■llririiiir'ifn — i i ■' 'ii
S
1
Si
■Mi
S
■ :^
f
LIBRARY
OF THE
University of California.
GIF^T OK
Class
. OMji^ -E.'^Jy^
■ft^^'-^iv^*
INTO. 9.
HYDROGRAPHIC OFFICE.
THE
AMEKICAS PRACTICAL lAVIGATOR
BEING AN
epitom:e
OF
NAVIGATION AND NAUTICAL ASTRONOMY.
BY
NATHANIEL BOWDITCH, LL. D.,
Fellow of the Royal Societies of London, Edinburgh, and Dublin; of the Astronomical Society in London; of the
American Philosophical Society, held at Philadelphia ; of the American Academy of Arts and Sciences ;
of the Connecticut Academy of Arts and Sciences ; of the Literary and Philosophical Society
of New York ; Corresponding Member of the Royal Societies of Berlin, Palermo, &c.
Revised in 1880, under the direction of the Bureau of Navigation,
Navy Department,
BY
Commander P. H. COOPER, U. s. Navy.
Revised in 1903, under the direction of the Bureau of Equipment,
Navy Department,
BY
Lieutenant G. W. LOGAN, U. S. Navy.
WASHINGTON:
GOVERNMENT PRINTING OFFICE.
1903.
OF THE
UNIVERSITY
n^
A
^^
^^
ORDERS RELATING TO REVISION.
Bureau of Navigation,
Navy Departtnent^ January 1\ 1881.
In accordance with the purpose contemplated in the purchase of the copyright of
the New American Practical Navigator, a thorough and complete revision has been
made by Commander P. H. Cooper, U. S. Navy, acting under the direction of the
Bureau. The revision consists principally in the substitution of the more concise and
convenient methods of the present day for the obsolete methods of the past, and a
complete rearrangement under proper chapters and paragraphs for ready reference,
keeping in view, however, the character of the work as a Practical Navigator.
The revision having been completed, it was submitted to Capt. Ralph Chandler,
U. S. Navy, for a final review, and having received a satisfactory report from that
officer it has been accepted by the Bureau and will hereafter be substituted for the
former editions of the work.
WiLLiA^r D. Whiting,
Chief of Bureau.
Bureau of Equipment,
Navy Department, March 18, 1903.
A revision of Bowditch's American Practical Navigator having become neces-
sar}'-, the work has been completed by Lieut. G. VV. Logan, U. S. Navy, under the
supervision of the Hydrographer to the Bureau of Equipment. The revision was
approved by a Board consisting of Capt. Colby M. Chester, U. S. Navy, Commander
C. J. Badger, U. S. Navy, and Lieut. Commander C. C. Rogers, U. S. Navy. It
is directed that this revised edition be substituted for all former editions.
R. B. Bradford,
Chief (f Bureau.
p»ref^ch:.
The copyright of the New American Practical Navigator, by the late Dr.
Bowditch, became the property of the United States Government under the provision
of an act of Congress to establish a Hydrographic Office in the Navy Department,
approved June 21, 1866.
Under the direction of the Bureau of Navigation, at that time charged with such
publications, the work was revised in 1880 by Commander P. H. Cooper, U. S. Navy,
certain chapters being contributed by Lieuts. Richard Wainwright and Charles H.
Judd, U. S. Navy, and the whole being reviewed by Capt. Ralph Chandler, U. S.
Navy. The object of this revision was to improve the general arrangement, and to
introduce the more convenient and precise methods of navigation that had come into
practice since the book was originally written.
The progress that has been made in the science of navigation since 1880 has
rendered necessary a second extensive revision, to take cognizance of the changes of
methods and instruments that have accompanied the general introduction of high-speed
vessels built of iron and steel. This work has been carried out, under the direction
of the Bureau of Equipment, by Lieut. G. W. Logan, U. S. Navy, who was aided in
the collection of data and preparation for publication b}^ Lieut. T. A. Kearney, U. S.
Navy; the chapters on AVinds and Cyclonic Storms were contributed by Mr. James
Page, nautical expert, Hydrographic Office.
There has been an extensive rewriting of the text, with the object of amplifying
those matters that are of the greatest importance in the modern practice of navigation,
and of omitting or condensing those of lesser importance; and the revision of the
tables has proceeded along similar lines. This has involved, among other things, a
much wider treatment of the subject of the compass; an extension of the traverse
table for degrees to distances up to 600 miles: an improved table for reducing circum-
meridian altitudes; the combination of the tables of maritime positions and tidal data;
the omission of certain special methods for finding position by two observations; the
addition of a series of annotated forms for the working of all sights, and the intro-
duction of a number of new tables of use to the navigator.
The explanation of the method of lunar distances, with its accompanying tables,
has been retained, in order to be available for use when required; but since this obser-
vation is so rarely employed in modern navigation, everything pertaining thereto has
been incorporated ih an appendix, that it may be distinct from matter of every-day
use to the navigator.
For convenience in use the work has been divided into two parts, of which the first
comprises the text and its appendices, and the second the tables.
W. H. H. SOUTHERLAND,
- Commander^ U. S. Navy^ Hydrographer.
Hydrographic Office,
Bureau of Equipment, Navy Department,
Washington^ D. C, March 19^ 1903.
3
1 1 1 140
Digitized by the Internet Archive
in 2008 with funding from
IVIicrosoft Corporation
http://www.archive.org/details/americanpracticaOObowdrich
P J^Pt T I.
TEXT AND APPENDICES,
OOISTTEISTTS O F I> A. R T I.
Page.
Orders relatipg to revision 2
Preface 3
Abbreviations ' 9
Chapter I. Definitions relating to Navigation 11
II. Instruments and Accessories in Navigation 13
III. The Compass Error 29
IV. Piloting 42
V. The Sailings 50
VI. Dead Reckoning 60
VII. Definitions relating to Nautical Astronomy 63
VIII. Instruments employed in Nautical Astronomy 66
IX. Time and the Nautical Almanac 74
X. Correction of Observed Altitudes 82
XI. The Chronometer Error 87
XII. Latitude 94
XIII. Longitude 103
XIV. Azimuth 109
XV. The Sumner Line 114
XVI. The Practice of Navigation at Sea 1 24
XVII. Marine Surveying 131
XVIIL Winds .' 142
XIX. Cyclonic Storms 147
XX. Tides 153
XXI. Ocean Currents 158
Appendix I. Extracts from the American Ephemerls and Nautical Almanac for the year 1879,
which have reference to examples for that year given in this Avork 163
II. A collection of Forms for working Dead Reckoning and various Astronomical
Sights, with notes explaining their application under all circumstances 171
III. Explanation of certain Rules and Principles of Mathematics of use in the Solu-
tion of Problems in Navigation 178
IV. Maritime Positions and Tidal Data 190
V. Lunar Distances 288
Index 333
7
ABBREVIATIONS USED IN THIS WORK.
Alt. {orh) Altitude.
A. M Ante meridian.
Amp Amplitude.
App . Apparent.
App. t Apparent time.
Ast Astronomical.
Ast. t Astronomical time.
Aug Augmentation.
Az. (or Z) Azimuth.
C Course.
C. C Chronometer correction.
C — W Chronometer minus watch.
Chro. t Chronometer time.
Co. L Co. latitude.
Col Column.
Corr Correction.
Cos Cosine.
Cosec Cosecant.
Cot Cotangent.
d (or Dec. ) Declination.
D ( or DLo ) Difference longitude.
Dep Departure.
Dev Deviation.
Diff Difference.
Dist Distance.
DL Difference latitude.
D. R Dead reckoning.
E., Ely East, easterly.
Elap. t Elapsed time.
Eq. eq. alt Equation equal altitude"
Eq. t Equation of time.
G. (or Gr. ) Greenwich.
G. A. T Greenwich apparent .ne.
G. M. T Greenwich mean time.
G. S. T : Greenwich sidereal time.
h Altitude.
H Meridian altitude.
H. A. (or /) Hour angle.
H. D Hourly difference.
H. P. (or Hor. par. ) . . . Horizontal parallax.
Hr-s Hour-8.
H. W High water.
I. C Index correction.
L. (or Lat. ) Latitude.
L. A. T Local apparent time.
L. M. T Local mean time.
L. S. T Local sidereal time.
Lo. (or Long) Longitude.
Log Logarithm.
Lun. Int Lunitidal interval.
L. W Low water.
m Meridional difference.
Merid Meridian or noon.
Mag Magnetic.
M. D Minute's difference.
Mid Middle.
Mid. L Middle latitude.
M. T Mean time.
N. , Nly North, northerly.
N. A. (or Naut. Aim. ). Nautical Almanac.
Np Neap.
Obs Observation.
p (or P. D. ) Polar distance.
p. c Per compass.
P. D. (or «) Polar distance.
P. L. (or Prop. Log.) .Proportional logarithm.
P. M Post meridian.
p. & r Parallax and refraction.
Par Parallax.
R. A Right ascension.
R. A. M. S Right ascension mean sun.
Red Reduction.
Ref Refraction.
S. , Sly South, southerly.
S. D Semi-diameter.
Sec Secant.
Sid Sidereal.
Sin Sine.
Spg Spring.
t Hour angle.
T Time.
Tab Table.
Tan Tangent.
Tr. (or Trans. ) Transit.
Var V'^ariation.
Vert Vertex or vertical.
W., Wlv West, westerly.
W. T . .' AVatch time
2 Zenith distance.
Z Azimuth.
0
The Sun.
° Degrees.
c
The Moon.
' Minutes of Arc.
*
A Star or Planet.
^^ Seconds of Arc.
(^C
Alt. upper limb.
" Hours.
(•)C
Alt. lower limb.
"" Minutes of Time
(l)0
Azimuthal angle.
•^ Seconds of Time.
GREEK LETTERS.
A a.
.Alpha.
N v....
.Nu.
B(i.
.Beta.
SI ....
.Xi.
ry.
.Gamma.
Oo ....
.Omicron.
J 6.
.Delta.
n n....
.Pi.
E s .
.Epsilon.
Pp. ...
.Rho.
ZC.
.Zeta.
26{i).
. Sigma.
Hr^.
.Eta.
Tr ....
.Tau.
t)0 .
.Theta.
Tv....
.Upsilon.
1 I ..
.Iota.
$ 0
.Phi.
Kk.
. Kappa.
^;«:..--
.Chi.
AX.
.Lambda.
Wrl)....
.Psi.
Mjii.
.Mu.
£1 00 ...
.Omega.
DEFINITIONS RELATING TO NAVIGATION.
11
BR .,
or THE
UNIVERSITY
CHAPTER I.
DEFINITIONS KELATINQ TO NAVIGATION.
1. That science, generally termed Navigatiou, which affords the knowledge necessary to conduct
a ship from point to point upon the earth, enabling the mariner to determine, with a sufficient degree
of accuracy, the position of his vessel at any time, is properly divided into two branches: Navigation
and Nautical Astronomy.
2. Navigation, in its limited sense, is that branch which treats of the determination of the position
of the ship by reference to the earth, or to objects thereon. It comprises {a) Piloting, in which the
position is ascertained from visible objects upon the earth, or from soundings of the depth of the sea,
and {h) Dead Reckoning, in which the position at any moment is deduced from the direction and
amount of a vessel's progress from a known point of departure.
3. Nautical Astronoim/ is that branch of the science which treats of the determination of the
vessel's place by the aid of celestial objects — the sun, moon, planets, or stars.
4. Navigation and Nautical Astronomy have been respectively termed Geo-Naviga^don and Celo-
Navigation, to indicate the processes upon which they depend.
5. As the method of piloting can not be employed excepting near land or in moderate depths of
water, the navigator at sea must fix his position either by dead reckoning or by observation {of celestial
objects) ; the latter method is more exact, but as it is not always available, the former must often be
depended upon.
6. The Earth. — The Earth is an oblate spheroid, being a nearly spherical body slightly flattened
at the poles; its longer or equatorial axis measures about 7,927 statute miles, and its shorter axis,
around which it rotates, about 7,900 statute miles.
The Earth (assumed for purposes of illustration to be a
sphere) is represented in figure 1.
The ^Lris of Rotation, usually spoken of simply as the
Axis, is PP''.
The Poles are the points, P and P', in which the axis
intersects the surface, and are designated, respectively, as
the North Pole and the South Pole.
The Equator is the great circle EQMW, formed by the
intersection with the earth's surface of a plane perpendicular
to the axis; the equator is equidistant from the poles, every
point upon it being 90° from each pole.
Meridians are the great c-ircles PQP^ PMP^ PM'P^
formed by the intersection with the earth's surface <4i planes
secondary to the equator (that is, passing through its poles
and therefore perpendicular to its plane) .
Parallels of Latitude are small circles NT/*, N^?/T', formed
by the intersection with the earth's surface of planes passed
parallel to the eciuator.
The Latitude of a place on the surface of the earth is the
arc of the meridian intercepted between the equator and •p'
that place. Latitude is reckoned JWr//* and »S'Ji<</i, from the Fig. 1.
equator as an origin, through 90° to the poles; thus, the
latitude of the point T is MT, north, and of the point T^ M^T', north. The Difference of Latitude
between any two places is the arc of a meridian intercepted between their parallels of latitude, and is
called North or South, according to direction; thus, the difference of latitude between T and T' is Tn^ or
T^», north from T or south from T'.
The Longitude of a place on the surface of the earth is the arc of the equator intercepted between
its meridian and that of some place from which the longitude is reckoned. Longitude is measured East
or West through 180° from the meridian of a designated place, such meridian being termed the Printe
Meridian; the prime meridian used by most nations, including the United States, is that of Greenwich,
England. If, in the figure, the prime meridian be PGQP^, then the longitude of the point T is QM, east,
and of T^, QM^, east. The Difference of Longitude between any two places is the arc of the equator inter-
cepted between their meridians, and is called East or West, accordmg to direction; thus, the difference
of longitude between T and T'' is MAP, east from M or west from AP. The Departure is the linear distance,
measured on a parallel of latitude, between two meridians; unlike the various quantities previously
defined, departure is reckoned in miles; the departure between two meridians varies with the parallel of
latitude upon which it is measured; thus, the departure between the meridians of T and T^ is the number
of miles corresponding to the distance Tji in the latitude of T, or to n'T' in the latitude of T'.
uy\
^yy Ny
1 T
« 1 M
M' r
12 DEBINITIONS RELATING TO NAVIGATION.
The curved line which joins any two places on the earth's surface, cutting all the meridians at the
same angle, is called the Rhumb Line, Loxodromic Chinr,, or Equiangular Spiral. In the figure, this line
is represented by TrT''. The constant angle which this line makes with the meridians is called the
Course; and the length of the line between any two places is called the Distance between those places.
The unit of linear measure employed by navigators is the Nautical or Sea Mile, or Knot. It is
equal to one minute of platitude — that is, to the length of that portion of a meridian which subtends at
the earth's center the angular measure of one minute; since, however, on account of the fact that the
earth is not a perfect sphere, this distance is not exactly the same in all latitudes, a mean value is adopted for
the length of the knot, and it is regarded as equal to 6,080.27 feet. For the purposes of navigation, the
variation from this value in different latitudes is so small that it may be neglected, and the knot may
be assumed equal to a minute of latitude in all parts of the earth; hence, when a vessel changes her
position to the north or south by one nautical mile, it may always be considered that the latitude has
changed 1''. Owing to the fact that the meridians all convei^e toward the poles, the difference of longi-
tude produced by a change of position of one mile to the east or west will vary with the latitude; thus
a departure of one mile will equal a difference of longitude of 1^.0 at the equator, of V.l in the latitude
of 30°, and of 2^0 in the latitude of 60°.
The Great Circle Track or Course between any two places is the route between those places along the
circumference of the great circle which joins them. In the figure, this line is represented by TgT^.
From the properties of a great circle (which is a circle upon the earth's surface formed by the inter-
section of a plane passed through its center) the distance between two points measured on a great circle
track is shorter than the distance upon any other line which joins them. Except when the two points
are on the same meridian or when both lie upon the equator, the great circle track will always differ
from the rhumb line, and the great circle track will intersect each intervening meridian at a different
angle.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 13
CHAPTER II.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
DIVIDERS OR COMPASSES.
7. This instrument consists of two legs movable about a joint, so that the points at the extremities
of the legs may be set at any required distance from each other. It is used to take and transfer dis-
tances and to describe arcs'and circles. When used for the former purpose it is termed didders, and
the extremities of both legs are metal points; when used for describing arcs or circles, it is called a com-
pass, and one of the metal points is replaced by a pencil or pen.
PARALLEL RXTLERS.
§. Parallel rulers are used for drawing lines parallel t(j each other in any direction, and are particu-
larly useful in transferring the rhuml)-]ine on the chart to the nearest compass-rose to ascertain the
course, or to lay off bearings and courses.
PROTRACTOR.
9. This is an instrument used for the measurement of angles upon paper; there is a wide variation in
the material, size, and shape in which it mav be made. (For a description of the Three Armed Protractor,
see art. 432, Chap. XVII. )
THE CHIP LOG.
10. This instrument, for measuring the rate of sailing, consists of three parts; viz, the log-chip,
the log-line, and the log-glass. A light substance thrown from the ship ceases to partake of the motion
of the vessel as soon as it strikes the water, and will be left behind on the surface; after a certain inter-
val, if the distance of the ship from this stationary object be measured, the approximate rate of sailing
will be given. The log-chip is the float, the log-line is the measure of the distance, and the log-glass
defines the interval of time.
The log-chip is a thin wooden quadrant of about 5 inches radius, loaded with lead on the circular
edge sufficiently to make it swim upright in the water. There is a hole in each comer of the log-
chip, and the log-line is knotted in the one at the apex; at about 8 inches from the end there is seized
a wooden socket; a piece of line of proper length, being knotted in the other holes, has seized into its
bight a wooden peg to fit snugly into the socket before the log-chip is thrown; as soon as the line is
checked this peg pulls out, thus allowing the log-chip to be hauled in with the least resistance.
The log-line is about 150 fathoms in length, one end made fast to the log-chip, the other to a
reel upon which it is wound. At a distance oi from 15 to 20 fathoms from the log-chip a permanent
mark of red bunting about 6 inches long is placed to allow sufficient stray line for the log-chip to clear
the vessel's eddy or Make. The rest of the line is divided into lengths of 47 feet 3 inches called knots,
by pieces of fish-line thrust through the strands, with one, two, three, etc., knots, according to the
number from stray -line mark; each knot is further subdivided into five equal lengths of two-tenths of a
knot each, marked by pieces of white rag.
The length of a knot depends upon the number of seconds which the log-glass measures; the length
of each knot must bear the same ratio to the nautical mile (^V of a degree of a great circle of the earth
or 6,080 feet) that the time of the glass does to an hour.
In the United States Navy all log-lines are marked for log glasses of 28 seconds, for which the
proportion is:
3600 : 6080 = 28' : x,
X being the length of the knot.
Ughcg
a: = 47".29, or47"3i".
The speed of the ship is estimated in knots and tenths of a knot.
The log-glass is a sand glass of the same shape and construction as the old hour-glass. Two glasses
are used, one of 28 seconds and one of 14 seconds; the latter is employed when the ship is going at a
high rate of speed, the number of knots indicated on a line marked for a 28-second glass being doubled
to obtain the true rate of speed.
11. The log in all its parts should be frequently examined and adjusted; the peg must be found to
fit sufficiently tight to keep the log-chip upright; the log-line shrinks and stretches and should often be
verified ; the log-glass should be compared with a watch. One end of the glass is stopped with a cork,
by removing which the sand may be dried or its quantity corrected.
12. A ground log consists of an ordinary log-line, with a lead attached instead of a chip; in shoal
water, where there are no well-defined objects available for fixing the position of the vessel and the
course and speed are influenced by a tidal or other current, this log is sometimes used, its advantage
being that the lead marks a stationary point to which motion may be referred, whereas the chip would
drift with the stream. The speed, which is marked in the usual manner, is the speed over the
:?round, and the trend of the line gives the course actually made good by the vessel.
14 INSTRUMENTS AND ACCJISSORIES IN NAVIGATION.
THE PATENT LOG.
1 3. This is a mechanical contrivance for registering the distance actually run by a vessel through the
water. There are various types of patent logs, but for the most part they act upon the same principle,
consisting of a registering device, a fly or rotator, and a log or tow line; the rotator is a small spindle
with a number of wings extending radially in such manner as to form a spiral, and, when drawn
through the water in4;he direction of its axis, rotates about that axis after the manner of a screw pro-
peller; the rotator is towed from the vessel by means of a log or tow line from 20 to 50 fathoms in I'^ngth,
made fast at its apex, the line being of special make so that the turns of the rotator are transmitted
through it to the worm shaft of the register, to which the inboard end of the line is attached; the regis-
tering device is so constructed as to show upon a dial face the distance run, according to the number of
turns of its worm shaft due to the motion of the rotator; the register is carried at some convenient point
on the vessel's quarter; it is frequently found expedient to rig it out upon a small boom, so that the
rotator will be towed clear of the wake.
14. Though not a perfect instrument, the patent log affords the most accurate means available for
determining the vessel's speed through the water. It will usually )je found that the indications of the
log are in error by a constant percentage, and the amount of this error should be determined l)y careful
experiment and apjilied to all readings.
Various causes may operate to produce inaccuracy of working in the patent log, such as the bending
of the wings of the rotator by accidental blows, fouling of the rotator by sea weed or refuse from the
ship, or mechanical wear of parts of the register. The length of the tow-line has much to do with the
wqrking of the log, and by varying the length the indications of the instrument may sometimes be
adjusted when the percentage of error is small; it is particularly important that the line shall not be too
short. The readings of the jjatent log can not be depended upon for accuracy at low speeds, when the
rotator does not tow horizontally, nor in a head or a following sea, when the effect depends upon the
wave motion as well as upon the speed of the vessel.
1 5. Electrical registers for patent logs are in use, the distance recorded by the mechanical register
being communicated electrically to some point of the vessel which is most convenient for the purposes of
those charged with the navigation.
16. A number of instruments based upon different physical principles have been devised for
recording the speed of a vessel through the water and have been used with varying degrees of success.
1 7. The revolutions of the screw i)ropeller afford in a steamer a valuable check upon the patent
log and a means of replacing it if necessary. To be of service the number of revolutions i)er knot must
be carefully determined for the vessel by experiment under varying conditions of speed, draft, and foul-
ness of bottom.
THE LEAD.
18. This device, for ascertaining the depth of water, consists essentially of a suitaljly marked line,
having a lead attached to one of its ends. It is an invaluaVjle aid to the navigator in shallow water,
particularly in thick or foggy weather, and is often of service when the vessel is out of sight of land.
Two leads are use<l for soundings — the htmd-ledd, weighing from 7 to 14 jjounds, with a line marked
to about 25 fathoms, and the deep-sea lead, weighing from 30 to 100 pounds, the line being 100 fathoms or
upward in length.
Lines are generally marked as follows:
2 fathoms from the lead, with 2 strips of leather.
3 fathoms from the lead, with 3 strips of leather.
5 fathoms from the lead, with a white rag.
7 fathoms from the lead, with a red rag.
10 fathoms from the lead, with leather having a
hole in it.
13 fathoms from the lead, same as at 3 fathoms. ! And so on.
15 fathoms from the lead, same as at 5 fathoms. |
Fathoms which correspond with the depths marked are called )nark-<; the intermediate fathoms are
called deeps; the only fractions of a fathom used are a half and a quarter.
A practice sometimes followed is to mark the hand-lead line in feet around the critical depths of
the vessel by which it is to be used.
Lead lines should be measured frequently while wet and the correctness of the marking verified.
The distance from the leadsman's hand to the water's edge should be ascertained in order that proper
allowance may be made therefor in taking soundings at night.
19. The deep-sea lead may be armed by tilling with tallow a hole lioUowed out in its lower end,
by which means a sample of the bottom is brought up.
THE SOUNDING MACHINE.
20. This machine possesses advantages over the deep-sea lead, for which it is a substitute, in that
soundings may be obtained at great depths and with rapidity and accuracy without stopping the ship.
It consists essentially of a stand holding a reel upon which is wound the sounding wire, and which is
controlled by a suitable Ijrake. Crank handles are provided for reeling in the wire after the sounding
has been taken. Attached to the outer end of the wire is the lead, which has a cavity at its lower end
for the rece[>tion of the tallow for arming. Above the lead is a cylindrical case containing the depth-
registering mechanism; various devices are in use for this purpose, all depending, however, upon the
increasing pressure of the water with increasing depths.
21. In the Lord Keliin machine z. slender glass tube is used, sealed at one end and open at the
other, and coated inside with a chemical substance which changes color upon contact with sea water;
this tube is placed, closed end up, in the metal cylinder; as it sinks the water rises in the tube, the
contained air being compressed with a force dependent upon the depth. The limit of discoloration is
marked by a clearly defined line, and the dei)th of the sounding corresponding to this line is read off
from a scale. Tubes that have been used in comparatively shallow water may be used again where the
water is known to be deeper.
17 fathoms from the lead, same as at 7 fathoms.
20 fathoms from the lead, with 2 knots.
25 fathoms from the lead, wi:h 1 knot.
30 fathoms from the lead, with 3 knots.
35 fathoms from the lead, with 1 knot.
40 fathoms from the lead, with 4 knots.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
15
22. A tube whose inner surface is ground has been substituted for the chemical-coated tube, ground
glass, when wet, showing clear. The advantage of these tubes is that they may be used an indefinite
number of times if thoroughly dried. To facilitate drying, a rubber cap is fitted to the upper end, which,
when removed, admits of a circulation of the air through the tube.
23. As a substitute for the glass tubes a mechanical depth recorder contained in a suitable case has
been used. In this device the pressure of the water acts upon a piston against the tension of a spring. A
scale with an index pointer records the depth reached. The index pointer must be set at zero before
each sounding.
24. Since the action of the sounding machine, when glass tubes are used, depends upon the com-
pression of the air, the barometric pressure of the atmosphere must be taken into account w^hen accurate
results are required. The correction consists in increasing the indicated depth bj' a fractional amount
according to the following table:
Bar. reading.
Increase.
//
29. 75
m. 00
.so. 50
30. 75
j
1 One-fortieth.
: One-thirtieth.
; One-tv.'entieth.
One-fifteenth.
THE MARINER'S COMPASS.
25. The Mariner^ s Compass i.s an instrument consisting either ot a single magnet, or, more usually,
of a series of magnets, which, being attached to a graduated circle i)iv<»ted at the center and allowed to
Fig. 2.
swing freely in a horizontal plane, has a tendency to lie with its magnetic axis in the plane of the earth's
magnetic meridian, thus affording a means of determining the azimuth, or horizontal angular distance
from that meridian, of the ship's c-ourse and of all visible objects, terrestrial or celestial.
/
16
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
26. The circular card of the compass (fig. 2) is divided on its periphery into 360°, numbered from 0°
at North and South to 90° at East and West; also into thirty-two divisions of 1^° each, called jmnts, the
latter being further divided into half-points and quarter-points ; still finer suMivisions, eighth-]>oints, are
sometimes used, though not indicated on the card. A system of numbering the degrees from 0° to 360°,
always increasing toward the right, is shown in the figure. This system is in use by the mariners of
some' nations, and itsgeneral adoption would carry with it certain undoubted advantages.
27. Boxing the (Mmpass is the process of naniing the points in their order, and is one of the first
things to be learned by the young mariner. The four principal points are called cardinal points and are
named North, South, East, and West; each differs in direction from the adjacent one by 90°, or 8 points.
Midway between the cardinal points, at an angular distance of 45°, or 4 points, are the inter-cardinal
points, named according to their posititm Northeast, Southeast, etc. Midway between each cardinal
and inter-cardinal point, at an angular distance of 22J°, or 2 points, is a point whose name is made up
of a combination of that of the cardinal with that of the inter-cardinal point: North-Northeast, East-
Northeast, East-Southeast, etc. At an angular distance of 1 point, or lli°, from each cardinaland inter-
cardinal point (and therefore midway between it and the 22J°-division last described), is a point
which bears the name of that cardinal or inter-cardinal point joined by the word by to that of the cardi-
nal point in the dire<'tion of which it lies: North by East, Northeast by North, Northeast by East, etc.
In boxing by fractional points, it is evident that each division may be referred to either of the
whole points to which it is adjacent; for instance, NE. by N. j N. and NNE. J E. would describe the
same division. It is the custom in the United States Navy to box from North and South toward East and
West, excepting that divisions adjacent to a cardinal or inter-cardinal point are always referred to that
point; as N. i E., N. by E. ^ E., NNE. J E., NE. j N., etc. Some mariners, however, make it a prac-
tice to box from each cardinal and inter-cardinal point tmiard a 22i°-point (NNE., ENE., etc.); as
N. i E., N. by E. J E., NE. by N. J N., NE. \ N., etc.
The names of the whole points, together with fractional points (according to the nomenclature of
the United States Navy), are given in the following table, which shows also the degrees, minutes, and
seconds from North or South to which each division corresponds:
- '•> ^
N. to E.
N. to W.
S. to E.
Pts.
Angular
measure.
North:
N. iE
N. JE
N. |E
N.byE
N. by E. i E..
N. by E. ^E..
N. by E. |E..
NNE
NNE. \E
NNE. iE
NNE. f E
NE. byN
NE. J N
NE. i N
NE. i N
NE
NE. iE
NE. i E
NH |E
NE. byE
NE. by E. i E.
NE. by E. i E.
NE. by E. I E.
ENE
ENE. iE
ENE. iE
ENE. f E
E. byN
E. IN
E. IN
v.. iN
East
North:
N. i W
N. J W
N. f W
N.byW
N. by W. iW..
N. by W.J W..
N. by W. f W..
NNW
NNW. } W....
NNW. iW....
NNW. f W . . . .
NW. byN
NW. |N
NW. IN
NW. iN
NW
NW. i W
NW. J W
NW. I W
NW. by W
NW.byW.iW.
NW.byW.JW.
NW.byW. JW.
WNW
WNW. J W....
WNW. J W....
WNW. f W....
W.byN
W. I N
W. JN
W. } N
West
South:
S. \E
S. JE
S. |E
S. byE
S. by E. i E .
S. by E. J E .
S. by E. I E .
SSE
SSE. iE
SSE. JE
SSE. f E....
SE. by S
SE. |S
SE. ^S
SE. i-S
SE
SE.iE
SE. JE
SUf E
SE. byE
SE. by E. i E
SE. by E. i E
SE. by E. f E
ESE
ESE. iE....
ESE. J E . . . .
ESE. f E . . . .
E.byS
E. f S
E. JS
E. }S
East
South :
S. J W
S. iW
S. |W
S. by W
S. by W. i W..
S. by W.J W..
S. by W. I W..
ssw
ssw. i w
ssw. J w
ssw. I w
SW. byS
SW. f s
SW. JS
SW. JS
SW
SW. i w
SW. J w
SW. f w
SW. by W
SW. by W. i W
SW. by W. J W
SW. by W. I W
WSW
wsw. nv....
WSW. J W....
WSW. iw....
W. byS
W. f s
W. JS
AV. iS
West
1
U
1|
2
2\
2i
2J
3
3i
3J
3i
4
^
4i
5
b\
5J
5J
6
6i
6i
61
7
n
n
71
2
5
8
11
14
16
19
22
25
28
30
33
36
39
42
45
47
50
53
56
59
61
64
67
70
73
75
78
81
84
87
90
48 45
37 30
26 15
15 00
03 45
52 30
41 15
30 00
18 45
07 30
56 15
45 00
33 45
22 30
11 15
00 00
48 45
37 30
26 15
15 00
03 45
52 30
41 15
30 00
18 45
07 30
56 15
45 00
33 45
22 30
n 15
00 00
2§. The compass card is mounted in a bowl which is carri^ in gimbals, thus enabling the card to
retain a horizontal position while the ship is pitching and rolling. A vertical black line called the bib-
ber's line is marked on the inner surface of the bowl, and the compass is so mounted that a line joining
its pivot with the lubber's line is parallel to the keel line of the vessel; thus the lubber's line always
indicates the compass direction of the ship's head.
29. According to the purpose which it is designed to fulfill, a compass is designated as a Standard,
Peering, Check, or Boat Compass.
INSTEUMENTS AND ACCESSORIES IN NAVIGATION. 17
30. There are two types of compass in use, the v:et or liquid and the dry; in the former the bowl i;j
filled with liquid, the card being thus partially buoyed, with consequent increased ease of working on
the pivot, and the liquid further serving to decrease the vibrations of the card when deflected by reason
of the motion of the vessel or other cause. On account of its advantages the liquid compass is used in
the United States Xavy.
31. The Navy Service 7^-ixch Liquid Compass. — This consists of a skeleton card 7 J inches in
diameter, made of tinned brass, resting on a pivot in liquid, with provisions for two pairs of magnets
symmetrically placed.
The magnet system of the card consists of four cylindrical bundles of steel wires; these wires are
laid side by side aiid magnetized as a bundle between the poles of a powerful electromagnet. They are
afterwards placed in a cylindrical case, sealed, and secured to the card. Steel wires made up into a
bundle were adopted Ijeckuse they are more homogeneous, can be more perfectly tempered, and for the
same weiglit give greater magnetic power than a solid steel bar.
Two of the magnets are placed parallel to the north and south diameter of the card, and on the
chords of 15° (nearly) of a circle passing through their extremities. These magnets penetrate the air
vessel, to which they are soldered, and are further secured to the bottom of the ring of the card. The
other two magnets of the system are placed parallel to the longer magnets on the chords of 45° (nearly)
of a circle passing through their extremities, and are secured to the bottom of the ring ofthe card.
The card is of a curved annular type, the outer ring being convex on the upper and inner side, and
is graduated to read to one-fourth point, a card circle being adjusted to its outer edge and divided to
half-degrees, with legible figures at each 3°, for use in reading bearings by an azimuth circle or in laying
the course to degrees.
The card is provided with a concentric spheroidal air vessel, to buoy its own weight and that of the
magnets, allowing a pressure of between 60 and 90 grains on the pivot at 60° F. ; the weight of the card
in air is 3,060 grains. The air vessel has within it a hollow cone, open at its lower end, and provided
with the pivot bearing, or cap, containing a sapphire, which rests upon the pivot and thus supports the
card; the cap is provided with adjusting screws for accurately centering the i-ard. The pivot is fastened
to the center of the bottom of the bowl by a flanged plate and screws. Through this plate aiid the
bottom of the bowl are two small holes which communicate Avith the expansion chamber and admit of
a circulation of the liquid between it and the bowl. The pivot is of gun metal with an iridium cap.
The card is mounted in a bowl of cast bronze, the glass cover of which is closely packed with rubber,
preventing the evaporation or leakage of the liquid, which entirely tills the bowl. This liquid is com-
posed of 45 per cent pure alcohol and 55 per cent distilled water, and remains liquid below —10° F. _
The luljber's line is a fine line drawn on an enameled plate on the inside of the bowl, the inner
surface of the latter l)eing covered with an insolul)le white paint.
Beneath the bowl is a metallic self-adjusting expansion chamber of elastic metal, by means of which
the bowl is kept constantly full Avithout the show of bubbles or the development of undue pressure
caused by the change in volume of the liquid due to changes of temperature.
The Vim of the compass bowl is made rigid and its outer edge turned strictly to gauge to receive the
azimuth circle.
32. The Dry Compass. — The Lord Kelrin Compass, which may be regarded as the standard for
the nonliquid type, consists of a strong paper card with the central parts cut away and its outer edge
stiffened 1)y a thin aluminum ring. The pivot is fitted with an iridium point, upon which. rests a small
light aluminum boss fitted with a sapphire Ijearing. Radiating from this boss are 32 silk threads whose
outer ends are made fast to the inner edge of the compass card; these threads sustain the weight of the
suspended card, and, as they possess some elasticity, tend to decrease the shocks due to motion.
Eight small steel wire needles, 3^ to 2 inches long, are secured normally to two parallel silk threads,
and are slung from the aluminum rim of the card by other silk threads which pass through eyes in the
ends of the outer pair of needles. The needles are below the radial threads, thus keeping the center of
gravity low.
33. The Azimuth Circle. — This is a necessary fitting for all compasses employed for taking
bearings — that is, noting the directions — of either celestial or terrestrial objects. The instrument varies
widely in its different forms; the essential features which all share consist in (a) a pair of sight vanes,
or equivalent device, at the extremities of the diameter of a circle that revolves concentrically with the
compass bowl, the line of sight thus always passing through the vertical axis of the compass; and (h)
a system, usually of mirrors and prisms, by which the point of the compass card cut by the vertical
plane through the line of sight — in other words, the compass direction — is brought into the field of view
of the person making the observation. In some circles, for observing azimuths of the sun advantage is
taken of the brightness of that body to reflect a pencil of light upon the card in such a manner as to
indicate the bearing; such an azimuth circle is used in the United States Navy.
34. Binnacles. — Compasses are mounted for use in stands known as Binnacles, of which there are
two principal types — the Compensating and the Non-Compensating Binnacle, so designated according as
they are or are not equipped with appliances by which the deviation of the compass, or error in its
indications due to disturbing magnetic features within the ship, may be compensated.
4 Binnacles may be of wood or of some nonmagnetic metal; all contain a compass chamber within
. which the compass is suspended in its gimbal ring, the knife edges upon which it is suspended resting
in V-shaped bearings; an appropriate method is supplied for centering the compass. A hood is proAided
for the protection of the compass and for lighting it at night. Binnacles must be rigidly secured to the
deck of the vessel in such position that the lubber's line of the compass gives true indications of the
direction of the ship's head.
The position of the various binnacles on shipboard and the height at which they carry the compas-^
must be chosen with regard to the purpose which the compass is to serve, having in mind the magnetic
conditions of the ship.
Compensating binnacles contain the appliances for carrying the various correctors used in the com-
pensation of the deviation of the compass. These consist of (a) a system of permanent magnets for
22489—03 2
18 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
semicircular deviation, placed in a magnet chamber lying immediately beneath the compass chamber,
so arranged as to permit variation in the height and direction of the magnets employed; (b) a pair of
arms projecting horizontally from the compass chamber and supporting masses of soft iron for quad-
rantal deviation; (c) a central tube in the vertical axis of the binnacle for a permanent magnet used to
correct the heeling error, and (d) an attachment, sometimes fitted, for securinjj a vertical soft iron rod,
or "Flinders bar," u^d in certain cases for correction of a part of the semicircular deviation. An
explanation of the various terms here used, together with the method of compensating the compass,
will be given in Chapter III.
THE PELORXJS.
35. This instrument consists of a circular plate, mounted horizontally in gimbals upon a vertical
standard, at some point on board ship affording a clear view for taking bearings; radial scores upon a
raised flange on the periphery of this plate indicate true directions from its center parallel with the keel
line of the vessel and perpendicular thereto — in other words, lines of bearing directly ahead, astern, and
abeam. Eevolving about a common center, which is also the center of the plate, are (a) a dumb com-
pass card, usually engraved on metal, whose face is level with the raised periphery of the plate on which
are marked the scores, and (6) a pivoted horizontal bar carrying at its extremities a pair of sight vanes
so arranged that the line of sight always passes through the vertical axis of the instrument, and having
an index showing the point at which the line of sight cuts the dumb compass. The dumb compass and
the sight-vane bar can each be rigidly clamped.
The instrument is used for taking bearings, and may be more convenient than the compass for that
purpose because of the better view that it affords, as well as because it may be made to eliminate the
compass error from observed bearings. Suppose that the dumb compass be revolved until the degree or
division which is coincident with the right-ahead score of the plate is the same as that which is abreast
the lubber's line of the ship's compass. Then all directions indicated by the dumb compass will be
parallel to the corresponding directions of the live one, and all bearings taken by the pelorus will be.
identical with those taken by the compass (leaving out of the question the diffence due to the distance
that separates them). Suppose, now, that it is known that the ship's compass has a certain error and
that the correct direction that we seek ( which is the one indicated on the charts ) is a certain angular
distance to the right or left of that which the compass shows; if, in such a case, instead of setting the
pelorus for the direction indicated by compass, we set it for the correct direction in which we know the
ship to be heading, all bearings observed by the pelorus will be correct bearings as given by the chart
and may be plotted directly thereon without the necessity for the intermediate i)rocess of correction to
which the bearings shown by compass are subject. It will at once be evident that the indications of the
pelorus will be accurate only when bearings are taken at an instant when the ship is heading exactly in
the direction for which it is set, and care must be taken accordingly in its use.
The most modern types of pelorus are fitted for illuminating the dumb compass, thus greatly facili-
tating night work.
THE CHART.
36. A nautical chart is a miniature representation upon a plane surface, in accordance with a defi-
nite system of projection or development, of a portion of the navigable waters of the world. It generally
incluaes the outline of the adjacent land, together with the surface forms and artificial features that are
useful as aids to navigation, and sets forth the depths of water, especially in the near approaches to the
land, by soundings that are fixed in position by accurate determinations. Except in charts of harbors
or other localities so limited that the curvature of the earth is inappreciable on the scale of construction,
a nautical chart is always framed over with a network of parallels of latitude and meridians of longitude
in relation to which the features to be depicted on the chart are located and drawn; and the mathematical
relation between the meridians and parallels of the chart and those of the terrestrial sphere determines
the method of measurement that is to be employed on the chart and the special uses to which it is
adapted
37. There are three principal systems of projection in use: (a) the Mercator, (h) the polyccmic, and
(c) the gnomonic; of these, the Mercator is by far the most generally used for purposes of navigation
proper, while the polyconic and the gnomonic charts are employed for nautical purposes in a more
restricted manner, as for plotting surveys or for facilitating great circle sailing.
3§. The Mercator Pro.iection. — The Mercator Projection, so called, may be said to result from
the development, upon a plane surface, of a cylinder which is tangent to the earth at the equator, the
various points of the earth's surface having l:>een projected upon the cylinder in such manner as they
would appear to an observer at the earth's center; this method of projection and development results
in a characteristic feature — namely, that the loxodrornic curve or rhumb line (art. 6, Chap. I) apjiears as
a right line preserving the same angle of bearing with respect to the intersected meridians as does the
ship's track.
In order to realize this condition, the line of tangency, which coincides with the earth's equator,
being the circumference of a right section of the cylinder, will appear as a right line on the develop-
ment; while the series of elements of the cylinder corresponding to the projected terrestrial meridians
will appear as equidistant right lines, parallel to each other and perpendicular to the equator of the
chart, maintaining the same relative positions and the same distance apart on that equator as the
meridians have on the terrestrial spheroid. The series of terrestrial parallels will also appear as a
system of right lines parallel to each other and to the equator, and will so intersect the meridians as to
form a system of rectangles whose altitudes, for successive intervals of latitude, must be variable,
increasing from the equator in such manner that the angles made by the rhumb line with the meridian
on the chart may maintain the required equality with the (iorresponding angles on the spheroid.
39. Meridional Parts. — At the equator a degree of longitude is equal to a degree of latitude, but
in receding from the equator and approaching the pole, while the degrees of latitude remain always of
the same length (save for a slight change due to the fact that the earth is not a perfect sphere), the
degrees of longitude become less and less.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 19
Since, in the Mereator projection, the degrees of longitude are made to appear everywhere of the
same length, it becomes necessary, in order to preserve the proportion that exists at different parts of
the earth's surface between degrees of latitude and degrees of longitude, that the former be increased
from their natural lengths, and such increase must become greater and greater the higher the latitude.
The length of the meridian, as thus increased, between the equator and any given latitude,
expressed in minutes at the equator as a unit, constitutes the number of Meridional Parts corresponding
to that latitude. The Table of Meridional Parts or Increased Latitudes (Table 3) , computed for every
minute of latitude between 0° and 80°, affords facilities for constructing charts on the Mereator pro-
jection and for solving problems in Mereator sailing.
40. To Construct a Mercator Chart. — If the chart for which a projection is to be made includes
the equator, the values to be measured off are given directly by Table 3. If the equator does not come
upon the chart, then the parallels of latitude to be laid down should be referred to a principal parallel,
preferably the lowest parallel to be drawn on the chart. The distance of any other parallel of latitude
from the "principal parallel is then the difference of the values for the two taken from Table 3.
The values so found may either be measured off, without previous numerical conversion, by means
of a diagonal scale constructed on the chart, or they may be laid down on the chart by means of any
properly divided scale of yards, meters, feet, or miles^ after having been reduced to the scale of proportions
adopted for the chart.
If, for example, it be required to construct a chart on a scale of one-quarter of an inch to five minutes
of arc on the equator, a diagonal scale may first be constructed, on which ten meridional parts, or ten
minutes of arc on the equator, have a length of half an inch.
It may often be desirable to adapt the scale to a certain allotment of paper. In this case, the lowest
and the highest parallels of latitude may first be drawn on the sheet on which the transfer is to be made.
The distance between these parallels may then be measured, and the number of meridional parts
between them ascertained. Dividing the distance by this number will then give the length of one
meridional part, or the quantity by which all the meridional parts taken from Table 3 must be multi-
plied. This quantity will represent the scale of the chart. If it occurs that the limits of longitude are
a governing consideration, the case may be similarly treated.
E.K ample: Let a projection be required for a chart of 14° extent in longitude between the parallels
of latitude 20° 30^ and 30° 25'', and let the space allowable on the paper between these parallels measure
10 inches.
Entering the column in Table 3 headed 20°, and running down to the line marked 30' in the side
column, will be found 1248 9; then, entering the column 30°, and running down to the line of 25', will
be found 1905.5. The difference, or 1905.5 — 1248.9 = 656.6, is the value of the meridional arc between
these latitudes, forjvhich 1' of arc of the_equator is taken as the unit. On the intended projection,
therefore, V of arc of longitude will measure J—-'. = 0.0152 inch, which will be the scale of the chart.
606.6
For the sake of brevity call it 0.015. By this quantity all the values derived from Table 3 will have to
be multiplied before laying them down on the projection, if they are to be measured on a diagonal scale
of one inch.
Draw in the center of the sheet a straight line, and assume it to be the middle meridian of the chart.
Construct very carefully on this line a perpendicular near the lower border of the sheet, and assume this
perpendicular to be the' parallel of latitude 20° 30'; this will be the southern inner neat line of the chart.
From the intersection of the lines lay off on the parallel, on each side of the middle meridian, seven
degrees of longitude, or distances each equal to 0.015 X 60 X 7 = 6.3 inches; and through the points thus
obtained draw parallel lines to the middle meridian, and these will be the eastern and western neat lines
of the chart.
In order to construct the parallel of latitude for 21° 00', find, in Table 3, the meridional parts for
21° 00', which are 1280.8. Subtracting from this number the number for 20° 30', and multiplying the
difference by 0.015, we obtain 0.478 inch, which is the di.stance on the chart V)etween 20° 30' and
21° 00'. On the meridians lay off distances equal to 0.478 inch, and through the three points thus
obtained draw a straight line, which will be the parallel of 21° 00'.
Proceed in the same manner to lay down all the parallels answering to full degrees of latitude; the
distances will be respectively :
0"'.015X (1344.9—1248.9) = 1.440 inches,
0'".015X (1409.5-1248.9) =2.409 inches,
0'°.015X (1474.5-1248.9) =3.384 inches, etc.
Thus will be shown the parallels of latitude 22° 00', 23° 00', 24° 00', etc. Finally, lay down in the same
way the parallel of latitude 30° 25', which will be the northern inner neat line of the chart.
' A degree of longitude will measure on this chart 0'".015x60=0'".9. Lay off, therefore, on the low-
est parallel of latitude drawn on the chart, on a middle one, and on the highest parallel, measuring
from the middle meridian toward each side, the distances of 0"'.9, 1"'.8, 2"'. 7, 3'". 6, etc., in order to
determine the points where meridians answering to full degrees cross the parallels drawn on the chart.
Through the points thus found draw the meridians. Draw then the outer neat lines of the chart at a
convenient distance outside of the inner neat lines, and extend to them the meridians and parallels.
Between the inner and outer neat lines of the chart subdivide the degrees of latitude and longitude as
minutely as the scale of the chart will permit, the subdivisions of the degrees of longitude being found
by dividing the degrees into equal parts, and the subdivisions of the degrees of latitude being accu-
rately found in the same manner as the full degrees of latitude previously described, though it will
generally be found sufficiently exact to make even subdivisions of the degrees, as in the case of the
longitude.
The subdivisions between the two eastern as well as those between the two western neat lines will
serve for measuring or estimating terrestrial distances. Distances between points bearing North and
South of each other may be ascertained by referring them to the subdivisions between the same paral-
lels. Distances represented by lines at an angle to the meridians (loxodromic lines) may be measured
X
20
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
by taking between the dividers a small number of the subdivisions near the middle latitude of the
line to be measured, and stepping them off on that line. If, for instance, the terrestrial length of a line
running at an angle to the meridians between the parallels of latitude of 24° 00^ and 29° OC be required,
the distance shown on the neat space between 26° 15' and 26° 45^ ( = 30 nautical miles) may be taken
between the dividers and stepped off on that line.
41. Coast lines an* other positions are plotted on the chart by their latitude and longitude. A
chart may be transferred from any other projection to that of Mercator by drawing a system of corre-
sponding parallels of latitude and" meridians over both charts so close to each other as to form minute
squares, and then the lines and characters contained in each square of the map to be transferred may
be copied by the eye in the corresponding squares of the Mercator projection.
Since the unit of measure, the mile or minute of latitude, has a different value in every latitude, there
is an appearance of distortion in a Mercator chart that covers any large extent of surface; for instance,
an island near the j^ole will be represented as being much larger than one of the same size near th6
equator, due to the different scale used to preserve the character of the ])rojection.
42. The Polyco.nic Projection. — This projection is based upon the development of the earth's
surface on a series of cones, a different one fi>r each parallel of latitude, each one having the parallel as
its base, and its vertex in the pointwhere a tangent to the earth at that latitude intersects the earth's axis.
The degrees of latitude and longitude on this chart are projected in their true length, and the general
distortion of the figure is less than in any other method of projection, the relative magnitudes being
closely preserved.
A straight line on the polyconic chart represents a great circle, making a slightly different angle
with each successive meridian as the meridians converge toward the pole and are theoretically curved
lines; but it is only on charts of large extent that this curvature is apparent; the parallels are also
curved, this fact being apparent to the eye upon all excepting the largest scale charts.
This method of projection is especially adapted to the plotting of surveys; it is also employed for
nearly all of the charts of the United States Coast and Geodetic Survey.
43. Gnomonic Peojectiox. — This is based upon a system in which the plane of projection is tangent
to the earth at some given point; the eye of the spectator is situated at the center of the sphere, where,
being at once in the plane of every great circle, it will see all such circles projected as straight lines
where the visual rays passing through them intersect the plane of projection. In a gnomonic chart, a
straight line between any two points is projected as an arc of a great circle, and is therefore the shortest
line l)etween those points.
Excepting in the Polar regions, for which latitudes the Mercator projection can not be constructed,
the gnomonic charts are not used for general navigating purposes. Their greatest application is to afford
a ready means of finding the course and distance at any time in great circle sailing, the method of doing
which will be explained in (^hapter \".
44. Meridiaxs Employed in Chart Construction. — The United States, England, Germany, Italy,
Russia, Norway, Sw^eden, Denmark, Holland, Austria, Portugal, and Japan adopt as a prime meridian
the meridian of Greemvich.
France adopts the meridian of Paris in Long. 2° 20'' 14'". 5 E. of Greenwich.
Spain adopts the meridian of Sun Fernando, Cadiz, in Long. 6° 12'' 20" W. of Greenwich.
The Pulkowa Observatory of St. Petersburg (sometimes referred to in Russian charts) is in Long.
30° 19' 39''.6 E. of Greenwich.
The Royal Observatory of Naples (sometimes referred to in Italian charts) is in Long. 14° 14' 06" V..
of Greenwich.
The meridian of Genoa is 8° 55' 21" E. ; of Lisbon, 9° 08' 36" W. ; of Rio de Janeiro, 43° 10' 21".2
W.; of Amsterdam, 4° 53' 03". 8 E.; of Washington, 77° 03' 56". 7 AV.
45. Quality of Bottom. — The following table shows the qualities of the bottom, as expressed on
charts of various nations:
United States.
English.
French.
Italian.
Spanish.
German.
Clay
Coral
Gravel . . .
Mud
Rocky
C.
Co.
G.
M.
Sh.
Sf.
Clay
Coral
Gravel . . .
Mud
Rock
Sand
Shells ...
Stones
Weed....
Fine
Coarse . . .
Stiff
Soft
Black ...
Red
Yellow . .
cl.
....cri.
g-
m.
....rk.
s.
....sh.
St.
...wd.
f.
c.
....Stf.
....sft.
...blk.
....rd.
V
Argile
Corail
Gravier ..
Vase
Roche
Sable
Coquille .
Pierre....
Herb
Fin
Gros
Dure
Molle....
Noire
Rouge ...
Jaune
....A.
...Cor.
....Gr.
....V.
....R.
S.
..Coq.
V. .Vh."
...fin.
m.
n.
r.
J-
Argila
CoRlllo
Rena orGhiaja
Fango
Roccia ; . .
Arcillo or Barro
Coral
Cascfljo
Fango or Luno .
I^iedra or Roca .
Arena
Conchuela
IMedra
Alga
Fina
Gruesa
Tenaz
Muelle
Negro
RoJo
Amarillo
.cl.
Co.
-F.
..P.
.A.
.ca.
..P.
.A.
..f.
! Lehm
Korallen...
1 Grob sand . .
' Schlemm ..
Fels
Sand
Muschel . . .
Stein.
Gras
L.
K.
....g. s.
....Sch.
F.
Sand
Shells....
Stone .
Sabia or Arena
Conc'higlia
S.
M.
Weed
Wd.
Alga
Fino
G rosso
Tenace
G.
Fine
fne.
— crs.
stf.
sft.
bk.
rd.
yi.
gy.
f.
Coarse . . .
Stiff
1 Grob
Zahe
; Welch
Schwarz...
Roth.
Gelb.
Soft
Molle
W.
Black
..schw.
Red
Rosse
Yellow...
Giallo
Gray
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
21
46. Measures of Depth. — The following table shows the measures of depth employed in the charts
of certain foreign nations, with their equivalents in English measures:
1 English feet. I EngH^h
Austrian fathom (klafter) . .
Danish and Norwegian fathom (farn) . .
Dutch fathom ( vaden ) . .
p , /fathom ( brasse) . .
^ ^^"^^ \meter ( metre ) . . .
Portuguese . .'. fathom ( braga) . .
Prussian fathom (faden) . .
Russian fathom (sajen) . .
Spanish fathom (braza ) . .
Swedish fathom (famn) . .
6.222
6.175
5.575
5.329
3.281
6.004
5.906
6.000
5.492
5.843
fathoms.
1.030
1.029
0.929
0.888
0.547
1.000
0.984
1.000
0.915
0.974
The Dutch elle, the Spanish, Portuguese, and Italian metro, and the French vu'tre are identical.
A pied usael=l3A2A inches, or 1.094 feet. A mPtre is 3 pieds; a pied da ro/=12.7896 inches; brasse
is used upon old French charts instead of vii'tre. I'^pon some Italian charts soundings are in French
pieds.
THE BAROMETER.
47. The barometer is an instrument for measuring the pressure of the atmosphere, and is of great
service to the mariner in affording a knowledge of existing meteorological con-
ditions and of the probable changes therein. There are two cla.sses of barome-
ter— mercurial and aneroid.
4§. The Mercurial Barometer. — This instrument, invented by Torricelli
in 1643, indicates the pressure of the atmosphere by the height of a column
of mercury.
If a glass tube of uniform internal diameter somewhat more than 30 inches
in length and closed at one end be completely filled with pure mercury, and
then placed, open end down, in a cup of mercury (the open end having been
temporarily sealed to retain the liquid during the process of inverting), it will
be found that the mercurv in the tube will fall until the top of the colunm is
about 30 inches above the level of that which is in the cup, leaving in the upper
part of the tube a perfect vacuum. Since the weight of the colunm of mercury
thus left standing in the tube is equal to the pressure by which it is held in
position — namely, that of the atmospheric air — it follows that the height of the
column is subject to variation upon variation of that pressure; hence the mer-
cury falls as the pressure of the atmosphere decreases and rises as that pres-
sure increases. The mean pressure of the atmosphere is equal to nearly 15
pounds to the square inch ; the mean height of the barometer is about 30 inches.
49. In the practical construction of the barometer the glass tube which
contains the mercury is encased in a brass tube, the latter terminating at the
top in a ring to be used for suspension, and at the bottom in a flange, to which
the several i)arts forming the cistern are attached. The upper part of the brass
tube is partially cut away to expose the mercurial column for observation ;
abreast this opening is fitted a scale for measuring the height, and along the
scale travels a vernier for exact reading; the motion of the vernier is controlled
by a rack and pinion, the latter having a milled head accessible to the observer,
by which the adjustment is made. In the mitldle of the brass tube is fixed a
thermometer, the bulb of which is covered from the outside but open toward
the mercury, and which, being nearly in contact with the glass tube, indicates
the temperature of the mercury and not that of the external air; the central
position of the column is selected in order that the mean temperature may be
obtained — a matter of importance, as the temperature of the mercurial colunm
must ])e taken into account in ever}' accurate application of its reading.
50. In the arrangement of further details mercurial barometers are di-
vided into two classes, according as they are to be used a« Standards (lig. 4)
on shore, or as Sea Bcironicter-'i (fig. 3) on shipboard.
In the Standard Barometer the scale and vernier are so graduated as to
enable an observer to read the height of the mercurial column to the nearest
0.002 inch, while in the Sea Barometer the reading can not be made closer
than 0.01 inch.
tThe instruments also differ in the method of obtaining the true height of
the mercurial column at varying levels of the liquid in the cistern. It is evi-
dent that as the mercury in "the tube rises, upon increase of atmospheric pres-
sure, the mercury in the cistern must fall; and, conversely, when the mercurial
column falls the amount of fluid in the cistern will thereby be increased and a
Fig 3 ^^^® ^^ level will occur. As the height of the mercurial colunm is required Yig. 4.
above the existing level -in the cistern, some means must be adopted to obtain
the true height under varying conditions. In the Standard Barometer the mercury of the cistern is
contained in a leather bag, against the bottom of which presses the point of a vertical screw, the milled
22
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
head of the screw projecting from the bottom of the instrument and thus placing it under control of the
observer. By this means the surface of the mercury in the cistern (which is visible through a glass
casing) may be raised or lowered until it exactly coincides with that level which is chosen as the zero
of the scale, and which is indicated by an ivory pointer in plain view.
In the Sea Barometer there is no provision for adjusting the level of the cistern to a fixed point,
but compensation for tke Aariable level is made in the scale graduations; a division representing an
inch on the scale is a certain fraction short of the true inch, proper allowance being thus made for the
rise in level which occurs with a fall of the column, and for the reverse condition.
Further modification is made in the Sea Barometer to adapt it to the special use for which intended.
The tube toward its lower end is much contracted to prevent the oscillation of the mercurial column
known as "pumping," which arises from the motion of the ship; and just below this point is a trap to
arrest any small bubbles of air from finding their way upward. The instrument aboard ship is sus-
pended ill a revolving center-ring, in giml)als, supported on a horizontal brass arm which is screwed
to the bulkhead; a vertical position is thus maintained by the tube at all times.
51. The ?'frn(Vr is an attachment for facilitating the exact reading of the scale of the barometer,
and is also applied to many other instruments of precision, as, for example, the sextant and theodolite.
It consists of a metal scale similar in general construction to that of the instrument to which it is fitted,
and arranged to move alongside of and in contact with the main scale.
The general principle of the vernier requires that its scale shall have a total length exactly equal
to some whole number of divisions of the scale of the instrument and that this length shall be subdivided
into a number of parts equal to 1 more or 1 less than the number of divisions of the instrument scale
which are covered; thus, if a space of 9 divisions of the main scale be designated as the length of the
vernier, the vernier scale would be divided into either 8 or 10 parts.
Suppose that a barometer scale be divided into tenths of an inch and that a length of 9
divisions of such a scale be divided into 10 parts for a vernier (fig. 5) ; and suppose that the
31 divisions of the vernier be numbered consecutively from zero at the origin to 10 at the upper
extremity. If, now, by means of the movable rack and pinion, the bottom or zero division
of the vernier be brought level with the top of the mercurial column, and that division falls
into exact coincidence with a division of the main scale, then the height of the column will
correspond with the scale reading indicated. In such a case the top of the vernier will also
exactly coincide with a scale division, but none of the intermediate divisions will be evenly
abreast of such a division; the division marked "1" will fall short of a scale division by one-
tenth of 1 divison of the scale, or by 0.01 inch; that marked "2" by two-tenths of a division,
or 0.02 inch, and so on. If the vernier, instead of having the zero coincide with a scale
30 division, has the division " 1 " in such coincidence, it follows that the mercurial column stands
at 0.01 inch above that scale division which is next below the zero; for the division "2," at
0.02 inch; and similarly for the others. In the case portrayed in figure 5, the reading of the
column is 29.81 inches, the scale division next below the zero being 29.80 inches, while the
fact that the first division is abreast a mark of the scale shows that 0.01 inch must be added
to this to obtain the exact reading.
Had an example been chosen in which 8 vernier divisions covered 9 scale divisions — that
is, where the number of vernier divisions was 1 less than the number of scale divisions
covered — the principle would still have applied. But, instead of the length of 1 division of
the vernier falling short of a division of the scale by one-tenth the length of the latter, it would
have fallen beyond by one-eighth. To read in such a case it would therefore be necessary to
number the vernier divisions from up downward and to regard the subdivisions as ^^ instead
of 0.01 inch.
It is a general rule that the smallest measure to which a vernier reads is equal to the
length of 1 division of the scale divided by the number of divisions of the vernier; hence, by varying
either the scale or the vernier, we may arrive at any subdivision that may be desired.
52. The Sea Barometer is arranged as described for the instrument assumed in the illustration; the
scale divisions are tenths of an inch, and the vernier has 10 divisions, whence it reads to 0.01 inch. It is
not necessary to seek a closer reading, as complete accunu->' is not attainable in observing the height of a
barometer on a vessel at sea, nor is it essential. The Standard Barometer on shore, however, is capa-
ble of very exact reading; hence each scale division is made equal to half a tenth, or 0.05 inch, while
a vernier covering 24 such divisions is divided into 25 parts; hence the column may be read to 0.002 inch.
53. To adjust the vernier for reading the height of the mercurial column the eye should be brought
exactly on a level with the top of the column; that is, the line of sight should be at right angles to the
scale. When properly set, the front and rear edges of the vernier and the uppermost point of the mer-
cury should all be in the line of sight. A piece of white paper, held at the back of the tube so as to
reflect the light, assists in accurately setting the Aeniier by day, while a small bull's-eye lamp held
behind the instrument enables the observer to get a correct reading at night. When observing the
barometer it should hang freely, not being inclined by holding or even by touch, because any inclina-
tion will cause the column to rise in the tube.
54. Other things being equal, the mercury will stand higher in the tube when it is warm than
when it is cold, owing to expansion. For the purjxjses of comparison, all barometric observations are
reduced to a standard which assumes 32° F. as the temperature of the mercurial column, and 62° F. as
that of the metal scale; it is therefore important to make this reduction, as well as that for instrumental
error (art. 56), in order to be enabled to compare the true barometric pressure with the normal that
may be expected for any locality. The following table gives the value of this correction for each 2° F.,
Fig. 5.
INSTKUMENTS AND ACCESSORIES IN NAVIGATION.
23
the plus sign showing that tiie correction is to be added to the reading of the ship's barometer and the
minus sign that it is to be subtracted:
Tempera-
ture.
Correction.
Tempera-
ture.
Correction.
Tempera-
ture.
Correction.
Tempera-
ture.
Correction.
o
Inch.
o
Inch.
o
Inch.
o
Inch.
20
+0.02
40
-0.03
60
-0.09
80
-0.14
22
+0.02
42
-0.04
62
-0.09
82
-0.14
24
+0.01
44
-0.04
64
,-0.09
84
-0.15
26
+0.01
46
-0. 05
66
-0.10
86
-0.15
28
0.00
48
-0.05
68
-0.10
88
-0.16
30
0.00
50
-0.06
70
-0.11
90
-0.16
32
-0. 01
52
-0.06
72
-0.12
92
-0.17
34
- 0. 02
54
-0.07
74
-0.12
94
-0.17
36
-0.02
56
-0.07
76
-0.13
1 96
-0.18
38.
-0.03
58
-0.08
78
-0. 13
98
-0.18
As an example, let the ol^served reading of the mercurial Vjarometer be 29.95 inches, and the tem-
perature as given by the attached thermometer 74°; then we have:
Observed height of the mercury 29. 95
Correction for temperature (74° ) —0. 12
Height of the mercury at standard temperature 29. 83
55. The Aneroid Barometer. — This is an instrument in. which the pressure of the air is measured
by means of the elasticity of a plate of metal. It consists of a cylindrical brass box, the metal in the
sides being very thin; the contained air having been partially, tnough not completely, exhausted, the
box is hermetically sealed . When the pressure of the atmosphere increases the inclosed air is compressed,
the capacity of the box is diminished, and the two flat ends approach each other; when the pressure of
the atmosphere decreases, the ends recede from one another in consequence of the expansion of the
inclosed air. By means of a combination of levers, this motion of the ends of the box is communicated
to an index pointer which travels over a graduated dial plate, the mechanical arrangement being such
that the motion of the ends of the box is magnified many times, a very minute movement of the box
making a considerable difference in the indication of the pointer. The graduations of the aneroid scale
are obtained by comparison with the correct readings of a standard mercurial barometer under normal
and reduced atmospheric pressure.
The thermometer attached to the aneroid barometer is merely for convenience in indicating the
temperature of the air, but as regards the instrument itself, no correction for temperature can be applied
with certainty. Aneroids, as now manufactured, are almost perfectly compensated for temperature by
the use of different metals having unequal coefficients of expansion; they ought, therefore, to show the
same pressure at all temperatures.
The aneroid barometer, from its small size and the ease with which it may be transported, can often
be usefully employed under circumstances where a mercurial barometer would not be available. It also
has an advantage over the mercurial instrument in its greater sensitiveness, and the fact that it gives
earlier indications of change of pressure. It can, however, be relied upon only when frequently com-
pared with a standard mercurial barometer; moreover, considerable care is required in its handling;
while slight shocks will not ordinarily affect it, a severe jar or knock may change its indications by a
large amount.
When in use the aneroid barometer may be suspended vertically or placed flat, but changing from
one position to another ordinarily makes a sensible change in the readings; the instrument should
always, therefore, be kept in the same position, and the errors determined by comparisons made while
occupying its customary place.
56. Comparison of Barometers. — To determine the reliability of the ship's barometer, whether
mercurial or aneroid, comparisons should from time to time be made with a standard barometer.
Nearly all instruments read either too high or too low by a small amount. These errors arise, in a
mercurial barometer, from the improper placing of the scale, lack of uniformity of caliber of the glass
tube, or similar causes; in an aneroid, which is less accurate and in which there is even more necessity
for frequent comparisons, errors may be due to derangement of any of the various mechanical features
upon which its working depends. The errors of the barometer should be determined for various
heights, as they are seldom the same at all parts of the scale.
In the principal ports of the world standard barometers are observed at specified times each day,
and the readings, reduced to zero and to sea level, are published. It is therefore only necessary to read
the barometer on shipboard at those times, and, if a mercurial instrument is used, to note the attached
thermometer and apply the correction for temperature (art. 54). It is evident that a comparison of the
heights by reduced standard and by the ship's barometer will give the correction to be applied to the
latter, including the instrumental error, the reduction to sea level, and the personal error of the
observer. In the United States, standard barometer readings are made by the Weather Bureau and
Branch Hydrographic offices.
Aneroid barometers may be adjusted for instrumental error by moving the index hand, but this is
usually done only in the case of errors of considerable magnitude.
57. Determination of Heights by Barometer. — The barometer may be used to determine the
difference in heights between any two stations by means of the difference in atmospheric pressure
24
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
between them. An approximate rule is to allow 0.0011 inch for each difference in level of one foot, or,
more roughly, 0.01 inch for every 9 feet.
A very exact method is afforded by Babinet's formula. If B^ and B represent the barometric pres-
sure (corrected for all sources of instrumental error) at the lower and at the upper stations respectively,
and to and t the corresponding temperatures of the air; then,
Diff. in height=Cx
B„-B
My
B„-B'
if the temperatures be taken by a Farhenheit thermometer,
C ( in feet) = 52,494 (^i+ h+^-
if a centigrade thermometer is used, ^
C (in meters)- 10,000(^1-^ V^^.
THE THERMOMETER. *
58. The Thermometer is an instrument for indicating temperature. In its construction advantage
is taken of the fact that bodies are expanded by heat and contracted by cold. In its most usual form
the thermometer consists of a bulb filled with mercury, connected with a tube of very fine cross-sectional
area, the liquid column rising or falling in the tube according to the volume of the mercury due to the
actual degree of heat, and the height of the mercury indicating upon a scale the temperature; the mer-
cury contained in the tube moves in a vacuum produced by the expulsion of the air through boiling the
mercury and then closing the top of the tube by means of the blowpipe.
There are three classes of thermometer, distinguished according to the method of graduating the
scale as follows: the Fahrenheit, in which the freezing point of water is placed at 32° and its boiling
point (under normal atmospheric pressure) at 212°; the Centifjraxh', in which the freezing point is at 0°
and the boiling point at 100°; and the R'aumur, in which these points are at 0° and 80°, respectively.
The Fahrenheit thermometer is generally used in the United States and England. Tables will be
found in this work for the interconversion of the various scale readings (Table 31).
59. The thermometer is a valuable instrument for the mariner, not only by reason of the aid it
affords him in judging meteorological conditions from the temperature of the air and the amount of
moisture it contains, but also for the evidences it furnishes at times, through the temperature of the sea
water, of the ship's position and the proVjable current that is being encountered.
60. The thermometers employed in determining the temperature of the air (wet and dry bulb)
and of the water at the surface, should be mercurial, and of some standard make, with the graduation
etched upon the glass stem; they should be compared
with accurate standards, and not accepted if their read-
ings vary more than 1° from the true at any point of
the scale.
61. The dry-bulb thermometer gives the tempera-
ture of the free air. The wet-bulb thermometer, an
exactly similar instrument the bulb of which is sur-
rounded by an envelope of moistened cloth, gives what
is known as the temperature of evaporation, whi(;h is
always somewhat less than the temperature of the free
air. From the difference of these two temperatures the
observer may determine the proximity of the air to
saturation; that is, how near the air is to that point
at which it will l)e obliged to precipitate some of its
moisture (water vapor) in the form of liquid. With
the envelope of the wet \)\\\h removed, the two ther-
mometers should read precisely the same; otherwi.se
hey are practically useless.
The two thermometers, the wet and the dry bulb,
should be hung within a few inches of each other, and
the surroundings should be as far as possible identical.
In ]iractice the two thermometers are generally inclosed
within a small lattice case, such as that shown in figure
6; the case should be placed in a j)osition on deck
remote from any source of artificial heat, sheltered
from the direct rays of the .«un, and from the rain and
spray, but freely exposed to the circulation of the air;
the door shouUl hi kept closed except during the ])roc-
ess of reading. The cloth envelope of the wet bulb
should be a single thickness of line muslin, tightly
stretched over the bulb, and tied with a fine thread.
The wick which serves to carry the water from the
cistern to the bulb should consist of a few threads of
lamp cotton, and should be of sufficient length to admit of two or three inches being coiled in the cistern.
The muslin envelope of the wet bulb should V)e at all times thoroughly moist, but not dripping.
When the temperature of the air falls to 32° F. the water in the wick freezes, the capillary action
is at an end, the bull) in con.sequence soon becomes quite dry, and the thermometer no longer shows
the temperature f)f evaporation. At such times the ImP) should be thoroughly wetted with ice-cold
water shortly before the time of observation, using for this purpose a camel's hair brush or feather; by
Fig. 6.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
25
this process the temperature of the wet bulb is temporarily raised above that of the dry, but only for a
brief time, as the water quickly freezes; and inasmuch as evaporation takes place from the surface of
the ice thus formed precisely as from the surface of the water, the thermometer will act in the same way
as if it had a damp bulb. The wet-bulb thermometer can not properly read higher than the dry, and
if the reading of the wet bulb should be the higher, it may always be attributed to imperfections in the
instruments.
62. Knowing the temperature of the wet and dry bulbs, the relative humidity of the atmosphere
at the time of observation may be found from the following table:
Tempera-
ture of the
air, dry-
r)ifference between dry-bulb and wet-bulb readings.
bulb ther-
mometer.
1°
2°
3°
40
5°
6°
7°
.8°
9°
10°
o
Perct.
Perct.
Per ct.
Per ct.
Per ct.
Perct.
Per ct.
Per ct.
Per ct.
Per ct.
24
87
75
62
50
38
26
26
88
76
65
63
42
30
28
89
78
67
56
45
34
24
30
90
79
68
58
48
38
28
32
90
80
70
61
51
41
32
23
34
90
81
72
63
53
44
35
. 27
36
91
82
73
64
55
47
38
30
22
38
92
83
75
66
57
50
42
34
26
40
92
84
76
68
59
52
44
37
30
22
42
92
84
77
69
61
54
47
40
33
26
44
92
85
78
70
63
56
49
43
36
29
46
93
85
79
72
65
58
51
45
38
32
48
93
86
79
73
66
60
53
47
41
35
50
93
87
80
74
67
61
55
49
43
37
52
94
87
81
75
69
63
57
51
46
40
54
94
88
82
76
70
64
59
53
48
42
56
94
88
82
77
71
65
60
55
50
44
58
94
89
83
78
72
67
61
56
51
46
60
94
89
84
78
73
68
63
58
53
48
62
95
89
84
79
74
69
64
59
54
50
64
95
90
85
79
74
70
65
60
56
51
66
95
90
85
80
75
71
66
61
57
53
68
95
90
85
61
76
71
67
63
58
54
70
95
90
86
81
77
72
68
64
60
55
72
95
91
86
82
77
73
69
65
61
57
74
95
91
86
82
78
74
70
66
62
58
76
95
91
87
82
78
74
70
66
63
59
78
96
91
87
83
79
75
71
67
63
60
80
96
92
87
83
79
75
72
68
64
61
82
96
92
88
84
80
76
72
69
65
62
84
96
92
88
84
80
77
73
69
66
63
86
96
92
88
84
81
77
73
70
67
63
88
96
92
88
85
81
77
74
71
67
64
90
96
92
88
85
81
78
74
71
68
65
The table may be readily understood. For example, if the temperature of the air (dry bulb) be
60°, and the temperature of evapoi'ation (wet bulb) be 56°, the difference being 4°, look in the column
headed "Temperature of the air" for 60°, and for the figures on the same line in column headed 4°;
here 78 will be found, which means that the air is 78 per cent saturated with water vapor; that is, that
the amount of water vapor present in the atmosphere is 78 per cent of the total amount that it could
carry at the given temperature (60°). This total amount, or saturation, is thus represented by 100, and
if there occurred any irtcrease of the quantity of vapor beyond this point, the excess would be precipi-
tated in the form of liquid. Over the ocean's surface the relative humidity is generally about 90 per
cent, or even higher in the doldrums; over the land in dry winter weather it may fall as low as 40 per
cent.
63. The sea water of which the temperature is to be taken should be drawn from a depth of 3
feet below the surface, the liucket used being weighted in order to sink it. The bulb of the thermome-
ter should remain immersed in the water at least three minutes before reading, and the reading should
be made with the bulb immersed.
THE LOG BOOK.
64. The Log Book is a record of the ship's cruise, and, as such, an important accessory in the navi-
gation. It should afford all the data from which the position of the ship is established by the method
of dead reckoning; it should also comprise a record of meteorological oteervations, which should be
made not only for the purpose of fortelling the weather during the voyage, luit also for contribution to
the general fund of knowledge of marine meteorology.
65. A convenient form for recording the data, which is employed for the log books of United States
naval vessels, is shown on page 26; beside the tabulated matter thus arranged, to which one page of the
book is devoted, a narrative of the miscellaneous events of the day, written and signed by the proper
officers, appears upon the ojipcjsite page.
26
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
•M 10
Ot»vS
oo "" «
^-
g^s
•
O <d o
as^f
i
o
-«! =•
tic
§2
o
S""
0!
S o
E b-C"
s-^a
a
«
5|fe-
«^>.
^
frN
s^ig
^saS
a5
^ "^
3
i
£^5
a
■<»^
s
(V
H
^
S S 0)2
■2
J3 o-S*s
■£
H3^<a
1
S S
^
^c^
n
01 •" u
W 5
i >>
a S3
H^l^
"3
0)
K
6
o
o
f^
>>
a
■^-o^
'^
a ^ uS
III
•a
Ill
» c a
III
2>>"
5-^
Sao ^
.5 c .
■C"- 4) !lO
g's^
« *
m
^
a
1
E-i
ft
M
2
o
c
s
S
-< W
o o
X GC !1Q DC OG
mi I
>.0 >-.H ^.'-S
>.-° >>'^ t*.'^ g
OJ
05 O « O 03 O ,,
J J ^ ^ ^ ^ g
■~1 ' ■; c
6C O
.S °
Ch OJ C
« S !=
.S
'x
o
o
a
o
O
03 Q
£ 2 o
bp 2
OJ -)H
S S
C C £
tc CO p
S 5 6
C 2
*- O o
•^ eS t;
> W Q
OS 5
S -^
2 «
6C c
'^
o
c 3
2:
1!
p.'-i
?J rt
tc c
ft'O
'fc
fi
-c
o
n fl
it:
-« o
.H
Tl 6C
C
<D a
crt
S c
1
11
o >^
tl
0)
ec
S3
'^ %
?i
;::-
O Q
INSTRUMEJSTTS AND ACCESSORIES IN NAVIGATION.
27
66. For the most part, the nature of the information called for, with the method of recording it,
will be apparent. A brief explanation is here given of "such points as seem to require it.
67. The Wind. — In recording the force of the wind the scale devised by the late Admiral Sir F.
Beaufort is employed. According to this scale the wind varies from 0, a calm, to 12, a hurricane, the
greatest velocity it ever attains. In the lower grades of the scale the force of the wind is estimated
from the speed imparted to a man-of-war of the early part of the nineteenth centurj^ sailing full and by;
in the higher grades, from the amount of sail which the same vessel could carry when closehauled.
The scale, with the estimated A-elocity of the wind in both statute and nautical miles per hour, is as
follows:
Conditions.
Velocity.
Mean pressure
in pounds
per square
foot.
Foree of wind.
Statute miles per
hour.
Nautical miles per
hour.
0.— Calm
Full-rigged ship, all sails set, no headway.
.lust sufficient to give steerage way
Speed of 1 or2knots, "full and by"
Speed of 3 or 4 knots, " full and by "
Speed of 5 or 6 knots, "full and by"
All plain sail, " full and by"
0 to 3
8
13
18
23
28
34
40
48
56
65
75
90 and over.
0 to 2. 6
6.9
11.3
15.6
20.0
24.3
29.6
34.7
41.6
48.6
56.4
65.1
78. 1 and over.
0 03
1.— Light air
2.— Light breeze
3.— Gentle breeze
4.— Moderate breeze . .
0.23
0.62
1.2
1.9
2 9
6.— Strong breeze
7.— Moderate gale —
8.— Fresh gale
9. — Strong gale
10.— Whole gale
11.— Storm
Topgallantsails over .single-reefed topsails
4.2
5 9
Treble-reefed topsails (or reefed upper-
top.sails and courses).
Close-reefed topsails and courses (or lower
topsails and courses).
Close-reefed main topsail and reefed fore-
sail (or lower main topsail and reefed
foresail).
8.4
11.5
15.5
20.6
12. — Hurricane
Under bare poles
29 6 ,
68. When steaming or sailing with any considerable speed, the apparent direction and force of
the wind, as determined from a vane, flag, (jr pennant aboard ship, may differ materially from the true
direction and force, the reason being that the air appears to come from a direction and with a force
dependent, not only upon the wind itself, but also upon the motion of the vessel. For instance,
suppose that the wind has a velocity of 20 knots an hour (force 4), and take the case of two vessels,
each steaming 20 knots, the first with the wind dead aft, the second with the wind dead ahead. The
former vessel will be moving with the same velocity as the air and in the same direction; the velocity
of the wind relatively to the ship will thus be zero; on the vessel an apparent calm will prevail and the
I^ennant will hang up and down. The latter vessel will be moving with the same velocity as the air, but
in the opposite direction; the relative velocity of the two will thus be the sum of the two velocities, or 40
knots an hour, and on the second vessel the wind will apparently have the velocity corresponding very
nearly with a fresh gale. Again, it might be shown that in the case of a vessel steaming west at the
rate of 20 knots, with the wind blowing from north with the velocity of 20 knots an hour, the velocity
with which the air strikes the ship as a result of the combined motion will be 28 knots an hour, and
the direction from which it comes will be NW. If, therefore, the effect of the the speed of the ship is
neglected the wind will be recorded as NW., force 6, when in reality it is north, force 4.
In order to make a proper allowance for this error and arrive at the true direction and force of the
wind. Table 32 may be entered with the ship's speed and the apparent direction and force of the wind
as arguments, and the true direction and force wall be found.
69. AVeather. — To designate the weather a series of symbols devised by the late Admiral Beaufort
is employed. The system is as follows:
b. — Clear blue sky.
c. — Clouds.
d. — Drizzing, or light rain.
/. — Fog, or foggy weather.
g. — Cloomy, or dark, stormy-looking weather.
^.— Hail.
I. — Lightning.
?». — Misty weather.
0. — Overcast.
p. — Passing showers of rain.
q. — Squally weather.
r. — Eainy weather, or continuous rain
s. — Snow, or snowv weather.
^— Thunder.
u.
r. — Visibility of distant objects.
v. — Wet, or heavy dew.
z. — Hazv.
Ugly appearances, or threatening weather.
Visib
To indicate great intensity of any feature, its symbol may be underlined; thus: r., heavy rain.
70. ("LorDS. — The following are the principal forms of clouds, named in the order of the altitude
above the earth at which they usually occur, beginning with the most elevated. The symbols by which
each is designated follows its name:
1. CiRKUs, (d). ^Detached clouds, delicate and fibrous looking, taking the form of feathers,
generally of a white color, sometimes arranged in belts which cross a portion of the sky in great circles,
and, by an effect of perspective, converging toward one or two opposite points of the horizon.
2. Cirro-Stratus, [CL-S.). — A thin, whitish sheet, sometimes completely covering the sky and
only giving it a whitish appearance, or at others presenting, more or less distinctly, a formation like a
tangled web. This sheet often produces halos around the sun and moon.
3. CiRRO-CuMULUs, {Ci.-Cu.). — Small globular masses or white flakes, having no shadows, or only
very slight shadows, arranged in groups and often in lines.
4. Alto-Cumulus, {A.-Cu.). — Rather large globular masses, white or grayish, partially shaded,
arranged in groups or lines, and often so closely packed that their edges appear confused. The detached
masses are generally larger and more compact at the center of the group; at the margin they form into
finer flakes. They often spread themselves out in lines in one or two directions.
28 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
5. Alto-Strati's, (^1.-»S'.)- — A thick sheet of a gray or bhiish color, showing a brilliant patch in the
neighborhood of the sun or moon, and which, without causing halos, may give rise to corome. This
form goes through all the changes like the Cirro-Stratus, but its altitude is only half so great.
6. STRATO-CrMiLrs, {S.-Ch.). — I^rge globular masses or rolls of dark cloud, frequently covering the
whole sky, especially in winter, and occasionally giving it a wavy appearance. The layer of Strato-
Cumulus is not, as a ^jple, very thick, and patches of blue sky are often visible through the intervening
spaces. All sorts of transitions between this form and the Alto-Cumulus are noticeable. It may be
distinguished from Nimbus by its globular or rolled appearance and also because it does not bring rain.
7. Nimbus, (N.). — Rain clouds; a thick layer of dark clouds, without shape and with ragged edges,
from which continued rain or snow generally falls. Through the openings of these clouds an upper
layer of Cirro-Stratus or Alto-Stratus may almost invariably be seen. If the layer of Nimbus separates
into shreds or if small loose clouds are visible floating at a low level underneath a large nimbus, they
may be described as Fracto-Nimlms (Fr.-N. ), the "scud " of sailors.
8. Cumulus, (Cm.). — Wool-pack clouds; thick clouds of which the upper surface is dome-shaped
and exhibits protuberances, while the base is horizontal. When these clouds are opposite the sun the
surfaces usually presented to the observer have a greater brilliance than the margins of the protuber-
ances. When the light falls aslant, they give deep shadows; when, on the contrary, the clouds are on
the same side as the sun, they appear dark, with bright edges. The true Cumulus has clear superior
and inferior limits. It is often broken up by strong winds, and the detached portions undergo continual
changes. These may be distinguished by the name of Fracto-Cumulus (Fr.-(1*«.).
9. CuMULO-NiMBus, ( Cn.-N. ). — The thunder-cloud or shower-cloud; heavy masses of clouds rising in
the form of mountains, turrets, or anvils, generally having a sheet or screen of fibrous appearance above,
and a mass of clouds similar to Nimbus underneath. From the base there usually fall local showers
of rain or of snow (occasionally hail or soft hail).
10. Stratus, (»S'. ). — A horizontal sheet of lifted fog; when this sheet is broken up into irregular
shreds by the wind or by the summits of mountains, it may be distinguished by the name of Fracto-
Stratus (Fr.-S.).
71. In the scale for the amount of clouds 0 represents a sky which is cloudless and 10 a sky which
is completely overcast.
72. State of Sea. — The state of the sea is expressed by the following system of symbols:
B. — Broken or irregular sea. M. — Moderate sea or swell.
C. — Chopping, short, or cross sea. R. — Rough sea.
Cr.^Ground swell. »S'. — Smooth sea.
H. — Heavy sea. T. — Tide-rips.
L. — Long rolling sea.
THE COMPASS EREOR. 29
CHAPTER III
THE COMPASS EKEOE.
CAUSES OF THE ERROT.
73. When two magnets are near enough together to exert a mutual intiuence, their properties are
such as to cause those poles which possess similar magnetism to repel, and those which possess magnet-
ism of opposite sorts to attract one another.
The earth is an immense natural magnet, having in each hemisphere a pole lying in the neighbor-
hood of the geographical pole, though not exactly coincident therewith; consequently, when a magnet,
such as that of a compass, is allowed to revolve freely in a horizontal plane, it will so place itself as to
be i>arallel to the lines of magnetic force in that plane created 1)y the earth's magnetic poles, the
end which we name north pointing to the north, and the south end in the opposite direction. The
north end of the compass — north-seeking, as it is sometimes designated for clearness — will be that end
Avhich has opposite polarity to the earth's north magnetic pole, this latter possessing the same sort of
magnetism as the so-called south pole of the comjiass.
74. By reason of the fact that the magnetic pole differs in position from the geographical pole, the
compass needle will not indicate true directions, but each compass point will differ from the correspond-
ing true point by an amount dependent upon the angle between the geographical and the magnetic pole
at the position of the observer. The amount of this difference, expressed in angular measure, is the
Variation of the Compass (sometimes called also the Declination, though this term is seldom employed by
navigators).
The variation not only changes as one travels from point to point on the earth, being different in
different localities, but, as it has Ijeen found that the earth's magnetic poles are in constant motion, it
undergoes certain changes from year to year. In taking account of the error it produces, the navigator
nmst therefore be sure that the variation used is correct not only for the place, but also for the time
under consideration. The variation is subject to a small diurnal fluctuation, but this is not a material
consideration with the mariner.
75. Besides the error thus produced in the indications of the compass, a further one, due to Local
Attraction, may arise from extraneous influences due to natural magnetic attraction in the vicinity of the
vessel. Instances of this are quite common when a ship is in port, as she may be in close jiroximity to
vessels, docks, machinery, or other masses of iron or steel. It is also encountered at sea in localities where
the mineral substan<'es in the earth itself possess magnetic qualities — as, for example, at certain places in
Lake Superior and at others off the coast of Australia. When due to the last-named cause, it may be a
source of great danger to the mai'iner, but, fortunately, the number of localities suVjject to local attraction
is limited. The amount of this error can seldom, if ever, be determined; if known, it might properly
be included with the variation and treated as a part thereof.
76. In addition to the variation, the compass ordinarily has a still further error in its indications,
which arises from the effect exerted upon it by masses of magnetic metal within the ship itself. This
is known as the Deviation of the Compass. For reasons that will be explained later, it differs in amount
for each heading of the ship, and, further, the character of the deviations undergo modification as a
vessel proceeds from one geographical locality to another.
APPLYING THE COMPASS ERROR.
77. From what has been explained, it may be seen that there are three methods by which bearings or
courses may be expressed: (a) true, when they refer to the angular distance from the earth's geographical
meridian; \h) magnetic, when they refer to the angular distance from the earth's magnetic meridian,
and must be corrected for variation to be converted into true; and (c) by compass, when they refer to
the angular distance from the north indicated ))y the compass on a given heading of the ship, and must
be corrected for the deviation on that heading for conversion to magnetic, and for both deviation and
variation for conversion to true bearings or courses. The process of applying the errors under all circum-
stances is one of which the navigator must make himself a thorough master; the various problems of
conversion are constantly arising; no course can be set nor liearing plotted without involving the applica-
tion of this problem, and a mistake in its solution may produce serious consequences. The student is
therefore urged to give it his most careful attention.
30
THE COMPASS ERROR.
7§. When the effect of a compass error, whether arising from variation or from deviation, is to
draw the north end of the compass needle to the right, or eastward, the error is named east, or is
marked +; when its effect is to draw the north end of the needle to the left or westward, it is named
west, or marked — .
Figures 7 and 8 represent, respectively, examples of easterly and westerly errors. In both cases
consider that the circles rep-
resent theobserver's horizon,
N and S being the correct
north and south points in
each case. If N^ and S' repre-
sent the corresponding pomts
indicated by a compass whose
needle is deflected by a com-
pass error, then in the first
qa.'-e, the north end of the
needle being drawn to the
right or east, the error will
Ije easterly or positive, and
in the second case, the north
end of the needle being drawn
to the left or west, the com-
pass error will be westerly or
negative.
Considering figure 7, if
we assume the easterly error to amount to one point, it will be seen that if a direction of N. by W. is
indicated by the compass, the correct direction should be north, or one point farther to the right. If
the compass indicates north, the correct bearing is N. by E. ; that is, still one point to the right.
If we follow around the whole card, the same relation will be found in every case, the corrected bearing
being always one point to the right of the compass bearing. Conversely, if we regard figure 8, assuming
the same amount of westerly error, a compass bearing of N. by E. is the equivalent of a correct bearing
of north, which is one point to the left; and this rule is general throughout the circle, the corrected
direction being always to the left of that shown by the compass.
79. Having once satisfied himself that the general rule holds, the navigator may save the necessity
of reasoning out in each case the direction in which the error must be applied, and need only charge
his mind with some single formula which will cover all cases. Such a one is the following:
When tlie correct direction is to tite right, the error is east.
The words correct-right-east, in such a case, would be the key to all of his solutions. If he had a
compass course to change to a corrected one with easterlj^ deviation, he would know that to obtain the
result the error must be applied to the right; if it were desired to change a correct course to the one indi-
cated by compass, the error being westerly, the converse presents itself — the correct must be to the
left — the uncorrected will therefore be to the right; if a correct bearing is to be compared with a com-
pass bearing to find the compass error, when the correct is to the right the error is east, or the reverse.
§0. It must be remembered that the word east is equivalent to right in dealing with the compass
error, and west to left, even though they involve an apparent departure from the usual rules. If a
vessel steers NE. by compass with one point easterly error, her corrected course is NE. by E. ; but if
she steers SE., the corrected course is not SE. by E., but SE. by S. Another caution may be necessary
to avoid confusion; the navigator should always regard himself as facing the point under consideration
when he applies an error; one point westerly error on South will bring a corrected direction to S. by
E. ; but if we applied one point to the left of South while looking at the compass card in the usual
way — north end up — S. by W. would be the point arrived at, and a mistake of two points would be the
result.
§1. In the foregoing explanation reference has been made to " correct" directions and " compass
errors" without specifying "magnetic" and "true" or "variation" and "deviation." This has been
done in order to make the statements apply to all cases and to enable the student to grasp the subject
in its general bearing without confusion of details.
Actually, as has already been pointed out, directions given may be true, magnetic, or by compass.
By applying variation to a magnetic bearing we correct it and make it true, by applying deviation to a
compass bearing we correct it to magnetic, and by applying to it the combined deviation and variation
we correct it to true. Whichever of these operations is undertaken, and whichever of the errors is
considered, the process of correction remains the same; the correct direction is always to the right,
when the error is east, by the amount of that error.
Careful study of the following examples will aid in making the subject clear:
Examples: A bearing taken by a compass free from deviation is ,^. 76° H; variation, 5° W. ;
required the true bearing. N. 71° E.
A bearing taken by a similar compass is NW. bv W. i W. ; variation, \ pt. W. ; requiretl the true
bearing. NW. by W. f W.
A vessel steers S. 27° ¥j. bv compass; deviation on that heading, 3° W. ; variation in the locality,
12° E. ; required the true course. S. 18° E.
A vessel steers S. bv W. § W. ; deviation, \ pt. W. ; variation, 1 pt. E. ; required the true course.
SSW. \ W.
It is desired to steer the magnetic course N. 38° W.; deviation, 4° E. ; required the course by com-
pass. N. 42° W. '
The true course between two points is found to be W. \ N. ; variation \\ pt. E. ; no deviation;
required the compass course. W. f S.
True course to be made, N. 55° E. ; deviation, 7° E.; variation, 14° W.; required the course by
compass. N. 62° E.
THE COMPASS ERROR. 31
A vessel passing a range whose direction is known to be S. 20° W., magnetic, observes the bearing
by compass to be S. 2° E. ; required the deviation. 22° E.
The sun's observed bearing l)y compass is S/i89° E. ; it is found by calculation to be N. 84° E. (true) ;
variation, 8° W.; required the deviation. 1° E.
FINDING THE COMPASS EBBOB. ^
§2. The variation of the compass for any giveiJ^locality is found from the charts. A nautical
chart always contains information from which the navigator is enabled to ascertain the variation for
any place within the region embraced and for any year. Beside the information thus to be acquired
from local charts, special charts are published showing the variation at all points on the earth's surface.
83. The deviation of the compass, varying as it does for every ship, for every heading, and for
every geographical locality, must be determined by the navigator, for which purpose various methods
are available.
Whatever method is used, the ship must be swung in azimuth and an observation made on each of
the headings upon which the deviation is required to be known. If a new iron or steel ship is being
swung for the first time, observations should be made on each of the thirty-two points. At later
swings, especially after correctors have been applied, or in the case of wooden ships, sixteen points
will suffice — or, indeed, only eight. In case it is not practicable to make observations on exact compass
points, they should be made as near thereto as practicable and platted on the Napier diagram (to be
explaine)'! hereafter), whence the deviations on exact points may be found.
84. In swinging ship for deviations the vessel should be on an evei^ keel and all movable masses
of iron in the vicinity of the compass secured as for sea. The vessel, upon being placed on any heading,
should be steadied there for three to four minutes before the observation is made in order that the
compass card may come to rest and the magnetic conditions assume a settled state. To assure the
greatest accuracy the ship should first be swung to starboard, then to port, and the mean of the two
deviations on each course taken. Ships may be swung under their own steam, or with the assistance
of a tug, or at anchor, where the action of the tide tends to turn them in azimuth (though in this case
it is difficult to get them steadied for the recjuisite time on each heading), or at anchor, by means of
springs and hawsers.
85. The deviation of all compasses on the ship may be obtained from the same swing, it being
required to make observations with the standard only. To accomplish this it is necessary to record the
ship's head by all compasses at the time of steadying on each even point of the standard; applying
the deviation, as ascertained, to the heading by standard, gives the magnetic heads, with which the
direction of the ship's head by each other compass may be compared, and the deviation thus obtained.
Then a complete table of deviations may be constructeii as explained in article 94.
86. There are four methods for ascertaining the deviations from swinging; namely, by reciprocal
hearings, by bearings of the sun, by ranges, and by a distant object.
87. Reciproc.vl Bearings. — One observer is stationed on shore with a spare compass placed in a
position free from disturbing magnetic influences; a second observer is at the standard compass on
board ship. At the instant when ready for observation a signal is made, and each notes the bearing
of the other. The bearing by the shore compass, reversed, is the magnetic bearing of the shore station
from the ship, and the difference between this and the bearing by the ship's standard compass repre-
sents the deviation of the latter.
In determining the deviations of compasses, placed on the fore-and-aft amidship line, when the
distribution of magnetic metal to starboard and port is symmetrical, the shore compass may be replaced
by a dumb compass, or pelorus, or bv a theodolite in which, for convenience, the zero of the horizontal
graduated circle may be termed north; the reading of the shore instrument will, of course, not represent
magnetic directions, but by assuming that they do we obtain a series of fictitious deviations, the mean
value of which is the error common to all. Upon deducting this error from each of the fictitious devia-
tions, we obtain the correct values.
If ship and shore observers are provided with watches which have been compared with one
another, the times may be noted at each observation, and thus afford a means of locating errors due to
misunderstanding of signals.
88. Bearings of the Sun. — In this method it is required that on each heading a bearing of the
sun be observed by compass and the time noted at the same moment by a chronometer or watch. By
means which will be explained in Chapter XIV, the true bearing of the sun may be ascertained from
the known data, and this, compared with the compass bearing, gives the total compass error; deducting
from the compass error the variation, there remains the deviation. The variation used may be that
given by the chart, or, in the case of a compass affected only by symmetrically placed iron or steel, may
be considered equal to the mean of all the total errors. Other celestial bodies may be observed for this
purpose in the same manner as the sun.
This method is important as being the only one available for determining the compass error at sea.
89. Ranges. —In many localities there are to be found natural or artificial range marks which are
clearly distinguishable, anil which when in line lie on a known magnetic bearing. By steaming about
on different headings and noting the compass bearing of the ranges each time of crossing the line that
they mark, a series of deviations may be obtained, the deviation of each heading being equal to the
difference between the compass and the magnetic bearing.
90. Distant Object. — A conspicuous object is selected which must be at a considerable distance
from the ship and upon which there should be some clearly defined point for taking bearings. The
direction of this object by compass is observed on successive headings. Its true or magnetic bearing is
then found and compared with the compass bearings, whence the deviation is obtained.
The true or the magnetic bearing may be taken from the chart. The magnetic bearing may also be
found by setting up a compass ashore, free from foreign magnetic disturbance, in range with the object
and the ship, and observing the bearing of the object; or the magnetic bearing maybe assumed to be the
mean of the compass l)earings.
32
THE COMPASS ERROK.
In choosing an oliject for use in this method care must.be taken that it is at such a distance that its
bearing from the shii)does not practically differ as the vessel swings in azimuth. If the ship is swung
at anchor, the distance should l)e not less than 6 miles. If swung under way, the object must be so far
that the parallax (the tangent of which may be considered equal to half the diameter of swinging
divided by the distance) shall not exceed about 30'.
91. in all of the inethods described it will be found convenient to arrange the results in tabular
form. In one column record the ship's head by standard compass, and aljreast it in successive colunms
the observations from which the deviation is determined on that heading, and finally write the deviation
itself. When the result of the swing has been worked up another table is constructed showing simply
the lieadings and the corresponding deviations. This is known as the Deriation Table of the compass.
If compensation is to l)e attempted, this table is the basis of the o])eration; if not, the deviation tables
of the standard and steering compass should be posted in such place as to be accessible to all i^ersons
concerned with the navigation of the ship.
92. Let it lie assumed that a deviation table has been found and that the values are as follows:
Deviation table.
Ship's head ht
Devia-
Ship's head by
standard compass.
Devia-
Ship's head by
Devia-
Ship's head bv
Devia-
standard compas.s.
tion.
tion.
standard compass.
tion.
1 standard compass.
tion.
North . . . .
o /
- 1 00
- 1 50
East
E.byS...
-19 55
-22 00
South
S. by W . .
0 00
+ 10 20
West
o /
+19 30
N. by E . . .
W.byN...
+17 00
NNE
- 3 00
ESE
-23 30
SSW
+ 17 00
WNW
+ 13 00
NE. by N . .
- 5 15
SE. bv E .
-24 00
SW.byS.
+21 50
1 NW.byW.
+11 10
NE :
- 7 10
SE :....
-23 30
SW
+24 30
' NW
+ 7 40
NE. by E . .
-10 15
SE.bvS..
-20 30
SW. bv W
T-26 20
NW. by N .
+ 5 05
ENE
-13 05
SSE
-16 00
WSW ....
+25 00
NNW
+ 3 00
E.by N ...
-17 10
S.byE...
- 8 50
1
W.bvS..
+23 30
N.byW...
+ 1 00
AVe have from the table the amount of deviation on each compass heading; therefore, knowing the
ship's head by compass, it is easy to pick out the corresponding deviation and thus to obtain the mag-
netic heading. But if we are given the magnetic direction in which it is desired to steer and have to
find the corresponding compass course, the problem is not so simple, for we are not given deviations
on magnetic heads, and where the errors are large it may not be assumed that they are the same as on
the corresponding compass headings. For example, with the deviation ta])le just given, suppose it is
required to determine the compass heading corresponding to N. 79° W., magnetic.
The deviation corresponding to N. 79° W., per compass, is + 17° 00'. If we apply this to N. 79°
W., magnetic, we have S. 84° W. as the compass course. But, consulting the table, it may be seen that
the deviation corresponding to S. 84° W., per compass, is + 21 J°, and therefore if Me steer that course
the magnetic direction will be N. 74^° AV., and not N. 79° W., as desired.
A way of arriving at the correct result is to make a series of trials until a course is arrived at which
fulfills the conditions. Thus, in the example given:
Mag. course required
Try dev. on X. 79° W., p. c
First trial.
N. 79° W.
17° E.
Trial comp. course S. 84° AV.
Dev. on S. 84° W., p. c 2U° E.
Mag. course made good N. 74i° A\'.
Since this assumption carries the course 4i° too
far to the right, assume next a deviation on a
course 5° farther to the left than tlie one used here.
Mag. course required
Try dev. on S. 79° A\'., p.
Trial comp. course
Dev. onS. 77i° W.
p. c
/Second trial.
N. 79° AA'.
..... 23^° E.
77 i° W
24° E.
Mag. course made good X. 782° AV.
This is as close to the required course as the ship
can be steered. It may occur that further trials
will be necessarv in some cases.
93. The Xapier Diagram. — A much more expeditious method for the solution of this problem is
afforded by the Xapier Diagram, and as that diagram also facilitates a number of other operations con-
nected with compass work it should be clearly understood by the navigator. This device admits of a
graphic representation of the table of deviations of the compass by means of a curve; besides furnishing
a ready means of converting compass into magnetic courses and the reverse, one of its chief merits is
that if the deviation has been determined on a certain number of headings it enables one to obtain the
most probable value of the deviation on any other course that the ship may head. The last-named
feature renders it useful in making a table of deviations of compasses other than the standard when their
errors are found as described in article 85.
THE COMPASS ERROR.
33
94. The Napier diagram (fig. 9) represents the margin of a compass card cut at the north point and
straightened into a vertical line; for convenience, it is usually divided into two sections, representing,
respectively, the eastern and western semicircles. The vertical line is of a convenient length and di\ided
into thirty-two equal parts corresponding to the points of the compass, beginning at the top with North
and continuing around to the right; it is also divided into 360 degrees, which are appropriately marked.
DEVIATION
WEST
DEVIATIOM
EAST
DEVIATION
WEST
DEVIATION
EAST
Fi(4. 9.
The vertical line is intersected at each compass point l)y two lines inclined to it at an angle of 60°,
that line which is inclined upward to the right being drawn plain and the other dotted.
To pl(jt a curve on the Napier diagram, if the deviation has been observed with the ship's head ou
given coi/(/)a.s-.s' courses (as is usually the case with the standard compass), measure off on the vertical
scale the number of degrees corresponding to the deviation and lay it down — to the right if easterly and
to the left if westerly — on the dotted line passing through the point representing the ship's head; or, if
the observation was not made on an even point, then lay it down on a line drawn parallel to the dotted
ones through that division of the vertical line which represents the compass heading; if the deviation
has been observed with the ship on given magnetic courses (as when deviations by steering compass are
obtained by noting the ship's head during a swing on even points of the standard) , proceed in the same
way, excepting that the deviation must be laid down on a plain line or a line parallel thereto. Mark
each point thus obtained with a dot or small circle, and draw a free curve passing, as nearly as possible,
through all the points.
224X0—0:";-
-3
34
THE COMPASS ERROR.
To obtain a complete curve, a suflicient number of observations should be taken while the t^hip
swings through an entire circle. Generally, observations on every alternate point are enough to estab-
lish a good curve, but in cases where the maximum deviation reaches 40° it is preferable to observe on
every i)oint.
The curve shown in the full line on figure 9 corresponds to the table of deviations given in article 92.
From a given compass course to find the corresponding magnetic course, through the point of the vertical
line representing the given compass course, draw a line parallel to the dotted lines until the curve is
intersected, and from the point of intersection draw another line parallel to the plain lines; the point on
the scale where this last line cuts the vertical line is the magnetic course sought. The correctness of
this solution will be ap])arent when we consider that the 60° triangles are e(iuilateral, and therefore the
distance measured along the vertical side will equal the distance measured along the inclined sides —
that is, the deviation; and the direction will be correct, for the construction is such that magnetic
directions will be to the right of compass directions when the deviation is easterly and to the left if
westerly.
From a given magnetic course to find the corresponding compass course, the process is I Ik same, exce])ting
that the first line drawn should follow, or be parallel to, the plain lines, and the second, or return line,
should be parallel to the dotted; and a proof similar to that previously employed will show the correctness
of the result. As an example, the problem given in article 92 may be solved by the diagram, and the
result will be found to accord with the solution previously given.
THE THEORY OF DEVIATION." '
95. Features of the Earth's MA(iNETisM. — It has already been stated that the earth is an
immense natural magnet, with a pole in each hemisphere which is not coincident with the geographical
pole; it has also a magnetic equator which lies close to, but not coincident with, the geographical
equator.
A magnetic needle freely suspended at a point on the earth's surface, and undisturbed by any
other than the earth's magnetic influence, will lie in the plane of the magnetic meridian and at an
angle with the horizon depending upon the geographical position.
The magnetic elements of the earth which must be considered are shown in figure 10. The earth's
total force is represented in direction and intensity by the line AB. Since compass needles are mechan-
ically arranged to move only in a horizontal plane, it becomes
necessary, when investigating the effect of the earth's mag-
netism upon them, to resolve the total force into two com-
ponents which in the figure are represented by AC and AD.
These are known, respectively, as the horizontal and vertical
components oi the earth's total force, and are usually designated
as H and Z. The angle CAB, which the line of direction
makes with the plane of the horizon, is called the magnetic
inclination or dip, and denoted by 0.
It is clear that the horizontal comj)onent will reduce to
zero at the magnetic poles, where the needle points directly
downward, and that it will reach a maximum at the magnetic
equator, where the free needle hangs in a horizontal direction.
The reverse is true of the vertical component and of the angle
of dip.
Values representing these different terms may be found
from special charts.
96. Induction; Hard and Soft Iron. — When a piece of
unmagnetized iron or steel is brought within the influence of
a magnet, certain magnetic properties are inunediately imparted
to the former, which itself becomes magnetic and continues to
remain so as long as it is within the sphere of influence of the
permanent magnet; the magnetism that it acquires under these
circumstances is said to he induced, and the properties of induc-
tion are such that that end or region which is nearest the pole
of the influencing magnet will take up a polarity opposite thereto. If the magnet is withdrawn, the
induced magnetism is soon dissipated. If the magnet is brought into proximity again, but with its
opposite pole nearer, magnetism will again \)e induced, but this time its polarity will be reversed. A
further property is that if a piece of iron or steel, while temporarily possessed of magnetic qualities
through induction, be subjected to blows, twisting, or mechanical violence of any sort, the magnetism
is thus made to acquire a permanent nature.
The softer the metal, from a physical point of view, the more quickly and thoroughly will induced
magnetism be dissipated when the source of influence is withdrawn; hard metal, on the contrary, is
slow to lose the effect of magnetism imparted to it in any way. Hence, in regarding the different features
which affect deviation, it is usual to denominate as hard iron that which possesses retained magnetism
of a stable nature, and as soft iron that which rapidly accjuires and parts with its magnetic qualities
under the varying influences to which it is subjected.
97. Magnetic Properties Acqutrkd by an Iron or Steel Vessel in Buildinc. — The inductive
action of the earth's magnetism affects all iron or steel within its influence, and the amount and
permanency of the magnetism so induced depends upon the position of the metal with reference to the
earth's total force, upon its character, and upon the degree or hammering, bending, and twisting that it
undergoes.
JforLxonttMl, Forc^ - H
Fig. 10.
o As it is probable that the Btudent will not have practical need of a knowledge of the theory of deviation and the
compensation of the compa.ss until after he has mastered all other subjects pertaining to Navigation and Nautical
Astronomy, it may be considered preferable to omit the remainder of this chapter at first and return to it later.
THE COMPASS EKKOE. 35
An iron bar held in the line of the earth's total force instantly becomes magnetic; if held at an
angle thereto it would acquire magnetic properties dependent for their amount upon its inclination to
the line of total force; when held at right angles to the line there would be no effect, as each extremity
would be equally near the pf)les of the earth and all influence would be neutralized. If, while such a
bar is in a magnetic state through inductive action, it should be hammered or twisted, a certain mag-
netism of a permanent character is impressed upon it, which is never entirely lost unless the bar i&
subjected to causes ecpial and opposite to those that produced the first effect.
A sheet of iron is affected by induction in a similar way, the magnetism induced l)y the earth
diffusing itself over the entire plate and separating itself into regions of opposite polarity divided by a
neutral area at right angles to the earth's line of total force. If the plate is hammered or bent, this
magnetism takes up a permanent character.
If the magnetic mass has a third dimension, and assumes the form of a ship, a similar condition
prevails. The whole takes up a magnetic character; there is a magnetic axis in the direction of the line
of total force, with poles at its extremities and a zone of no magnetism perpendicular to it. The distri-
bution of magnetism will depend upon the horizontal and vertical components of the earth's force in
the locality and upon the direction of the keel in building; its permanency will depend upon_ tho
amount of "mechanical violence to which the metal has been subjected by the riveting and other inci-
dents of construction, and upon the nature of the metal employed.
98. Causes that Produce Deviation. — There are three influences that operate to produce devia-
tion; namely, (o) si(bpernutneni magnetism; (b) transient magnetism induced in reHical soft iron, and (c)
transient magnetism induced in horizontal soft iron. Their effect will be explaineil.
Suhpernianent magnetism is the name given to that magnetic force which originates in the ship while
building, through the process explained in the preceding article; after the vessel is launched and has
an opportunity to swing in azimuth, the magnetism thus induced will suffer material diminution until,
after the lapse' of a certain time, it will settle down to a condition that continues practically unchanged;
the magnetism that remains is denominated subpermanent. The vessel will then approximate to a
permanent magnet, in which the north polarity will lie in that region which was north in building, and
the south polarity (that which exerts an attracting influence on the north pole of the compass needle),
in the region which was south in building.
Transient magnetism induced in vertical soft iron is that developed in the soft iron of a vessel through
the inductive action of the vertical component only of the earth's total force, and i.-^ transient in nature.
Its value or force in any given mass varies with and depends upon the value of the vertical component
at the place, and is proportional to the sine of the dip, being a maximum at the magnetic pole and zero
at the magnetic equator.
Transient magnetism induced in horizontal soft iron is that developed in the soft iron of a vessel through
the inductive action of the horizontal component only of the earth's total force, and is transient in
nature. Its value or force in any given mass varies with and depends upon the value of the horizontal
component at the place, and is proportional to the cosine of the dip, being a maximum at the magnetic
equator and reducing to zero at the magnetic pole.
The needle of a compass in any position on board ship will therefore be acted upon by the earth's
total force, together with the three forces just described. The poles of these forces d(j not usually lie in
the horizontal plane of the compass needle, bTit as this needle is constrained to act in a horizontal plane,
its movements will be affected solely by the horizontal component*? of these forces, and its direction will
be determined by the resultant of those components.
The earth's force operates to retain the compass needle in the plane of the magnetic meridian, but
the resultant of the three remaining forces, when without this plane, deflects the needle, and the
amount of such deflection constitutes the deviation.
99. Classes of Deviation. — Investigation has developed the fact that the deviation produced as
described is made up of three parts, which are known respectively as semicircular, qnadrantal, and con-
stant deviation, the latter being the least important. A clear understanding of the nature of each of
these classes is essential for a comprehension of the methods of compensation.
100. Semicircular Deviation is that due to the combined influence, exerted in a horizontal plane, of
the subpermanent magnetism of a ship and of the magnetism induced in soft iron by the vertical com-
ponent of the earth's force. If we regard the effect of these two forces as concentrated in a single
resultant pole exerting an attracting influence upon the north end of the compass needle, it may be seen
that there will be some heading of the ship whereon that pole will lie due north of the needle and
therefore produce no deviation; now consider that, from this position, the ship's head swings in azi-
muth to the right; throughout all of the semicircle first described an easterly deviation will be produced,
and, after completing 180°, the pole will be in a position diametrically opposite to that from which it
started, and will again exert no influence that tends to produce deviation. Continuing the swing,
throughout the next semicircle the direction of the deviation produced will be always to the westward,
until the circle is completed and the ship returns to her original neutral position. From the fact that
this disturbing cause acts in the two semicircles with equal and opposite effect it is given the name of
semicircular deviation.
In figure 9, a curve is depicted which shows the deviations of a semicircular nature separated from
those due to other disturbing causes, and from this the reason for the name will be apparent.
101. Returning to the two distinct sources from which the semicircular deviation arises, it may
be seen that the force due to subpermanent magnetism remains constant regardless of tlie geographical
position of the vessel; but since the horizontal force of the earth, which tends to hold the needle in the
magnetic meridian, varies with the magnetic latitude, the deviation due to subpermanent magnetism
varies inversely as the horizontal force, or as tt; this may be readily understood if it is considered that
the stronger the tendency to cling to the direction of the magnetic meridian, the less will be the deflec-
tion due to a given disturbing force. On the other hand, that part of the semicircular force due to
magnetism induced in vertical soft iron varies as the earth's vertical force, which is proportional to the
36 THE COMPASS ERROR.
sine of the dip; its effect in producing deviation, as in the preceding case, varies inversely as the earth's
horizontal force — that is, inversely as the cosine of the dip; hence the ratio representing' the change of
deviation arising from this cause on change of latitude is f., or tan 9.
If, then, we consider the change in the semicircular deviation due to a change of magnetic latitude,
it will be necessary tt> separate the two factors of the deviation and to remember that the portion pro-
V duced bv subpermanent magnetism varies as , and that due to vertical induction as tan 0. But for
\ ' H
any consideration of the effect of this class of deviation in one latitude only, the two parts may be
joined together and regarded as having a single resultant.
102. If we now resume our former assumption, that all the forces tending to produce semicircular
deviation are concentrated in a single pole exerting an attracting influence upon the north pole of the
compass, we maj' consider a line to be drawn joining that theoretical pole with the center of the com-
pass, then the angle made by this line with the keel line of the vessel, measured from right ahead,
around to the right is called the starboard angle. From this it follows that the disturbing force producing
semicircular deviation may be considered to have the same effect as a single magnet whose center is in
the vertical axis of the compass, and whose south pole (attracting to the north pule of the compass) is in
the direction given by the starboard angle; if, therefore, a magnet be placed with its center in the ver-
tical axis of the compass, its north (or repelling) pole in the direction of the starboard angle, and its
distance so regulated that it exerts upon the compass a force equal to that of the ship's combined sub-
permanent magnetism and vertical induced magnetism, the disturbing effect of these two forces will be
counterbalanced, and, so far as they are concerned, the compass deviations will be corrected, provided
that the ship does not change her magnetic latitude.
103. It is evident that the force of the single magnet may be resolved into two components — one
fore-and-aft, and one athwartship; in this case, instead of being represented by a single magnet with its
south pole in the starboard angle, the semicircular forces will be represented by two magnets, one fore-
and-aft and the other athwartship, and compensation
may be made by two separate magnets lying respec-
tively in the directions stated, but with their north
or repelling poles in the position occupied by the
south or attracting poles of the ship's force.
Figure 11 represents the conditions that have been
described. If O be the center of the compass, XX''
"* and YY'', respectively, the fore-and-aft and athwart-
ship lines of the ship, and OS the direction in which
the attracting pole of the disturbing force is exerted,
then XOS is the starboard angle, usually designated
a. Now, if OP be laid off on the line OS, represent-
ing the amount of the disturbing force according to
some convenient scale, then Oh and Oc, respectively,
represei^t, on the same scale, the resolved directions
of that force in the keel line and in the transverse
line of the ship. Each of these resolved forces will
exert a maximum effect when acting at right angles
to the needle, the athwartship one when the ship
Yio. 11. heads north or south by compass, and the longitu-
dinal one when the heading is east or west. On any
other heading than those named the deviation produced by each force will be a fraction of its maximum
whose magnitude will depend upon the azimuth of the ship's head. The maximum deviation produced,
therefore, forms in each case a basis for reckoning all of the various effects of the disturbing force, and is
called a coefficient.
The coefficient of semicircular deviation produced by the force in the fore-and-aft line is called B,
and is reckoned as positive when it attracts a north pole toward the bow, negative when toward the
stern; that produced by the athwartship force is C, and is reckoned as positive to starboard and nega-
tive to port. These coefficients are expressed in degrees. «
Referring again to figure 11, it will be seen that:
Oc.
or (what may be shown to be the same thing):
tan a-^^^,
, sm C.
tan a= , --
sin B
and when the maximum deviations are small, this becomes:
tan '^1'= ,
X)
Since the starboard angle is always measured to the right, it will be seen that, for positive values of
B and C, a will Ije between 0° and 90°; for a negative B and a positive C, between 90° and 180°; for
a It should be remarked that in a mathematical analysis of the deviations, it would be necessar.v to distinguish between
the approximate coefficients, B and C, here described, as also A, D, and E, to be mentioned later, and the exact coefficients
denoted by the corresponding capital letters of the German alphabet. In the practical discussion of the subject here given,
the question of the diflference need not be entered into.
THE COMPASS ERROE.
37
negative values of both B and C, between 180° and 270°; and for a positive B and negative 0, between
270° and 360°.
104. The coefficient B is approximately equal to the deviation on East; or to the deviation on
West with reversed sign; or to the mean of these two. Thus in the ship having the table of deviations
previously given (art. 92), B isequal to -19° 55', or to —19° 80', or to ^ (—19° 55' —19° 30')= -19° 43'.
The coefficient C is approximately equal to the deviation on North; or to the deviation on South
with reversed sign; or to the mean of these two. In the example C is equal to —1° 00' or 0° 00', or
i (-1° 00'±0° 00')= -0° 30'.
105. The value of the subpermanent magnetism remaining practically constant under all condi-
tions, it will not alter when the ship changes her latitude; but that due to induction in vertical softiron
undergoes a change when, by change of geographical position, the vertical component of the earth's
force assumes a different value, and in such case the correction by means of one or a pair of permanent
magnets will not remain effective. If, however, by series of observations in two magnetic latitudes, the
values of the coefficients can be determined under the differing circumstances, it is possible, by solving
equations, to determine what effect each force has in producing the semicircular deviation; having done
which, the subpermanent magnetism can be corrected by permanent magnets after the method previ-
ously described, and the vertical induction in soft iron can be corrected by a piece of vertical soft iron
placed in such a position near the compass as to produce an equal but opposite force to the ship's vertical
soft iron. This last corrector is called a Flinders bur.
Having thus opposed to each of the component forces a corrector of magnetic character identical with
its own, a change of latitude will make no difference in the effectiveness of the compensation, for in every
case the modified conditions will produce identical results in the disturbing and in the correcting force.
106. Qiiadrantal, Deviation is that which arises from horizontal induction in the soft iron of the
vessel through the action of the horizontal component of the earth's total force. Let us consider, in figure
12, the effect of any piece of soft iron which is symmetrical with respect to the compass — that is, which
lies wholly within a plane passing through the center of the needle in either a fore-and-aft or an ath wart-
ship direction. It may be seen («) that such iron produces no deviation on the cardinal points (for
on north and south headings the fore-and-aft iron, though strongly magnetized, has no tendency to draw
the needle from a north-and-south line, while the athwartship
iron, being at right angles to the meridian, receives no magnetic
induction, and therefore exerts no force; and on east and west
headings similar conditions prevail, the athwartship and the
fore-and-aft iron having simply exchanged positions) ; and {li)
the direction of the deviation produced is opposite in successive
quadrants. The action of unsymmetrical soft iron is not (juite
so readily apparent, but investigation shows that part of its effect
is to produce a deviation which becomes zero at the inter-cardinal
points and is of opposite name in successive quadrants. From
the fact that deviations of this class change sign every 90°
throughout the circle, they gain the name of qiiadraidal deviations.
One of the curves laid down in the Napier diagram (fig. 11) is
that of quadrantal deviations, whence the nature of this disturb-
ance of the needle may be observed.
107. All deviations produced by soft iron may be considered
as fractions of the maximum deviation due to that disturbing
influence; and consequently the maximum is regarded as a
coefficient, as in the case of semicircular deviations. The coeffi-
cient due to symmetrical soft iron is designated as D, and is Fui. 12.
considered positive when it produces easterly deviations in the
quadrant between North and P^ast; the coefficient of deviations arising from unsymmetrical soft iron is
called E, and is reckoned as positive when it produces easterly deviations in the quadrant between NW.
and NE. ; this latter attains importance only when there is some marked inetpiality in the distribution
of metal to starboard and to port, as in the case of a compass placed off the midship line.
10§. 1) is approximately equal to the mean of the deviations on NE. and SW. ; or to the mean of
those on SE. and NW., with sign reversed; or to the mean of those means. In the table of deviations
given in article 92, D is equal to \ {—1° 10' - 24° 30') = J- 8° 40'; or to h (-i-23° 30' — 7° 40')
= -f 7° 55'; or to ^ ( 4- 8° 40' + 7° 55') = — 8° 23'. By reason of the nature of the arrangement of iron
in a ship, D is almost invariably positive.
E is approximately P(iual to the mean of the deviations on North and South; or to the mean of tho.se
on East and West with sign reversed; or to the mean of those means. In the example, E is equal to
i (-1° 00'±0° 00') = -0° 30'; or to \ (+ 19° 55'- 19° 30') = + 0° 13'; or to i (-0° 30' J-0° 13')
= _ 0° 09'.
109. Quadrantal deviation does not, like semicircular, undergo a change upon change of magnetic
latitude; being due to induction in horizontal soft iron, the magnetic force exerted to produce it is propor-
tional to the horizontal component of the earth's magnetism ; but the directive force of the needle likewise
depends upon that same component; consequently, as the disturbing force exerted upon the needle
increases, so does the power that holds it in the magnetic meridian, with the result that on any given
heading the deflection due to soft iron is always the same.
no. Quadrantal deviation is corrected by placing masses of soft iron (usually two hollow spheres
in the athwartship line, at equal distances on each side of the compass), with the center of mass in the
horizontal plane of the needle. The distance is made such that the force exerted exactly counteracts
that of the ship's iron. As the correcting effect of this iron will, like the directive force and the quad-
rantal disturbing force, vary directly with the earth's horizontal component, the compensation once
properly made will be effective in all latitudes.
In practice, the quadrantal deviation due to unsymmetrical iron is seldom corrected; the correction
may be accomplished, however, by placing the soft iron masses on a line which makes an angle to the
athwartship line through the center of the card.
38 THE COMPASS EEROR.
111. Constant Deviation is due to induction in horizontal soft iron unsymmetrically placed about the
compass. It has already been explained that one effect of such iron is to produce a quadrantal <leviation,
represented by the coefficient E; another effect is the conMant deviation, so called because it is uniform
in amount and direction on every heading of the ship. If plotted on a Napier diagram, it would appear
as a straight line parallel with the initial line of the diagram.
112. Like other classes of deviation, the effect of the disturbing force is represented by a coeffi-
cient; this coefficient IS designated as A, and is considered plus for easterly and minus for westerly errors.
It is approximately equal to the mean of the deviations on any number of equidistant headings. In the
case previously given, it might be found from the four headings, North, p]ast, South, and West, and
would then be equal to i ( -1° 00^-19° 55^±0° (KK-f 19° 3(K)=— 0° 2V; or from all of the 32 headings,
when it would equal -f 0° 16^.
For the same reason as in the case of E, the value of A is usually so small that it may be neglected;
it only attains a material size when the compass is placed off the midship line, or for some similar
cause.
113. Like quadrantal deviation, since its force varies with the earth's horizontal force, the con-
stant deviation will remain uniform in amount in all latitudes.
No attempt is made to compensate this class of error.
114. Coefficients. — The chief value of coefficients is in mathematical analyses of the deviations
and their causes. It may, however, be a convenience to the practical navigator to find their approxi-
mate values by the methods that have been given, in order that he may gain an idea of the various
sources of the error, with a view to ameliorating the conditions, when necessary, by moving the bin-
nacle or altering the surrounding iron. The following relation exists between tbe coefficients and the
deviation:
d=A + B sin z' + C cos z' + D sin 'Zi/ + K cos 2z^,
where d is the deviation, and s/ the ship's heading by compass, measured from compass North.
115. Me.\n Directive Force. — The effect of the disturbing forces is not confined to causing devi-
ations; it is only those components acting at right angles to the needle which oi)erate to produce
deflection; the effect of those acting in the direction of the needle is exerted either in increasing or
diminishing the directive force of the compass, according as the resolved component is northerly or
southerly.
It occurs, with the usual arrangement of iron in a vessel, that the mean effect of this action
throughout a complete swing of the ship upon all headings is to reduce the directive force — that is,
while it varies with the heading the average value upon all azimuths is minus or southerly. The result
of such a condition is unfavorable from the fact that the compass is thus made more "sluggish," is
easily disturbed and does not return quickly to rest, and a given deflecting force produces a greater
deviation when the directive force is reduced. The usual methods of compensation largely correct this
fault, but do not entirely do so; it is therefore the case that the mean combined horizontal force of earth
and ship to north is generally less than the horizontal force of the earth alone; but it is only in extreme
cases that this deficiency is serious.
116. Heeling Error. — This is an additional cause of deviation that arises when the vessel heels to
one side or the other. Heretofore only those forces have been considered which act when the vessel is
on an even keel; but if there is an inclination from the vertical certain new forces arise, and others
previously inoperative become effective. These forces are (a) the vertical com])onent of the subperma-
nent magnetism acquired in building; (b) the vertical component of the induced magnetism in vertical
soft iron, and {(■) the magnetism induced by the vertical component of the earth's total force in iron
which, on an even keel, Mas horizontal. The first two of these disturbing causes are always present,
but, when the ship is upright, have no tendency to produce deviation, simply exerting a downward
pull on one of the poles of the needle; the last is a new force that arises when the vessel heels.
The maximum disturbance due to heel occurs when the ship heads North or South. When heading
East or AVest there will be no deviation produced, although the directive force of the needle will be
increased or diminished. The error will increase with the amount of inclination from the vertical.
117. For the same reason as was explained in connection with semicircular deviations, that part of
the heeling error due to subpermanent magnetism will vary, on change of latitude, as , while that
H
due to vertical induction will vary as tan 0. In south magnetic latitude the effect of vertical induction
will be opposite in direction to what it is in north.
118. The heeling error is corrected by a ])ermanent magnet placed in a vertical position directly
under the center of the compass. Such a magnet has no effect upon the compass when the ship is
upright; but since its force acts in an opjwsite direction to the force of the ship which causes heeling
error, is equal to the latter in amount, and is exerted under the same conditions, it affords an effective
compensation. For similar reasons to those affecting the compensation of B and C, the correction by
means of a permanent magnet is not general, and nmst be rectified upon change of latitude.
PRACTICAL COMPENSATION.
119. In the course of explanation of the different classes of deviation occasion has been taken to
state generally the various methods of compensating the errors that are produced. The practical
methods of applying the correctors will next be given.
120. Order of Correction. — The following is the order of steps to be followed in each case. It
is assumed that the vessel is on an even keel, that all surrounding ma.sses of iron or steel are in their
normal positions, all correctors removed, and that the binnacle is one in which the semicircular
deviation is corrected by two sets of permanent magnets at right angles to each other.
1. Place quadrantal correctors by estimate.
2. Correct semicircular deviations.
THE COMPASS ERROR. 39
3. Correct quadrantal deviations.
4. Swing ship for residual deviations.
The heeling corrector may be placed at any time after the semicircular and quadrantal errors are
corrected. A Flinders bar can be put in place only after observations in two latitudes.
121. The ship is first placed on some magnetic cardinal point. If North or South, the only force
(theoretically speaking) which tends to produce deflection of the needle will be the athwartship com-
ponent of the semicircular force, whose effect is represented by the coefficient C If East or West, the
only deflecting force will be the fore-and-aft component of the semicircular force, whose effect is repre-
sented by the coefficient B. This will be apparent from a consideration of the direction of the forces
producing deviation, and is also shown by the equation connecting the terms (where A and E are zero) :
(7 = B sin 2^ + C cos 2' + D sin 2z'.
If the ship is headed North or South, z' being equal to 0° or 180°, the equation becomes d = ± C.
If on East or West, z' being 90° or 270°, we have d = i B.
This statement is exact if we regard only the forces that have been considered in the problem, but
experience has demonstrated that the various correctors when in place create certain additional forces
by their mutual action, and in order to correct the disturbances thus accidentally produced, as well as
those due to regular causes, it is necessary that the magnetic conditions during correction shall approxi-
mate as closely as possible to those that exist when the compensation is completed; therefore the quad-
rantal correctors should first be placed on their arms at the positions which it is estimated that they
will occupy later when exactly located. An error in the estimate will have but slight effect under
ordinary conditions. It should be understood that the placing of these correctors has no corrective
effect while the ship is on a cardinal point. Its object is to create at once the magnetic field with which
we shall have to deal when compensation is perfected.
This having been done, proceed to correct the semicircular deviation. If the ship heads North or
South, the force producing deflection is, as has been stated, the athwartship component of the semi-
circular force, which is to be corrected by permanent magnets placed athwartships; therefore enter in
the binnacle one or more such magnets, and so adjust tlieir height that the heading of the ship by
compass shall agree with the magnetic heading. When this is done all the deviation on that azimuth
will be corrected.
Similarly, if the ship heads East or West, the force producing deviation is the fore-and-aft com- "
ponent of the semicircular force, and this is to be corrected by entering fore-and-aft permanent magnets
in the binnacle and adjusting the height so that the deviation on that heading disappears.
With the deviation on two adjacent cardinal points corrected, the semicircular force has been com-
pletely compensated. Next correct the quadrantal deviation. Head the ship NE., SH, SW., or NW.
The coefficients B and C having been reduced to zero by compensation, and 2z' , on the azimuths named,
being equal to 90° or 270°, the equation becomes d = =b D. The soft-iron correctors are moved in or
out from the positions in which they were placed by estimate until the deviation on the heading (all of
which is due to quadrantal force) disappears. The quadrantal disturbing force is then compensated.
122. Deter.mixation of Magnetic Headings. — To determine when the ship is heading on any
given magnetic course, and thus to know when the deviation has been corrected and the correctors are
in proper position, four methods are available:
(a) Swing the ship and obtain by the best available method the deviations on a sufficient number
of compass courses to construct a curve on the Napier diagram for one quadrant, and thus find the com-
pass headings corresponding to two adjacent magnetic cardinal points and the intermediate intercardinal
point, as North, NE., and East, magnetic." Then put the ship successively on these courses, noting the
corresponding headings by some other compass, and when it is desired to head on the various magnetic
azimuths during the process of correction the ship may be steadied upon them by the auxiliary com-
pass. Variations of this method will suggest themselves and circumstances may render their adoption
convenient. The compass courses corresponding to the magnetic directions may be obtained from
observations made with the auxiliary compass itself, or while making observations with another com-
pass the headings by the auxiliary may be noted and a curve for the latter constructed, as explained
in article 94, and the required headings thus deduced.
(6) By the methods to be explained hereafter (Chap. XIV), ascertain in advance the true bearing
of the sun at frequent intervals during the period which is to be devoted to the compensation of the
compasses; apply to these the variation and obtain the magnetic bearings; record the times and
bearings in a convenient tabular form; set the watch accurately for the local apparent time; then
when it is required to steer any given magnetic course, set that point of the pelorus for the ship's
head and set the sight vanes for the magnetic bearing of the sun corresponding to the time by watch.
Maneuver the ship with the helm until the sun comes on the sight vanes, when the azimuth of the
ship's head will be that which is required. The sight vanes must be altered at intervals to accord with
the table of times and bearings.
(c) Construct a table showing times and corresponding magnetic bearings of the sun, and also set
the watch, as explained for the previous method. Then place the sight vanes of the azimuth circle of
the compass at the proper angular distance to the right or left of the required azimuth of the ship's
head; leave them so set and maneuver the ship with the helm until the image of the sun comes on with
the vanes. The courserwill then be the required one. As an example, suppose that the table shows that
the magnetic azimuth of the sun at the time given by the watch is N. 87° E., and let it be required to
head magnetic North; when placed upon.this heading, therefore, the sun must bear 87° to the right, or
east, of the direction of the ship's head; when steady on any course, turn the sight vane to the required
bearing relative to the keel. If on N. 11° W., for example, turn the circle to N. 76° E.; leave the vane
"This is all that is required for the purposes of compensation, but if there is opportunity it is always well to make a
complete swing and obtain a full table of deviations, which may give interesting information of the existing magnetic
conditions.
40 THE COMPASS ERROR.
undisturbed and alter course until the sun comes on. The magnetic heading is then North, and adjust-
ment may be made accordingly.
(d) When ranges are available, they may be utilized for determining magnetic headings.
123. Summary of Ordinary Corrections. — To summarize, the following is the process of correct-
ing a compass for a single latitude, where magnets at right angles are employed for compensating the
semicircular deviation ^pd where the disturbances due to unsymmetrical soft iron are small enough to be
neglected:
First. All correctors being clear of the compass, place the quadrantal correctors in the position
which it is estimated that they will occupy when adjilstment is complete. The navigator's experience
will serve in making the estimate, or if there seems no other means of arriving at the probable position
they may be placed at the middle points of their supports.
Second. Steady the ship on magnetic North, East, South, or West, and hold on that heading by such
method as seems best. By means of permanent magnets alter the indications of the compass until the
heading coincides with the magnetic course. If heading North, magnets must be entered N. ends to
starboard to correct easterly deviation and to port to correct westerly, and the reverse if heading
South. If heading East, enter N. ends forward for easterly and aft for westerly deviations, and the
reverse if heading W^est. (Binnacles differ so widely in the methods of carrying magnets that details
on this point are omitted. It may be said, however, that the magnetic intensity of the correctors may
be varried by altering either their number or their distance from the compass; generally si)eaking,
several magnets at a distance are to be preferred to a small number close to the compass. )
Third. Steady the ship on an adjacent magnetic cardinal point and correct the compass heading
by permanent magnets to accord therewith in the same manner as described for the first heading.
Fourth. Steady the ship on an intercardinal point (magnetic) and move the quadrantal correctors
away from or toward the compass, keeping them at equal distances therefrom, until the compass and
magnetic headings coincide.
124. The compensation being complete, the navigator should proceed immediately to swing ship
and make a table of the residual deviations. Though the remaining errors will be small, it is seldom
that they will be reduced to zero, and it must never be assumed that the compass may be relied upon
without taking the deviation into account. Observations on eight equidistant points will ordinarily
suffice for this purpose.
^ 125. To Correct Semicircular Deviation avith a Single Magnet. — In certain binnacles provision
is made for correcting the semicircular deviation by a single magnet (or series of magnets) in the star-
board angle, the magnet tray having motion in azimuth as well as vertically. In this case the i^rocess of
correcting semicircular deviation is somewhat different from that described for correction by rectangular
magnets. Either of the two following methods may be employed:
(o) By computation determine the starboard angle. An approximate method for doing this is
given in article 103, and a more exact one may be found in works treating this subject mathematically.
Head the ship on a cardinal point (magnetic); enter the magnets in the tray and revolve it until their
N. ends lie at an angular distance from ahead (measured to the right) equal to the starboard angle;
raise or lower the tray until the deviation disappears.
(6) Head the ship on a cardinal point (magnetic), enter the magnets, and turn the tray to an east-
and-west position, the N. ends in such direction as will tend to reduce the deviation; raise or lower the
tray until the deviation disappears. Alter course 90° and head on an adjacent magnetic cardinal point;
observe the amount of deviation that the compass shows; correct half of this by altering the starboard
angle and the other half by raising or lowering the tray. Return to first course, note deviation, and
correct one-half in each way, as before. Continue the operation, making a series of trials until the
deviations disappear on both headings, when the compensation will be correct. This operation may be
considerably hastened by finding the first position of the magnets from a rough calculation of the
starboard angle (art. 103).
126. Correcting the Heeling Error. — The heeling error may be corrected by a method
involving computation, together with certain observations on shore. A more practical method, however,
is usually followed, though its results may be less precise. The heeling corrector is placed in its vertical
tube, N. end uppermost in north latitudes, as this is almost invariably the required direction; the ship
being on a course near North or South and rolling, observe the vibrations of the card, which, if the
error is material, will be in excess of those due to the ship's real motion in azimuth; slowly raise or
lower the corrector until the abnormal vibrations disappear, when the correction will be made for that
lalitude; but it must be readjusted upon any considerable change of geographical position.
In making this observation care must be taken to distinguish the vessel's "j'awing" in a seaway,
from the apparent motion due to heeling error; for this reason it may be well to have an assistant to
w^atch the ship's head and keep the adjuster informed of the real change in azimuth, by which means
the latter may better judge the effect of the heeling error.
In the case of a sailing vessel, or one which for any reason maintains a nearly steady heel for a
continuous period, the amount of the heeling error may be exactly ascertained by observing the azi-
muth of the sun, and corrected with greater accuracy than is possible with a vessel which is constantly
rolling.
127. Flinders Bar. — The simplest method that presents itself for the placing of the Flinders
bar is one which is available only for a vessel crossing the magnetic equator. Magnetic charts of the
world show the geographical positions at which the dip becomes zero — that is, where a freely suspended
needle is exactly horizontal and where there exists no vertical component of the earth's total magnetic
force. In such localities it is evident that the factor of the semicircular deviation due to vertical induc-
tion disappears and that the whole of the existing semicircular deviation arises from subpermanent
magnetism. If, then, w'hen on the magnetic equator the compass be carefully compensated, the effect
of the subpermanent magnetism will be exactly opposed by that of the semicircular correcting magnets.
Later, as the ship departs from the magnetic equator, the semicircular deviation will gradually acquire
a material value, which will be known to be due entirely to vertical induction, and if the Flinders bar
be so placed as to correct it, the compensation of the compass will be general for all latitudes.
THE COMPASS ERROR. 41
In following this method it may usually be assumed that the soft iron of the vessel is symmetrical
with respect to the fore-and-aft line and that the Flinders bar may be placed directly forward of the
compas^ or directly abaft it, disregarding the effect of components to starboard or port. It is therefore
merely necessary to observe whether a vertical soft iron rod must be placed forward or abaft the
compass to reduce the deviation, and, having ascertained this fact, to find by experiment the exact
distance at which it completely corrects the deviation.
The Flinders bar frequenth^ consists of a bundle of soft iron rods contained in a case, which is
secured in a vertical position near the compass, its upper end level with the plane of the needles; in
this method, the distance remaining fixed, the intensity of the force that it exerts is varied by increasing
or decreasing the number of rods; this arrangement is more convenient and satisfactory than the
employment of a single rod at a variable distance.
128. When it is not possible to correct the compass at the magnetic equator there is no ready
practical method by which the Flinders bar may be placed; the operation will then depend entirely upon
computation, and as a mathematical analysis of deviations is beyond the scope laid out for this work
the details of procedure will not be gone into; the general principles involved are indicated, and students
seeking more must consult the various works that treat the subject fully.
It has been explained that each coeflBcient of semicircular deviation ( B and C ) is made up of a sub-
permanent factor varying as vj and of a vertical induction factor varying as tan 6. If we indicate by the
subscripts ^ and ,., respectively, the parts due to each force, we may write the equations of the coefficients:
B=B, X j^ + B, X tan 0; and
C = C,X^+C, X tane.
Now if we distinguish by the subscripts i and ^ the values in the first and in the second position of
observation, respectively, of those quantities that vary with the magnetic latitude, we have;
Bi = B,Xjj- + B,Xtan6„
B2 = B, X JJ-+ B^ X tan&,; and
C, = C,x4- + CvXtane„
C, = C, X jj- 4- ('v X tan 0.,.
The values of the coefficients in both latitudes are found from the observations made for deviations;
the values of the horizontal force and of the dip at each place are known from magnetic charts; hence
we may solve the first pair of equations for B^ and B,., and the second pair for (\ and C,.; and having
found the values of these various coefficients, we may correct the effects of B, and C^ by permanent mag-
nets in the usual way and correct the remainder — that due to B^. and C, — by the Flinders bar.
Strictly, the Flinders bar should be so placed that its repelling pole is at an angular distance from
ahead equal to the "starboard angle" of the attracting pole of the vertical induced force, this angle
depending upon the coefficients B^, and C^.; but since, as before stated, horizontal soft iron may usually
be regarded as symmetrical, C». is assumed as zero and the bar placed in the midshi]i line.
129. To Correct Ad-itstment on Change of Latitude. — The compensation of quadrantal devia-
tion, once properly made, remains effective in all latitudes; but unless a Flinders bar is used a correction
of the semicircular deviation made in one latitude will not remain accurate when the vessel has
materially changed her position on the earth's surface. With this in mind the navigator must make
frequent observations of the compass error during a passage and must expect that the table of residual
deviations obtained in the magnetic latitude of compensation will undergo considerable change as that
latitude is departed from. The new deviations may become so large that it will be found convenient
to readjust the semicircular correcting magnets. This process is very simple.
Wien correctors at right angles are used, provide for steadying tte> ship, by an auxiliary compas^s or
by the pelorus, upon two adjacent magnetic cardinal points (art. l3^). Put the ship on heading North
or South (magnetic), and raise or lower the athwartship magnets or alter their number until the
deviation disappears; then steady on East or West (magnetic) and similarly adjust the fore-and-aft
magnets. Swing ship for a new table of residual deviations.
When correctors in the starboard angle are nsed, arrange as before for heading on two adjax-ent cardinal
magnetic courses. Steady on one of these, observe amount of compass error, correct half by changing
the starboard angle and half by raising or lowering magnets; steady on the adjacent cardinal point and
repeat the operation. Continue until adjustment is made on both headings, then swing for residual
deviations.
42 PILOTING.
CHAPTER IV.
PILOTING.
130. Definition'. — Piloting, in the sense given the word by modern and popular usage, is the
art of conducting a vessel in channels and harbors and along coasts, where landmarks and aids to
navigation are available for fixing the position, and where the depth of water and dangers to navigation
are such as to require a constant watch to be kejit upon the vessel's course and frequent changes to be
made therein.
131. Reqiisites. — As requisites to successful piloting, the navigator should be provided with
the best available chart of the locality to be traversed, together with the sailing directions and descrip-
tions of aids to navigation; and all of these should be corrected for the latest information, published in
notices to mariners or otherwise, that bear upon the locality. The vessel should be equipped with the
usual instruments employed in navigation. The deep-sea sounding-machine, if i)rovided, should be ready
for use when there is a chance that it may be needed. The lead lines should be correctly marked, and
as shoal water is entered one or two men should be stationed to sound. The index errors of the sextants
should be known, and, above all, there should be at hand a table showing correctly the deviation of
the compass on each heading.
132. Laying the Course. — Mark a point upon the chart at the ship's position; then mark another
point for which it is desired to steer; join the two by a line drawn with the parallel ruler, and, main-
taining the direction of the line, move the ruler until its edge passes through the center of the compass
rose and note the direction. If the compass rose indicates true directions, this will be the true course,
and must be corrected for variation and deviation ( by applying each in the opposite direction to its
name) to obtain the compass course; if it is a magnetic rose, the course need be corrected for deviation
only.
Before putting the ship on any course a careful look should be taken along the line over which it
leads to be assured that it clears all dangers.
1 33. Methods of Fixing Position. — A navigator in sight of objects whose positions are shown ujjon
the chart may locate his vessel by either of the following methods: («) cross bearings of two known
objects; {h) the bearing and distance of a known object; {(•) the bearing of a known object and the
angle between two known objects; {d) two bearings of a known object separated by an interval of time,
with the run during that interval; [e] sextant angles between three known objects. Besides the fore-
going there are two methods by which, without obtaining the precise position, the navigator may assure
himself that he is clear of any particular danger. These are: (/) the danger angle; {g) the danger
bearing.
The choice of the method will be governed by circumstances, depending upon which is best adapted
to prevailing conditions.
1 34. Cross Bearings of two Known Objects. — Choose two objects whose i^osition on the chart
can ])e unmistakably identified and whose respective bearings from the ship differ, as nearly as possible,
bv90°; observe the bearing of each, either by compass or pelorus, taking one as quickly as possible
at\er tlie othep; see that the ship is on an even keel at the time the observation is made, and, if using
the pelorus, be sure also that she heads exactlj- on the course for which the i)elorus is set. Correct the
bearings so that they will be either true or magnetic, according as they are to be plotted by the true or
magnetic compass rose of the chart — that is, if observed by compass, api)ly deviation and variation to
obtain the true bearing, or deviation only to obtain the magnetic; if
/" / observed by pelorus, that instrument should be set for the true or mag-
n/ti. netic heading, according as one or the other sort of reading is required,
y/r\ and no further correction will be necessary. Draw on the chart, by
y^ I means of the parallel rulers, lines which shall pass through the respec-
y^ \ five objects in the direction that each was observed to bear. As the
/ \ shi%Ls position on the chart is known to be at some point of each of
jT \ the« lines, it must l>e at their intersection, the only point that fulfills
^^/ ) c botn conditions.
/\ ^" figure 13, if A and B are the objects and OA and OB the lines
X N. ( passing through them in the observed directions, the ship's position
/ N. I will be at O, their intersection.
N. 1 * 135. If it be possible to avoid it, ol)jects should not be selected
' i N. ^ \ for a cross bearing»which subtend an angle at the ship of less than 30°
\/ or more than 150°, as, when the lines of bearing approach parallelism,
f^B a small error in an observed bearing gives a large error in the result.
VTS. For a similar reason objects near the ship should be taken in prefer-
^ N ence to those at a distance.
Fig. 13. 1 36. When a third object is available a bearing of that may be
taken and ])lotted. If this line intersects at the same point as the other
two (as the bearing OC of the object C in the figure), the navigator may have a reasonable assurance
that his " fix " is correct; if it does not. it indicates an error somewhere, and it may have arisen from
inaccurate observation, incorrect determination or application of the deviation, or a fault in the chart.
PILOTING.
43
V-t;::
Fui. 15.
137. What may be considered as a form of this method can be used when only one known object
is in sight by taking, at the same instant as the bearing, an altitude of the sun or other heavenly l)ody
and noting the time; work out the sight and obtain the Sumner line (as explained in Chapter XV), and
the intersection of this with the direction-line from the object will give the observer's position in the
same way as from two terrestrial bearings.
13§. Bearing and Distance of a Known Object. — When only one object is available, the ship's
position may be found by observing its bearing and distance. Follow the preceding method in the mat-
ters of taking, correcting, and plotting the bearing; then, on this
line, lay off the distance from the object, which will give the
point occupied by the observer. In figure 1-i, if A represents the
object and AO the bearing and distance, the position sought will
be at O.
139. It is not ordinarily easy to find directly the distance
of an object at sea. The most accurate method is when its height
is known and it subtends a fair-sized angle from the ship, in
which case the angle may be measured by a sextant," and the
distance computed or taken from a table. Table 83 of this work
gives distances up to 5 miles, corresponding to various heights
and angles. Captain Lecky's "Danger Angle and Offshore Dis-
tance Tables" carries the computation much further. The use
of this method at great distances must not be too closely relied
upon, as small errors, such as those due to refraction, may throw
out the results to a material extent; but it affords an excellent approximation, and as this method of fixing
position is employed only when no other is available the best possible approximation has to suflice.
In measuring vertical angles, strictness requires that the
observation should be so made that the angle at the foot of the
object should equal 90° and that the triangle be a right triangle,
as OMN, figure 15, where the line OM is truly horizontal, and
not as in the triangle O^MN, where the condition is not fulfilled.
This error is inapprecial>le, however, save at very close dis-
tances, when it may be sufficiently corrected by getting down
as low as possible on board the vessel, so that the eye is near
the water-line. One condition exists, however, where the
error is material — that shown in figure 16, where the visible
shorjp-line is at M^, a considerable distance from M, the point
vertically below the summit. In this case there is nothing to
mark M in the observer's eye, and it is essential that all angles
be measured from a point dose down to the water-line.
If a choice of objects can be made, the best results will l)e
obtained by observing that one which subtends the greatest
angle, as small errors will then have the least effect.
There is another method for determining the distance of
an o)>ject, Avhich is available under certain circumstances. This consists in observing, from a position
aloft, the angle between the object and the line of the sea horizon beyond. By reference to Table 34
will be found the distance in yards corresponding to different angles for various heights of the observer
from 20 to 120 feet. The method is not accurate beyond moderate distances (the table being limited to
5,000 yards) and is obviously only available for finding the distance of an isolated object, such as an
islet, vessel, or target, over which the horizon may be seen. In employing this method the higher the
l)osition occupied by the observer the more precise will be the results.
140. In observing small angles, such as those that occur in the methods just described, it is some-
times convenient to measure them on and off the limb of the sextant. Firet look at the bottom of the
object and reflect the top down into coincidence; then look through the transparent part of the horizon
glass at the top and bring the bottom up by its reflected ray. The mean of the two readings will be the
true angle, the index correction having been eliminated by the operation.
141. When the methods of finding distance by a vertical or a horizon angle are not available, it
must be obtained by such means as exist. Fstimate the distance by the appearance; take a sounding, and
note where the depth falls upon the line of bearing; at night, if atmospheric conditions are normal,
consider that the distance of a light when sighted is equal to its maximum range of visibility, remem-
l^ering that its range is stated for a height of eye of 15 feet; or employ such method as suggests itself
under the circumstances, regarding the result, however, as an approximation only.
142. The Bearing of a Known Object and the Ancjle between two Known Objects. — This
method is seldom employed, as the conditions always permit of cross bearings being taken, and the
latter is generally considered preferable.
Take a bearing of a known object by compass or pelorus and observe the sextant angle between some
two known objects. The line of bearing is plotted as in former methods. In case one of the objects of
the observed angle is that whose bearing is taken, the angle is applied, right or left as the case may be,
to the bearing, thus giving the direction of the second object, which is plotted from the compass rose
and parallel rulers. If the object whose bearing is taken is not one of the objects of the angle, lay off
the angle on a three-armed proti-actor, or piece of tracing paper, and swing it (keeping the legs or lines
always over the two objects) until it ])asses over the line of bearing, which defines the position of the
ship; there will, except in special cases, be two points of intersection of the line with the circle thus
described, and the navigator must know his position with sufficient closeness to judge which is correct.
143. Two Bearin(;s of a Known Object. — This is a most useful method, which is frequently
employed, certain special cases arising thereunder being particularly easy of application. The process
iThe use of the sextant is explained in Chapter VIII.
44
PILOTING.
is to take a careful bearing and at the same moment read the patent log; then, after running a convenient
distance, take a second bearing and again read the log, the difference in readings giving the intervening
run; when running at a known speed, the time interval will also afford a means for determining the
distance run.
The problem is as follows: In figure 17, given OA, the direction of a known object, A, at the first
observation; PA, the direction at the second observation; and 01*, the distance
• traversed between the two; to find AP, the distance at the second observation.
Knowing the angle PC) A, the angular distance of the object from right ahead
at the first bearing; OPA, the angular distance from right astern at the secontl
bearing; and OP, the distance run; we have by Plane Trigonometry:
PAO = 180°- (POA + OPA) ; and
AP = OP X
sin POA
sin PAO*
If, as is frequently the case, we desire to know the distance of passing abeam^
we have:
AQ = AP X sin OPA.
Tables 5A and 5B give solutions for this problem, the former for intervals
of bearing of quarter points, the latter for intervals of two degrees. The first
column of each of these tables gives the value of AP, the distance of the ship
from the observed object at the time of taking the last bearing, for values of
OP equal to unity; that is, for a run V)etween bearings of 1 mile. The second
P 1- column gives AQ, the distance of the object when it bears abeam, likewise for
a value of OP of 1 mile. When the run between bearings is other than 1 mile,
the number taken from the table must be used as a multiplier of that run to give the required distance.
Example: A vessel steering north takes a bearing of a light XW. J W. ; then runs 4.3 miles, when
the bearing is found to be WSW. Required the distance of the light at the time of the second bearing.
Difference between course and first bearing, 4i pts.
Difference between course and second bearing, 10 pts.
Multiplier from first column, Table 5A, 0.88.
4.3 miles X 0.88 = 3.8 miles, distance at second bearing.
Example: A vessel on a course S. 52° E. takes the first bearing of an object at S. 26° E., and the
second at S. 2° W., running in the interval 0.8 mile. Required the distance at which she will pass
abeam.
Difference between course and first bearing, 26°.
Difference between course and second bearing, 54°.
Multiplier from second column. Table 5B, 0.79.
0.8 mile X 0.79 = 0.6 mile, distance of passing abeam.
144. As has been said, there are certain special cases of this problem where it is exceptionally
easy of application; these arise when the multiplier is equal to unity, and the distance run is therefore
equal to the distance from the object. When the angular distance on the bow
at the second bearing is twice as great as it was at the first bearing, the distance
of the object from the ship at fiecond bearing is equal to the run, the multiplier
being 1.0. For if, in figure 18, when the ship is in the first position, O, the ol)ject
A bears ar°on the bow, and at the second position, P, 2cir°, we have in the triangle
APO, observing that APO = 180° — 2ix, and POA = tx:
PAO = 180° -(POA -r- APO),
= 180°-(cr + 180°-2a),
= a.
Or, since the angles at O and at A are equal to each other, the sides OP and AP
are equal, or the distance at second bearing is equal to the run. This is known
as doubling the angle on the buic.
145. A case where this holds good is familiar to every navigator as the botv
and beambearing, where the first bearing is taken when the object is broad on
the bow (four points or 45° from ahead) and the second when it is abeam (eight
points or 90° from ahead); in that case the distance at second bearing and the
distance abeam are identical and etiual to the run between bearings.
146. When the first bearing is 26i° from ahead, and the second 45°, the
distance at which the object irill be passed abeam will equal the run between bear-
ings; this may be proved by computation or by reference to the tables and is a
very convenient fact to remember, as it shows the navigator at once, it about to pass a point, how wide
a berth he is going to give the offiying dangers.
147. There is a graphic method of solving this problem that is considered by some more convenient
than the use of multipliers. Draw upon the chart the lines OA and PA (fig. 19), pa^^sing through the
object on the two observed bearings; set the dividers to the distance run, OP; lay down the parallel
rulers in a direction parallel to the course and move them toward or away from the observed object
until some point is found where the distance between the lines of bearing is exactly equal to the
distance between the points of the dividers; in the figure this occurs when the rulers lie along the line
PILOTING.
45
Fig. 19.
OP, and therefore O represents the position of the ship at the first bearing and P at the second. For
any other positions O^P', O'^P^', the condition is not fulfilled.
14§. Another jiraiihic solution is given by the Dintance Finder, devised by Lieut. J. B. Blish, U. S.
Navy. This consists of a semicircle whose circumference is graduated in degrees. Two pieces of thread,
made to swing aljout a pin-head at the center, are laid down to
represent the lines of bearing, and ease in measuring distances is
afforded l)y series of cross lines similar to those on a piece of profile ^ ^
paper.
149. The methoil of obtaining position by two bearings of the
same object is one of great value, by reason of the fact that it is
frequently necessary to locate the ship when there is but one land-
mark in sight. Careful navigators seldom, if ever, miss the opjwr-
tunity for a bow and beam bearing in passing a light-house or other
well-plotted ol:)ject; it involves little or no trouble, and always gives
a feeling of added security, however little the position may be in
doubt. If about to pass an object abreast of whii-h there is a
danger — a familiar example of which is when a light-house marks a
point off which are rocks or shoals — a good assurance of clearance
should l:)e obtained before bringing it abeam, either by doubling
the angle on the bow, or by using the 26i°-45° bearing; the latter
has the advantage over the former if the object is sighted in time
to permit of its use, as it may be assumed that the 45° (bow) bear-
ing will always be observed in any event, and this gives the distance
al>eam directly, saving the necessity of plotting the position at
second Ijearing (as obtained by .doubling the angle) and then carry-
ing it forward.
150. It nuist be remembered that, however convenient, the
fix obtained by two bearings of the same object will be in error unless
the course and distance are correctly estimated, the course "made
good" and the distance "over the ground" being required. Difficulty will occur in estimating the
exact course when there is bad steering, a cross current, or when a ship is making leeway; errors in
the allowed run will arise when she is being set ahead or back by a current or when the logging is
inaccurate. To take a not extreme case, a vessel making 10 knots through the water, running against a
2-knot tide, will overestimate her distance one-fifth of its true amount in taking a bow and beam bear-
ing if no allowance is made for the tide, or she will underestimate her distance by one-fifth of its
apparent amount if going with the same tide. Therefore, if in a current of any sort, due allowance
must be made, and it should be remembered that more dependence can be placed upon a position fixed
by simultaneous bearings or angles, when two or more objects are available, than by two bearings of a
single ol)ject.
151. Sextant Anules between Three Known Objects. — This method, involving the solution of
the three-}ioint 2)rof>len>, will, if the objects be well cho.sen, give the most accurate results of any. It is
largely employed in surveying, because of its precision; and it is especially valuable in navigation,
because it is not subject to errors arising from imperfect knowledge of the compass error, improper log-
ging, or the effects of current, as are the methods previously described.
Three objects represented on the chart are selected and the angles measured with sextants of
known index error between the center one and each of the others. Preferably there should be two
observers and the two angles be taken sinuiltaneously, but one observer may fii-st take the angle which
is changing more slowly, then take the other, then repeat the first angle, and consider the mean of the
first and last observations as the value of the first angle. The position is usually plotted by means of
the three-armed protractor, or station-jwinter (see art. 432, Chap. XVII). Set the right and left
angles on the instrument, and then move it over the chart until the three beveled edges pass respectively
and simultaneously through the three objects. The center of the instrument will then mark the ship's
position, which may be pricked on the chart or marked with a pencil point through the center hole.
When the three-armed protractor is not at hand, the tracing-paper protractor will prove an excellent
substitute, and may in some cases be preferable to it, as, for instance, when the objects angled on are
so near the observer as to be hidden by the circle of the
instrument. A graduated circle printed upon tracing
l)aper j^ermits the angles being readily laid off, but a
plain ])iece of tracing paper may be used and the angles
marked by means of a small protractor. The tracing-
paper protractor pernnts the laying down, for simultane-
ous trial, of a number of angles, where special accuracy is
s>ought.
1.52. The three-point problem, by which results are
obtained in this method, is: "To find a point such that
three lines drawn from this point to three given points
shall make given angles with each other.
Let A, B, and C, in figure 20, be three fixed objects on
shore, and from the ship, at D, suppose the angles CDB
and ADB are found equal, respectively, to 40° and 60°.
With the complement of CDB, 50°, draw the lines
BE and CE; the point of intersection will be the center
of a circle, on some point of whose circumference the
ship must be. Then, with the complement of the angle ADB, 30°, draw the lines AF and BF, meeting
at F, which point will be the center of another circle, on some point of whose circumference the ship
must be. Then D, the point of intersection of the circumference of the two circles, will be the position
of the ship.
Fig. 20.
46
PILOTIKG,
The correctness of this sohation may be seen as follows: Take the first circle, DBC; in the triangle
EBC, the angle at E, the center, cquah i80°— 2x50°= 2 (90° -50° ), twice the complement of 50°, which
is twice the observed angle; now if the angle at the center subtended by the chord BC' equals twice the
observed angle, then the angle at any point on the circumference subtended by that chord, which equals
half the angle at the center, eiiuals the observed angle; so the required condition is fulfilled. Should
either of the angles exceed 90°, the excess of the angle over 90° must be laid off on the opposite side of
the lines joining the stations.
153. It may be seen that the intersection of the circles becomes less sharp as the centers 'E and F
approach each other; and finally that the problem becomes indeterminate when the centers coincide,
that is, when the three observed points and the observer's position all fall upon the same circle; the
two circles are then identical and there is no intersection; such a case is called a "revolver," because
the protractor will revolve around the whole circle, everywhere passing through the observed points.
The avoidance of the revolver and the employment of large angles and short distances form the keys
to the selection of favorable objects.
Generally speaking, the observer, in judging which objects are the best to be taken, can picture
in his eye the circle passing through the three points and note whether it comes near to his own
position. If it does, he must reject one or more of the objects for another or others. It should be
remembered that he must avoid not only the condition where the circle passes exactly through his
position (when the problem is wholly indeterminate), but also all conditions approximating thereto,
for in such cases the circles will intersect at a very acute angle, and the inevitable small errors of the
observation and plotting will produce large errors in the resulting fix.
Without giving an analysis of reasons, which may be found in various works that treat the
problem in detail, the following may be enumerated as the general conditions which result in a (/ood fix:
(a) When the center object of the three lies between the observer and a line joining the other two,
or lies nearer than either of the other two. ,
(b) When the sum of the right and left angles is equal to or greater than 180°.
(c) When two of the objects are in range, or nearly so, and the angle to the third is not less than 30°.
(d) When the three objects are in the same straight line.
A condition that limits all of these is that angles should be large — at least as large as 30° — excepting
in the case where two objects are in range or nearly so, and then the other angle must be of good size.
When possible, near objects should be used rather than distant ones. The navigator should not fall into
the error of assuming that objects which would give good cuts for a cross bearing are necessarily
favorable lor the three-point solution.
In a revolver, the angle formed by lines drawn from the center object to the other two, added to
the sum of the two observed angles, equals 180°. A knowledge of this fact may aid in the choice of
objects.
If in doubt as to the accuracy with which the angles will plot, a third angle to a fourth object may
be taken. Another way to make sure of a dou1)tful fix is to take one compass
bearing, by means of which even a revolver may be made to give a good
position.
154. The Danger Angle. — When running in sight of the land, it is
frequently of the greatest importance for the navigator to assure himself that
the course leads clear of outlying dangers, and the Danger Angle affords a con-
venient means of so doing. There are two sorts of danger angles — the hori-
zontal angle taken between two objects, and the vertical angle of a single one.
The former will be first described.
155. Suppose, in figure 21, that a vessel standing along the coast on the
course indicated nmst pass an offshore danger between two well-marked
objects, A and B, and that, allowing a safe margin, it is desired to approach
no closer than the point O. Through the points A, B, and O draw a circle,
by the usual methods of geometry, and observe that no portion of the danger
lies without the circle. Measure the angle AOB with a protractor, and con-
sider this the danger angle; as the ship draws near, take frequent observa-
tions with a sextant of the angle subtended by the objects A and B. As
long as the angle is less than the danger angle the
ship is without the circle; but if the angle increases
to the amount of the danger angle, she is on the
circle, and should at once sheer off to avoid approach-
ing closer. The reason will be evident from the con-
sideration that all angles AOB, AO'B, AO'^B, AC^B,
subtended at points on the circumference of the
circle by the chord AB, are equal.
1 56. The vertical danger angle is an application of the same principle
where there is in sight only one well-charted object and that is of known height.
Draw a circle with that object as a center and of such radius that no neighboring
dangei"s lie beyond its circumference; note, from Table 33, the vertical angle
which is subtended by the known height at the distance chosen as a radius,
and, by frequent observations in i)assing, make sure that this danger angle is
not exceeded. By a simple modification, a ship passing inshore of an isolated z
rock or shoal could be navigated clear by means of a vertical danger angle which
was not allowed to decrease below that corresponding to a safe distance.
Considerations governing the taking of vertical angles are given in the
description of finding position by one bearing and the distance (arts. 139, 140). Y''
157. The Danger Bearing. — This is a method by which the navigator is
warned by a compass bearing when the course is leading into danger. Suppose
a vessel to be steering a course, as indicated in figure 22, along a coast which must not be approached
within a certain distance, the landmark A being a guide. Let the navigator draw through A the line
A
Fig. 22.
PILOTING. 47
XA, clear of the danger at all points, and note its direction bj- the compass rose; then let frequent
bearings be taken as the ship proceeds, and so long as the bearings, YA, ZA, are to the right of XA he
may be assured that he is on the left or safe side of the lines.
If, as in the case given, there is but one object in sight and that nearly ahead, it would be very
difficult to get an exact position, but this method would always show whether or not the ship was on a
good course, and would, in consequence, be of the greatest value. And even if there were other objects
visible by which to get an accurate fix it would be a more simple matter to note, by an occasional glance
over the' sight-vane of the pelorus or compass, that the ship was making good a safe course than to be
put to the necessity of plotting the position each time.
15§. It will occasionally occur that two natural objects will so lie that when in range they mark
a danger bearing; advantage should be taken of all such, as they are easier to observe than a compass
bearing; but if in a locality with which the navigator has not had previous acquaintance the compass
bearing of all ranges should be observed and compared with that indicated on the chart in order to
make sure of the identity of the objects. The utility of ranges, either artificial or natural, as guides in
navigation is well recognized.
159. SouNDiX(iS. — The practice should be followed of employing one or two leadsmen to take and
report soundings continuously while in shoal water or in the vicinity of dangers. The soundings must
not be regarded as fixing a position, but they afford a check upon the positions obtained by other
methods. An exact agreement with the soundings on the chart need not be expected, as there may be
some little inaccuracies in reporting the depth on a shij) moving with speed through the water, or the
tide may cause a discrepancy, or the chart itself may lack perfection; but the soundings should agree in
a general way, and a marked departure from the characteristic bottom shown on the chart should lead
the navigator to verify his position and proceed with caution; especially is this true if the water is more
shoal than expected.
160. But if the soundingsinshallow water when landmarks are in sight serve merely as an auxiliary
guide, those taken (usually with the patent sounding machine or deep-sea lead) when there exist no
other means of locating the ])osition, fulfill a nuich more important purpose. In thick weather, when
approaching or running close to the land, and at all times when the vessel is in less than 100 fathoms
of water and her pf)sition is in doubt, soundings should be taken continuously and at regular intervals,
and, with the character of the bottom, systematically recorded. By laying the soundings on tracing
paper, along a line which represents the track of the ship according to the scale of the chart, and then
moving the i)aper over the chart, keeping the various courses parallel to the corresponding directions
on the chart, until the observed soundings agree with those laid down, the ship's position will in general
be quite well determined. While some localities, by the sharpness of the characteristics of their
soundings, lend themselves better than others to accurate determinations by this method, there are few
places where the mariner can not at least keep out of danger by the indications, even if they tell him no
more than that the time has come when he must anchor or lie off till conditions are more favorable.
161. Lights. — Before coming within range of a light the navigator should ac(iuaint himself with
its characteristics, so that when sighted it will be recognized. The charts, sailing directions, and light
lists give information as to the color, character, and range of visibility of the various lights. Care should
be taken to note all of these and compare them when the light is seen. If the light is of the flashing,
revolving, or occulting variety the duration of its periods should be noted to identify it. If a fixed
light, a method that may be employed to make sure that it is not a vessel's light is to descend several
feet inunediately after sighting it and observe if it disappears from view; a navigation light will usually
do so, excepting in misty weather, while a vessel's light will not. The reason for this is that naviga-
tion lights are as a rule sufficiently powerful to be seen at the farthest point to which the ray can reach
without being interrupted by the earth's curvature. They are therefore seen at the first moment that
the ray reaches an observer on a ship's deck, and are cut off if he lowers the eye. A vessel's light, on
the other hand, is usually limited by its intensity and does not carry beyond a distance within which it
it is visible at all heights.
Care nuist be taken to avoid being deceived on first sighting a light, as there are various errors into
which the inexperienced may fall. The glare of a powerful light is often seen beyond the distance of
visibility of its direct rays by the reflection downward from particles of mist in the air; the same mist
may also cause a white light to have a distinctly reddish tinge, or it may obscure a light except within
shoVt distances. AVhen a light is picked up at the extreme limit at which the height of the observer
will permit, a fixed light may appear flashing, as it is seen when the ship is on the crest of a wave, and
lost when in the hollow.
Many lights are made to show different colors in different sectors within their range, and by con-
sulting his chart or books, the navigator may be guided by the color of the ray in which he finds himself;
in such lights one color is generally used on bearings whence the approach is clear, and another covers
areas where dangers are to be encountered.
The visibility of lights is usually stated for an assumed height of the observer's eye of 15 feet, and
must be modified accordingly for any other height. But it should be remembered that atmospheric and
other conditions considerably affect the visibility, and it nmst not he positively assumed, on sighting a
light, even in perfectly clear weather, that a vessel's distance is equal to the range of visibility; it may be
either greater or less, as the path of a ray of light near the horizon receives extraordinary deflection under
certain circumstances; the conditions governing this deflection are discussed in article 301, Chapter X.
162. Buoys. — While buoys are valuable aids, the mariner should always employ a certain amount
of caution in being guided by them. In the nature of things it is never possible to be certain of finding
buoys in correct position, or, indeed, of finding them at all. Heavy seas, strong currents, ice, or collisions
with passing vessels may drag them from their places or cause them to disappear entirely, and they are
especially imcertain in unfrequented waters, or those of nations that do not keep a good lookout upon
their aids to navigation. When, therefore, a buoy marks a place where a ship must be navigated with
caution, it is well to have a danger angle or bearing as an additional guide instead of placing too much
dependence upon the buoy being in place.
Different nations adopt different systems of coloring for their buoys; an important feature of
many such systems, including those adopted by the United States and various other great maritime
48 PILOTING.
nations (though not all), consists in placing black l)uoyH to be left on the starboard hand of a vessel
(johu/ out of a liarbor or fairway, and red biioys (the color of the port side light) on the port hand. ,In
these various systems the color and character of the buoy are such as to denote the special purpose for
which it is employed.
163. Fogs and Fog Signals. — As with lights, the navigator should, in a fog, acquaint himself
with the characteristics of the various sound signals which he is likely to pick up, and when one is
heard, its jjeriods sh<Jbld be timed and comjjared with those given in the light lists to insure its proper
identity.
Experiment has demonstrated that sound is convej'ed through the atmosphere in a very uncertain
way; that its intensity is not always increased as its origin is approached, and that areas within its range
at one time will seem silent at another. Add to these facts the possibility that, for some cause, the
signal may not be working as it should be, and we have reason for observing the rule to proceed with
the utmost caution when running near the land in a fog.
The best guide is the lead, and that should be kept going constantly. The method of plotting
soundings descril^ed in article 160 will give the most reliable position that is obtainable. Moreover,
the lead will warn the navigator of the approach to shallow water, when, if his position is at all in
doubt, it is wisest to anchor before it becomes too late.
"When running slowly in a fog (which caution, as well as the law, requires that one should do) it
must be borne in mind that the relative effect of current is increased; for instance, the angle of deflec-
tion from the course caused by a cross-set is greater at low than at high speed.
It is worth remembering that when in the vicinity of a bold bluft" shore vessels are sometimes
warned of a too close approach by having their own fog signals echoed back from the cliffs; in<leed, from
a knowledge of the velocity of sound (art. 314, Chap. XI) it is possible to gain some rough idea of the
distance in such a case.
164. Tides and Currents. « — The information relating to the tides given on the chart and in other
publications should be studied, as it is of importance for the navigator to know not only the height of
the tide above the plane of reference of the chart, but also the direction and force of the tidal current.
The plane of reference adopted for soundings varies with different charts; on a large number it is
that of mean low water, and as no plane of reference above that of mean low water is ever employed,
the navigator may with safety refer his soundings to that level when in doubt.
When traversing waters in which the depth exceeds the vessel's draft by but a small margin,
account must be taken of the fact that strong winds or a high barometer may cause the water to fall
below even a very low plane of reference. On coasts where there is much diurnal inequality in the
tides, the amount of rise and fall can not be depended upon, and additional caution is necessary.
A careful distinction should be made between the vertical rUe and fall of the tide, which is marked
at the transition periods by a stationary height, or stand, and the tidal current, which is the horizontal
transfer of water as a result of the difference of level, producing the flood and ehb, and the intermediate
condition, or slack. It seldom occurs that the turn of the tidal stream is exactly coincident with the
high and low water, and in some channels the current may outlast the vertical movement which pro-
duces it by as much as three hours, the effect being that when the water is at a stand the tidal stream
is at its maximum, and when the current is slack the rise or fall is going on with its greatest rapidity.
Care must be taken to avoid confounding the two. Usually, more complete data is furnished in charts
and tide tables regarding the rise and fall, and it frequently occurs that the information regarding the
tidal current is comparatively meager; the mariner must therefore take every means to ascertain for
himself the direction and force of the tidal and other currents, either from the set shown between suc-
cessive well-located jiositions of the ship, or by noting the ripple of the water around buoys, islets, or
shoals, the direction in which vessels at anchor are riding, and the various other visible enacts of the
current.
Current arrows on the chart must not be regarded as indicating absolutely the conditions that are
to be encountered. They represent the mean of the direction and force observed, but the observations
upon which they are based may not be complete, or there may be reasons that bring about a departure
from the normal state.
Generally speaking, the rise and fall and strength of current are at their minimum along straight
stretches of coast upon the open ocean, while bays, bights, inlets, and large rivers operate to augment
the tidal effects, and it is in the vicinity of these that one finds the highest tides and strongest currents.
The navigator need therefore not be surprised, in cruising along a coast, to notice that his vessel is set
more strongly toward or from the shore in passing an indentation, and that the evidences of tide will
appear more marked as he nears its mouth.
1 65. Charts. & — The chart should be carefully studied, and among other things all of its notes should
be read, as valuable information may be given in the margin which it is not practicable to place upon
the chart abreast the locality affected.
The mariner will do well to consider the source of his chart and the authority upon which it is based.
He will naturally feel the greatest confidence in a chart issued by the Government of one of the more
important maritime nations which maintains a well-equipped office for the especial purpose of acquiring
and treating hydrographic information. He should note the character of the survey from which the
chart has been constructed; and, finally, he should be especially careful that the chart is of recent issue
or bears correction of a recent date — facts that should always be clearly shown upon its face.
It is well to proceed with caution when the chart of the locality is based upon an old survey, or one
whose source does not carry with it the presumption of accuracy. Even if the original survey was a
good one, a sandy bottom, in a region where the currents are strong or the seas heavy, is liable to
undergo in time marked changes; and where the depth is affected by the deposit or removal of silt, as
in the vicinity of the estuaries of large river systems, the behavior is sometimes most capricious. Large
blank spaces on the chart, where no soundings are shown, may be taken as an indication that no sound-
oSee also Chapter XX. bSee also article 86 and following articles, Chapter II.
PILOTING. 49
ings were made, and are to be regarded with suspicion, especially if the region abounds in reefs or pin-
nacle rocks, in which case only the the closest sort of a survey can be considered as revealing all the
dangers. AH of these facts must be duly weighed.
When navigating by landmarks the chart of the locality which is on the largest scale should be
used. The hydrography and topography in such charts appear in greater detail, and — a most important
consideration — bearings and angles may be plotted with increased accuracy.
166, Records. — It will be found a profitable practice to pay careful attention to the recording of
the various matter relating to the piloting of the ship. A notebook should be kept at hand on deck or
on the bridge, in which are to be entered all bearings or angles taken to fix the position, all changes of
course, important soundings, and any other facts bearing upon the navigation. (This book should be
different from the one in which astronomical sights and offshore navigation are worked.) The entries,
though in memorandum form, should be complete; it should be clear whether bearings and courses are
true, magnetic, or by compass; and it is especially important that the time and patent log reading should
be given for each item recorded. The value of this book will make itself apparent in various directions;
it will afford accurate data for the writing of the ship's log; it will furnish interesting information for
the next run over the same ground; it will provide a means by which, if the ship be shut in by fog,
rain, or darkness, or if there be difficulty in recognizing landmarks ahead, the last accurate fix can be
plotted and brought forward; and, finally, if there should be a mishap, the notebook would furnish
evidence as to where the trouble has been.
The chart on which the work is done should also be made an intelligible record, and to this end
the pencil marks and lines should not be needlessly numerous, heavy, or long. In plotting bearir\gs,
draw lines only long enough to cover the probable position. Mark intersections or positions by drawing
a small circle around them, and writing neatly abreast them the time and patent log reading. Indicate
the courses and danger bearings by full lines and mark them appropriately, preferably giving both
magnetic (or true) and compass directions. A great number of lines extending in every direction may
lead to confusion; however remote the chance may seem, the responsibilities of piloting are too serious
to run even a small risk.
Finally, on anchoring, record and plot the position by bearings or angles taken after coming to;
observe that the berth is a safe one, or, if in doubt, send a boat to sound in the vicinity of the ship to
make sure.
22489—03 4
50
THE SAILINGS.
CHAPTER V.
THE SAILINGS.
167. In considering a ship's position at sea with relerence to any other place, either one that has
been left or one toward which the vessel is bound, five terms are involved — the Course, the Distance,
the Difference of Latitude, the Difference of Longitude, and the Departure. "^ The solutions of the various
problems that arise from the mutual relation of these quantities are called Sailings.
16§. Kinds of Sailin(js. — When the only quantities involved are the course, distance, difference
of latitude, and departure, the process iw denominated Plane Sailing. In this method the earth is
regarded as a plane, and the operation prt)ceeds as if the vessel sailed always on a perfectly level sur-
face. When two or more courses are thus considered, the^- are comV)ined by the method ot Traverse
Sailing. It is evident that the number of miles of latitude and departure can thus be readily deduced;
but, while one mile always equals one minute in difference of latitude, one mile of departure corre-
sponds to a difference of longitude that will vary with the latitude in which the vessel is sailing. Plane
sailing, therefore, furnishes no solution where difference of longitude is considered, and for such solu-
tion resort must be had to one of several methods, which, by reason of their taking account of the
spherical figure of the earth, are called Spherical Sailings.
When a vessel sails on an east or west course along a parallel of latitude, the method of converting
departure into difference of longitude is called Parallel Sailing. When the course is not east or w-est,
and thus carries the vessel through various latitudes, the conversion may be made either by Middle
Latitude Sailing, in which it is assumed that the whole run has been made in the mean latitude, or by
Mercator Sailing, in which the principle involved in the construction of the Mercator chart (art. 38,
Chap. II) is utilized.
Great Circle Sailing deals with the courses and distances between any two points when the track
followed is a gre^t circle of the terrestial sphere. A modification of this method which is adopted
under certain circumstances is called (Jonipositc Sailing.
PLANE SAILING.
169. In Plane Sailing, the curvature of the earth being neglected, the relation between the elements
1-' of the rhumb track joining any two points may be considered from the plane
right triangle formed by the meridian of the place left, the parallel of the place
arrived at, and the rhumb line. In figure 23, T is the point of departure;
T^, the point of destination; Tn, the meridian of departure; T^n, the parallel
of destination; and XT'*, the rhumb line between the points. Let C repre-
sent the course, T^Tn; Dist., the distance, TT^; DL, the difference of latitude,
Tn; and Dep., the departure, T^/i. Then from the triangle TT^h, we have
the following:
8inC=^;
Dist. '
cos C
DL.
Diet.'
Fig. 23.
tanC=^.
From these equations are derived the following formulse for working the various problems that may
arise in Plane Sailing:
Given.
Required.
Course and distance .
("Difference of latitude . . .
(Departure
Difference of latitude jfCourse
and departure.
Distance -
Course and difference of [Distance.,
latitude. I [Departure
Formulse.
D L =Dist. cosC. Log D L = log Dist. + log cos C.
Dep. =Di8t. sin C. Log Dep. =log Dist. + log sin C.
TanC=?^P-.
D L
Dist. =5^.
sinC
Dist.
Dep.
_ DL
cos C
=D L tan C.
Log tan C= log Dep.— log D L.
Log Dist. = log Dep. —log sin C.
Log Dist. =log D L — log cos C.
LogDep.=log D L-flogtanC.
(I For the definition of tliese terms, see article 6, Chapter 1.
THE SAILINGS.
51
Given.
Course and departure.
Required.
I Distance
Difference of latitude.
Distance and difference y ^" '"
of latitude. ' \ Departure
Distance and departure.
I Course
Difference of latitude.
Formulae.
Dist.
Dep.
sin C
D L =5^.
tan C
Log Dist. = log Dep. —log sin C.
Log D L =log Dep. —log tan C.
^"^^=Di^
Log cos C=log D L —log Dist.
Dep. =Dist. sin C. LogDep. = log Dist. + log sin C.
SinC=;^fP:
Dist.
Log sin C= log Dep. —log Dist.
D L =Dist. cosC. Log D L =logDist.+logcosC.
1 70. The solution of the plane right triangle may be accomplished either by Plane Trigonometry, by
Traverse Tables, or by construction. If the former method is adopted, the logarithms of numbers may
be found in Table 42, and of the functions of angles in Table 44. A more expeditious method is avail-
able, however, in the Traverse Tables, which give by inspection the various solutions. Table 1 contains
values of the various parts for each unit of Di.«t. from 1 to 300, and for each quarter-point (2° 49'), of C;
Table 2 contains values for each unit of Dist. from 1 to 600, and for each degree of C. The method of
solving by construction consists in laying down the various given terms by scale upon a chart or plain
paper, and measuring thereon the terms required.
171. Of the various problems that may arise, the first two given in the foregoing table are of much
the most frequent occurrence. In the first, the given quantities are course and distance, and those to be
found are difference of latitude and departure; this is the case where a navigator, knowing the distance
run on a given course, desires to ascertain the amount made good to north or south and to east or
west. In the second case the conditions are reversed; this arises where the course and distance between
two points are to be obtained from their known difference of latitude and departure.
Example: A ship sails SW. byW., 244 miles,
made good.
By Computation.
Dist.
C
DL
Dist.
C
244
56° 15'
135.6
244
56° 15'
log 2.38739
log cos 9.74474
2.13213
log ^^
log 2.38739
log sin 9.91985
Required the <lifference of latitude and the departure
Bi/ Inspection.
In Table 1, find the course SW. by W. (5 points); it
occurs at the bottom of the page, therefore take the names
of the columns from the bottom as well; opposite 244 in
the Dist. column will be seen Lat. 135.6 and Dep. 202.9.
Dep. 202.9 log
2.30724
Example: A ship sails N. 5° E., 188 miles. Required the difference of latitude and the departure.
By Computation.
Dist.
C
DL
Dist.
C
Dep.
188
5°
187.3
188
5°
16.4
log 2.27416
log cos 9.99834
log
2.27250
By Inspection.
In Table 2, find the course 5°; it occurs at the top of the
page, therefore take the names of the columns from the
top; opposite 188 in the Dist. column will be seen Lat.
187.3 and Dep. 16.4.
log 2.27416
log sin 8.94030
log
1.21446
Example: A vessel is bound to a port which is 136 miles to the north ami 203 miles to the west of
her position. Required the course and distance.
By Inspection.
Enter Table 1 and turn the pages until a course
is found whereon the numbers 136 and 203 are
found abreast each other in the columns marked
respectively Lat. and Dep. This occurs most nearly
at the course for 5 points, the angle being taken
from the bottom, because the appropriate names
of the columns are found there. The course is
therefore NW. by W. Interpolating for interme-
diate values, the corresponding number in tke
Dist. column is about 244.3.
By Computation.
Dep. 203 log 2.30750
DL 136 log 2.13354
C (N.) 56° 11' (\V.)
log tan 0.17396
Dep. 203
C 56° 11'
log 2.30750
log sin 9.91951
Dist.
244.3
log
2.38799
52
THE SAILINGS.
Example: A.s the result of a day's run a vessel changes latitude 244 miles to the south and makes a
departure of 171 miles to the east. What is the course and distance made good?
By Inspection.
Enter Table 2 and the nearest agreement will
be found on course (S.) 35° (E. ), the appropriate
names being found at the top of the page. The
nearest corresponding Dist. is 298 miles.
By Computation.
Dep. 171
DL • 244
log 2.23300
log 2.38739
C (S.) 35°02^ (E.)
log tan 9.84561
Dep. 171
C 35° 02'
log 2.23300
log sin 9.75895
Dist,
297.9
log
2.47405
TRAVERSE SAILING.
1 72. A Traverse is an irregular track made by a ship in sailing on several different courses, and the
method of Traverse Sailing consists in finding the difference of latitude and departure corresponding to
several courses and distances and reducing all to a single equivalent course and distance. This is done
by determining the distance to north or south and to east or west made good on each course, taking the
algebraic sum of these various differences of latitude and departure and finding the course and distance
corresponding thereto. The work can be most expeditiously performed by adopting a tabular form for
the computation and using the traverse tables.
Example: A ship sails SSE., 15 miles; SE., 34 miL>s; W. by S., 16 miles; WNW., 89 miles; S. by E.,
40 miles. Required the course and distance made good.
Courses.
Dist.
N.
s.
E.
w.
SSE.
15
13.9
5.7
SE.
34
24.0
24.0
W. by S.
16
3.1
15.7
WNW.
39
14.9
36.0
S. by E.
40
39.2
7.8
14.9
80.2
37.5
51.7
S. by W.
66.8
14.9
37.5
65.3
14.2
The result of the various courses is, therefore, to carry the vessel S. by W., 66.8 miles from her origrnal
position.
PARALLEL SAILING.
173. Thus far the earth has been regarded as an extended plane, and its spherical figure has not
been taken into account; it has thus been impossible to consider one of the important terms involved —
namely, difference of longitude. Parallel Sailing is the simplest of the various forms of Spherical Sailing,
being the method of interconverting departure and difference of longitude when the ship sails upon an
east or west course, and therefore remains always on the same parallel of latitude.
In figure 24 T and T' are two places in the same latitude; P, the adjacent pole;
TT'', the arc of the parallel of latitude through the two places; MM^, the corre-
sponding arc of the equator intercepted between their meridians PM and PM';
and TT', the departure on the parallel whose latitude is TCM = OTC, and whose
radius is OT.
Let DLo represent the arc of the equator MM^, which is the measure of
MPM', the difference of longitude of the meridians PM and PM''; R, the equa-
torial radius of the earth, CM = CT; r, the radius OT of the parallel TT''; and L,
the latitude of that parallel.
Then, since TT' and MM' are similar arcs of two circles, and are therefore
-^proportional to the radii of the circles, we have:
TT' ^ OT.
MM' CM'
From the triangle COT, r = R cos L; lience
Dep. R cos L
or,
Dep. _ r
DLo ~R'
DLo
R
or, DLo = Dep. sec. L; or, Dep. = DIxi cos L.
Thus the relations are expressed between minutes of longitude and miles of departure.
174. Two cases arise under Parallel Sailing: First, where the difference of longitude between two
places on the same parallel is given, to find the departure; and, second, where the departure is given,
to find the difference of longitude.
THE SAILINGS. 53
/
In working these problems, the computation can be made by logarithms; but the traverse tables
may more conveniently be employed. Kemembering that those tables are based upon the formuhe,
DL=Dist. cos C, and Uist.=DL sec C,
we may substitute for the column marked Lat. the departure, for that marked Dist. the difference of
longitude, and for the courses at top and bottom of the page the latitude. The tables then become
available for making the required conversions.
Example: A ship in the latitude of 49° 30' sails directly east until making good a difference of
longitude of 3° 30'. Required the departure.
By Computation. By Inspection.
L 49° 30' log cos 9.81254 Enter Table 2 with the latitude as C and the difference
DLo 210' log 2.32222 of longitude as Dist. As the table is calculated only to
single degrees, we must find the numbers in the pages of
Dep. 136. 4 log 2.13476 49° and 50° and take the mean. Corresponding to Dist.
210 in the former is Lat. 137.8, and in the latter Lat. 135.0.
The mean, which is the required departure, is 136.4.
Example: A ship in the latitude of 38° sails due west a distance of 215.5 miles. Required the
difference of longitude.
By Computation. By Inspection.
L 38° log sec 0.10347 Entering Table 2 with the latitude, 38°, as a course,
Dep. 215. 5 log 2.33345 corresponding with the number 215.5 in column of Lat.,
is 273.5 in the column of Dist. This is therefore the
y^j / 273'. 5 log 2.43692 required difference of longitude, being equal to 4° 33'. 5.
JJ1.0 ^ 40 33/ 5
MIDDLE LATITUDE SAILING.
175. When a ship follows a course obliquely across the meridian the latitude is constantly
changing, and the method of converting departure and difference of longitude T)y Parallel Sailing, just
described, ceases to be applicable.
In figure 25, T is the point of departure; T', the point of destination ; P, ?
the earth's pole; TT', the rhumb tracrk; r^TT', the course; Tn, «iT', the
respective parallels of latitude; and MM', the equator.
The difference of longitude between T and T' is MPM', wliich may
be measured by the arc of the equator, MM', intercepted between their
meridians. This corresponds to a departure Tn in the latitude of T, and
to the smaller departure T'rzi in the higher latitude of T'; but since the
vessel neither makes all of the departure in the latitude T, nor all of it
in the latitude T', the departure actually made in the passage must have
some intermediate value between these extremes. Dividing the total
difference of longitude into a number of equal parts MPwii, hjjPhIj, etc.,
of such small extent that, for the purposes of conversion, the change of
latitude corresponding to each may be neglected, we have the total
departure made up of the sum of a number of small departures, each
equal to the same difference of longitude, but each different from the
other. These will be c/j r^ in the latitude T, d^ r^ in the latitude ?•,,
etc. Hence we have: „ ^_
MM'=d, r-i sec MT-|-f?2 ''21 sec m, rj + da r^, sec 7U2 r^, + etc. *-'•
Now, if LL' be a parallel of latitude lying midwav between Tn and T'jij, since there will be as many
of the small parts lying above as below it, and since for moderate distances the ratio to be employed in
the conversion of departure and difference of longitude may be regarded as varying directly with the
latitude, it maybe assumed for such distances that the sum of all of the different small departures
equals the single departure between the meridians measured in the latitude LL', and therefore that the
departure obtained by the method of plane sailing on any course may be converted into difference of
longitude by multiplying by the secant of the Middle Latitude.
The niethod of conversion based upon this assumption is denominated Middle lAtitude Sailing, and
by reason of its convenience and simplicity is usually employed for short distances, such as those covered
by a vessel in a day's run.
176. In Middle Latitude Sailing, having found the mean of the latitudes, the solution is identical
with that of Parallel Sailing (art. 173), substituting the Middle Latitude for the single latitude therein
employed.
177. It niay be remarked that the Middle Latitude should not be used when the latitudes are of
opposite name; if of different names and the distance is small, the departure may be assumed equal to
the difference of longitude, since the meridians are sensibly parallel near the equator; but if the distance
is great the two portions of the track on opposites of the equator must be treated separatelv.
] Example: A ship in Lat. 42° 30' N., Long. 58° 51' W., sails SE. by S., 300 miles. Required the
latitude and longitude arrived at.
From Table 1: Course SE. by S., Dist., 300, we find Lat., 249.4 S. (4° 09'.4), Dep., 166.7 E.
Latitude left, 42° 30'.0 N. Latitude left, 42° 30' N.
DL, 4 09 .4 S. Latitude arrived at, 38 21 N.
Latitude arrived at, 38 20 .6 N. 2)80 51
Mid. latitude, 40 25 N.
54
THE SAILINGS.
/^~V
Enter Table 2 with the middle latitude, 40°, as a course; the difference of longitude (DLst. ) cor-
responding to the departure (Lat.) 166.7 is 217.6; entering with 41°, it is 220.9; the mean is 219.2
(3° 39'. 2). ^
KjA Longitude left, 58° 51'.0 W.
DLo, 3 39 .2 E. *
Longitude arrived at, 55 11 .8 W.
Example: A ship in I^t. 39° 42' S., Long. 3° 31' E., sails S. 42° W.
tude and longitude arrived at.
From Table 2: Course, S. 42°
Latitude left,
DL,
236 miles. Required the lati-
^
W., Dist., 236 miles; we find I^t., 175.4 S. (2° 55'.4), Dep., 157.9 W.
39° 42'.0 S. Latitude left, 39° 42' S.
2 55 .4 S. Latitude arrived at, 42 37 S.
I^atitude arrived at, 42 37 .4 S.
2)82 19
Mid. latitude, 41 09 S.
From Table 2: Mid. Lat.. (course), 41°, Dep. (Lat.), 157.9; we find DLo (Dist.), 209.3 (3=
Longitude left, 3° 31'.0 E. •
DLo, 3 29 .3 W.
29'.3).
Longitude arrived at, 0 01 .7 E.
Example: A vessel leaves Lat. 49° 57' N., Long. 15° 16' W., and arrives at T^at. 47° 18' N., Long.
20° 10' AV. Required the course and distance made good.
Latitude left, 49° 57' N. Longitude left, 15° 16' W.
Latitude arrived at, 47 18 N. Longitude arrived at, 20 10 W.
l^L, {^°159'}S- ^'^' ■ {%S'K
2)97° 15' N.
Mid. latitude, 48 38 N.
From Table 2: Mid. Lat. (course), 49°, DLo (Dist.), 294; we find Dep. (Lat.), 192.9.
From Table 2: DL 159 S., Dep. 192.9 W., we find course S. 51° W., Dist., 251 miles.
17§. The assumption upon which Middle Latitude sailing is based — that the conversion may be
made as if the whole distance were sailed upon a parallel midway between the latitudes of departure and
destination — while sufficiently accurate for moderate distances, may be materially in error where the
distances are large. In such case, either the method of Mercator Sailing (art. 179) must be employed,
or else the correction given in the following table should be applied to the mean latitude to obtain what
may be termed the latitude of conversion, being that latitude in which the required conditions are
accurately fulfilled. The table is computed from the formula:
cos Lc=— ,
■m
where Lc represents the latitude of conversion, and / and m are respectively the differences of latitude
and of meridional parts (art. 39, Chap. II) between the latitudes of departure and destination. «
Mid.
Lat.
Difference of latitude.
Mid.
Lat.
1°
2° 3°
4°
6°
6°
7° 8°
9°
10° 12°
14°
16°
18°
20°
o
15
18
21
/
-86
-67
-54
-85
-67
-54
/
-84
-66
-53
-44
-29
-21
-15
-11
- 7
/
-83
-65
-52
-42
-29
-21
-14
-10
- 6
- 3
- 1
- 1
0
1
2
/
-81
-63
-51
/
-79
-61
-49
/
-76
-59
-47
-38
-24
-17
-73
-56
-44
-.36
-23
-15
/
-69
-53
-42
-33
-20
-12
/
-65
-50
-39
-56
-43
-32
/
-46
-34
-24
/
-34
-23
-15
/
-21
-12
- 5
1
11
18
'
- 6
1
7
o
15
18
21
24
30
35
24
30
35
-44 1 —44
-31 -30
-23 -22
-41
-28
-19
-13
- 8
- 5
-40
-26
-18
-12
- 7
- 3
0
2
3
4
5
6
-31 1 -24
-18 -12
-10 - 5
-17
- 6
2
8
14
20
- 8
1
10
T6
22
28
12
21
28
■ 40
45
50
-17
-12
- 8
- 5
- 4
- 3
-16
-10
- 5
- 1
2
4
5
7
8
9
- 8
- 3
1
- 6
- 1
3
- 4
1
6
10
13
14
17
18
20
2
7
12
25
31
38
34
41
49
40
45
50
55
58
60
- 5
- 3
- 3
- 4
-3
- 2
— 2
0
1
2
3
4
5
7
8
9
11
12
7
10
11
13
14
16
17
20
22
25
29
32
35
39
43
46
51
55
60
65
71
58
64
69
55
58
60
62
64
66
- 3 - 2 - 1
- 2 - 1 0
-2-1' 0
25
27
30
35
38
42
46
50
55
75
81
89
62
64
66
68
70
72
- 1: 0; 1
-1 0: 1
0 0 2
2
3
4
5
5
7
8
10
10
12
13
14
16
18
18
20
23
22
25
?8
33
37
41
46
51
57
61
67
76
78
87
97
98
109
123
68
70
72
a The statement often made, that the latitude of conversion is always greater than the middle latitude, is not correct
when the compression of the earth is taken into account, as an inspection of the table will show; that statement is based
upon an assumption that the earth is a perfect sphere, and it was iipon that assumption that a table which appeared in early
editions of this work was computed. The value of the compression adopted for this table is - .
THE SAILINGS.
55
Example: A vessel sails from Lat. 10° 13' S. to Lut. 20° 2K S., making a departure of 432 miles.
Required the difference of longitude.
Latitude left, 10° 13' S.
Latitude arrived at, 20 21 S.
2)30 34
For Mid. Lat. 15° and Diff. of Lat. 10°, ('orrection, —65'
Mid. latitude.
Correction,
15 17 S.
- 1 05
14° 12'
432
445'. 6
log sec
log
log
Lc,
14''-12 S.
L<,
Dep.
DLo
.01348
2.63548
2.64896
MERCATOR SAILING.
1 79. Mercator Sailing is the method by which values of the various elements are determined from
<'onsidering them in the relation in which they are .plotted upon a chart constucted according to the
Mercator projection.
180. Upon the Mercator chart (art. 38, Chap. II), the meridians being parallel, the arc of a par-
allel of latitude is shown as equal to the corresponding arc of the equator; the length of every such
arc is, therefore, expanded; and, in order that the rhumb line may appear as a straight line, the merid-
ians are also expanded by such amount as is necessary to preserve, in any latitude, the proper propor-
tion existing between a unit of latitude and a unit of longitude. The lengths of small portions of the
meridian thus increased are called meridional parts (art. 39, Chap. II), and these, computed for every
minute of latitude from 0° to 80°, form the Table of Meridional Parts (Table 3),
by means of which a INIercator chart may be constructed and all problems of
Mercator Sailing may be solved.
In the triangle ABC (fig. 26), the angle ACB is the course, C; the side AC, the b
distance, Dist. ; the side BC, the difference of latitude, DL; and the side AB, the
departure, Dep. Then corresponding to the difference of latitude BC in the lati-
tude under consideration, if CE be laid off to represent the meridional difference
of latitude, in, completing the right triangle CEF, EF will represent the differ-
ence of longitude, DLo. The triangle ABC gives the relations involved in Plane dl
Sailing as previously described; the triangle CEF affords the means for the con-
version of departure and difference of longitude by Mercator Sailing.
181. To find the arc of the expanded meridian intercepted between any two
parallels, or the meridional difference of latitude, when both places are on the same
side of the equator, subtract the meridional parts of the lesser latitude, as given
by Table 3, from the meridional parts of the greater; the remainder will be the
meridional difference of latitude; but if the places are on different sides of the
equator, the sum of the meridional parts will be the meridional difference of
latitude.
1§2. To solve the triangle CEF by the traverse tajbles it is only necessary to substitute merid-
ional difference for Lat., and difference of longitude for Dep. Where long distances are involved,
<-arrying the computation beyond the limits of the traverse table, as frequently occurs in this method,
either of two means may be adopted : the problems may be worked by the trigonometrical formulae,
using logarithms, or the given quantities involved may all be reduced b}' a common divisor until they
fall within the traverse table, and the results, when obtained, correspondingly increased. The former
method is generally preferable, especially when the distances are quite large and accurate results are
sought. The formulae for the various conversions are as follows:
tan C=5^; DLo=m tan C; r/i=DLo cot C.
Example: A ship in Lat. 42° 3(' N., Long. 58° 51' W., sails SE. by S., 300 miles,
latitude and longitude arrived at.
From Table 1: Course, SE. by S., Dist, 300; we find Lat. 249.4 S. (4° 09/4).
Latitude left, 42° 30'. 0 N. Merid. parts, +2806.4
DL, 4 09 .4 S.
Required the
Latitude arrived at, 38 20 .6 N.
Merid. parts,
m,
2480.4
DLo
By Computation.
326.0 log
33° 45'
; 217'.8
\3° 37'. 8
2.51322
og tan 9.82489
log
2.33811
326.0
By Inspection.
Enter Table 1, course 3 points; since the quantities
involved exceed the limits of the table, divide by 2;
abreast '|(Lat.), 163.0, find g— (Dep.), 108.9; hence
DLo=217'.8 or 3° 37'.8.
Longitude left,
DLo,
58° 51'.0 W,
3 37 .8 E.
Longitude arrived at, 55 13 .2 W.
56
THE SAILINGS.
Example: A ship in Lat. 4° 37' S., Ix)ng. 21° 05' W., sails N. 14° W., 450 miles. Required th«
latitude and longitude arrived at.
From Table 2: Course, (N.) 14° (W.), Dist., 450; we find Lat. 436.6 N. (7° 16'.6).
Latitude left, 4° 37'.0 S.
i)L, 7 16 .6 N.
Merid. parts, -f 275.4
Latitude arrived at, 2 39 .6 N.
Merid. parts, -f 159.0
m, 434.4
tation.
By Inspection.
DLo
434.4
14'
log 2.63789 From Table 2: Course, 14°, m (Lat.), 434.4, we tind
log tan 9.39677 DLo (Dep. ) 108'. 3 W., or 1° 48'. 3.
{v
108'. 3
' 48'. 3
log
2.03466
Longitude left,
DLo,
21° 05'.0 W.
1 48 .3 W.
Longitude arrived at, 22 53 .3 W.
Example: Required the course and distance by rhumb line from a jwint in Lat. 42° 03' N., Long.
70° 04' W., to another in Lat. 36° 59' N., Long. 25° 10' W.
Lat. departure, 42° 03' N.
Lat. destination, 36 59 N.
DL
Merid. pts., -f 2770.1
Merid. pts., —2377.3
Long, departure, 70° 04' W.
Long, destination, 25 10 W.
/ 5° 04'1 g
\ 304'/^-
DLo 2694
m 392.8
(E.)
m, 392.8
log 3.43040
log 2.59417
DLo
C (S.) 81° 42'
DL 304'
log tan .83623
log sec .84056
log 2.48287
/44° 54'\t
\ 2694'/^
Dist.
2106
log 3.32343
The course is therefore S. 81° 42' E., and the distance is 2,106 miles. Since the figures involved
are so large, it is best to employ only the method by computation. The formula by which the Dist. is
obtained comes from Plane Sailing.
GREAT CIRCLE SAILING.
1§3. The shortest distance between any two points on the earth's surface is measured by the arc of
the great circle which passes through those points; and the method of sailing in which the arc of a great
circle is employed for the track of the vessel, taking advantage of the fact that it is the shortest route
possible, is denominated (ireat Circle Sailing.
184. It frequently happens when a great circle route is laid down that it is found to lead across
the land, or to carry the vessel into a region of dangerous navigation or extreme cold which it is expe-
dient to avoid; in such a case a certain parallel should be fixed upon as a limit of latitude, and a route
laid down such that a great circle is followed as far as the limiting parallel, then the parallel itself, and
finally another great circle to the port of destination. Such a modification of the great circle method is
called Composite Sailing.
1§5. The rhiuah line (art. 6, Chap. I) also called the loxodromic curve, which cuts all the meridi-
ans at the same angle, has been largely employed as a track by navigators on account of the ease with
which it may be laid down on a Mercator chart. But as it is a longer line than the great circle between
the same i)oints, intelligent navigators of the jiresent day use the latter wherever practicable. On the
Mercator chart, however, the arc of a great circle joining two points (unless both are on the equator or
both on the same meridian) will not be projected as a straight line, but as a curve which seems to be
longer than the rhumb line; hence the shortest route appears as a circuitous one, and this is doubtless
the reason that a wider use of the great circle has not been made.
It should be clearly understood that it is the rhumb line which is in fact the indirect route, and
that in following the great circle the vessel is always heading for her port, exactly as if it were in sight,
while on the course which is shown as a straight hue on the Mercator chart the vessel never heads for
her port until at the very end of the voyage.
186. The method of great circle sailing is of especial value to steamers, as such vessels need not,
in the choice of a route, have regard for the winds to the same extent as must a sailing vessel ; but even in
navigating vessels under sail a knowledge of the great circle cour.se may proveof great value. For example,
suppose a ship to be bound from Sydney to Valparaiso; the first great circle course is SE. by S., while
the Mercator course is almost due east. The distance is 748 miles shorter by the former route (if the
THE SAILINGS. 57
p;reat circle is followed throughout, though this would lead to a latitude of 61° S.). With the wind at
E. J S. the ship would lie nearer to the Mercator course on the starboard tack, assuming that she sailed
within six points of the wind; but if she took that tack she would be increasing her distance from the
port of destination by 45 miles in every 10 that she sailed; while on the port tack, heading one point
farther from the rhumb, the gain toward the port would be 9i miles out of every 10. Any course
between East and SSW. would be better than the Mercator course; and if the wind were anything to
the eastward of SE. by S., the ship would gain by taking the port tack in preference to the starboard.
1§7. As the great circle makes a different angle with each meridian that is crossed, it becomes
necessary to make frequent changes of the ship's course; in practice, the course is a series of chords
joining the various points on the track line.
If, while endeavoring to follow a great circle, the ship is driven from it, as by unfavorable weather,
it will not serve the purpose to return to the old track at convenience, but it is required that another
great circle l)e laid down, joining the actual position in which the ship finds herself with the port of
destination.
1§S. The methods of determining the great circle course may be divided generally into four
classes; namely, by Great Circle Hailiny Charts, by Computation, by the methods of the Time Azimuth,
and by Graphic Approximations.
1 89. Great Circle Sailing Charts. — Of the available methods, that by means 'of charts espe-
cially constructed for the purpose is considered greatly superior to all others.
A series of great circle .sailing charts covering the navigable waters of the globe is published by the
United States Hydrographic Office. Being on the gnoinonic projection (art. 43, Chap. II), all great
circles are represented as straight lines, and it is only necessary to join any two points by such a line to
represent the great circle track between them. The courses and distance are readily obtainable by a
method explained on the charts. The track may be transferred to a chart on the Mercator projection
by plotting a number of its points by their coordinates and joining them with a curved line.
The navigator who contemplates the use of great circle
tracks will find it of the greatest convenience to be pro-
vided with these gnomonic charts for the regions which
his vessel is to traverse.
190. By CoMPiTATiON. — This method consists in de-
termining a series of points on the great circle by their
coordinates of latitude and longitude, plotting them upon
a Mercator chart, and tracing the curve that joins them.
The first point determined is the vertex, or point of highest
latitude, even when, as sometimes occurs, it falls without
that portion of the great circle which joins the points of
departure and destination. Fig. 27.
In figure 27, A represents the point of departure; B, the
point of destination; AV'B, the great circle joining them, with its vertex at V; and P, the pole of tlie
earth.
Let Ca = PAB, the initial course;
Cb = PBA, the final courser
La , Lv, Lb = the latitudesof the respective points A, V, B = (90° — PA), (90° — PV), (90° - PB).
Loab, Loav, Lobv = the differences of longitude between A and B, A and V, B and V, respectively, =
APB, APV, BPV.
D = the great circle distance between A and B; and
q> — an auxiliary angle introduced for the computation.
We then have:
tan cp — cos Loab cot Lb;
cot Ca = cot Loab cos (La + <p) cosec cp;
cot D = cos Ca tan (La + ^);
cos Lv = sin Ca cos La;
cot Loav = tan Ca sin L a .
Bv these formul.T are determined the initial course and the total distance by great circle; also the
latitude of the vertex and its longitude with respect to A. By interchanging the subscript letters a and
B throughout, we should ol)tain the final course, and the longitude of the vertex with respect to B; also
the same total distance and latitude of the vertex as before.
In performing this computation, strict regard must be had to the signs of the quantities. If the
points of departure and destination are in different latitudes, the latitude of one of these points must he
regarded as negative with respect to the other, and they must be marked with opposite signs. Should
Loav or Lobv assume a negative value, it indicates that the vertex does not lie between A and B, and is
to be laid off accordingly.
To find other points of the great circle, M, N, etc. , let their latitudes be represented by L m , L jj , etc. ,
and their longitudes from the vertex by Lovj:, Lovx, etc.; then
tan Lji = tan Lv cos Lovm ; or, cos Lovm = tan Lm cot L v;
tan Ln = tan Lv cos Lo v.\ ; or, cos Lo vn = tan L x cot v ;
and so on. By these formulpe intervals of longitude from the vertex of 5°, 10°, or any amount, may be
assumed, and the corresponding latitudes deduced; or any latitude may be assumed and its correspond-
ing interval of longitude from the vertex found. Two positions will result from each solution, and the
appropriate ones may be chosen by keeping in mind the signs involved.
68
THE SAILINGS.
Example: Given two places, one in Lat. 40° X., Long. 70° AV., the other in Lat. 30° S., Long. 10°
W., find the great circle distance between them; also the initial course, and the longitude of equator
crossing.
La = 4-40°; Lb = -30°; Loab=60°.
Loab 60° cos 9.69897.. cot 9.76144
Lb - 30° fot (-) .23856
La +40° cos 9.88425 sin 9.80807
<p - 40° 54' tan (-) 9.93753.. co8ec(-) .18393
(La + <p) - 0° 54' cos 9.99995 tan (-) 8.19616
Ca 131° 24' orS.48°36'E cot (-)9.94532 cos {-) 9.82041 sin 9.87513 tan (-) .05472
P 89° 24' or 5,364 miles cot 8.01657
Ly + 54° 56' CDS 9.75938
Loav - 53° 54' ...cot (-)9.86279
The initial course is therefore S. 48° 36' E., and the distance 5,364 nautical miles. (It may be
found that the course by rhumb line is S. 38° 45' E. and the distance 5,751 miles.) The vertex of the
freat circle is in Lat. 54° 56' N., and is 53° 54' in longitude from the point A, in a direction away from
\\ hence it is in Long. 123° 54' W. To find the longitude of equator crossing let Lm = 0°; then in the
^nation,
cos LovM=tan Lm cot Lv,
since tan Lm equals zero, cos I^oi also equals zero, or the longitude interval from the vertex is 90°, which
is evident from the properties of the great circle; thtjrefore the longitude of equator crossing is
123° 54' W.— 90°=33° 54' W.
191. By Time Azimtth Methods. — A convenient method of obtaining the initial and final courses
in great circle sailing is afforded by the tables and graphic methods which are prepared for the solution
of the Tone Azimuth problem (art. 359, Chap. XIV). It will be found by comi)arison that if the lati-
tude of the point of departure be substituted for the latitude of the observer in that problem, the latitude
of destination for the declination of the celestial body, and the longitude interval for the hour angle, the
solution for the initial course will coincide with that for the azimuth; by interchanging the latitudes of
the points of departure and destination the final course will be similarly obtained. Advantage may
thus be taken of the various methods provided for facilitating the determination of the azimuth to ascer-
tain the great circle courses from one jwint to another.
192. By Graphic Approximations. — Of the numerous methods that fall w'ithin this class only two
need be given.
193. By the use of a TerreKtrial Globe the two given points tetween which the great circle track
is required may be joined by the shortest line between them, either by means of a piece of thread or
by moving the globe until they are brought to the fixed horizon which is usually provided; the coordi-
nates of the various points of the track are then transferred to the chart. The number of minutes of
arc, as measured on the scale of the horizon between the points, equals the number of miles of distance;
if there be no horizon, the measure may be made by a thread along the equator or a meridian.
194. The Method of Professor Airy consists in drawing on the chart a rhumb line joining the two
points, and erecting at its middle point a perpendicular; the following table should then be entered
with the middle latitude as an argument, and the "corresponding parallel" of latitude taken out
(noting whether it is the same or opposite in name to the middle latitude); where this parallel is inter-
sected by the perpendicular that was drawn will be the center from which may be swept an arc approx-
imately representing the great circle between the two points.
Middle lati-
Correspond-
Name.
Middle lati-
Correspond-
Name.
tude.
ing parallel.
tude.
o
ing parallel.
o
o /
o /
20
81 13
Opposite.
52
11 33
Opposite.
22
78 16
Do.
54
6 24
Do.
24
74 59
Do.
56
1 13
Do.
26
71 26
Do.
58
4 00
Same.
28
67 38
Do.
60
9 15
Do.
30
63 37
Do.
62
14 32
Do.
32
59 25
Do.
64
19 50
Do.
34
55 05
Do.
66
25 09
Do.
36
50 36
Do.
68
30 30
Do.
38
46 00
Do.
70
35 52
Do.
40
41 18
Do.
72
41 14
Do.
42
36 31
Do.
74
46 37
Do.
44
31 38
Do.
76
52 01
Do.
46
26 42
Do.
78
57 25
Do.
48
21 42
Do.
80
62 51
Do.
50
16 39
Do.
THE SAILINGS. 59
COMPOSITE SAILING.
195. It has already been stated that when, for any reason, it is impracticable or imadvisable to
follow the great circle track to its highest altitude, a limiting parallel is chosen and the route moditied
accordingly. This method is denominated Composite Sailing.
196. The shortest track between points where a fixed latitude is not exceeded is made up as
follows:
1. A great circle through the point of departure tangent to the limiting parallel.
2. A course along the parallel.
3. A great circle through the point of destination tangent to the limiting parallel.
The composite track may be determined by Oreat Circle Sailing Chart, by CompuUUion, or by
Graph ic Approximation.
197. On a Great Circle Sailing Chart, draw lines from the points of departure and destination,
respectively, tangent to the limiting parallel; transfer these great circles to a Mercator chart in the
usual manner, by the coordinates of several points, including in each case the point of tangency to the
parallel. Follow the first great circle to the parallel; then follow the parallel; then the second great
circle. Determine great circle courses and distances from the gnomonic chart as thereon described;
determine the distance along the parallel by Parallel Sailing.
19§. Bi/ computation, the problem consists in finding the great circles which pass, respectively,
through the points of departure and destination and have their vertices in the latitude of the limiting
parallel. Resuming the designation of terms already employed (art. 190), we have:
cos LovA=tan La cot Lv ;
cos LovB=tan Lb cot Lv ;
where Lova and Lovb represent the distances in longitude from A and from B to the respective points of
tangencv; other features of each of the great circles mav be determined in the usual manner.
Example: A vessel in Lat. 30° S., Long. 18° W., is* bound to a point in Lat. 39° S.. Long. 145° E.,
and it is decided not to go south of the parallel of 55° S. Find the longitude of reaching that parallel
and the longitude at which it should be left.
La =30° S.; Lb =39° 8.; Lv=55°S.
Loa =18° W.; Lob =145° E.
La 30° tan 9.76144 L„ 39° tan 9.90837
Ly 55° cot 9.84523 Lv 55° cot 9.84523
LovA 66° 09^ E. cos 9.60667 Lovb 55° 27' W. cos 9.75360
Loa 18 00 W. Lob 145 00 E.
Lov 48 09 E. Lov 89 33 E.
199. A graphic approximation to the composite track may be obtained by drawing a straight line
between the given points on a Mercator chart and erecting at its middle point a perpendicular, which
shoulii be extended until it intersects the limiting parallel. Then through this intersection and
the two points describe the arc of a circle, and this will approximate to the shortest distance within the
assigned limit of latitude.
200. A terrestrial glol^e may be employed for the determination of the composite track; the
method of its use will suggest itself.
201. Another approximation is obtained by joining the two points with a single great circle,
and following this to its intersection with the limiting parallel; thence sailing along the parallel until
the great circle is again intersected; then resuming the circle and following it to the destination.
60 DEAD RECKONING.
chaptp:r vl
dead keckoning.
203. Dead Reckoning is the process by which the position of a ship at any instant is found by
applying to the last well-determined position the run that has since been made, using for the purpose
the ship's course and the distance indicated by the log.
203. Positions by dead reckoning, also spoken of as positions by account, differ from those
determined by bearings of terrestrial objects or by observations of celestial bodies in being less exact,
as the correctness of dead reckoning depends upon the accuracy of the estimate of the run, and this is
always liable to be at fault to a greater or less extent. The course made good by a ship may differ from
that which it is believed that she is making good, by reason of imperfect steering, improper allowance
for compass error and leeway, and the effects of unknown currents; the allowed distance over the
ground may be in error on account of inaccurate logging and unknown currents.
Notwithstanding its recognized defects as comparetl with the more exact methods, the dead
reckoning is an invaluable aid to the mariner. It affords him a means of plotting the position of the
ship at any desired time between astronomical determinations; it also gives him an approximate
position at the moment of taking astronomical observations which is a great convenience in working up
those observations; and finally it affords the only available means of determining the location of a
vessel at sea during those periods (which may continue for several days together) when the weather is
such as to render the observation of celestial bodies an impossibility.
204. Taking Departure. — Before losing sight of the land, and preferably while objects remain in
good view, it is the duty of the navigator to take a departure; this consists in fixing the position of the
ship by the best means available (Chap. IV), and using this position as the origin for dead reckoning.
There are two methods of reckoning the departure. The first and simpler consists in taking from the
chart the latitude and longitude of the position found, and applying the future run thereto. The other
requires that the bearing and distance of an object of known latitude and longitude be found; the
position of the object then forms the basis of the reckoning, and the reversed direction of the bearing,
with the distance, forms the first course and distance; thus it may be considered that the ship starts from
the position of the object and sails to the position where the bearing was taken; the correction for
deviation in such a case should be that due to the heading of the ship when the bearing was taken.
Each time that a new position is determined it is used as a new departure for the dead reckoning.
This meaning of the term departure should not be confounded with the other, which refers to the
distance run toward east or west.
205. Methods. — The working of dead reckoning merely involves an application of the methods of
Traverse Sailing (art. 172) and Middle Latitude Sailing (art. 175), as explained in Chapter V.
The various compass courses are set down in a column, and abreast each are written the errors by
reason of which the course steered by compass differs from the true course made good over the ground;
thence the true course made good is determined and recorded; next, the distance is written in, and
afterwards, by means of Tables 1 or 2 (according as the courses are expressed in cjuarter points or
degrees), the difference of latitude and departure are found, separate columns being kept for distances to
the north, south, east, and west.
When the position of the ship at any moment is required, add up all the differences of latitude and
departure, and write in the column of the greater the difference between the northing and southing,
and the easting and westing. Apply the difference of latitude to the latitude of the last determined
position, which will give the latitude by D. R., and from which may be found the middle latitude; with
the middle latitude find the difference of longitude corresponding to the departure, apjjly this to the
longitude of last position, and the result will be the longitude by D. R.
The employment of the tabular form will be found to facilitate the work and guard against errors.
It will be a convenience to include in that form colunnis showing the hour, together with the reading
of the patent log (if used) each time that the course is changed or the dead reckoning worked up.
The employment of minutes and tenths in dead reckoning rather than minutes and seconds is
recommended.
E.XAMPLE: A vessel under sail heading NE. f E. (on which course deviation is \ pt. Easterly) takes
departure from Cape Henry light-house (see Appendix IV for position ), bearing SSVV. ^ A\\ per compass,
distant 1.4 miles. She then sails on a series of courses, with errors and distances as indicated below;
wind about SE. by E. Required the position by dead reckoning; also the course and distance made
good by dead recokning.
DEAD RECKONING.
61
Comp. course.
Var.
Dev.
Leeway.
Error.
True course.
Dist. i N.
s.
E.
w.
D.
NNE. 1 E.
iw.
iE.
i w.
NNE. i E.
1.4
1.3
0.6
NE. 1 E.
*w.
iE.
iw.
iw.
NE. i E.
27.6
18.5
20.5
S. by W.
*vv.
0
iE.
iw.
S. f W.
31.5 1
81.2
4.6
ENE.
iw.
iE.
iW.
f w.
NE. bv E. i E.
14.2 1 7.3
12.2
S. iE.
iW.
0
^E.
0
S. i E.
11.0 !
11.0
0.5
NE. i N.
i\\.
iE.
i W.
iw.
NE. by N.
87.0
72.3
48.3
99.4
42.2
82.1
4.6
Made good,
NE. i E.
96.5
57.2
77.5
97.0
Point of departure,
Run,
Bv D. K.
Latitude.
36° 55^6 N.
57 .2 N. Mid. L., 37°
37 52 .8 N.
Longitude.
76° 00^5 W.
1 37 .OE.
74 23 .5 W.
Example: A steamer's position by observation at noon, patent log reading 27.3, is Lat. 49° 15'' N.,
Long. 7° 32' W. Thence she steers S. 82° W. ( per compass ) , the total compass error on that course being
20° W., until 12.30, at which time, patent log reading 33.9, the course is changed to S. 80° W. (p. c),
same error. At 4.12, patent log 80.5, sights are taken from which it is found that the true longitude is
8° 46' W., and the compass error 19° W. At 6.15, patent log reading 6.1, a sight is taken from which
it is found that the true latitude is 48° 34' 30" N. At 8 j). m. the patent log reads 27.5. Required the
positions by D. R. at each sight and at 8 o'clock.
Time.
Comp. course.
Error.
True course.
Pat. Log.
Dist.
S.
w.
D.
Noon,
12.30
4.12
6.15
8.00
8. 82° W.
8. 80° W.
8. 80° W.
8. 80° AV.
20° W.
20° W.
19° W.
19° W.
8. 62° W.
8. 60° W.
8. 61° W.
S. 61° W.
27.3
33.9
80.5
6.1
27.5
6.6
46.6
25.6
21.4
3.1
23.3
5.8
40.3
70.3
34.1
27.9
26.4
12.4
10.4
46.1
22.4
18.7
By obs. at noon,
Run to 4.12 sight.
Latitude.
49° 15'.0 N.
26.4 S.
Mid.
Mid.
Mid.
L., 49°
L., 49°
L., 48°
Longitude.
7° 32'.0 W
1 10.3 W
By D. R. at 4.12 sight.
48
48.6 N.
12.4 8.
8
42.3 W
By obs. at 4.12 sight,
Run to 6.15 sight.
8
46.0 W
34.1 W
By 1). R. at 6.15 sight.
48
36.2 N.
9
20.1 W
By obs. at 6.15 sight,
Run to 8 p. m.,
48
34.5 N.
10.4 8.
27.9 W
By 1). R. at 8 p. m., 48 24.1 N. 9 48.0 W.
206. Allowance for Current. — When a vessel is sailing in a known current whose strength may
be estimated with a fair degree of accuracy, a more correct position may be arrived at by regarding the
set and drift of the current as a course and distance to be regularly taken account of in the dead
reckoning.
Example: A vessel in the Gulf Stream at a point where the current is estimated to set N. 48° E. at
the rate of 1.8 miles an hour, sails 8. 3° W. (true), making 9.5 knots an hour through the water for
S^ 30"". Middle latitude 35°. Required the course and distance made good.
True course. Dist.
N.
S. E. W.
D.
Run
Current
Made good
8. 3° W.
N. 48° E.
8. 6° E.
33.3
6.3
29.3
4.2'
33.3 1.7
i i.7
3.6
29. 1 ; 3. 0
62
DEAD RECKONING.
207. Finding the Current. — It is usual, upon obtaining a gocnl position by observation (as the
navigator usually does at noon), to compare that position with the one obtained by dead reckon-
ing, and to attribute such discrepancy as may be found to the effects of current. It has already been
pointed out that other causes than the motion of the water tend to make the dead reckoning inaccurate,
80 that it must not be assumed that currents proper are thus determined with complete correctness.
Current is said to have set and drift, referring respectively to the direction toward which it is flow-
ing and the velocity ^<'!th which it moves.
It is evident that, in calculating current by the method of comparing positions by observation with
those by account, the navigator must limit himself to the periods during which the (lead reckoning has
been brought forward independently, without receiving any corrections due to new points of departure.
In ca.se it is desired to find the current covering a period during which fresh departures have been used,
as from noon to noon, find the algebraical sums of all the differences of latitude and longitude from the
table, and apply these to the latitude and longitude of original departure — that of the preceding
noon; this gives the position from the ship's run proper, and the difference between this and the posi-
tion by observation gives the set and drift for the twenty-four hours; if an allowance has been made
for current, as explained in the preceding article, that must l)e omitted in bringing up the position
which is to take account of the run only.
20§. Day's Run. — It is usual to calculate, each day at noon, the ship's total run for the preceding
twenty-four hours. Having the positions at noon of esu-h day, the course and distance between them is
found as explained in article 175, Chapter V. The position by observation is used in each case, if such
has been found; otherwise, the position by dead reckoning.
Example: At noon, January 22, the position of a vessel by observation was Lat. 35° ICK N., Long.
134° 01^ W. During the next 24 hours, tlie run by account was 60.1 miles north and 153.2 miles east.
At noon, January 23, the position by observation was Lat. 36° 03^ N., Long. 131° 14^ VV. Required
the position by D. R. at the latter time; also the run and current for the 24 hours.
Bv obs., noon, 22d,
Run,
Latitude.
35° 10^0 N. 1
1 00.1 N.
Mid.
Dep.
D,
Dep.
L., 36°
, 153.2 E.
189.4 E.
22.4 W.j
, 18.1 W.j
Langittide.
134°0r.0W.
3 09 .4 E.
By D. R., noon, 23d,
By obs., noon, 23d,
36 10 .IX.
36 03 .ON. 1
130 51.6W.
131 14 .OW.
Current,
6 .9 R. 1
22.4W.
Current for 24 hours, 6.9 S., 18.1 W.= S. 69° W., 19.4 miles.
Current per ho\ir, S. 69° W., 0.8 mile.
By obs., noon, 23d,
By obs., noon, 22d,
Run,
Latitude.
36° 03^0 N.
35 10 .ON.
0 53 .0 N.
Mid. L., 36°
}D, 167.0 E.
Dep., 135.1
Longittide.
131° 14'.0W.
134 01 .OW.
2 47 .0 E.
Run for 24 hours, 53.0 N., 135.1 E.=N. 68° E., 146 miles.
DEFINITIONS RELATING TO NAUTICAL ASTRONOMY.
63
CHAPTER VII.
DEFINITIONS RELATING TO NAUTICAL ASTRONOMY.
209. Nautical Astronomy, or Celo-Xavigafio)i, has been defined (art. 8, Chap. I) as that branch of
the science of Navigation in which the position of a ship is determined by the aid of celestial objects —
the sun, moon, planets, or stars.
210. The Celestial Sphere. — An observer upon the surface of the earth appears to view the
heavenly bodies as if they were situated upon the surface of a vast hollow sphere, of which his eye is
the center. In realit\^ we know that this apparent vault has no existence, and that we can determine
only the relative directions of the heavenly bodies — not their distances from each other or from the
observer. But by adopting an imaginary spherical surface of an infinite radius, the eye of the observer
being at the center, the places of the heavenly bodies can be projected upon this Celestial Sphere, or Celes-
tial Concave, at points where the lines joining them with the center intersect the surface of the sphere.
Since, however, the center of the earth should be the point from which all angular distances are meas-
ured, the observer, by transferring himself there, will find projected on the celestial sphere, not only the
heavenly bodies, but the imaginary points and circles of the earth's surface. The actual position of the
observer on the surface will be projected in a point called the zenith; the meridians, equator, and all other
lines and points may also be projected.
211. An observer on the earth's surface is constantly changing his position with relation to the
celestial bodies projected on the sphere, thus giving to the latter an apparent motion. This is due to
three causes: first, the diurnal motion of the earth, arising from its rotation upon its axis; second, the
annual motion of the earth, arising from its motion about the sun in its orbit; and third, the actual
motion of certain of the celestial bodies themselves. The changes produced by the diurnal motion are
different for observers at different points upon the earth, and therefore depend upon the latitude and
longitude of the observer. But the changes arising from the other causes named are independent of the
observer's position, and may therefore be considered at any instant in their relation to the center of the
earth. To this end the elements necessary for any calculation are tabulated in the Xuritical Almanac
from data based upon laws which have been found by long series of observations to govern the actual and
apparent motion of the various bodies.
212. The Zenith, of an observer on the earth's surface is the point <^>f the celestial sphere vertically
overhead. The Nadir is the point vertically beneath.
213. The Celestial Horizon is the great circle of the celestial sphere formed by passing a plane
through the center of the earth at right angles to the line which joins that point with the zenith of the
observer. The celestial horizon differs somewhat
from the Visible Horizon, which is that line appearing
to an observer at sea to mark the intersection of earth
and sky. This difference arises from two causes:
first, the eye of the observer is always elevated above
the sea level, thus permitting him a range of vision
exceeding 90° from the zenith; and second, the
observer's position is on the surface, instead of at the
center of the earth. These causes give rise, respec-
tively, to dip of the horizon and parallax, which will
be explained later (Chap. X).
214. In figure 28 the celestial sphere is considered
to be projected upon the celestial horizon, represented
by NESW. ; the zenith of the observer is projected at
Z, and that pole of the earth which is elevated above
the horizon, assumed for illustration to be the north
pole, appears at P, the Elevated Pole of the celestial
sphere. The other pole is not shown in.the figure.
215. The Equinoctial, or Celestial Equator, is the
great circle formed by extending the plane of the
earth's equator until it intersects the celestial sphere.
It is shown in the figure in the line EQW. The equi-
noctial intersects the horizon in E and W, its east and
west points.
216. Hour Circles, Declination Circles, or Celestial Meridians are great circles of the celestial sphere
passing through the poles; they are therefore secondary to the equinoctial, and may be formed by
extending the planes of the respective terrestrial meridians until they intersect the celestial sphere. In
the figure, PW, PS, PE, are hour circles, and that one, PS, which contains the zenith and is therefore
formed by the extension of the terrestrial meridian of the observer, intersects the horizon in N and S, its
north and south points.
217. Vertical Circles, or Circles of Altitude, are great circles of the celestial sphere which pass through
the zenith and nadir; they are therefore secondary to the horizon. In the figure, ZH, WZE, NZS, are
projections of such circles; the vertical circle NZS, which passes through the poles, coincides with the
Fig
64 DEFINITIONS RELATING TO NAUTICAL ASTRONOMY.
meridian of the observer. The vertical cintle WZE, whose plane is at right angles to that of the merid-
ian, intersects the horizon in its eastern and western points, and, iheretV)re, at the points of intersection
of the equinoctial; this circle ia distinguished as the Prime Vertk-al.
21 S. The Declination of any point in the celestial sphere is its angular distance from the equinoctial,
measiured upon the hour or declination circle which passes through that jxtint; it is designated as North
cr South according to the direction of the point from the equinoctial; it is customary to regard north
declinations as positive (~r ), and south declinations as negative ( ~ ). In the figure, DM is the declina-
tion of the point M. Declination upon the celestial sphere corresponds with latitude upon the earth.
219. The Polar Distance of any point is its angular distance from the jjole (generally, the elevated
pole of an observer), measured upon the hour or declination circle passing through the point; it must
therefore equal 90° minus the declination, if measured from the pole of the same name as the declina-
tion, or 90° pins the declination, if measured from the pole of opposite name. The polar distance of the
point M from the elevated. pole, P, is PM.
220. The Altitude of any point in the celestal sphere is its angular distance from the horizon,
measured upon the vertical circle passing through the point; it is regarded as positive when the body
is on the same side of the horizon as the zenith The altitude of the point ]\I is HM.
5-21. The ZenitJi Distance of any ])oint is its angular distance from the zenith, measured upon the
vertical circle passing through the ]>oint; the zenith distance of any point which is above the horizon of
an observer must therefore equal 90° )nimis the altitude. The zenith distance of M, in the figure, is ZM.
222. The Hour Angle of any point is the angle at the pole between the meridian of the observer
and the hour circle passing through that point; it may also be regarded as the arc of the equinoctial
intercepted between those circles. It is measured tuward the west as a positive direction through the
twenty-four hours, or 360 degrees, which constitute the interval between the successive returns to the
meridian, due to the diurnal rotation of the earth, of any point in the celestial sphere. The hour angle of
M is the angle C^PD, or the arc QD.
223. The Azimuth of a point in the celestial sphere is the angle at the zenith between the meridian
of the observer and the vertical circle passing through the point; it may also be regarded as the arc of
the horizon intercepted between those circles. It is measured from either the north or the south point
of the horizon (usually that one of the same name as the elevated pole) to the east or west through 180°,
and is named accordingly; as, N. 60° W., or S. 120° W. The azimuth of M is the angle NZH, or the arc
NH, from the north point, or the angle SZH, or the arc SH, from the south point of the horizon.
224. The Amplitude of a point is the angle at the zenith between the prime vertical and the vertical
circle of the point; it is measured from the east or the west jioint of the horizon through 90°, as W. 30°
N. It is closely allied with the azimuth and may always be deduced therefrom. In the figure, the
amplitude of H is the angle WZH, or the arc WH. The amplitude is only used with reference to points
in the horizon.
225. The Ecliptic is the great circle representing the path in which, by reason of the annual revo-
lution of the earth, the sun appears to move in the celestial sphere; the plane of the ecliptic is inclined
U) that of the equinoctial at an angle of 23° 21 Y, and this inclination is called the obliquity of the ecliptic.
The ecliptic is represented by the great circle CVT.
226. The Equinoxes are those points at which the ecliptic and the equinoctial intersect, and when
the sun occupies either of these positions the days and nights are of equal length throughout the earth.
The Vernal Equinox is that one at which the sun appears to an observer on the earth when passing from
southern to northern declination, and the Aidumnal Equinox that one at which it appears when passing
from northern to southern declination. The Vernal Equinox is also designated as the Ftrst Point of Aries,
and is used as an origin for reckoning right ascension; it is indicated in the figure at V.
227. The Solstitial Points, or Solstices, are points of the ecliptic at a distance of 90° from the equinoxes,
at which the sun attaiiis its highest declination in each hemisphere. They are called respectively the
Summer and the Winter Solstice, according to the season in whicn the sun appears to pass these points in
its path.
22S. The Right Ascension of a point is the angle at the pole between the hour circle of the point
and that of the First Point of Aries; it may also be regarded as the arc of the equinoctial intercepted
between those circles. It is measured from the First Point of Aries to the eastward as a positive
direction, through twenty-four hours or 360 degrees. The right ascension of the point M is YD.
229. Celestial Latitude is measured to the north or south of the ecliptic upon great circles secondary
thereto. Celestial Longitude is measured upon the ecliptic from the First Point of Aries as an origin,
being regarded as positive to the eastward throughout 360°.
230. Coordinates. — In order to define the position of a jwint in space, a system of lines, angles, or
planes, or a combination of these, is used to refer it to some fixed
line or plane adopted as the primitive; and the lines, angles, or
l)lanes by which it is thus referred are called coordinates.
231. In figure 29 is shown a system of rectilinear coordinates
for a plane. A fixed line FE U chosen, and in it a definite point C,
as the origin. Then the position of a point A is defined by CB = x,
the distance from the origin, C, to the foot of a perpendicular let
■ fall from A on FE; and by AB = y, the length of the perpendicular.
The distance x is called the abscissa and y the ordinate. Assuming
two intersecting right lines FE and HI as standard lines of refer-
ence, the location of the point A is defined by regarding the dis-
FiG. 29. tances measured to the right hand of HI and above FE af> positive;
those to the left hand of HI and below FE as negative.
An exemplification of this system is found in the chart, on which FE is represented by the equator,
Hi by the prime meridian; the coordinates x and y being the longitude and latitude of the point A.
DEFINITIONS RELATING TO NAUTICA-L ASTEONOMY. 65
332. The great circle is to the sphere wliat tlie straight line is to the i)lane; hence, in order to
define the position of a point on the surface of a sphere, some great circle must be selected as the
primary, and some particular point of it as the origin. Thus, in figure 30, which represents the case of a
sphere, some fixed great circle, CBQ, is selected as the axis and called the
primary; and a point C is chosen as the origin. Then to define the pos-ition
of any point A, the abscissa x equals the distance from C to the point B,
where the secondary great circle through A intersects the primary; the
ordinate y equals the distance of A from the primary measured on the
secondary — that is, x — C-B and // = AB.
233. In the case of the earth, the primary selected is the equator (its
])lane being j)erpendicular to the earth's axis), and upon this are measured
the abscissa', while upon the secondaries to it are measured the ordinates of
all points on the earth's surface. The initial point for reference on the
equator is determined by the prime meridian chosen, West longitudes and
North latitudes being called positive, East longitudes and South latitudes,
negativt'.
234. In the case of the celestial si)here, there are four systems of coor-
dinates in use for defining the position of any point; these vary according to the circle adopted as the
primary and the point used as an origin. They are as follows:
1. Altitude and azimuth.
2. Declination and hour angle.
3. Declination and right ascension.
4. Celestial latitude and longitude.
235. In the system of Altitude and Azimuth, the primary circle is the celestial horizon, the seconda-
ries to which are the vertical circles, or circles of altitude. The horizon is intersected by the celestial
meridian in its northern and southern points, of which one — usually that adjacent to the elevated pole — is
selected as an origin for reckoning coordinates. The azimuth indicates in Avhich vertical circle the point
to be defined is found, and the altitude gives the position of the point in that circle. In figure 28 the
point M is located, according to this system, by its azimuth NH and altitude HM.
236. In the system of Dedination and Hour Angle, the primary circle is the equinoctial, the seconda-
ries to which are the circles of declination, or hour circles. The pcjint of origin is that poiht of inter-
section of the equinoctial and celestial meridian which is above the horizon. The hour angle indicates
in which declination circle the point to be defined is found, and the declination gives the position of
the point in that circle. In figure 28 the point M is located, according to this system, by its hour angle
QD and declination DM.
237. Inthe system of Dedination and Right Ascension, the primary and secondaries are the same as in
the system just described, but the point of origin differs, being assumed to be at the First Point of Aries, or
vernal equinox. The right ascension indicates in which declination circle the point to be defined may
be found, and the declination gives the position in that circle. In figure 28 the point M is located by YD,
the right ascension, and DM, the declination. It should be noted that this system differs from the
preceding in that the position of a point is herein referred to a fixed point in the celestial sphere and is
independent of the zenith of the observer as well as of the position of the earth in its diurnal motion,
while, in the system of declination and hour angle, both of these are factors in determining the coordinates.
23§. In the system of Celestial Latitude and Longitude, the primary circle is the ecliptic; the point
of origin, the First Point of Aries. The method of reckoning by this system, which is of only slight
importance in Nautical Astronomy, will appeaj from the definitions of celestial latitude and longitude
already given (art. 229).
22489—03 5
66
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
CHAPTER VIII.
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
THE SEXTANT.
239. The sextant if? an instrument fur measuring the angle between two o))jeets by Itringing into
coincidence at the eye of the observer rays of light received directly from the one and by reflection from
the other, the measure being afforded by the inclination t)f the reflecting surfaces. By reason of its
small dimensions, its accuracy, and, above all, the fact that it does not recjuire a permanent or a stable
mounting but is available for u.se under the conditions existing on shipboard, it is a most important
instrument for the purposes of the navigator. While the sextant is not capable of the same degree of
accuracy as fixed instruments, its measurements are sufficiently exact for navigation.
240. Description. — A usual form of the sextant is represented in figure 31. The frame is of brass
or some similar alloy. The graduated arc, AA, generally of silver, is marked in approi)riate divisions;
in the finer sextants, each divir
sion represents 10^, and the
vernier affords a means of
reading to 10^'. A wooden
handle, H, is provided for
holding the instrument. The
index mirror, 31, and horizon
mirror, m, are of plate glass,
and are silvered, though the
upper half of the horizon glass
is left plain to allow direct rays
to pass through unobstructed.
To give greater distinctness to
the images, a small telescope,
E, is placed in the line of
sight; it is supported in a ring,
K, which can he moved by a
screw in a direction at right
angles to the plane of the sex-
tant, thus shifting the axis of
the telescope, and therefore the
plane of reflection; this plane,
however, always remains par-
allel to that of the instrument,
the motion of the telescope
being intended merely to regu-
late the relative brightness of
the direct and reflected images. In the ring K are small screws for the purpose tif adjusting the tele-
scope by making its axis parallel with the plane of the sextant. The vernier is carried on the end of an
index bar pivote<l beneath the index mirror, M, and thus travels along the graduated scale, affording a
measure for any change of inclination of the index mirror; a reading glass, 11, attached to the index bar
and turning upon a pivot, S, facilitates the reading of vernier aiul scale. The index mirror, 31, is attached
to the head of the index bar, with its suil'ace perjiendicular to the plane of the instrument; an adjust-
ing screw is fitted at the back to permit of adjustment to the peritendicular i)lanc. The fixed gla.'^s m,
half silvered and half plain, is called the horizon glass, as it is through this tiiat the horizon is observed
in measuring altitudes of celestial bodies; it is provided with screws, by which its perpendicularity to
the i)lane of the instrument may l>e adjusted. At I' and Q are colored glasses of different shades, which
may be used separately or in comlMnation to protect tlie eye from th 3 intense light of the sun. In order
to observe with accuracy and make the images come i)recisely in contact, a tanijent-screir, B, is fixed to
the index, by means of which the latter may be moved with great;-r ))recision than by hand; but this
screw does not act until the index is fixed by the screw C at the back of the sextant; when the index
is to be moved any considerable amount, the screw C is loosened; when it is brought near to its required
position the screw must be tightened, and the index may then be moved gradually by the tangent-screw.
Besides the telescope, E, the instrument is usually provided with an inverting telescope, I, and a
tube without glasses, F; also, with a cap carrying colored glasses, which may be put on the eye-end of
the telescope, thus dispensing with the necessity for the use of the colored shades, Pand Q, and elimina-
ting any possible errors which might arise from nonparallelism of their surfaces.
341. The rerm«r is an attachment for facilitating the exact reading of the scale of a sextant, by
which aliquot parts of the smallest divisions of the graduated scale are measured. The principle of the
sextant vernier is identical with that of the barometer vernier, a complete description of which will
be found in article 51, Chapter II. The arc of a sextant is usually divided into 120 or more parts, each
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 67
division representing 1°; each of these degree divisions is further subdivided to an extent dependent
upon the accuracy of reading of which the sextant is capable. In the instruments for finer work, the
divisions of the scale correspond to 10' each, and the vernier covers a length corresponding to 59 such
divisions, which is subdivided into 60 parts, thus permitting a reading of ICK'; all sextants, however, are
not so closely graduated.
Whatever the limits of subdivision, all sextants are fitted with verniers which contain one more
division than the length of scale covered, and in which, therefore, scale-readings and vernier-readings
increase in the same direction — toward the left hand. To read any sextant, it is merely necessary to
observe the scale divi.sion next below, or to the right of, the zero of the vernier, and to add thereto the
angle corresponding to that division of the vernier scale which is meet nearly in exact coincidence with
a division of the instrument scale.
242. Optical Principle. — When a ray of light is reflected from a plane surface, the angle of inci-
dence is equal to the angle of reflection. From this it ^^
may be proved that when a ray of light undergoes two
reflections, in the same plane the angle between its
first and its last direction is equal to twice the inclina-
tion of the i-eflecting surfaces. Upon this fact the con-
struction of the sextant is based.
In figure 32 let B and C represent respectively the
index mirror and horizon mirror of a sextant; draw
EF perpendicular to B, and CF perpendicular to C;
then the angle CFB represents the inclination of the
two mirrors. Suppose a ray to proceed from A and
undergo reflection at B and at C, its last direction I leing
CD; then ADC is the angle between its first and last
directions, and we desire to prove that ADC = 2 CFB.
From the eciuality of the angles of incidence and ^m 3'>
reflection:
ABE = EBC, and ABC = 2 EBC;
BCF ^ FCD, and BCD = 2 BCF.
From Geometry:
ADC = ABC - BCD = 2 (EBC - BCF) = 2 CFB,
which is the relation that was to be pro'^ed.
24;?. In the sextant, since the index mirror is immovably attached to L.ie index arm, which also
carries the vernier, it follows that no change can occur in the inclination between the index mirror and
the horizon mirror, excepting such as is registered l)y the travel of the vernier upon the scale.
If, when the index mirror is so placed that it is nearly parallel with the horizon mirror, an observer
direct the telescope toward some well-defined object, there will be seen in the field of view two separate
images of the object; and if the inclination of the index mirror be slightly changed bv moviug the index
bar, it will be seen that while one of the images remains fixed the other moves. 'The fixed image is
the direct one seen through the unsilvered part of the horizon glass, while the movable image is due to
rays reflected by the index and horizon mirrors. When the two images coincide these mirrors m^^t be
parallel (assuming that the object is sufficiently distant to disregard the space which separates the mir-
rors); in this position of the index mirror the vernier indicates the true zero of the scale. If, however,
instead of observing a single object, the instrument is so placed that the direct ray from one object
appears in coin<'idence with the reflected ray of a second object, then the true angle between the objects
will be twice the angle of inclination between the mirrors, or twice the angle. measured by the vernier
from the true zero of the scale. To avoid the necessity of doubling the angle on the scale, the latter is
so marked that each half degree appears as a whole degree, whence its indications give the whole anple
directly.
244. AD.irsTMENTS OF THE Sextaxt. — The theory of the sextant requires that, for accurate indi-
cations, the following conditions be fulfilled:
(o) The two surfaces of each mirror and shade glass must be parallel plants.
{h) The graduated arc or limb must be a plane, and it:; graduations, as well as those of the vernier,
must be exact.
(c) The axis must be at the center of the limb, and perpendicular to the plane thereof.
(d) The index and horizon gla.sses must be perpendicular, and the line of sight parallel, to the
plane of the limb.
Of these, only the last named ordinarily require the attention of the navigator who is to make use of
the sextant; the others, which may be called the perrnaueiit adjvstinenl.^, should be made before the
instrument leaves the hands of the maker, and with careful use will never be dranged.
245. The Adjustmi'iit of the Index Mirror consists in making the reflecting surface of tiiis mirror
truly perpendicular to the jtlane of the sextant. In onltr to test this, set the index iv ar the middle of
the arc, then, placing the eye very nearly in the plane of the sextant and close to the index mirror,
observe whether the direct image of the arc and its image reflected from the mirror appear to form one
continuous arc; if so, the glass is perpendicular to the plane of the sextant; if the reflected image appears
to droop from the arc seen directly, the glass leans backward; if it seems to rise, the glass leans forward.
The adjustment is made by the screws at the back of the mirror.
246. The Adjmtment of the Horizon Mirror consists in making the reflecting surface of this i.iirror
gerpendicular to the plane of the sextant. The index mirror having been adjusted, if, in revolving it
y means of the index arm, there is found one position in which it is parallel to the horizon glass, then
the latter must also be perpendicular to the plane of the sextant. In order to test this, put in the tele-
scope and direct it toward a star; move the index until the reflected image appears to pass the direct
image; if one ymsses directly over the other the mirrors must be parallel; if one passes on either side of
the other the horizon glass needs adjustment, which is accomplished by means of the screws attached.
68 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
The sea horizon may also be used for making this adjustment. Hold the sextant vertically and
bring the direct and the reflected images of the horizon line into coincidence; then incline the sextant
until its plane makes l)ut a small angle with the horizon; if the images still coincide the glasses are
parallel; if not, the horizon glass needs adjustment.
247. The Adjustineiit of the Telescope must be so made that, in measuring angular distances, the line
of sight, or axis oit th« telescope, shall be parallel to the plane of the instrument, as a deviation in that
respect, in measuring large angles, will occasion a considerable error. To avoid such error, a tele.scope is
employed irv which are placed two wires, ])arallel to each other and equidistant from the center of the
telescope; by means of these wires the adjuMtment may be made. Screw on the telescope, and turn the
tube containing the eyeglass till the wires are parallel to the plane of tlie instrument; then select two
dearly-defined objects whose angular distance must be not less than 90°, because an error is more easily
discovered when the distance is great; bring the reflected image of one object into exact eoincideuce
with the direct image of the other at the inner wire; then, by altering slightly the ])osition of the instru-
ment, make the objects appear on the other wire; if the contact still remains perfect, the axis of the
telescope is in its right situation; but if the two objects aj)pear to separate or lap over at the outer wire
the telescope is not parallel, and it must be rectified by turning one of the two screws of the ring into
which the telescope is screwed, having previously unturned the other screw; by repeating this operation
a few times the contact will be precisely the same at both wires, and the axis of the telescope will be
parallel to the plane of the instrument.
Another method of making this adjustinent is to place the sextant upon a tal>le in a horizontal
position, look along the plane of the limb, and make a mark upon a wall, or other vertical surface, at a
distance of about 20 feet; draw another mark above the first at a distance equal to the height of the axis
of the telescope above the plane of the limb; then so a<ljust the telescope that the upper mark, as
viewed through the telescope, falls midway between the wires. Some sextants are accompanied by
small sights whose height is exactly equal to the distance between the telescope and the plane of the
limb; by the use of these, the necessity for employing the second mark is avoided and the adjustment;
can be very accurately made.
24§. The errors which arise from defects in what have been denominated the permanent adjustments
of the sextant may be divided into three classes, namely: Errors due to faulty centering of the axes,
called eccentricity; errors of graduation; and errors arising from lack of parallelism of surfaces in index
mirror and in shade glasses-
The errors due to eccentricity and faulty graduation are constant for the same angle, and should be
determined once for all at some place where proper facilities for doing the work are at hand; these
errors can only be ascertained by measuring known angles with the sextant. If angles of 10°, 20°, 30°,
40°, etc., are first laid off with a theodolite or similar instrument and then measured by the sextant, a
table of errors of the sextant due to eccentricity and faulty graduation may be made, and the error at
any intermediate angle found by interpolation; this table will include the error of graduation of the
theodolite and also the error due to inaccurate reading of the sextant, but such errors are small. Another
method for determining the combined errors of eccentricity and graduation is by measuring the angular
distance between stars and comparing the observed and the computed arc between them, but this process
is liable to inaccuracies by reason of the uncertainty of allowances for atmospheric refraction.
Errors of graduation, when large, may be detected by "stepping off " distances on the graduated
arc with the vernier; place the zero of the vernier in exact coincidence with a division of the arc, and
observe whether the final division of the vernier also coincides with a division of the arc; this should be
tried at numerous positions of the graduated limb, and the agreement ought to be perfect in every case.
The error due to a prismatic index mirror may be found by measuring a certain unchangeable angle,
then taking out the glass and turning the upper edge down, and measuring the angle again; half the dif-
ference of these two measures will be the error at that angle due to the mirror. From a number of meas-
ures of angles in this manner, a table similar to the one for eccentricity and faulty graduation can be
made; or the two tables may be combined. When possible to avoid it, however, no sextant should be
used in which there is an index mirror which produces a greater error than that due to the probable error
of reading the scale. Mirrors having a greater angle than 2'^ between their faces are rejected for use in
the United States Navy. Index mirrors may be roughly tested by noting if there is an elongated image
of a well-defined point at large angles.
Since the error due to a prismatic horizon mirror is included in the index correction (art. 2-19), and
consequently applied alike to all angles, it may be neglected.
Errors due to prismatic shade glasses can be determined by measuring angles with and without the
shade glasses and noting the difference. They may also be determined, where the glasses are so arranged
that they can be turned through an angle of 180°, by measuring the angle first with the glass in its
usual position and then reversed, and taking the mean of the two as the true measure.
249. Index Error. — The Index Error of a sextant is the error of its indications due to the fact
that when the index and horizon mirrors are parallel the zero of the vernier does not coincide with
the zero of the scale. Having made the adjustments of the index and horizon mirrors and of the
telescope, as previously described, it is necessary to find that point of the arc at which the zero of the
vernier falls when the two mirrors are parallel, for all angles measured by the sextant are reckoned from
that point. If this point is to the left of the zero of the limb, all readings will be too great; if to the
right of the zero, all readings will be too small.
If desirable that the reading should be zero when the mirrors are parallel, place the zero of the
vernier on zero of the arc; then, by means of the adjusting screws of the horizon glass, move that glass
until the direct and reflected images of the same object coincide, after which the perpendicularity of
the horizon glass should again be verified, as it may have been deranged by the operation. This adjust-
ment is not essential, since the correction may readily be determined and applied to the reading. In
certain sextant work, however, such as surveying, it will be very convenient to be relieved of the
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 69
necessity of correcting each angle observed. The sextant should never be relied upon for maintaining
a constant index correction, and the error should be ascertained frequently. It is a good practice to
verify the correction each time a sight is taken.
250. The Index Correction may be found (a) by a star, {b) by the sea horizon, and (c) by the sun.
(a) Bring the direct and reflected images of a star into coincidence, and read off the arc. The
index correction is numerically equal to this reading, and is positive or negative according as the read-
ing is on the right or left of the zero.
(b) The same method may be employed, substituting for a star the sea horizon, though this will be
found somewhat less accurate.
(c) Measure the apparent diameter of the sun by first bringing the upper limb of the reflected
image to touch the lower limb of the direct image, and then bringing the lower limb of the reflected
image to touch the upper limb cf the direct image.
Denote the readings in the two cases by r and r^; then, if S = apparent diameter of the sun, and
R = the reading of the sextant when the two images are in coincidence, we have:
r =R + S,
r' = R - S,
R = ^(r + rO.
As R rei^resents the error, the correction will be — R. Hence the rule : Mark the readings when on
the arc with the negative sign; when off, with the positive sign; then the index correction is one-half the
algebraic sum of the two readings.
Example: The sun's diameter is measured for index correction as follows: On the arc, 31^ 20^'; off
the arc, 33^ 10^^. Required the correction.
On the arc, - 31^ 20^^
Off the arc, - 33 10 '
1 50.
I. ('., -r- 0 55
251. From the equations previously given, it is seen that:
8 = i (r-rO;
hence, if the observations are correct, it will be found that the sun's semidiameter, as given in the
Nautical Almanac for the day of observation, is equal to one-half the algebraic difference of the readings.
If required to obtain the index correction with great precision, several observations should be taken and
the mean used, the accuracy being verified by comparing the tabulated with the observed semidiameter.
If the sun is low, the horizontal semidiameter should be observed, to prevent the error that may arise
from unequal refraction.
252. Use of the Sextant. — To measure the angle between any two visible objects, point the tele-
scope toward the lower one, if one is above the other, or toward the left-hand one, if they are in nearly
the same horizontal plane. Keep this object in direct view through the unsilvered part of the horizon
glass, and move the index arm until the image of the other object is seen by a double reflection from the
index mirror and the silvered portion of the horizon glass. Having gotten the direct image of one
object into nearly exact contact with the reflected image of the other, clamp the index arm and, by
means of the tangent-screw, complete the adjustment so that the contact may be perfect; then read the
limbs.
In measuring the altitude of a celestial body above the sea horizon, it is necessary that the angle
shall be measured to that point of the horizon which lies vertically beneath the object. To determine
this point, the observer should move the instrument slightly to the right and left of the vertical, swinging
it about the line of sight as an axis, taking care to keep the object in the middle of the field of view.
The object will appear to describe the arc of a circle, and the lowest point of this arc marks the true
vertical.
The shade-glasses should be employed as may be necessary to protect the eye when observing
objects of dazzling brightness, such as the sun, or the horizon when the sun is reflected from it at a low
altitude. Care must be taken that the images are not too bright or the eye will be so affected as to
interfere with the accuracy of the observations.
253. Choice of Sextants. — The choice of a sextant should be governed by the kind of work which
is required to be done. In rough work, such as surveying, where angles need only be measured to the
nearest 30'^ the radius may be as small as 6 inches, which will permit easy reading, and the instrument
can be correspondingly lightened. Where readings to 10" are desired, as in nice astronomical work, the
radius should be about 7j inches, and the instrument, to be strongly built, should weigh about 3 J pounds.
The parts of an instrument should move freely, without binding or gritting. The eyepieces should
move easily in the telescope tubes; the bracket for carrying the telescope should be made very strong.
It is frequently found that the parallelism of the line of sight is destroyed in focusing the eyepiece,
either on account of the looseness of the fit or because of the telescope bracket being weak. The vernier
should lie close to the limbs to prevent parallax in reading. If it is either too loose or too tight at either
extremity of its travel, it may indicate that the pivot is not perpendicular. The balls of the tangent-
screw should fit snugly in their sockets, so that there may be no lost motion.
Where possible, the sextant should always be submitted to expert examination and test as to the
accuracy of its permanent adjustments before acceptance by the navigator.
254. Resilverinu Mirrors. — Occasion may sometimes arise for resilvering the mirrors of a
sextant, as they are always liable to be damaged by dampness or other causes. For this purpose some
70 INSTRUMENTS EMi-LOYED IN NAUTICAL ASTRONOMY.
clean tin foil and mercury are required. Upon a piece of glass about 4 inches square lay a piece of
tin foil whose dimensions exceed by about a quarter of an inch in each direction those of the glass to be
silvered; smooth out the foil carefully by rubbing; put a small drop of mercury on the foil and spread
it with the finger over the entire surface, being careful that none shall find its Avay untler the foil;
then put on a few more drops of mercury until the whole surface is fluid. The glass which is to be
silvered having been carefully cleaned, it should l)e laid upon a piece of tissue paper whose edge just
covers the edge of the foil and transferred carefully from the paper to the tin foil, a gentle pressure
being kept upon the glass to avoid the formation of bubbles; finally, place the mirror face downward
and leave it in an inclined position to allow the surjilus mercury to flow off, the latter operation being
hastened by a strip of tin foil at its lower edge. After five or six hours the tin foil around the edges
may be removed, and the next day a coat of varnish made from spirits of wine and red sealing wax
should l)e applied. For a horizon mirror care must be taken to avoid silvering the plain half. The
mercury drawn from the foil should not be placed with clean mercury with a view to use in the artificial
horizon or the whole will be spoiled.
255. Octants and Quintants. — Properly speaking, a sextant is an instrument whose arc covers
one-sixth of a complete circle, and which is therefore capable of measuring an angle of 120°. Other
instruments are made which are identical in princijile with the sextant as heretofore described, and
which differ from that instrument only in the length of the arc. These are the octant, an eighth of a
circle, by which angles may be measured to 90°, and the (jitinlant, a fifth of a circle, which measures
angles up to 144°. The distinction between these instruments is not always carefully made, and in
such matters as have been touched upon in the foregoing articles the sextant may be regarded as the
type of all kindred reflecting instruments.
THE ARTIFICIAL HORIZON.
256. The Artificial Horizon is a small, rectangular, shallow basin of mercury, over which, to protect
the mercury from agitation ])y the wind, is placed a roof consisting of two plates of glass at right angles
to each other. The mercury affords a perfectly horizontal surface
*\ which is at the same time an excellent mirror. The different parts
N. of an artificial horizon are furnished in a compact form, a metal
\v bottle being i)rovided for containing the mercury when not in use,
N. together with a suitable funnel for pouring.
\v If MX, in figure 33, is the horizontal surface of the mercury; S^]}
N^ a raj' of light from a celestial object, incident to the surface at B;
^ \^ BA the reflected ray; then an observer at A will receive the ray BA
\v Nv as if it proceeded from a point S^^, Avhose angular depression, ^IBS''',
N. N. below the horizontal plane is equal to the altitude, ]MBS^, of the
>v ^A object above that plane. If, then, SA is a direct ray from the object
N. / parallel t~) S'B, an observer at A can measure with the sextant the
. \^ / angle 8A8''= S'BS''= 2 S'BM, by bringing the image cf the object
N. / reflected by the index mirror into coincidence with the image S''
\^^ / reflected by the mercury and seen through the horizon glass. The
\/ instrumental measure, corrected for index error, will be double the
/» apparent altitude of the body.
/ The sun's altitude will be measured by bringing the lower limb
/ of one image to touch the upper liml) of "the other. Half the cor-
/ reefed instrumental reading will l)e the apparent altitude of the
^./ sun's loirer or upper limb, according as the lower or upper limb of
Pj^, .>.> the reflected image was the one employed in the observation.
In observations of the sun with the artificial horizon, the eye is
protected by a single dark glass over the eyepiece of the telescope through which direct and reflected
rays must pass alike, thereby avoiding the errors that might possibly arise from a difference in the
separate shade glasses attached to the frame of the sextant.
The glasses in the roof over the mercury should be made of plate-glass, with perfectly parallel faces.
If they are at all prismatic, the ol)served altitude will l)e erroneous. The error may be removed by
observing a second altitude with the roof reversed, and, in general, by taking one halfVjf a set of obser-
vations with the roof in one ])osition and the other half with the roof reversed. On the rare occasions
when the atmosphere is so calm that the unsheltered mercury Mill remain undisturbed, most satisfac-
tory observations may be made by leaving off the roof.
257. In setting up an artificial horizon, care should be taken that the basin is free from dust and
other foreign matter, as small particles floating upon the surface of the mercury interfere with a perfect
reflection. The basin should be so i)laced that its longer edge lies in the direction in which the observed
body will bear at the middle of the observations. The spot selected for taking the sights should lie as
free as possible from causes which will produce vibration of the mercury, and precautions should be
taken to shelter the horizon from the wind, as the mere placing of the roof will not ordinarily be suf-
ficient to accomplish this. Embedding the roof in earth serves to keep out the wind, while setting the
whole horizon upon a thick towel or a piece of such material as heavy felt usually affords ample protec-
tion from wind, tends to reduce the vibrations from mechanical shoc^ks, and also aids in keeping out the
moisture from the ground. In damp climates the roof should lie kept dry by wiping, or the moisture
deposited from the inclosed air will form a cloud upon the glass.
Molasses, oil, or other viscous fluid may, when necessary, be employed a.s a substitute for mercury.
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 71
iiJ.jS. Owing to the perfection of manufacture that is required to insure accuracy of results with the
artificial horizon, navigators are advised to accept only such instrument as has satisfactorily stood the
necessary tests to prove the correctness of its adjustment as regards the glasses of the roof.
THE CHRONOMETER.
259. The Chronometer is simply a correct time-measurer, differing from an ordinary watch in
having the force of its main-spring rendered uniform by means of a variable lever. Owing to the fact
that on a sea voyage a chronometer is exposed to many changes of temperature, it is furnished with an^
expansion balance, formed of a combination of metals of different expansive qualities, which produces
the required compensation. In order that its working may not be deranged by the motion of the ship
in a seaway, the instrument is carried in gimbals.
As the regularity of the chronometer is essential for the correct determination of a ship's position,
it is of the greatest importance that every precaution be taken to insure the accuracy of its indications.
There is no more certain way of doing this than to provide a vessel with several of these instruments —
preferably not less than three — in order that if an irregularity develop in one, the fact may be revealed
V)y the others.
260. Care of Chronometers ox Shipboard. — The box in which the chronometers are kept
should have a permanent place as near as practicable to the center of motion of the ship, and where it
will be free from excessive shocks and jars, such as thos^e that arise from the engines or from the firing
of heavy guns; the location should be one free from sudden and extreme changes of temperature, and
as far removed as possible from masses of vertical iron. The box should contain a separate compart-
ment for each clironometer, and each compartment should be lined with baize cloth padded with
curled hair, for the double purpose of reducing shocks and ecpializing the temperature within. An
outer cover of l^aize cloth should be provided for the lx)x, and this should be changed or dried out
frequently in damp weather. The chronometers should all be placed with the XII mark in the same
position.
For transportation for short distances by hand, an instrument should he rigidly clamped in its
gimbals, for if left free to swing, its performance may be deranged by the violent oscillations that are
imparted to it.
For transportation for a considerable distance, as l)y express, the chronometer should l)e allowed
to run down, and should then be dismounted and tlie balance corked.
2611. Since it is not possible to make a perfect in.strument which will be uninfluenced by the dis-
turbing causes incident to a sea voyage, it becomes the duty of the navigator to determine the error and
to keep watch upon the variable rate of the chronometer.
The error of tlte dtronometer .i>i t\w difference l)etween the time indicated and the standard time to
which it is referred — usually (ireonwich mean time.
The amount the chronometer gai)!.^ or loses daily is the daih/ rate.
The indications of a chronometer at any given instant require a correction for the accumulated error
to that instant; and this can be found if the error at any given time, together with the daily rate, are
known.
262. Winding. —Chronometers are ordinarily constructed to run for 56 hours without rew inding,
and an indicator on the face always shows how many hours have elapsed since the last winding. To
insure a uniiorm rate, they mr.st l)e wound regularly every day, and, in order to avoid the serious conse-
quences of their running down, the navigator shoultl take some means to guard against neglecting this
duty thnnigh a fault of memory. To wind, turn the clironometer gently on its sicle, enter the key in its
hole and ])ush it home, steadying the instrument with the hand, and wind t(j the left, the last half turn
being made so as to bring up gently against the stop. After winding, cover the keyhole and return the
instrument t(^ its natural position. Chronometers should always be wound in the same order tofirevent
omissions, and the jn-ecaution taken to insjiect the indicators, as a further assurance of the proper
performance of the oj)eralion.
After winding each day, the comparisons should Ix; made, and, with the readings of the maximum-
and-mininunn thermometer and other necessary data, recorded in a book kept for the purpose.
The maximum-and-mininuuu thermometer is one so arranged that its highest and lowest readings
are marked by small steel indices that remain in ]>lace imtil reset. Every chronometer box should be
provided with such an instrument, as a knowledge of the temperature to which chronometers have
been subjected is essential in any analysis of tiie rate. To draw down the indices for the purpose of
resetting, a magnet is used. This magnet should be kept at all times at a distance from the chronometers.
263. Comparison of Chronometers.— The instrument believed to be the best is regarded as the
Standard, and each other is compared with it. It is usual to designate the Standard as A, and the
others as B, C, etc. Chronometers a-e made to beat half-seconds, and any two may be compared by
following the beat of one with the ear and of the other with the eye.
To make a comparison, say of A and B, open the boxes of these two instruments and close all
others. Cret the cadence and, commencing when A has just completed the beat of some even 5-second
division of the dial, count "half-one-half-two-half-three-half-four-half-five," glancing at B in time to
note the position of its second-hand at the last count; the seconds indicated by A will be five greater
than the number at the beginning of the count. The hours and minutes are also recorded for each
chronometer, and the subtraction made. A good check upon the accuracy is afforded by repeating the
operation, taking the tick from B.
Where necessary for exact work, it is possible to estimate the fraction between beats, and thus
make the comparison to tenths of a second; but the nearest half-second is sufficiently exact for the
purposes of ordinary navigation at sea.
72
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
364. The following form represents a convenient method of recording comparisons:
Stand. A, No. 777. Chro. B, No. 1509. Ghro. C, No. 1802,
Date, 1903.
Designation of
comparisvis.
Chro. B
Chro. C
with
Stand. A.
2ddifl.
Therm.
Bar.
Remarks.
Stand. A. !
Max.
Mln.
Air.
Jan'uary
1
Stand. A.
B and C.
Difference.
h. m. s.
1 13 40
1 12 21.5
s.
h. m. s.
1 14 20
2 04 11
«.
0
63
o
59
o
60
//
30.07
Fomid errors
by t i m e -
ball.
1 18^5
11 10 09
2
Stand. A.
B and C.
Difference.
1 16 30
1 15 10
+ 1.5
1 17 00
2 06 51.5
-0.5
64
58
57
30.12
Left New
York for
San Juan,
P. R.
1 20
11 10 08. 5
265. The second difference in the form is the difference between the comparisons of the same
instruments for two successive days. When a vessel is equipped with only one chronometer there is
nothing to indicate any irregularity that it may develop at sea — and even the best instruments may
undergo changes from no apparent cause. When there are two chronometers, the second difference,
which is equal to the algebraic difference between their daily rates, remains uniform as long as the rates
remain uniform, but changes if one of the rates undergoes a change; in such a case, there is no means
of knowing which chronometer has departed from its expected performance, and the navigator must
proceed with caution, giving due faith to the indications of each. If, however, there are three chro-
nometers, an irregularity on the part of one is at once located by a comparison of the second differ-
ences. Thus, if the predicted rates of the chronometers were such as to give for the second difference of
A — B, + 1'.5, and of A — C, —0^.5, suppose on a certain day those differences were -;-4*.5 and — 0'.5,
respectively; it would at once be suspected that the irregularity was in B, and that that chronometer
had lost 3* on its normal rate during the preceding day. Suppose, however, the second differences
were -f 4^5 and +2^.5; it would then be apparent that A had gained 3^
266. Temperature Curves. — Notwithstanding the care taken to eliminate the effect of a change
of temperature upon the rate of a chronometer, it is rare that an absolutely perfect compensation is
attained, and it may therefore be assumed that the rates of all chronometers vary somewhat with the
temperature. Where the voyage of a vessel is a long one and marked changes of climate are encoun-
tered, the accumulated error from the use of an incorrect rate may be very material, amounting to sev-
eral minutes' difference of longitude. Careful navigators will therefore take every means to guard
against such an error. By the employment of a temperature curve in connection with the chronometer
rate the most satisfactory results are arrived at.
267. There should be furnished with each chronometer a statement showing its daily rate under
various conditions of temperature; and this may be supplemented by the observations of the navigator
during the time that the chronometer remains on board ship. AVith all available data a temperature
curve should be constructed which will indicate graphically the performance of the instrument. It is
most convenient to employ for this purpose a piece of "profile paper," on which parallel lines are ruled
at equal intervals at right angles to each other. Let each horizontal line represent, say, a degree of tem-
perature, numbered at the left edge, from the bottom up; draw a vertical line in red ink to represent
the zero rate, and let all rates to the right be plus, or gaining, and those to the left minus, or losing; let
the intervals between vertical lines represent intervals of rate (as one-tenth of a second) numbered at
the top from the zero rate; then on this scale plot the rate corresponding to each temperature; when
there are several observations covering one height of the thermometer, the mean may be used.
Through all the plotted points draw a fair curve, and the intersection of this curve with each tempera-
ture line gives the mean rate at that temperature. The mean temperature given by the maximum and
minimum thermometer shows the rate to be used on any day.
26§. Hack or Comparing Watch. — In order to avoid derangement, the chronometers should
never be removed from the permanent box in which they are kept on shipboard. When it is desired to
mark a certain instant of time, as for an astronomical observation or for obtaining the chronometer
error by signal, the time is marked by a "hack " (an inferior chronometer used for this purpose only),
or by a comparing watch. Careful comparisons are taken — preferably both before and afterwards — and
the chronometer time at the required instant is thus deduced. The correction represented by the chro-
nometer time minus the watch time (twelve hours being added to the former when necessary to make
the subtraction possible) is referred to as C — W.
Suppose, for example, the chronometer and watch are compared and their indications are as follows:
Chro. t., 5''27'"30»
W. T., -2 36 45.5
C-W, 2 50 44.5
If then a sight is tak«n when the watch shows 3'' 01"' 27.* 5, we have:
W. T., 3" 01" 27^5
C-W, +2 50 44.5
Chrn.t., 5 52 12.0
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 73
It may occur that the values of C — W, as obtained from comparisons before and after marking the
desired time, will vary; in that case the value to be used will be the mean of the two, if the time marked
is about midway between comparisons, but if much nearer to one comparison than the other, allowance
should be made accordingly.
Thus suppose, in the case previously given, a second comparison had been taken after the sight as
follows:
Chro. t, 6M2»'45'
W. T., -3 21 59.5
C-W, 2 50 45.5
The sight having been taken at about the middle of the interval, the C — W to be used would be the
mean of the two, or 2'' 50™ 45*. 0.
Let us assume, however, that the second comparison showed the following:
Chro.t., 6''38™25» ^
W. T., -3 47 39
' C-W, 2 50 46
Then, the sight having been taken when only about one-third of the interval had elapsed between
the first and second comparisons, it would be assumed that only one-third of the total change in the
C — W had occurred up to the time of sight, and the value to be used would be 2** 50'" 45". 0.
269. It is considered a good practice always to subtract watch time from chronometer time
whatever the relative values, and thus to employ C — W invariably as an additive correction. It is equally
correct to take the other difference, W — C, and make it subtractive; it may sometimes occur that a few
figures will thus be saved, but a chance for error arises from the possibilitj' of inadvertently using the
wrong sign, which is almost impossible by the other method. Thus, the following example may be
taken:
rC, 10* 57'" 38' W, U"* 42" 35»
Comparison
Sight
|W, -11 42 35 C, -10 57 38
[C-W, 11 15 03 W-C, 0 44 57
f\V, 11 50 21 W, 11 50 21
I C-W, +11 15 03 W-C- 0 44 57
[C, 11 05 24 C, n 05 24
74 TIME AND THE NAUTICAL ALMANAC.
CHAPTER IX.
TIME AND THE NAUTICAL ALMANAC.
270. The subjects of Tinu aii<l the Xauiical Almanac are two of the most important ones to be
mastered in the study of Nautical Astronomy, as they enter into every oi>eration for the astronomical
determination of a ship's position. They will be treated in conjunction, as the two are interdependent.
METHODS OF RECKONING TIME.
271. The instant at which any point of the celestial sphere is on the meridian of an observer is
termed the tramit, cubni)iation, or meridian passaye of that point; when on that half of the me.idian
which contains the zenith, it is designated as superior or tipper transit; when on the half containing the
nadir, as inferior or lotcer transit.
272. Three different kinds of time are employed in astronomy — (a) apparent or mhn- time, [h] mean
time, and (e) sidereal time. These depend ujwn the hour angle from the meridian of the points to which
they respectively refer. The point of reference for apparent or solar time is the Center of the >Sun; for
mean time, an imaginary point called the Mean Sun; and for sidereal time, the Vernal Equinox, also called
the First Point of Aries.
The unit of time is the Day, which is the period between two successive transits over the same
branch of the meridian of the point of reference. The day is divided into 24 equal parts, called Hours;
these into (50 equal parts, called Minutes, and these into 60 equal parts, called Seconds.
273. Apparent or Solar Time. — The hour angle of the center of the sun affords a measure of
Apparent or Solar Time. An Apjiarcnt or Sular Jkni is the interval of time between two successive transits
over the same meridian of the center of the sun. It is Ajyparent Noou when the suti's hour circle coin-
cides with the celestial meridian. This is the most natural and direct measure of time, and the unit of
time adopted by the navigator at sea is the apparent solar day. Apparent noon is the time when the
latitude can be most readily determined, and the ordinary method of determining the longitude by the
sun involves a calculation to deduce the apparent time first.
Since, however, the intervals between the successive leturns of the sun to the same meridian are not
equal, apparent time can not be taken as a standard. The apparent day varies in length from two causes:
fii-st, the sun does not move in the equator, the great circle perpendicular to the axis of rotation of the
earth, but in the ecliptic; and, secondly, the sun's motion in the ecliptic is not uniform. Sometimes the
sun describes an arc of 57^ of the ecliptic, and sinnetimes an arc of hV in a day. At the points where
the ecliptic and equinoctial intersect, the direction of the sun's ajyparent motion is inclined at an angle
of 23° 27' to the equator, while at the solstices it moves in a direction parallel to the equator.
274. Mean Time. — To avoid the irregularity of time caused by the want of uniformity in the sun's
motion, a fictitious sun, called the Mean Sun, is supposed to move in the equinoctial with a imiform
velocity that equals the mean velocity of the true sun in the ecliptic. This mean sun is regarded as being in
coincidence with the true sun at the vernal equinox, or First Point of Aries.
Mean Time is the hour angle of the mean sun. A Mean Ihuj is the interval between two successive
transits of the mean sun over the meridian. Mean Noon is the instant when the mean sun's hour circle
coincides with the meridian.
Mean time lapses uniformly; at certain times it agrees with apparent time, while sometimes it is
behind, and at other times in advance of it. It is this time that is measured by the clocks in ordinary
use, and to this the chronometers used by navigators are regulated.
275. The difference between apparent and mean time is called the Equation of Time; l)y this
quantity, the conversion from one to the other of these times may be made. Its magnitude and the
direction of its application may be found for any moment from the Nautical Almanac.
270. Sidereal Ti.me. — Sidereal Time is the hour angle of the First Point of Aries. This point,
which is identical with the vernal equinox, is the origin of all coordinates of right ascension. Since the
position of the point is fixed in the celestial si)here and does not, like the sun, moon, and planets, have
actual or apparent motion therein, it shares in this re.spect the i)roperties of the fixed stars. It may
therefore be said that intervals of sidereal time are those which are measured by the stars.
A Sideretd Day is the interval between two successive transits of the First Point of Aries across
the same meridian. Sidereal Xoon is the instant at which the hour circle of the First Point of Aries
coincides with the meridian. In order to interconvert sidereal and mean times an element is tabulated
in the Nautical Almanac. This is the Sidereal Time of Mean Noon, which is also the Right A.^cension
of the Mean Sun.
277. Civil and Astronomical Ti.me. — The Civil Day commences at midnight and comprises the
twenty-four hours until the following midnight. The hours are counted from 0 to 12, from midnight to
noon; then, again, from 0 to 12, from noon to midnight. Thus the civil day is divided into two periods
of twelve hours each, the first of which is marked a. m. (ante meridian), while the last is marked p. m.
(post meridian) .
TIME AND THE NAUTICAL ALMANAC.
75
The Astronomical or Solar Day commences at noon of the civil day of the same date. It comprises
twenty-four hours, reckoned from 0 to 24, from noon of one day to noon of the next. Astronomical time
(apparent or mean) is the hour angle of the sun (true or mean) measured to the westward throughout
its entire circuit from the time of .its upper transit on one day to the same instant of the next.
The civil day, therefore, begins twelve hours before the astronomical day, and a clear under-
standing of this fact is all that is required for intercon verting these times. For example:
January 9, 2 a. m., civil time, is January 8, 14'', astronomical time.
January 9, 2 p. m., civil time, is January 9, 2'', astronomical time.
278. Hour Angle. — The hour angle of a heavenly body is the angle at the pole of the celestial
concave between the declination circle of the heavenly body and the celestial
meridian. It is measured by the arc of the celestial equator between the decli-
nation circle and the celestial meridian.
In figure 34 let P be the pole of the celestial sphere, of which YMQ is the
equator, PQ, the celestial meridian, and PM, PS, PV, the declination circles of
the mean sun, a heavenly body, and the First Point of Aries, respectively.
Then QPM, or its arc, QM, is the hour angle of the mean sun, or the mean v<
time; QPS, or QS, the hour angle of the heavenly body; QPV, or QV, the hour
angle of the First Point of Aries, or the right ascension of the meridian, both of
which are e(]uivalent to the sidereal time; VPS, or YS, the right ascension of
the heavenly body; and VPM, or V^I, the right ascension of the mean sun.
279. Time at Different ^Ieridians. — The hour angle of the true sun at any meridian is called the
local apparent time; that of the mean sun, the heal vieaii time; that of the First Point of Aries, the local
sidereal time. The hour angles of the same body and points from Greenwich are respectively the Green-
vrich apparent, mean, and sidereal times. The difference between the local time at any meridian and the
Greenwich time is e(]ual to the longitude of that place from Greenwich expressed in time; the conver-
sion from time to arc may be effected by a simple mathematical calculation or by the use of Table 7.
In comparing corresponding times of different meridians the most easterly meridian may be distin-
guished as that at which the time is greatest or latest.
In figure 35 P3I and PM^ represent the celestial meridians of two places;
PS, the declination circle through the sun, and PG, the Greenwich meridian;
let To = the Greenwich time = GPS;
Tm = the corresponding local time at all places on the meridian PM = MPS ;
Tji'^the corresponding local time at all places on the meridian PM'' =
M^PS;
Lo — west longitude of meridian PM = GPM ; and
Lo^ = east longitude of meridian PM' = GPM'.
If west longitudes and hour angles be reckoned as positive, and east lon-
gitudes and hour angles as negative, we have:
Lo = T«~T„; and
Lo' = To — TmS therefore,
Lo — Lo' = Tm— Tm.
Thus it may be seen that the difference of longitude between two places equals the difference of
their local times. This relation may be shown to hold for any two meridians whatsoever.
Both local and Greenwich times in the above formula^ must be reckoned westward, always from
their respective meridians and from O*" to 24''; in other words, it is the astronomical time which should
be used in all astronomical computations.
The formula Lo = Tg — Tj, is true for any kind of time, solar or sidereal; or, in general terms,
To and T>i are the hour angles of any point of the sphere at the two meridians whose difference of
longitude is Lo. S may be the sun (true or mean) or the vernal equinox.
2§0. Fi.vDiNG THE (jREENwicH TiME. — Siuce nearly every computation made by the navigator
requires a knowledge of the Greenwich date and time as a preliminary to the use of the Nautical
Almanac, the first operation necessary is to deduce from the local time the corresponding (rreenwich
date, either exact or approximate, and thence the Greenwich time expressed astronomically.
The formula is:
To=Tm+Lo,
remembering that west longitudes are positive, east longitudes are negative. Hence the following rule
for converting local to Greenwich time:
Having expressed the local time astronomically, add the longitude if west, subtract it if east; the result
is the corresponding Greenwich time.
• Example: In longitude 81° 15' \V. the local time is, 1879, April, 15'' 10'' 17'" 30" a. m. Required the
Greenwich time.
Local Ast. time, April, 14'' 22" 17"' 30"
Longitude, + 5 25 00
Fig. 35.
Greenwich time,
15 8 42 30
Example: In longitude 81° 15' E. the local time is, August, 5^ 2" 10"' 30^ p. m. Required the Green-
wich time.
Local Ast. time, 5'' 2" 10'" 30'
Longitude, - 5 25 00
Greenwich time.
4 20 45 30
76 TIME AND THE NAUTICAL ALMANAC.
I
Example: In longitude 17° 28' AV. the local time is, May, 1"* S*" 10™ p. m. Required the Greenwich
time. ^
Local Agt. time, l"* S** 10™ 00'
Longitude, + 1 09 52
_ Greenwich time, 1 4 19 52
Example: In longitude 125° SO' E. the local time ia, May, l"* S*" 10™ 30» a. m. Required the Green-
wich time.
Local Ast. time, April, SO** 20" 10"' 30'
Longitude, — 8 22 00
Greenwich time, 30 11 48 30
2§1. From the preceding article we have:
To = Tm + Lo; hence,
Tm = Tg — Lo;
thus it will be seen that, to find the local time corresponding to any Greenwich time, the above process
is simply reversed.
Since all observations at sea are referred to chronometers regulated to Greenwich mean time, and
as these instruments are usually marked on the dial from 0" to 12", it becomes necessary to distinguish
whether it is a.m. or p.m. at Greenwich. Therefore, an approximate knowledge of the longitude and
local time is necessary to determine the Greenwich date.
Example: In longitude 5" 00™ 00* W., about 3" 30"' p.m. April 15th, the Greenwich chronometer
read 8" 25™, and was fast of Gr. time 3™ 15^ Required the local astronomical time.
Aprox. local time, 15" 3" 30™ Gr. chro., 8" 25™ 00* Gr. Ast. time \b^, 8" 21™ 45
Longitude, -f 5 00 Corr., — 3 15 Longitude, — 5 00 00
Approx. Gr. time, 15 8 30 Gr. Ast. time 15\ 8 21 45 Local Ast. time 15*, 3 21 45
Example: In longitude 5" 00™ 00* E., about 8 a. m. May 3d, the Gr. chro. read 3" 15™ 20% and was
fast of Gr. time 3™ 15*. Required the local astronomical time.
Approx. local time. May, 2" 20" Gr. chro., 3" 15™ 20* Gr. Ast. time 2'», 15" 12™ 05
Longitude, — 5 Corr., — 3 15 Longitude, — 5 00 00
Approx. Gr. time, 2 15 Gr. Ast. time 2"», 15 12 05 Local Ast. time 2", 20 12 05
THE NAUTICAL ALMANAC. «
2§2. The American Ephemeris and Nautical Almanac is divided into four parts, a.s follows: Part I,
Ephemeris for the meridian of Greenwich, gives the ephemerides of the sun and moon, the geocentric
and heliocentric positions of the major planets, the sun's coordinates, and other fundamental astronom-
ical data for equidistant intervals of Greenwich mean time; Part II, Ephemeris for the meridian of
Washington, gives the ephemerides of the fixed stars, sun, moon, and major planets for transit over the
meridian of Washington; Part III, Phenomena, contains predictions of phenomena to be observed, with
data ior their computation; and Part IV, Star Numbers and other data, contains matter relating to cer-
tain fixed stars. Tables are also appended for the interconversion of mean and sidereal time and for
finding the latitude by an altitude of Polaris.
The American Nautical Almanac is a, smaller book made up of extracts from the " Ephemeris and
Almanac" just described, and is designed especially for the use of navigators, being adapted to the
meridian of Greenwich. It contains the positions of the sun and moon, the distances of the moon from
the center of the sun, from the centers of the four most conspicuous planets, and from certain fixed
stars, together with the ephemerides of the planets Mercury, Venus, Mars, Jupiter, and Saturn, and the
mean places of 150 fixed stars; solar and lunar eclipses are described, and the tables for the interconversion
of mean and sidereal time and for finding the latitude by Polaris are included.
The elements dependent upon the sun and moon are placed at the beginning of the book,
arranged according to the months of the year; eighteen pages are devoted to each month, numbered in
Roman notation from I to XVIII. Of these, page I contains the Apparent Right Ascension and Declina-
tion of the sun and the Equation of Time for the instant of Greenwich apparent noon; throughout the
remaining seventeen pages Greenwich mean time forms the basis of reckoning. Page I is used in com-
putations from observations that depend upon the time of the sun's meridian passage, at which instant
the local apparent time is 0", and the Greenwich apimrent time is equal to the longitude, if west, or to
24" minus the longitude, if east; this page therefore affords a means for reducing the elements for such
observations from a knowledge of the longitude alone. In all other observations the calculation is
made for some definite instant of Greenwich mean time (usually as noted by the chronometer) , in which
case Pages II to XVIII are employed.
2S3. Rediction' of Elements. — The reduction of elements in the Nautical Almanac is usually
accomplished by Interpolation, but in certain cases where extreme preiision is necessary the method of
Second Differences must be used.
a See extracts from Ephemeris and Nautical Almanac for 1879, Appendix I.
TIME AND THE NAUTICAL ALMANAC. 77
The Ephemeris, being computed for the Greenwich meridian, contains the right ascensions, declina-
tions, equations of time, and other elements for given equidistant intervals of Greenwich time. Hence,
before the value of any of these quantities can be found for a given local time it is necessary to determine
the corresponding Greenwich time. Should that time be one for which the Nautical Ahnanac gives the
value of the required element, nothing more is necessary than to employ that value. But if the time
falls between the Almanac times, the required quantity must be found by interpolation.
The Almanac contains the rate of change or difference of each of the principal quantities for some
unit of time, and, unless great precision is required, the first differences only need be regarded. In
order to use the difference columns to advantage, the Greenwich date should be expressed in the unit
of time for which the difference is given. Thus, for using the hourly differences, the Greenwich tin.e
should be expressed in hours and decimal parts of an hour; when using the differences for one minute,
the time should be in minutes and decimal parts of a minute. Instead of using decimal parts, some may
prefer the use of aliquot parts.
Since thequan titles in the Almanac are approximate numbers, given to a certain decimal, any inter-
polation of a lower order than that decimal is unneces.«ary work. Moreover, since, in computations at
sea, the Greenwich time is more or less inexact, too great refinement need not be sought in reducing the
Ahnanac elements.
Simple interpolation assumes that the differences of the quantities are proportional to the differences
of the times; in other words, that the differences given in the Almanac are constant; this is seldom the
case, but the error arising from the assumption will be smaller the less the interval between the times
in the Almanac. Hence those quantities which vary most irregularly are given for the smallest units
of time; as the variations are more regular, the units for which the differences are given increase.
In taking from the Almanac the elements relating to the fixed stars the data may be found either
in the table which gives the "mean place" of each star for the year or in that which gives the
"apparent place " occupied by each one on every tenth day throughout the year. As the annual varia-
tion of position of the fixed stars is small, the results will not vary greatly whichever ta])le may be used.
Yet, as it is proper to seek always the greatest attainable accuracy, the use of the table showing the
exact positions is recommended. That table is, however, published in the "Ephemeris and Nautical
Almanac" only, and is omitted from the abridged " Nautical Almanac; " hence, where the larger book
is not at hand, the tiible of mean places nmst be employed.
2§4. To find from the Nautical Almanac a required element for any given time and place, it is
first necessary to express the time astronomically and to convert it to Greenwich time and date. Then
take from the Almanac, for the nearest given precedivg instant, the required quantity, together with its
corresponding "Diff. for l*" " or "Diff. for 1""," noting the name or sign in each cat^e; for the sun use
Page I of the proper month in the Almanac when apparent time is to be the I)asi8 for correction, but
otherwise use Page II. Multiply the "Diff. for l**" by the number of hours and fraction of an hour,
or the "Diff. for 1'"" by the number of minutes and fraction of a minute, corresponding to the interval
between the time for which the quantity is given in the Almanac and the time for which required;
apply the correction thus obtained, having regard to its sign.
A modification of this rule may be adopted if the time for which the quantity is desired falls con-
siderably nearer a subsequent time given in the Almanac than it does to one preceding; in this case the
interpolation may be made backward, the sign of application of the correction being reversed.
Example: At a place in longitude 81° 15' W., April 17, 1879, find the sun's declination and the
equation of time at apj)arent noon.
Long. =81° 15' W. G. A. T. = 17'* b^ 25™ = 17'» + 5\42.
Eq. t., 17'» 0^ O-" 24\46
Corr., + 3 .18
Dec, 17"'0h,
Corr.,
(-r)
+
+
+
+
10°
26' 42". 3 N
4 46 .2
Dec, 17'* 5'> 25™
10
31 28 .5 N
H. D.,
G. A. T.,
52". 80
5\42
Corr.,
/ 286". 18
14'46".18
Eq. t, 17''5h25"', 0 27.64
H. D., + 0-\587
G. A. T., + 5^.42
Corr., -f 3M82
{Subtract from apparent time.)
Example: At a place in Long. 81° 15' E., April 17, 1879, find the sun's declination and the equation
of time at apparent noon.
Long. =81° 15' E. G. A. T. = 16'» 18" 35™ = 17* — 5h.42.
Dec, 17'* 0\ ( + ) 10° 26'42".3N. Eq. t., I71 0^ 0" 24'.46
Corr., - 4 46 .2 Corr., - 3.18
Dec, 16* 18" 35™,
10 21 56 .1 N.
Eq. t., 16* 18" 35"
H. D.,
G. A. T.,
Corr.,
', 0 21 .28
H. D.,
G. A. T.^
+ 52". 80
— 5". 42
-f 0«.587
- 5". 42
Cor.\,
( 286". 18
\4'46".18
— 3M82
78
TIME AND THE NAUTICAL ALMANAC.
Example: April 16, 1879, at U** 55"" 30^ a. m., local mean time, in Long. 81° 15' W., required the
declination and semidiameter of the sun, the equation of time, and the right ascension, declination,
horizontal parallax, and semidiameter of the moon and Jupiter.
Local mean time,
Longitude,
Greenwich mean time.
IS-i 23'> 55™ 30"
5" 25'" 00"
16* 5" 20"' 30"
16'' 5" 20™.5
16-1 5\34
Dec, 0^ ( + ) 10° 05' 30''. 1 N.
Corr., + 4 44 . 3
For the Sun.
S. D., 15' 58". 0
(Same as at G. A. Noon.)
Dec.,
H. D.,
G. M. T.,
Corr.,
10 10 14 . 4 N.
53". 24
5\ 34
Eq. t,
Corr.,
+
+
0'"
10'
3
.15
. 22
Eq. t.,
0
13
.37
H. D.
G. M.
0\
5".
604
34
+{
284". 30
4' 44". 30
Corr.,
+
3'. 22
{Add to mean time. ]
For the Moon.
R. A., 5h,
Corr.,
R. A.,
M. D.,
No. min.,
Corr.,
•J'Jt' 14'" 39'.29
+ 38.31
22 15 17 .60
1».869
20^.5
Dec, 5'',
Corr.,
Dec,
M. D.,
No. mln.,
(-) 7°59'36".l S.
+ 4 27 .1
7 55 09 .0 S.
]3".03
20'". 5
38'.31
f 267". 12
t 4'27".l
Hor. Par-.O!-,
Corr.,
Hor. Par.,
H. D.,
G. M. T.,
Corr.,
5,5' 13".6
7 .2
l."34
5i'.34
S-D-.C,
•Corr.,
S. D.,
H. D.,
G. M. T.,
15' 04".7
1 .8
15 02 .9
- 0".34
7".15 Corr.,
1".81
R. A.,0\ 22" 26'" ;^^ 54
Corr., + 9.71
For Jupiter.
Dec, 0^ (-) 10° 40' 28". 0 S.
Corr., + 53 . 6
R. A.,
H. D., +
G. M. T., +
Corr., +
22 26 45 . 25
1". 819
5\ 34
". 71
Dec,
H. D.,
G. M. T.,
Corr. ,
10 39 34 . 4 S.
10". 03
5". 34
Hor. Par., 16'^, 1". 6
S. D., 16^ 16".{
53". 6
2§5. Should greater precision be required than that attainable by niraple interpolation, resort must
be had to the reduction for second differences.
The differences between successive values of the quantities given in the Nautical Almanac are called
the first differences; the differences between successive first differences are called the second, differences.
Simple interpolation, which satisfies the necessities of sea computations, assumes the first differences to
be constant; but if the variation of the first differences be regarded, a further interpolation is required
for the second difference.
The difference for a unit of time in the American Nautical Almanac abreast any element expresses
the rate at which the element in changing at that precise instant of Greenwich time. Now, regarding
the second difference as constant, the first difference varies uniformly with the Greenwich time; there-
fore it« value may be found for any intermediate time by simple interpolation.
Hence the following rule for second differences: Employ the interpolated value of th6 first differ-
ence which corresponds to the middle of the interval for which the correction is to be computed.
Example: For the Greenwich date 1879, April, 10"* 18'' 25'" 30", find the moon's declination.
Dec, 18", (-)26° 19' 41".l S.
Corr., + 2 .1
First diff., + 0". 044
Corr., +0 .039
Dec,
26 19 39 .0 S.
M. D., 4^0 .083
No. min., +25°'.5
Second diff..
Interval,
Corr. ,
0".181
f Oh. 213
+ 0".039
Corr. ,
2". 12
The difference for one minute being 4- 0".044 at 18'', and +0".225 at 19'', the difference for one
minute undergoes a change of 4 0".181 during one hour. The time for which it is desired to obtain the
difference is at the middle instant between 18*' 0'" and 18'' 25'".5 — that is, at 18'' 12"'. 75, or its equivalent,
18'' 213. With a change of -f 0".181 in one hour, the change in 0''.213 is readily obtainable; correcting
the minute's difference at 18''. 0 accordingly, the proces ' of correcting the declination becomes the same
as in simple interpolation.
TIME AND THE NAUTICAL ALMANAC. 79
CONVERSION OF TIMES.
iiS6. Conversion of Time is the process by which any instant of time that if< defined according to one
system of reckoning may be defined according to some other system; and also
by Avhich any interval of time expressed in units of one system may be con-
verted into units of another.
287. Sidereal and Meax Times. — Mean time is the hour angle of the
Mean Sun; sidereal time is the hour angle of the First Point of Aries. Since
the Right Ascension of the Mean Sun is the angular distance between the hour
circles of the Mean Sun and of the First Point of Aries, mean time may be con-
verted into sidereal time by adding to it the Right Ascension of the Mean Sun;
and similarly, sidereal time may be converted into mean time by subtracting from
it the Right Ascension of the ^fean Sun.
This is explained in figure 36, vhich represents a projection of the celestial
sphere upon the equator. If P be the pole; QPQ', the meridian; V, the First
Point of Aries; M, the position of the mean sun (west of the meridian); then
QPV, or the arc QV, is the sidereal time; QPM, or the arc QM, is the mean
time; and VPM, or the arc VM, is the Right Ascension of the Mean Sun. From tl^s it will appear that:
QV=QM+VM, or
Sidereal f.me=Mean time-j- Right Ascension of Mean Sun.
If the mean sun be on the opposite side of the meridian, at 3F, then the mean time equals
24"— M^Q. In this case:
QV = VM'— M'Q, or
Sidereal time=Right Ascension of Mean Sun — (24''— Mean time),
=Right Ascension of Mean Sun -^ Mean time— 24".
Right ascension being measured to the east and hour angle to the west, the sidereal time
will therefore always equal the sum of these two; but 24" must be subtracted when the sum exceeds
that amount.
From the preceding equations, we also have:
QM=QV-VM; and
M^Q=VM'-QV, or
(24"-M'Q) = (24"+QV)-VM^
From this it may be seen that the mean time equals the sidereal time minus the Flight Ascension
of the Mean Sun, but the former must be increased by 24" when necessary to make the subtraction
possible.
28§. Apparent and Mean Times. — Apparent time is the angle between the meridian and the
hour circle which contains the center of the sun; mean time is the angle between the meridian and the
hour circle which contains the mean sun. Since the equation of time ref>resents the angle between
the hour circles of the mean and apparent suns, it is clear that the conversion of mean time to apparent
time may be accomplished by the api)lication of the ecpiation of time, with its j>roper sign, to the mean
time; and the reverse operation by the application of the same quantity, in an opposite direction, to the
apparent time.
The resemblance of these operations to the interconversion of mean and sidereal times may be
observed if, in figure 36, we assume that PV is the hour circle of the true sun, PM remaining that of the
mean sun; then the arc Q3I will be the mean time; QV, the apparent time; and VM, the equation of
time; whence \.e have as before:
QV = QM+VM, or
Apparent time — ^lean time — Equation of time;
the equation of time will be positive or negative according to the relative position-of the two suns.
2§9. Sidereal and Mean Time Intervals. — The sidereal year consists of 366.25636 sidereal days
or of 365.25636 mean solar days. If, therefore, M be any interval of mean time, ami S the corresponding
interval of sidereal time, the relations between the two may be expressed as follows:
Therefore, S = 1.0027379 M = M + . 0027379 M;
M = 0.9972696 S = S -.0027304 S.
If M = 24", S = 24" + 3"' 56^6; or, in a mean solar day, sidereal time gains on mean time 3™ 56'.6, the
gain each hour being 9'. 8565.
If S = 24", M = 24" — 3"' 55'.9; or, in a sidereal day, mean time loses on sidereal time 3'" 55'.9, the
loss each hour being 9^.8296.
If 'M and S be expressed in hours and fractional parts thereof,
S = M + 9^8565 M;
M = S - 9^8296 S.
Tables for the conversion of the intervals of mean into those of sidereal time and the reverse are
based upon these relations. Tables 8 and 9 of this work give the values for making these conversions,
and similar tables are to b^ found in the Nautical Almanac.
80 TIME AND THE NAUTICAL ALMANAC.
390. To Convert Meax Solar ixto Sidereal Time. — Apply to the local mean time the longitude,
adding if west and subtracting if east, and thus obtain the Greenwich mean time. Take from tlie Nau-
tical Almanac the Right Ascension of the Mean Sun at Greenwich mean noon, and correct it for the
Greenwich mean time l)y Table 9 or by the hourly difference of 9". 857. Add to the local mean time this
corrected right a.scension, rejecting 24'' if the sum is greater than that amount. The result will be the
local sidereal time.
Example: April ^2, 1879, in Long. 81° 15^ W., the local mean time is 2" 00"' 00» p. m. Required
the corresponding local sidereal time:
L. M. T., 22*' 2" 00"' Oa- R. A. M. S., 22» 0^ 2" 00"' 41^24 L. M. T., 2" 00'" 00^
Long., -t 5 25 00 Red. for 7" 25"" (Tab. 9), -f 1 13.10 R.A.M.S., r 2 01 54.34
G.M.T., 22 7 25 00 R. A. M. S., 7" 25"', 2 01 54.34 L. S. T., 4 01 54.34
Example: April 22, 1879, in Long. 75° E., the local mean time is 4'' 00"' 00" a. m. Ketjuired the
local sidereal time.
L. M. T., 21'» 16" 00'" 00^ R. A M. S. 21'» 0", 1" 56"" 44^69 L.M.T., 21" 16" 00"' OO''
Long., - 5 00 00 Red. for 11" (Tab. 9), ^ 1 48.42 R.A.M.S.,4 1 58 33.11
G. M. T., 21 11 00 00 R. A. M. S., 11", 1 58 33 .11 L. S. T., 21 17 58 33.11
In these examples the reduction of the R. A. M. S. has formed a separate operation in order to
make clear the process. It would be as accurate to add together directly L. M. T., R. A. M. S., and
Red., and the work would thus be rendered more brief.
291. To CoxvERT Sidereal ixto Meax Solar Time. — Take from the Nautical Almanac the
Right Ascension of the Mean Sun for Greenwich mean noon of the given astronomical day, and apply
to it the reduction for longitude, either by Table 9 or by the hourly difference of 9^857, and the result
will be the Right Ascension of the Mean Sun at local mean noon, which is equivalent to the local
sidereal time at that instant. Subtract this from the given local sidereal time (adding 24" to the latter
if necessary), and the result will be the interval from local mean noon, expressed in units of sidereal
time. Convert this sidereal time interval into a mean time interval by subtracting the reduction as
given by Table 8 or by tlie hourly difference of 9^830; the result will be the local mean time.
Example: April 22, 1879, a. m., in Long. 75° E., the local sidereal time is 17" 58"' 33M1. AVhat is
the local mean time?
Astronomical day, April 21.
L. S. T., 17" 58-" 33M1 R. A. M. S., Gr. 21" 0", 1" 56"' 44\69
R. A M.S., — 1 55 55.41 Red. for -5" long. (Tab. 9), — 49.28
Sid. interval from L. M. noon, 16 02 37.70 R. A. M. S., local 0", 1 55 55.41
Red. for sid. interval (Tab. 8), 2 37 .70
L. M. T., 21", 16 00 00 .00
Example: April 22, 1879, p. m., at a place in Long. 81° 15^ W., the sidereal time is 4" 01"' 54».34.
What is the corresponding mean time?
Astronomical day, April 22.
L. S. T., 4" 01"" 54'.34 R. A. M. S , Gr. 22" 0", 2" 00"' 4P.24
R. A. M. S., - 2 01 34 .63 Red. for +5" 25™ long. (Tab. 9), + 0 53 .39
Sid. interval from L. M. Noon, 2 00 19 .71 R. A. M. S., local 0", 2 01 34 .63
Red. for sid. interval (Tab. 8), — 0 19 .71
L. M. T., 22", 2 00 00 .00
392. To Covert Mean into Apparent Time and the Reverse. — Find the Greenwich time corre-
sponding to the given local time. If apparent time is given, find the Greenwich apparent time and take
the equation of time from Page I of the Almanac. It mean time, find the Greenwich mean time and
take the equation of time from Page II. Correct the equation of time for the required instant and
apply it with its proper sign to the given time.
IExample: April 21, 1879, in Long. 81° 15^ W., find the local apparent time corresponding to a local
mean time of 3" 05"" 00' p. m.
L. M. T., 21"3"05"'00'
Long., + 5 25 00
G. M. T., 21 8 30 00
L. M, T., 21" 3" 05"' 00"
Eq. t., + 1 22.01
Eq. t., 0", 1'" 17.61
Corr., + 4.40
L. A. T., 21 3 06 22.01
. Eq.t., 1 22.01
H.D., + 0\518
G.M.T.,+ 8".5
Corr., + f.403
{Add to mean time.)
TIME AND THE NAUTICAL ALMANAC. 81
Example: April 3, 1879, in Long. 81° 15' E., the local apparent time is 8'' 45™ 00' a. m. Required
the mean time.
L. A. T., 2^ 20" 45"' 00' L. A. T., 2" 20" 45™ 00' Eq. t., 0", 3™ 42'.46
Long., - 5 25 00 Eq. t., + 3 30.90 Corr., — 11 .56
G. A. T., 2 15 20 00 L. M. T., 2 20 48 30.90 Eq. t., 3 30 .90
H. D., - 0'.754
G. M. T., — 15''.33
Corr., — 11\56
{Add to apparent time.)
293. To Find the Hour Angle of a Body from the Time, and the Eeverse. — In figure 36, if M
and M' represent the positions of celestial bodies instead of those of the mean sun as before assumed,
then the hour angles of the bodies will be Q M and 24'' - M' Q, respectively, and their right ascen-
sions will be V M and V M^
As before, we have:
Q V = Q M + V M,
, = V M' - M' Q;
QM =QV-VM;
M' Q = V M' - V Q, or
(24" - M' Q) = (24" + Q V) - Y W.
Substituting, therefore, hour angle of the body for mean time, and right ascension of the body for Right
Ascension of the Mean »S'u«, the rules previously given for the conversion of mean and sidereal times will
be applicable for the conversion of hour angle and sidereal time. Thus, the sidereal time is equal to the
sum of the right ascension of the body and its hour angle, subtracting 24" when the sum exceeds that
amount; and the hour angle equals the sidereal time minus the right ascension of the body, 24" being
added to the former when necessary to render the subtraction possible.
Example: In Long. 81° 15' W.', on April 25, 1879, at 12" 10'" 30' (astronomical) mean time, find the
hour angle of Sirius.
L. JVI. T., 12" 10"' 30' L. M. T., 12" 10°' 30"
Long., + 5 25 00 R. A. M. S., 0",+ 2 12 30.91
Red. (Tab. 9) , + 2 53.39
G. M. T., 17 35 30
L. S. T., 14 25 54.30
R. A. Sirius, — 6 39 49.83
H. A. Sirius, 7 46 04.47
Example: May 9, 1879, Arcturus being 2" 27"' 42*.52 east of the meridian, find the local sidereal time
24" 00"' 00* H. A., 21" 32'° 17'.48
H. A., 2 27 42.52 E. R. A., ^ 14 10 11 .71
H. A., 21 32 17.48 W. L. S. T., 11 42 29.19
Or thus:
H. A., - 2"27"'42'.52
R. A., + 14 10 11 .71
L. S. T., 11 42 29 .19
22489—03 6
82
OOBRECTION OF OBSERVED ALTITUDES.
CHAPTER X.
OOEEEOTION OF OBSEEVED ALTITUDES.
294. The true altitude of a heavenly body at any place on the earth's surface is the altitnde of its
center, as it would be measured by an observer at the center of the earth, above the plane passed
through the center of the earth at right angles to the direction of the zenith.
Tne obsen'ed altitude of a heavenly body, as measured at sea, may be converted to the true altitude
by the application of the following-named corrections: Index Correction, Dip, Refraction, ParallcLv, and
Semidiaynefer. The corrections for parallax and semidiameter are of inappreciable magnitude in
observations of the fixed stars, and with planets are so small that they need only be regarded in refined
calculations. In observations with the artificial horizon there is no correction for dip.
For theoretical accuracy, the corrections should be applied in the order in which they are named,
but in ordinary nautical practice the order of application makes no material difference, except in the
case of the parallax of the moon as explained in article 306.
INDEX CORRECTION.
295. This correction is fully explained in articles 249 and 250, Chapter VIII.
REFRACTION.
296. It is known by various experiments that the rays of light deviate from their rectilinear
course in passing obliquely from one medium into another oi a different density; if the latter be more
dense, the ray will be bent toward the perpendicular to the line of junction of the media; if less dense,
it will be bent away from that perpendicular.
The ray of light before entering the second medium is called the incident ray ; after it enters the
second medium it is called the refracted ray, and the
difference of direction of the two is called the refraction.
The rays of light from a heavenly body must pass
through the atmosphere before reaching the eye of an
observer upon the surface of the earth. The earth's
atmosphere is not of a uniform density, but is most
dense near the earth's surface, gradually decreasing in
density toward its upper limit; hence the path of a ray
of light, by passing from a rarer medium into one of
continually increasing density becomes a curve, which
is concave toward the earth. The last direction of the
ray is that of a tangent to the curved path at the eye of
the observer, and the difftsrence of the direction of the
ray before entering the atmosphere and this last direc-
tion constitutes the refraction.
297. To illustrate this, consider the earth's atmos-
phere as shown in figure 37; let SB be a ray from
a star S, entering the atmosphere at B, and bent into
the curve BA; then the apparent direction of the star
is AS'', the tangent to the curve at the point A, the
refraction being the angle between the lines BS and
AS'. If CAZ is the vertical line of the observer, by a
law of Optics the vertical plane of the observer which
contains the tangent AS'' must also contain the whole
curve BA and the incident ray BS. Hence refraction
increases the apparent altitude of a star without affect-
ing its azimuth.
At the zenith the refraction is nothing. The less
the altitude the more obliquely the rays enter the atmosphere and the greater will be the refraction. At
the horizon the refraction is the greatest.
298. The refraction for a mean state of the atmosphere (barometer 30'", Fahr. thermometer 50°)
is given in Table 20 A; the combined refraction and sun's parallax in Table 20 B; and the combined
refraction and moon's parallax in Table 24.
Since the amount of the refraction depends upon the density of the atmosphere, and the density
varies with the pressure and the temperature, which are indicated by the barometer and thermometer,
the true refra<;tion is found by applying to the mean refraction the corrections to be found in Tables 21
and 22; these are deduced from Be&sel's formuhe, and are regarded as the most reliable tables
constructed. It should be remembered, however, that under certain conditions of the atmosphere a
very extraordinary deflection occurs in rays of light which reach the observer's eye from low altitudes
Fig. 37.
CORRECTION OE^ OBSERVED ALTITUDES.
83
(that is, from points near the visible horizon), the amount of which is not covered by the ordinary-
corrections for pressure and temperature; the error thus created is discussed under IHp (art. 301); on
account of it, altitudes less than 10° should be avoided.
Example: Required the refraction for the apparent altitude 5°, when the thermometer is at 20°
and the barometer at 30'" .67.
The mean refraction by Table 20 A is, 9^ 52'''
The correction for height of barometer is, + 13
The correction for the temperature, + 42
True refraction, 10 47
299. The correction for refraction should always be subtracted, aa also that for combined refraction
and parallax of the sun; the correction for combined refraction and parallax of the moon is invariably
additive.
DIP.
300. Dip of the Horizon is the angle of depression of the visible sea horizon below the true horizon,
due to the elevation of the eye of the observer above the level of the sea.
In figure 38 suppose A to be the position of an
observer whose height above the level of the sea is
AB. CAZ is the true vertical at the position of the
observer, and AH is the direction of the true hori- \^ z
zon, S being an observed heavenly body. Draw
ATH' tangent to the earth's surface at T. Disre-
garding refraction, T will be the most distant point
visible from A. Owing to refraction, however, the
most distant visible point of the earth's surface is h-
more remote from the observer than the point T,
and is to be found at a point T', in figure 39. But
to an observer at A the point T'' will appear to lie
in the direction of AH''', the tangent at A to the curve
AT''. If the vertical plane were revolved about CZ
as an axis, the line AH would generate the plane of
the true horizon, while the point T' would generate
a small circle of the terrestrial sphere called the
ViMble or Sea Horizon. The Dip of the Horizon is
HAH", being the angle between the true horizon and
the apparent direction of the sea horizon. Values
of the dip are given in Table 14 for various heights
of the observer's eye, and in the calculation of the
table allowance has been made for the effect of at-
mospheric refraction as it exists under normal con-
ditions.
Fig. 38.
301. The fact must be emphasized, however, that
under certain conditions the deflection of the ray in its path
from the horizon to the eye is so irregular as to give a value
of the dip widely different from that which is tabulated for
the mean state of atmosphere. These irregularities usually
occur when there exists a material difference between the
temperature of the sea water and that of the air, and they
attain a maximum value in calm or nearly calm weather,
when the lack of circulation permits the air to arrange itself
in a series of horizontal strata of different densities, the
denser strata being below when the air is warmer, and the
reverse condition obtaining when the air is cooler. The
effect of such an arrangement is that a ray of light from the
horizon, in passing through media of different densities,
undergoes a refraction quite unlike that which occurs in the
atmosphere of much more nearly homogeneous density that
exists under normal conditions.
Various methods have been suggested for computing
the amount of dip for different relative values of tempera-
ture of air and water, but none of these afford a satisfactory
solution, there being so many elements involved which are not susceptible of determination by an
observer on shipboard that it will always be difficult to arrive at results that may be depended upon. «
As the amount of difference between the actual and tabulated values of the dip due to this cause
may sometimes be very considerable — reliable observations having frequently placed it above 10', and
values as high as 32'' having been recorded — it is necessary for the navigator to be on his guard against
the errors thus produced, and to recognize the possible inaccuracy of all i esults derived from observations
taken under unfavorable conditions. Without attempting to give any method for the determination of
the amount of the extraordinary variation in dip, the following rules may indicate to the navigator the
conditions under which caution must be observed, and the direction of probable error:
(a) A displacement of the horizon should always be suspected when there is a marked difference
between the temperatures of air and sea water; this fact should be especially kept in mind in regions
such as those of the Red Sea and the Gulf Stream, where the difference frequently exists.
Fig. 39.
« A sextant attachment devised by Lieutenant-Commander J. B. Blish, U. S. Navy, enables an observer to measure the
actual dip at any time.
84
CORRECTION OF OBSERVED ALTITUDES.
(6) The error in the tabulated value of the dip will increase with an increase in the difference of
temperature, and Mill diminish with an increase in the force of the wind.
(c) The error will decrease with the height of the observer's eye; hence it is expedient, especially
when error is suspected, to make the observation from the most elevated position available.
( d) When the sea water is colder than the air the visible horizon is raised and the dip is decreased;
therefore the true al^tude is greater than that given by the use of the ordinary dip table. AVhen the
water is warmer than the air, the horizon is depressed and the dip is increased. At such times the
altitude is really less than that found from the use of the table.
The same cause, it may be mentioned here, affects the kindred matter of the visibility of objects.
When the air is warmer, terrestrial objects are sighted from a greater distance and appear higher above
the horizon than under ordinary conditions. When the water is warmer than the air, the distance of
visibility is reduced, and terrestrial objects appear at a less altitude.
302. What has been.said heretofore about the dip supposes the horizon (o be free from all inter-
vening land or other objects; but it often happens that an observation is required to be taken from a
ship sailing along shore or at anchor in harbor, when the sun is over the land and the shore is nearer the
ship than the visible sea-horizon would be if it were unconfined; in this case the dip will be different from
that of Table 14, and will be greater the nearer the ship is to that point of the shore to which the sun's
image is brought down. In such case Table 15 gives the dip at different heights of the eye and at
different distances of the ship from the land.
303. The dip is always to be subtracted from the observed altitude.
PARALLAX.
304. The parallax of a heavenly body is, in general
terms, the angle between two straight lines drawn to the
body from different points. But in Nautical Astronomy
geocentric parallax is f.lone considered, this being the differ-
ence between the positions of a heavenly body as seen at
the same instant from the center of the earth and from a
])oint on its surface.
The zenith distance of a body, S (fig. 40), seen from A, on
tlie surface of the earth, is ZAS; seen from C it is ZCS; the
I) irallax is the difference of these angles, ZAS— ZCS=ASC.
Parallax in altUnde is, then, the angle at the heavenly
iody subtended by the radius of the earth.
If the heavenly body is in the horizon as at H', the
ra lius, being at right angles to AH'', subtends the greatest
possible angle at the star for the same distance, and this
angle is called the horizontal parallax. The parallax is less
an the bodies are farther from the earth, as will be evident
Yicr. 40. from the figure.
Let par. = parallax in altitude, ASC;
Z = SAZ, the apparent zenith distance (corrected for refraction);
R = AC, the radius of the earth; and
D = CS, the distance of the object from the center of the earth.
Then, since SAC = 180° — SAZ, the triangle ASC gives:
R sin Z
sm par. =
D
If the object is in the horizon at H^, the angle AH^C is the horizontal parallax, and denoting it by
H. P. the right triangle AH''C gives:
sin H. P. = ^-
Substituting this value of r^ i" the above, .
sin par. — sin H. P. sin Z.
If h = SAH'', the apparent altitude of the heavenly body, then Z = 90° — /;; hence,
sin par. = sin H. P. cos h.
Since par. and H. P. are always small, the sines are nearly proportional to the angles; hence,
par. = H. P. cos h.
305. The Nautical Almanac gives the horizontal parallax of the moon, as well as of the planets
Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune.
COERECTION OF OBSERVED ALTITUDES. 85
In Table 16 will be found the values of the sun's parallax for altitude intervals of 5° or 10°, while
Table 20 B contains the combined values of the sun's parallax and the refraction. In Table 24 is given
the parallax of the moon, combined with the refraction, at various altitudes and for various values of
the horizontal parallax.
306. Parallax is always additive; combined parallax and refraction additive in the case of the
moon, but eubtractive for the sun.
Aa the correction for parallax of the moon is so large, it is essential that it be taken from the table
with considerable accuracy; the corrections for index correction, semidiameter, and dip should there-
fore be applied first, and the "approximate altitude" thus obtained should be used as an argument in
entering Table 24 for parallax and refraction.
SEMIDIAMETEB.
307. The semidiameter of a heavenly body is half the angle subtended by the diameter of the
visible disk at the eye of the observer. For the same body the semidiameter varies with the distance;
thus, the difference of the sun's semidiameter at different times of the year is due to the change of the
earth's distance from the sun; and similarly for the moon and the planets.
In the case of the moon, the earth's radius bears an appreciable and considerable ratio to the moon's
distance from the center of the earth; hence the moon is materially nearer to an observer when in or
near his zenith than when in or near his horizon, and therefore the semidiameter, besides having a
menstrual change, has a semidiurnal one also.
The increase of the moon's semidiameter due to increase of altitude is called its augmentation. This
reduction may be taken from Table 18.
The semidiameters of the sun, moon, and planets are given in their appropriate places in the Nautical
Almanac.
30§. The semidiameter is to be added to the observed altitude in case the lower limb of the body
is brought into contact with the horizon, and to be subtracted in the case of the upper limb. When the
artificial horizon is used, the limb of the reflected image is that which determines the sign of this correc-
tion, it being additive for the lower and subtractive for the upper.
Example: May 6, 1879, the observed altitude of the sun's upper limb was 62° 10' 40''; I. C, + 3' 10";
height of the eye, 25 feet. Required the true altitude.
Obs. alt. 0, 62° 10' 40" I. C, + 3' 10"
Corr., - 18 04
S. D. (NautAlm.), - 15' 53"
True alt., 61 52 36 dip (Tab. 14), - 4 54
p.&r. (Tab. 20 B), - 27
-21 14
Corr., -18' 04"
Example: The altitude of Sirius as observed with an artificial horizon was 50° 59' 30"; I. C,
V 30". Required the true altitude.
Obs. 2 alt.
I.e.,
20 A)
50°
59' 30"
1 30
2)50
58 00
Obs. alt.,
ref. (Tab.
25
29 00
2 02
True alt..
25
26 58
Example: April 16, 1879, observed altitude of Venus 53° 26' 10"; I. C, + 2' 30"; height of eye, 20
feet. Required the true altitude.
Obs. alt. *, 53° 26' 10" par. (Tab. 17), -r 0' 04" Hor. Par. (Naut. Aim.), 7"
Corr., - 2 32 I. C, + 2 30
53 23 38 -r2 34
dip (Tab. 14), - 4' 23"
ref. (Tab. 20 A),- 43
- 5 06
Corr., - 2' 32"
«6
CORRECTION OF OBSERVED ALTITUDES,
Example: May 6, 1879, at 13*" 24™ G. M. T., the observed altitude of the moon's lower limb was 25°
30' 30"; I. C, —1' 30"; height of eye, 20 feet. Required the true altitude.
Oba. alt.£, 25° 30' 30"
Istcorr., + 10 57
S. D. (Naut. Aim.),
Aug. (Tab. 18),
dip (Tab. 14),
I.e.,
+ 16'
42"
08
Hor. Par.
(Naut. Aim.), 61'
Approx. alt., « 41 27
p. & r. (Tab. 24), + 53 07
True alt., 26 34 34
+ 16
- 4'
— 1
50
23"
30
- 5
53
Ist corr..
+ 10' 57"
Or, the following modification
may be adopted:
Obs. alt.C, 25° 30' 30"
Istcorr., + 8 56
S. D.,
Aug.,
dip,
ref.,
I.e.,
+ 16' 42"
+ 08
A- 16 50
- 4' 23"
- 2 01
- 1 30
H. P.
App.
par..
3670"
alt., 25° 39'
/ 3308"
155' 08"
log 3. 56467
cos 9. 95494
Approx. alt., 25 39 26
par., + 55 08
log 3.51961
True alt., 26 34 34
— 7
54
1st corr.,
+ 8'
56"
THE CHRONOMETER ERROR. 87
CHAPTER XI.
THE OHRONOMETEE EREOR.
309. It has already been explained (art. 261, Chap. VIII) that the error of a chronometer is the
difference between the time indicated by it and the correct standard time to which it is referred; and
that the dailn rate is the amount that it gains or loses each day. In practice, chronometer errors are
usually stated with reference to Greenwich mean time. It is not required that either the error or the
rate shall be zero, but in order to be enabled to determine the correct time it is essential that both rate
and error be known, and that the rate shall have been uniform since its last determination.
310. Determining the Rate. — Since all chronometers are subject to some variation in rate under
the changeable conditions existing on shipboard, it is desirable to ascertain a new rate as often as possible.
The process of obtaining a rate involves the determination of the error on two different occasions sepa-
rated by an interval of time of such length as may be convenient; the change of error during this interval,
divided by the number of days, gives the daily rate.
Example: On March 10, at noon, found chronometer No. 576 to be 0™ 32".5 fast of G. M. T. ; on March
20, at noon, the same chronometer was 0"' 48*.0 fast of G. M. T. What was the rate?
Error, March IC* 0\ + 0"' 32'. 5
Error, March 20<* 0^ -f-O 48 . 0
Change in 10 days, + 15 . 5
Daily rate, + 1'.55
The chronometer is therefore gaming 1'.55 per day.
311. Determining Error from Rate. — The error on any given day being known, together with
the daily rate, to find the error on any other day it is only necessary to multiply the rate by the number
of days that may have elapsed, and to apply the product, with proper sign, to the given error.
Example: On December 17 a chronometer is 3'" 27^5 slow of G. M. T. and losing 0^.47 daily. What
is the error on December 26?
Error Dec. 17,-3'" 27'.5 Daily rate, — 0».47
Correction, — 4.2 No. days, 9
Error Dec. 26, - 3 31 .7 Corr., - 4 .23
The chronometer is therefore f<Joiv of G. M. T. on Decem1)er 26, 3"" 3P.7.
312. It is necessary to distinguish between the signs of the chronometer correction and of the
chronometer error. A chronometer fast of the standard time is considered as having a positive error,
since its readings are positive to (greater than) those of an instrument showing correct time; but the
same chronometer has a negative correction, as the amount must be subtracted to reduce chronometer
readings to correct readings.
313. Numerous methods are available for determining the error of a chronometer in port. The
principal of these will be given.
BY TIME SIGNALS.
314. In nearly all of the important ports of the world a time signal is made each day at some
defined instant. In many cases this consists in the dropping of a time-ball — the correct instant being
given telegraphically from an observatorj'. In a number of places where there is no time-ball a signal
may be received on the instruments at the telegraph offices, whereby mariners may ascertain the errors
of their chronometers. Such signals are to be had in almost every port of the United States.
The time signal may be given by a gun-fire or other sound, in which case allowance must be made
by the observer for the length of time necessary for the sound to travel from the point of origin to his
position. Sound travels 1,090 feet per second at 32° F., and its velocity increases at the rate of 1.15 feet
per second with each degree increase of temperature. If V be the velocity of sound in feet per second
at the existing temperature, and D the distance in feet to be traversed, y is the number of seconds to
be subtracted from the chronometer reading at the instant of hearing the signal, to ascertain the reading
at the instant the signal was made.
This method of obtaining the chronometer error consists in taking the difference between the
standard time and chronometer time at the time of observation and marking the result with appropriate
sign.
88 THE CHRONOMETER ERROR.
Example: A time-ball drops at 5^ 0™ 0% G. M. T., and the reading of a chronometer at the same
moment is 4'' 57" 52'. 5. What is the chronometer error?
G. M. T., 5h OO"' 00» 1
Chro. t., 4 57 52 .5
• Chro. error, — 2 07 .5
That is, chronometer slow 2™ 07'. 5; chronometer correction additive.
BY TRANSITS.
315. The most accurate method of finding the chronometer correction is by means of a transit
instrument well adjusted in the meridian, noting the times of transit of a star or the limbs of the sun
across the threads of the instrument.
At the instant of the body's passage over the meridian<(\vire, mark the time by the chronometer.
The hour angle at the instant is O*"; therefore the local sidereal time is equal to the right ascension of
the body in the case of a star, or the local apparent time is O** in the case of the sun's center. By con-
verting this sidereal or apparent time into the corresponding mean time and applying the longitude, the
Greenwich mean time of transit is given. By comparing with this the time shown by chronometer the
error is found.
Example: 1879, May 9 (Ast. day), in Long. 44° 39' E., observed the transit of Arcturus over the
middle wire of the telescope, the time noted by a chronometer regulated to Greenwich mean time being
S*" 05'" 33^5. Required the error.
L. S. T. (R. A. *), 14» 10"' IP. 71
Long., - 2 58 36
G. S. T.,
R. A. M. S., 9^ 0^ -
11
- 3
11
07
35
42
.71
.69
Sid. int. from 0^
Reduction (Tab. 8), -
8
03
1
53.
19.
,02
.27
G. M. T.,
Chro. t,
8
8
02
05
33.
33.
.75
,50
Chro. fast.
2
59.
. 75
Example: June 25, 1879, in Long. 60° E., observed the transit of both limbs of the eun over the
meridian wire of the telescope, noting the times by a chronometer. Find the error of the chronometer
on G. M. T.
Transit of western limb, S^ 04"' 02^ 5 Eq. t., 2'" 16^ 72
Tran-it of eastern limb, 8 06 20 . 0
H. D., + 0\532
Chro. time, loc. app. noon, 8 05 11 .25 Long., — 4''
8
05
11 .
.25
O"
00"
• 2
' 00'
14
.59
0
4
02
00
14
00
.59
8
8
02
05
14
11 .
.59
.25
L. A. T., loc. app. noon, 0" 00"' 00' Corr., — 2M28
Eq. t, - - ^-
Eq. t., 2"' 14^59
L. M. T., loc. app. noon, 0 02 14 .59 Add to apparent time.
Long., -
G. M. T., loc. app. noon,
Chro. time, loc. app. noon,
Chro. fast, 2 56 . 66
BY A SINGLE ALTITUDE iTIME SIGHT).
316. The problem involved in this solution, by reason of its frequent application in determining
the longitude at sea, is one of the most important ones in Nautical Astronomy. It consists in finding
the hour angle from given values of the altitude, latitude, and polar distance. The hour angle thus
obtained is converted by means of the longitude and equation of time in the case of the sun, or longi-
tude and right ascension in the case of other celestial bodies, into Greenwich mean time; and this, com-
pared with the chronometer time, gives the error.
317. It should be borne in mind that the most favorable position of the heavenly body for time
observations is when near the prime vertical. When exactly in the prime vertical a small error in the
latitude produces no appreciable effect. Therefore, if the latitude is uncertain, good results may be
obtained by observing the sun or other body when bearing east or west. If observations are made at
the same or nearly the same altitude on eacli side of the meridian and the mean of the results is taken,
various errors are eliminated of which it is otherwise impossible to take account, and a very accurate
determination is thus afforded.
31§. With a sextant and artificial horizon or good sea horizon, several altitudes of a body should
be observed in quick succession, noting in each case the time as shown by a hack chronometer or com-
jMiring watch whose error upon the standard chronometer is known. Condensing the observation into
THE CHRONOMETER ERROR.
89
a brief interval justifies the assumption that the altitude varies uniformly with the time. A very satis-
factory method is to set the sextant in advance at definite intervals of altitude and note the time as con-
tact is observed.
319. Correct the observed altitude for instrumental and other errors, reducing the apparent to the
true altitude.
If the sun, the moon, or a planet is observed, the declination is to be taken from the Nautical
Almanac for the time of the observation. If the chronometer correction is not approximately known
and it is therefore impossible
X jr to determine the Greenwich
mean time of observation
with a fair degree of accu-
racy, the first hour angle
found will be an approximate
()ne; thedeclination corrected
by this new value of the time
will i^roduce a more exact
value of the hour angle, and
the operation may be re-
l)eated until a sufficiently
jirecise value is determined.
320. In figure 41 there
are given:
AO = /*, the altitude of
the body O;
DO = d, the declination;
and
QZ = L, the latitude of the place.
In the astronomical triangle POZ there may be found from the foregoing:
ZO = z, the zenith distance of the body, = 90° — h;
PO =p, the polar distance, = 90° it d; and
PZ = co-L, the co-latitude of the place, =90° — L.
From this data it is required to find the angle POZ, the hour angle of the body, = /.
by the formula:
. 2 1 COS ^ (h-T-L+p) sin ^ {L+p —h)
SHI 5 r —
This is given
If we let 8 = J {h-\-L -\-p), this becomes:
cos L sin p
sin i t — ■^ sec L cosec^ cos » sin (« — h).
The polar distance is obtained by adding the declination to 90° when of different name from the
latitude and subtracting it from 90° when of the same name. Like latitude and altitude it is always
I)ositive.
If the sun is the body observed, the resulting hour angle is the local apparent time and is to be
taken from the a. m. or p. m. column of Table 44 according as the altitude is observed in the forenoon
or afternoon. If the moon, a star, or a planet be taken, the hour angle is always found in the p. m.
column.
Local apparent time as deduced from an observation of the sun is converted to local mean time by
the application of the equation of time; then, by adding the longitude if west, and subtracting it if east,
the Greenwich mean time is obtained.
The hour angle of any other body, added to its right ascension when it is west of the meridian at
observation or subtracted therefrom when east, gives the local sidereal time, which may be reduced to
Greenwich sidereal time by the application of the longitude, and thence to Greenwich mean time by
methods previously explained.
A comparison of the Greenwich mean time with the chronometer time of sight gives the error of
the chronometer.
Example: January 20, 1879, p. m., in Lat. 48° -iV 00^' S., Long. 69° 03' 00"' E., observed a series
of altitudes of the sun with a sextant and artificial horizon; mean double altitude, 59° 03'' 10''', images
approaching; mean of times by comparing watch, 4*" 40™ 56*; C — W,7''23"'25*; index correction,— 1^30''';
approximate chronometer correction, —0'" 10'. AVhat was the exact chronometer error?
W. T., 4'' 40"' 56» Obs. 2 alt. Q, 59° 03' 10" Dec, 20° 08' 26". 6 S. Eq. t., ll" 14'.60
C_W, ^ - -„ - -
Chro
t.
0
04
21
App.
C.
c.
—
0
10
7 23 25 I. C.
Q
App. G. M. T., 0 04 11 Corr.
S. D..
p. & r.,
Corr., +
—
1 30
2)59
01 40
29
-1-
30 50
14 43
29
45 33
^ 16' 17"
- 1' 34"
H. D.,
G. M. T.
Corr. ,
Dec,
P,
32". 5
0^.07
H. D., 4- 0».74
G. M. T., 0\07
+ 2". 275 Corr., + 0^.052
20° 08' 24". 3 8. Eq. t. , ll"" 14^ 7
69° 51' 36"
(Add to apparent
time. )
14' 43"
'90 THE CHRONOMETER ERROR.
h
h
29°
48
69
45' 33"
41 00
51 36
sec
cosec
cos
sin
.18031
.02740
9.43631
9.84483
L. A. T.,
Eq. t.,
L. M. T.,
Long.,
G. M. T.,
Chro. t.,
Chro. slow
4"
+
29"
11
'46'. 7
14.7
p
4
—4
41
36
01.4
12.0
2)148
• 74
44
18 09
09 05
23 32
8
0
0
04
04
49.4
21.0
2)19.48885
, 0
00
28.4
L. A.T., 4''29"'46».7 sin J < 9.74442
Example: May 18, 1879, p. m., in Lat. 8° 03' 22" S., Long. 34° 51' 57" W., observed a series of
altitudes of the star Arcturus, east of the meridian, using artificial horizon; mean double altitude,
60° 10'; mean w^atoh time, 0'' 50-" 32'; C— W, 2" 20'" 59^5; I. C, -f 2' 00". Find the true error of the
chronometer.
W. T., 6" 50"' 32^ Obs. 2 alt. *, 60° 10' 00" R. A. *, 14" 10"' IP. 7
C— W, 2 20 59.5 I. C, " + 2 00
Chro. t., 9 11 31.5 2)60 12 00
30 06 00
ref., - 1 41
Dec.*, 19° 48' 33". 5 ^^
p, 109° 48' 34"
h, 30 04 19
h 30° 04' 19" R. A, *, 14" 10™ 11».7
L 8 03 22 sec .00431 H. A., - 3 35 41
p 109 48 34 cosec .02650
L. S. T.,
2)147 56 15 Long.,
t 73 58 08 cos 9.44116 G. S. T.,
( — /i 43 53 49 sin 9.84096 R. A. M. S., 0",
H. A. 3" 35'" 41' E. sin ^ t 9.65647
2)19.31293 Sid. int. from 0",
Red. (Tab. 8), -
G. M. T.,
Chro. t.,
10 34
+ 2 19
30.7
27.8
12 53
- 3 43
58.5
11.7
9 10
- 1
46.8
30.2
9 09
9 11
16.6
31.5
Chro. fast, 2 14 .9
BY EaUAL ALTITUDES.
321. The method of observing equal altitwhs of the same body on opposite sides of the meridian
is usually employed for accurate determinations of the chronometer error when the method of transits is
not available.
In the case of a star, the mean of the two chronometer times corresponding to the equal altitudes
is the chronometer time of transit; but in the case of the sun the mean of these times differs somewhat
from the time of transit, since, in consequence of the change of the sun's declination between the
observations, the equal altitudes do not occur at equal intervals before and after the transit.
The small correction necessary, when the sun is observed, to reduce the mean of the times to the
time of transit ia called the equation of equal altitudes.
322. Equal Altitudes of the Sun.« — On shore, at a place whose longitude is accurately known,
and whose latitude is approximately known, observe, with an artificial horizon, the same altitude both
before and after meridian passage, as near the prime vertical as convenient when the altitude is more
than 10°, noting the times. In low latitudes the method of equal altitudes will often give very accurate
results, even when the observations are quite near the meridian.
It is most convenient, as well as conducive to accuracy, to take the observations in series, setting
the sextant in advance of the altitude and marking the time at the instant that the contact is observed;
about five or seven sights may compose a series, and several series may be observed, with the images of
the sun alternately approaching and separating; thus the mean of the results (working each series of
sights separately) will eliminate various possible errors. Ten minutes of double altitude will usually
be found a convenient interval for observing.
The sights may be taken on opposite sides of the meridian for either upper or lower transit. If at
upper transit, the first altitudes are taken in the forenoon and the times recorded; then in the afternoon
the times corresponding to the same altitudes are observed, the last altitude taken in the morning being
the first to come on in the afternoon; series taken with separating images in the forenoon should be
observed with approaching images in the afternoon, and the reverse. If the time of lower transit is to
be determined, the first set of sights is taken in the afternoon of one day and the second set in the
forenoon of the next, care being taken as beforer to observe with im^es moving in opposite directions
on opposite sides of the meridian.
a Chauvenet's method.
THE CHRONOMETER ERROR.
91
323. The mean of the a. m. times call the A. M. Chronometer Time, the mean of the p. m.
times, the P. M. Chronometer Time. If, instead of noting the times by the chronometer, a watch is
used (compared with the chronometer both before and after each observation), it will generally be
found necessary to make an allowance for its gain or loss on the chronometer, so as to obtain the exact
difference between the watch and chronometer at the instant of observation. The difference applied
to the mean of the watch times gives the mean chronometer time the same as would have been found
by employing the chronometer directly.
The half sum of the A. M. and P. M. Chronometer Times is the Middle Chronometer Time; the P. M.
minus the A. M. time in the case of observations for upper transit, or the A. M. minus the P. M. time
for lower transit, gives the Elapsed Time. Twelve hours should be added to the chronometer time at
second observation in any case where the chronometer has passed XII'' during the interval between
sights.
Take from the Nautical Almanac, page I, the sun's declination, the hourly difference of declination,
and the equation of time, reducing each to the instant of local apparent noon by applying the differences
due to the longitude.
Mark ttorth latitude and declination +> south latitude and declination — .
Mark hourly difference of declination when tovmrd north -{-, when toward south — .
Enter Table 37 with the elapsed time, and take out log A and log B, prefixing to each its proper
sign as given in the table at the head of the page.
To log A add the logarithm of the hourly diff. (Table 42) and the log tangent of the latitude (Table
44). Prefix to each logarithm the sign of the quantity it represents, and to their sum the sign which
results from the algebraic multiplication of the quantities. This sum is the logarithm (Table 42) of the
number of seconds of time in the first part of equation of equal altitudes, to be marked + or — , like its
logarithm.
To log B add the logarithm of the hourly diff. and the log tangent of the declination, marking the
signs as before. The sum is the logarithm of the second part of the equation of equal altitudes, to be
marked + or — like its logarithm.
Combine the two parts, having regard to signs, to obtain the equation of equal altitudes; apply this,
with proper sign, to the Middle Chronometer Time and the result is the Chronometer Time of Local
Apparent Noon or Chronometer Time of Local Apparent Midnight, according as observations were taken on
opposite sides of the meridian at upper or at lower transit.
Apply the equation of time (adding when it is additive to mean time, otherwise subtracting); the
result is the Chronometer Time of Local Mean Noon, or Midnight, which, if the chronometer is regulated
to local time, will be 12'' 0'" 0* when the chronometer is right, more than 12'' when fast, less than 12*"
when slow.
If the chronometer is regulated to Greenwich time, apply the longitude (in time) to the chronom-
eter time of mean noon (subtracting in west, adding in east longitude) ; the result will be more or less
than 12'', according as the chronometer is fast or slow.
Example: April 13, 1879, at a place in Lat. 30° 25^ N., Long. 5" 25"' 42' W., observed the following
equal altitudes of the sun with a sextant and artificial horizon, noting the times by a watch compared
Avith a chronometer regulated to Greenwich mean time. What is the error of the chronometer?
A. M. COMPARISONS.
Chro., 2'> 22" 30»
Watch,
C-W,
Chro.,
Watch,
C-W,
8 52
02
5 30
28
2'' 56"
9 26
'30«
02
5 30
28
P. M. COMPARISONS.
Chro., 8'> 04=' 30"
Watch, 2 34 01
C-W,
Dec,
9° 00' 54". 1 N.
H. D. (13th),+54".40
H. D. (14th), +54 .03
WATCH, A. M.
9h 12m 30s
12 55
13 20
13 46
14 10
Chro.,
Watch,
C-W,
ALTS.
91° 00'
10
20
30
40
5 30
29
8" 33"
3 03
'30«
01
5 30
29
H. D. at iioon,+
Long., +
54".32
5''.43
Corr.,
Dec,
(•294".96
t 4'55".0
9° 05' 49" N.
Dlfl., 24 hrs.,- 0 .37
Diff., 1 hr., -0".015
Diff., 5''.43, -0 .08
H.D.atnoon,+54".32
WATCH, P. M.
2h 45"' 45"
45 20
44 55 Tab. 37 log A(-)9.4445 logB( + )9.3193
44 30 H. D. +54".32 log ( + )1.7350 log ( + )1.7350
44 05 Lat. +30° 25' tan (+) 9.7687 d + 9°6' tan ( + )9.2045
Mean, W. T., A. M.,
C-W,
A. M. Chro. T.,
P. M. Chro. T.,
Mid. Chro. T.,
Eq. eq. alt.,
Chro. t. L. A. Noon,
Eq. t,
Chro. t. L. M. Noon,
Long.,
Chro. fast.
9hl3"-
20"
+ 5
30
28
2
43
48
+ 8
15
24
2)10
69
12
5
29
36
-
7.1
5
29
28.9
-
0
31.5
5
28
67.4
- 5
25
42.0
Mean, W. T., P. M.
C-W.
P. M. Chro. T.,
A. M. Chro. T.,
Elapsed Time,
Eq. t.,
H. D.,
Long.,
2h 44m 5.5* 1st Part>-8».88 log (_)0.9482
+ 5 30 29 2d Part+1 .81
log ( + ) 0.2588
16 24 Eq. eq.l _^ ^
43 48 alt. /
- 2 43 48 alt
5 31 36
0"> 36'.02
0«.65
5h.43
Corr.,
Eq. t.,
{Minug to mean time.)
0 03 16.4
92
THE CHRONOMETER ERROR.
324. A quicker method of solving the same problem « is available when results are not required to
be accurate to the fraction of a second.
If /i' is the change of altitude in minutes of arc, due to the total change in declination in the
time elapsed between sights (the latitude and hour angle remaining the same), and i' the number of
seconds it requires for the sun to change its altitude one minute of arc, then:
• 1
Equation of equal altitudes =7^h^ X t' .
Table 25 gives the change of altitude of an object arising from a change of 100 seconds in declination
at various altitudes, declinations, and latitudes. By multiplying the appropriate quantity taken from
this table by the total change of declination between sights, dividing by 100, and converting the result
from seconds to minutes of arc, // is found. It is marked with the sign indicated in the table.
By dividing the number of seconds of time between the first and last sights of one of the series by
the number of minutes difference of altitude, we find i' . When the sights are taken on opposite sides
of the upper meridian t' is minus; for the lower meridian it is plus.
When the artificial horizon is used, if i^ is computed on a basis of the change of the double altitude,
its value is only half of the true one and the second term of the equation becomes h^ X t^' instead of as
given above.
The example given in illustration of the preceding method when worked by this method is as
follows:
Change in declination between sights = H. D. X elapsed time
Change in altitude due to lOO'^ declination (Tab. 25) = + 56'^
54'''.32 X 5\53 = 300^'.
V =
100 X 60
2'»45'"45' — 2''44°K)5"
91° 40^ — 91° 00^
Eq. equal alt. = + 2.80 X -
100^
40'
2\o
= - 2«
7^oo.
325. If equal altitudes of a planet were observed, the correction due to change of declination could
be computed as in the case of the sun. It is not ordinarily expedient to use a planet, however, for if
night sights are to be taken facility of working would make it preferable to employ a fixed star.
On account of its rapid and excessive change of declination the moon would never be observed for
equal altitudes.
326. Equal Altitudes op a Fixed Star. — In selecting stars for this observation, it is to be
remarked that the nearer to the zenith the star passes the less may the elapsed time be; and when a
star passes exactly through the zenith the two altitudes may be taken within a few minutes of each
other. But, with the ordinary sextants, altitudes near 90° can not be taken with the artificial horizon,
as the double altitude is then nearly 180°. A limit is thus placed upon the extreme altitude that it
is practicable to observe.
The sextant should be set and the coincidences of the two images of the star awaited, as in the case
of the sun's limb, and the times by chronometer or watch noted as usual.
327. Take the mean of the times before the meridian passage as the A. M. Chronometer Time, and
the mean of those after the meridian passage as the P. M. Chronometer Time. The mean of these two
(adding 12'' to the later one in case the chronometer has passed XII*" in the interval between sights) is
the Chronometer Time of Star's Transit. At the instant of transit the local sidereal time will equal the
right ascension of the star in case of the upper transit, or it will equal the right ascension plus 12'' in
case of the lower transit. By converting local sidereal into Greenwich sidereal and thence into Green-
wich mean time in the usual way, the chronometer error is found.
Example:— June 8, 1879, at Cape Town, Lat. 33° 56' S., Long. 18° 28' 40" E., using sextant and arti-
ficial horizon, observed equal altitudes of star Antares before and after upper transit, as stated below.
Required the chronometer error on Greenwich mean time.
Chro. A. M.
7" 32'" 10^5
32
32
35.0
59.3
Altitudes.
125° 30^
40
50
A. M.
P. M.
Chro. t., 7
Chro. t., 11
32
33
34.9
56.1
2)19
06
31.0
Chro.
G. M.
t. Transit, 9
T. Transit, 9
33
59
15.5
30.9
Chro. slow,
26 15.4
Chro. P. M.
11" 34"' 20^3
11 33 56.0
11 33 32.0
P. M. Chro. t..
n
33
56.1
L. S. T.(R.A. *),
Long.,
16"
— 1
22"'
14
03%5
54.7
G. S. T.,
R. A. M. S., 0",
15
— 5
07
05
08.8
59.4
Sid. int. from 0",
Red. (Tab. 8),
10
01
1
09.4
38.5
G. M. T.,
9
59
30.9
a Suggested by Commander W. E. Sewell, U. S. Navy.
THE CHRONOMETER ERROR. 93
32§. Degrek of Dependence. — An error of 5'' in the latitude would not affect the corresponding
part of the equation of equal altitudes by more than one-hundredth of its amount in the most unfavorable
case, and in general would have no sensible effect. It is one of the advantages of the equal altitude
method, therefore, that it does not require an accurate knowledge of the latitude. It is also plain that
errors in the longitude affecting the declination and its hourly difference produce but small propor-
tionate effects upon the computed equation. The absolute error of the chronometer on Greenwich will
be affected by the whole error in the longitude, but the rate v^dll still be correct. Hence, we conclude
that by this method the chronometer may be accurately rated at a place whose latitude and longitude
are both imperfectly known.
The chief source of error is in the observation itself. The best observers with the sextant can not
depend on the noted time of a single contact within 0^.5, and hence the intervals between the successive
chronometer times (which, if observations could be perfectly taken, would be sensibly equal) may
differ 2". But the greatest probable error of the chronometer time of sun's or star's transit, from the
mean of six such observations on each side of the meridian, is found to be not more than 0*.2, provided
the rate of the chronometer between the observations is uniform.
94
LATITUDE.
CHAPTER XII.
LATITUDE.
BY MERIDIAN ALTITUDE.
329. The latitude of a place on the surface of the earth, being its angular distance from the equator,
is measured by an arc of the niieridian between the zenith and the equator; hence, if the zenith distance
of any heavenly body when on the meridian be known, together
with the declination of the body, the latitude can thence be found.
Ivet figure 42 represent a projection of the celestial sphere on
the plane of the meridian NZS; C, the center of the sphere; NS, the
horizon; P and P', the poles of the sphere; QCQ'', the equator; Z,
the zenith of the observer. Then, by the above definition, ZQ will
be the latitude of the observer; and NP, the altitude of the elevated
pole, will also equal the latitude.
Let A be the position of a heavenly body north of the equator,
but south of the zenith; QA = (/, its declination; AS = /i, its altitude;
and ZA = 2 = 9U°— /i, its zenith distance.
From the figure we have:
QZ = QA4-AZ, or
Fig. 42. • ^y attending to the names of z and d, marking the zenith dis-
tance north or south according as the zenith is north or south of the
body, the above equation may be considered general for any position of the body at upper transit, as
A, A^ A''.
In case the body is below the pole, as at A''^^ — that is, at its lower culmination — the same formula
may be used by substituting 180°— d for d. Another solution is given in this case by observing that:
NP = PA^'' + NA^'^ or
L=p + h.
330. A common practice at sea is to commence observing the altitude of the sun's lower limb
above the sea horizon about 10 minutes before noon, and then, by moving the tangent-screw, to follow
the sun as long as it rises; as soon as the highest altitude is reached, the sun begins to fall and the lower
limb will appear to dip. When the sun dips the reading of the limb is taken, and this is regarded as
the meridian observation.
It will, however, be found more convenient, and frequently more accurate, for the observer to have
his watch set for the local apparent time of the prospective noon longitude, or to know the error of the
watch thereon, and to regard as the meridian altitude that one which is observed when the watch indi-
cates noon. This will save time and try the patience less, for when the sun transits at a low altitude it
may remain "on a stand|" without appreciable decrease of altitude for several minutes after noon; more-
over, this method contributes to accuracy, for when the conditions are such that the motion in altitude
due to change of hour angle is a slow one, the motion therein due to change of the observer's latitude
may be very material, and thus have considerable influence on the time of the sun's dipping. This
error is large enough to take account of in a fast-moving vessel making a course in which there is a good
deal of northing or southing.
In observing the altitude of any other heavenly body than the sun, the watch time of transit
should previously be computed and the meridian altitude taken by time rather than by the dip. This
is especially important with the moon, whose rapid motion in declination may introduce still another
element of inaccuracy.
331. The watch time of transit for the sun, or other heavenly body, may be found by the forms
given below, knowing the prospective longitude, the chronometer error, and the amount that the watch
18 slow of the chronometer.
For the Sun.
For other Bodies.
L. A. T. noon.
Long. (+ if west),
G. A. T.,
Eq. t.,
G. M. T.,
C. C. (sign reversed)
Chro. time,
C-W,
Watch time noon,
0" 00'" OO"
L. S. T. transit,
Long. (+ if west),
G. S. T.,
R. A. M. S., 0\
Sid int. from O*",
Red. (Tab. 8),
G. M. T.,
C. C. (sign reverse*!),
Chro. time,
C-W,
Watch time transit,
( Right ascension. )
LATITUDE. 95
332. From the observed altitude deduce the true altitude, and thence the true zenith distance.
Mark the zenith distance North if the zenith is north of the body when on the meridian, South it the
zenith is south of the body.
Take out the declination of the body frorti the Nautical Almanac for the time of meridian passage,
having regard for its proper sign or name.
The algebraic sum of tlie declination and zenith distance will be the latitude. Therefore, add
together the zenith distance and the declination if they are of the same name, but take their difference if of
opposite names; this sum or difference will be the latitude, which will be of the same name as the greater.
Example: At sea, June 21, 1879, in Long. 60° W., the observed meridian altitude of the sun's lower
limb was 40° 4'; sun bearing south ; I. C.j + S'O''; height of the eye, 20 feet; required the latitude.
Obs. alt.,
Corr.,
40°
+
04^
13
00'^
21
S. D.,
LC,
dip,
p. <&r.
+ 15^
+ 3
46'^
00
Dec,
H. D.,
Long.,
Corr.,
Dec,
23° 27^ 20^''.5
, + 0'''.32
4".
h,
40
17
21
+ 18
- ¥
, - 1
46
23'^
02
2,
49°
23
42^
27
39'^ N.
22 N.
+ F''.28
23° 27^ 22^'
L,
73
10
01 N.
- 5
25
Corr., + 13^ 21'-'
Example: At sea, April 14, 1879, in Long. 140° E., the observed meridian altitude of the sun's lower
limb was 81° W 30'^; sun bearing north; I. C.,— 2' 30'-'; height of the eye, 20 feet.
Obs. alt., 81° 15' 30'^ S. D., + 15' 59'' Dec, 9° 22' 35".4 N.
Corr., + 8 59
H. D., + 54^.03
h, 81 24 29 p.'&r., - 0 07 Long., - 9\33
z, 8° 35' 31" S. p r 504". 1
d, 9 14 II N. - 7 00 *"""•' \8' 24". I
L, 0 38 40 N. Corr., + 8' 59" Dec, 9° 14' 11" N.
Example: At sea. May 15, 1879, Long. 0°, the observed meridian altitude of the sun's lower limb
was 30° 13' 10"; sun bearing north; I. C, + 1' 30"; height of the eye, 15 feet.
Obs. alt., 30° 13' 10" S. D., + 15' 51" Dec, Gr. 0^, 18° 50'48".5 N.
Corr., + 12 02 . I. C, + 1 30
h, 30 25 12 + 17 21
z, 59° 34' 48" S. dip, - 3' 48"
d, 18 50 49 N. p.&r., - 1 31
L, 40 43 59 S. - 5 19
Corr., + 12' 02"
Example: January 1, 1879, the observed meridian altitude of Sirius was 53° 23' 40", bearing south;
I. C., + 5' 0"; height of the eye, 17 feet.
Dec. *, 16° 33' 04" S.
Obs. alt.,
Corr. ,
53°
+
23'
40"
15
N.
S.
N.
LC,
dip,
ref.,
Corr.,
+
+
5' 00"
*,
53
23
55
43
%
36°
16
36'
33
05"
04
4 45
0' 15"
L»
20
03
01
Example: June 13, 1879, in Long. 65° W., and in a high northern latitude, the meridian altitude of
the sun's lower limb was 8° 16' 10", below the pole; height of the eye, 20 feet; I. C, 0' 00".
Greenwich apparent time of lower culmination, June 13, !&" 20'" ( =Long. +12'').
S. D., -^r 15' 47" Dec, 23° 13' 03".8 N.
dip, - 4 23
p. &T., - 6 12
Obs. alt.,
Corr., -
8° 16' 10"
5 12
K
8 21 22
z,
180°-(7,
81° 38' 38" S.
156 44 36 N.
75 05 58 N.
Alternative method,
h, 8° 21' 22"
p, 66 44 36
10 35
Corr., -h 5 12
H. D., +
G. M. T.,
8".58
16" .33
Corr., + -(
2'
140". 5
20". 5
Dec, 23°
15'
24"
p, 66°
44'
36"
180°-J, 156°
44'
36"
N.
L, 75 05 58 N.
96 LATITUDE.
Example: June 26, 1879, in Long. 80° W., the observed meridian altitude of the moon's upper limb
was 59° 6' 4(y', bearing south; I. C, + 1' ^'\ height of the eye, 19 feet.
G. M. T., Gr. trans., 5i> 27'».0 Dec. (llh), 4° 51' 36".5 S.
Corr. for Long (Tab. 11),+ 11 .0
h, 59° 18' 00"
Obs. alt.,
I. C,
S. D.,
Aug.,
dip,
1st Corr.,
+
59° 06' 40"
z, 30° 42' 00" N.
d, 4 51 06 S.
2' 00"
L, 25 50 54 K.
14
4 16
20 33
18' 33"
L. M. T., local trans., 5 38 .0
Long., -*- 5 20 .0
G. M. T., local trans., + 10 58 .0
M. D.,
No. min.,
+
15".07
2n'.0
Corr.,
30".l
Dec,
4° 51'
06" S.
Approx. alt., 58° 48' 07"
l>.<tr. (Tab. 24), + 29 53
Example: At sea, September 16, 1879, in Long. 75° E., the observed meridian altitude of Jupiter
was 51° 2W 24'^ bearing north; I. C, -^3^ 0'''; height of the eye, 16 feet.
Obs. alt., 51° 25' 24" par., +0'01" G. M. T., Gr. trans., 10i> 49'».8 Dec, 10° 44' 20".5 S.
CJorr., - 1 41 I.e., +3 00 Corr. for Long., - 0 .9 — .— —
H. D., • - 6".58
h, 51 23 43 +3 01 L. M. T., local trans., 10 .50.7 G. M. T., 5'' .84
— ^— — Long., - 5 00 .0 •
z, 38° 36' 17" S. dip, -3' 55" Corr., - 38".43
d, 10 44 59 S. ref., - 47 G. M. T. local trans., 5' 50 .7 — — ^—
Dec, 10° 44' 53" S.
L, 49 21 16 S. -4 42
• H. P., 2".2
Corr.. -1' 41" par. (Tab. 17) , 1"
333. Constant. — In working a meridian altitude, especially the daily noon observation of the sun,
it is frequently a convenience to so arrange the terms of the problem that all computation, excepting
the application of the observed altitude, is completed beforehand; then the ship's latitude will be known
immediately after the sight has been taken, it benig necessarj^ only to add or subtract the altitude.
It is assumed that the noon longitude will be sufficiently accurately known in advance to enable the
navigator to correct the declination; also the approximate meridian altitude to correct the parallax and
refraction; if the latter is not known, it may readily be found from the declination and approximate
latitude.
Generally speaking,
Lat. = Zenith distance — Dec,
= 90° — True alt. + Dec,
= 90° - (Obs. alt. + Corr.) + Dec,
= (90° -f Dec. - Corr.) - Obs. alt.,
in which the quantity (90° -f Dec. — Corr.) may be termed a Constant for the meridian altitude of the
day, as it remains the same regardless of what the observed altitude may prove to be. The constant
having been worked up before the observation is made, the latitude will be known as soon aa the
observed altitude is applied.
To avoid the confusion that might arise from the necessity of combining the terms algebraically
according to their different names, it may be convenient to divide the problem into four cases and lay
down rules for the arithmftical combination of the terms, disregarding their respective names as follows:
Case I. Lat. and Dec. same name, Lat. greater, + 90° + Dec. — Corr. — Obs. alt.
Case II. Lat. and Dec. same name, Dec. greater, — 90° + Dec. + Corr. + Obs. alt.
Case III. Lat. and Dec. opposite names, + 90° — Dec. — Corr. — Obs. alt.
Case IV. Lat. and Dec. same name, lower transit,-!- 90° — Dec. -f- Corr. + Obs. alt.
The correctness of such an arrangement will become readily apparent from an inspection of figure 42.
The assumption has been made that the correction to the observed altitude is positive; when this is
not true the sign of the correction must be reversed.
As examples of this method, the first, second, third, and fifth of the examples previously given
illu-strating the meridian altitude will be worked, using the constant; the details by which Corr. and
Dec. are obtained are omitted, being the same as in the originals.
1st Example. 2i> Example. 3d Example. 5th Example.
Case I. Case II. Case III. Case I V.
+ 90° 00' 00'^ -90° 00' 00'' +90° 00' 00" -f 90° 00' 0(7'
Dec, + 23 27 22 Dec, -f 9 14 11 Dec, -18 50 49 Dec, -23 15 24
Corr., - 13 21 Corr., -f 8 59 Corr., - 12 02 Corr., -f 5 12
Constant, -4-113 14 01 Con8tant,-80 36 50 Constant, + 70 57 09 Constant,+66 49 48
Obs. alt., - 40 04 00 Obs. alt., -f 81 15 30 Obs. alt., -30 13 10 Obs. alt.,-^ 8 16 10
Lat., 73 10 01 (N.) Lat, 0 38 40 (N.) Lat., 40 43 59 (S.) Lat., 75 05 58 (N.)
LATITUDE. 97
BY REDUCTION TO THE MERIDIAN.
334. Should the meridian observation be lost, owing to clouds or for other reason, altitudes may be
taken near the meridian and the times noted by a watch compared with the chronometer, from which,
knowing the longitude, the hour angle may be deduced.
If the observations are within 26'" from the meridian, before or after, the correction to be applied
to the observed altitude to reduce it to the meridian altitude may be found by inspection of Tables 26
and 27. Table 26 contains the variation of the altitude for one minute from the meridian, expressed in
seconds and tenths of a second. Table 27 contains the product obtained by multiplying the square of
the minutes and seconds by the change of altitude in one minute.
Let a = change of altitude (in seconds of arc) in one minute from the meridian:
H = meridian altitude;
h = corrected altitude at observation; and
t = interval from meridian passage.
The value of the reduction to the meridian altitude of each altitude is found by the formula:
H = /* ^ at-,
a being found in table 26, and af in Table 27; hence the following rule:
Find the hour angle of the body in minutes and seconds of time. Take from Table 26 the value of
a corresponding to the declination and the latitude. Take from Table 27 the value of at^ corresponding
to the fi thus found and to the interval, in minutes and seconds, from meridian passage. This quantity
will represent the amount necessary to reduce the corrected altitude at the time of observation to the
corrected altitude at the meridian pa-ssage; it is always additive when the body is near upper transit,
and always to be subtracted when near lower transit.
If the mean of a number of sights is to be taken, determine each reduction separately, take the
mean of all the reductions, and apjily it U) the mean of the altitud(!s; it is incorrect, in such a case, to
take the mean of the times and work the sight with this single value of t. The differences of altitude
being small, the parallax and refraction will be sensibly the same for all, and one computation of the
correction to the observed altitude will suffice.
Knowing the meridian altitude, the latitude is to be found as previously explained.
335. When several sights are taken, the most expeditious method of calculating will be to find
first the watch time of transit, and thence obtain the hour angle of each observation by comparing the
watch time of observation. The watch time of transit may be found as already explained (art. 331)
for computing that quantity as a guide in taking the meridian altitude, but the hour angle thus obtained
is subject to a correction. The difference l;etween watch time of transit and watch time of observation
^ives the watch time — that is, the mean time — elapsing between transit and observation. A fixed star
covers in that time an angle corresponding to the sidereal and not to the mean time interval, and a
reduction should be made accordingly to give its true hour angle at the instant of observation. A
planet's hour angle should be corrected in the same way (for we may disregard its very small change
m right ascension). The correction may be entirely neglected in the case of the sun, as the difference
between mean and apparent time intervals is immaterial. The reduction of the hour angle in the ca.se
of the moon becomes rather cumbersome, so much so that it is better to find the hour angle of this body
by the more usual method of converting watch time to G. M. T., and thence to L. 8. T., and finding
the difference between the latter and the R. A.; an additional reason for this is that the G. M. T. of
observation must be known exactly, with the moon, for the correction of the declination (art. 338).
336. Table 26 includes values of the latitude up to 60°, and those of the declination up to 63°,
thus taking in all frequented waters of the globe and all heavenly bodies that the navigator is likely to
employ. No values of (i are given when the altitudes are above 86° or below 6°, as the method of reduc-
tion to the meridian is not accurate when the body transits very near the zenith, and the altitudes
themselves are questionable when very low. In case it is desired to find the change of altitude in one
minute from noon for conditions not given in the tables, it may be computed by the formula:
l'^9635 cos L cos d
sm (L — a)
In working sights by this method where great accuracy is required, as in determining latitudes on
shore for surveying purposes, it is well to compute the a rather than to take it from the table, as one
is thus enabled to employ the value as found to the second decimal jilace.
Due regard must be paid to the names of the declination and latitude in working this formula; if
thev are of opposite names, the declination is negative, and L and d should be added together to obtain
L— '(/.
337. Table 27 contains values of af up to the limits within which the method is con.sidered to
apply with a fair degree of accuracy. It nuist not be understood that the plan of reduction to the
meridian is not available for wider limits, but it would seem ]ireferable to employ the tp^ cp" formula,
described hereafter, when the hour angle falls beyond that for which the table is computed. On the
other hand, the reduction is not exact in all cases covered by the table; while sufiiciently so for sea
navigation, the limits given are far too wide for the precise determinations required in surveying, where
the aim should l)e to observe bodies under such conditions that the total reduction a(^ shall not exceed V.
33§. It should be kept clearly in mind when employing the method of reduction to the meridian
that the resulting latitude is that of the ship at the instant of observation, and to bring it up to noon
the run nuist be applied. The declination should properly be corrected for the instant of observation;
with the sun or a planet, it is sufiiciently accurate to use the declination at meridian passage, unless the
interval from the meridian be quite large; but the moon's declination changes so rapidly that the exact
time of observation nmst be used in its correction when working with this body.
22489—03—7
98
LATITUDE.
Ex.\mplk: In latitude 47° S., having previou.-^ly worked up the constant for meridian altitude;
78° 42^ 10'^ observed altitude of sun near meridian,' 31° 11' 50'';.Dec 11° X.; watch time, 11" 40™ 21%
watch fast of L. A. T., 7*. Find the latitude.
Watch time, 11" 40°' 21^
AVatch fast,
•
07
L.
A. T.,
11
40
14
t,
19''
I.46S
Obs. alt., 31° 11^50''
at\ + 10 24
a (Tab. 26), 1.'''6
Mer. alt., 31 22 14
ConsUnt, 78 42 10
a<2(Tab.27),
Lat.,
47 19 56 8.
l.'''0= 6^30'^
. 6= 3 54
1. 6 = 10 24
Example: At sea, July 12, 1879, in Lat. 50° N., Long. 40° W., observed circum-meridian altitude of
the sun's lower limb, 61° 48' 30^', the time bv a chronometer regulated to Greenwich mean time being
2" 41'" 39^; chro. corr., -2"" 30'; I. C, —3' O''; height of the eye, 15 feet. Find the latitude.
Chro.t.,
C.C,
2h 4i«
- 2
'39'
30
Q
Corr. ,
h,
S. D.,
dip,
p. & r.
L C,
Corr.,
h
61°
' 48' 30"
8 31
Dec,
H.D.,
Long.,
Corr.,
Dec,
22° 00' 23". 2 N.
Eq.t.,
H. D.,
Long.,
Corr.,
Eq. t,
{Suhtrac
time. )
[Tab. 26), 2.
2.
(Tab. 27), r^-
5'" 17^99
20". 7
2". 7
+ 0^32
2". 7
G.M.T.,
Eq.t.,
2 39
— 5
09
19
61
57 01
-T
15' 46"
55". 9
~ .86
G.A.T.,
Long.,
, 2 33
- 2 40
50
00
)
3 48
0 27
3 00
21° 59' 27" X.
a 1
at'
5"' 18».9
L.A.T.,
11 53
50
t,
6
10
-
7 15
61° 57'
1
8 31
01"
35
"5
"0 = 1' 16"
5 = 0 19
H, 61 58 36
1 35
28 01 24 N.
21 59 27 N.
L, 50 00 51 X.
Example: May 31, 1879, in Lat. 30° 25' X., Lonsf. 5" 25"' 42' W., about 9 p. m., observed with a
sextant and artificial horizon a series of altitudes of Spica; mean observed double altitude 98° 06' 34";
noted times as enumerated below bv a watch compared with a chronometer which was 2"' 33'' fast of
G. M. T.; C-W, 5" 29"" 40^ I. C, -3' 00". Find the latitude.
R. A. * (L. S. T.transit) , 13" 18'" 52^2 Mean 2 all
Long.,
G. S. T.,
R. A. M. S. Gr. 0",
Sid. int. from 0",
Red. (Tab. 8),
G. M. T.,
C. C. (sign reversed),
Chro. time transit,
C— W,
Watch time transit.
+ 5 25 42
Watch times.
8" 31'" 18^0
33 19.5
36 07.0
38 50.0
41 07.5
43 45.5
45 46.0
47 33.0
51 12.5
18 44
4 34
34.2
26.9
14 10
2
07 .3 re
19.4
;,
14 07
_U 9
> 1 -^
47 .9
33
14 10
- 5 29
20.9
40
8 40 41
Intervals from transit.
Meantime.
— 9'" 23^0
21 .5
34.0
51.0
-r 0 26.5
3 04.5
5 05.0
6 52.0
31 .5
10
Sid. time.
- 9™ 24'
7 23
4 35
1 51
-0 27
3 05
5 06
6 53
10 33
98°
06' 34"
3 00
R. A. *,
Dec,
a (Tab. 26),
13" 18'" 52^2
10° 32' 04" S.
98
03 34
2".5
49
01 47
50
49
00 57
at^ (Tab. 27).
£o 05^ 2!5 '
2' 56" 0' 44" 3' 40"
1 49 0 27 2 16
0 42 0 10 0 52
0 07 0 01 0 08
0 01 0 00 0 01
0 19 0 04 0 23
0 52 0 13 1 05
1 35 0 23 1 58
3 42 0 55 4 37
h, 49° 00' 57"
«<*,+ 1 40
H,
49 02 37
40 57 23 N.
10 32 04 S.
30 25 19 N.
9)15 00
1 40
LATITUDE.
99
Example: August 6, 1S79, Lat. 59° S., Long. 175° 27^ E., during evening twilight, observed an
altitude of Achernar, near lower transit, 26° 52'; watch time, 4" 31"' 12^; C — W, 0" 18"' 07^; chro. fast of
G. M. T., 12"' 42^; I. C, -f V 20^'; height of eye, 24 ft. Find hour angle by both methods; thence the
latitude.
R. A. JJC -t- 12 1 1 Oh oom 1 Ka A
L. S. T. lower trans./ ^'^ ^^^ ^^ '^
Long., - 11 41 48
Watch time,
C-W,
Chro. t.,
C. C,
G. M. T. 5^
R.A.M.S. Gr.5''0S
Red. (Tab. 9),
G. S. T.,
Long.,
L. S. T.,
R. A. * + 12h,
R. A. *, 1" 33°'
4" 31"
+ 0 18
'12^
07
4 49
— 12
19
42
G. S. T., 1
R. A.M. S. Gr.5'»0^- 8
51
54
27.4
39.8
16 36
+ 8 54
+ 2
37
39.
43,
Sid. int., 16
Red. (Tab. 8), -
56
2
47.6
46.6
,8
,7
G. M. T., 16
C. C. (sign reversed ),+
54
12
01.0
42
1 34
+ 11 41
00.
48
.5
Chro. time, 5
C-W, - 0
06
18
43
07
13 15
13 33
48.
15.
,5
,4
Watch time transit, 4
Watch time obs., 4
48
31
36
12
17
15^4
27
, fMean time,
\Sid. time,
Obs. alt: *, 26°
17
17
52'
24
27
00"
L C, +
4'
1
20"
48"
55
Dec, 57°
50'
■ 28" S.
dip, —
ref., -
p, 32=
■ 09' 32"
a (Tab. 26),
at^ (Tab. 27),
0".6
3' 03"
-
6
43
Corr. , —
y
2.3"
/(, 26°
at\ -
46'
3
37"
03
H, 26
P, 32
43
09
34
32
L, 58
53
06 S.
BY A SINGLE ALTITUDE AT A GIVEN TIME.
339. This observation should be limited to conditions where the body is within three hours of
meridian passage and where it is not more than 45° from the meridian in azimuth. On the prime
vertical the solution by this method is inexact, and when the hour angle is 6'' it is impracticable.
The problem is: Given the hour angle, declination, and altitude, to find the latitude. The solution
is accomplished by letting fall, in the usual astronomical triangle, a perpendicular from the body to the
meridian, and considering separately the distances on the meridian, from the pole and zenith, respec-
tively, to the point of intersection of the perpendicular; the sum or difference of these distances is the
co-latitude.
Following the usual designation of terms and introducing the auxiliaries <?>' and <p", the formulae are
as follows:
tan ^'=tan d sec t;
cos (p' = sin h sin <p" cosec d;
The terms 9)' and ^" will have different directions of application according to the position of the
body relatively to the observer. From a knowledge of the approximate latitude, the method of com-
bining them will usually be apparent; it is better, however, to have a definite plan for so doing, and
this may be based upon the following rule:
Mark ^" north or south, according to the name of the declination; mark ^' north or south, accord-
ing to the name of the zenith distance, it being north if the body bears south and east or south and west,
and south if the body bears north and east or north and west. Then combine 95" and <p^ according to
their names; the result will be the latitude, except in the case of bodies near lower transit, when
180° — <p" must be substituted for ^' to obtain the latitude.
It may readily be noted that if we substitute <p'^ for declination and cp' for zenith distance, the
problem takes the form of a meridian altitude; indeed, the method resolves itself into the finding of
the zenith distance and declination of that point on the meridian at which the latter is intersected by a
perpendicular let fall from the observed body.
The time should be noted at the instant of observation, from which is found the local time, and
thence the hour angle of the celestial object.
100
LATITUDE.
If the sun i.s observed, the hour angle is the L. A. T. in the case of a p. m. sight, or 12'' — L. A. T.
for an a. m. sight. If any other body, the hour angle may be found as hitherto explained.
Example: June 7, 1879, in Lat. 30° 25' N., Long. 81° 25' 30" W., by account; chro. time, 6" 22'" 52»;
obs. Q 75° 13', bearing south and east; I. C. — 3' 00"; height of the eye, 25 feet; chro. corr. — 2"' 36».
Find the latitude.
Chro.t,
C.C,
G. M. T.
Eq.t.,
G.A.T.,
Long. ,
6" 22"' §2*
2 36
6 20
+ 1
16
26
6 21
- 5 25
42
42
Obs. alt. Q, 75° 13' 00"
Corr., + 7 40
S.D.,
L.A
■T.=r, {
dip,
p. & r. ,
0''56"00^E. I.e.,
14° 00' 00"
Corr.,
75
20
40
+
15'
48"
—
4' 54"
14
3 00
-
8
08
Dec,
H.D.. +
G.M.T., +
22° 45' 09".9 N. Eq.t., 1"' 28».85
14".6
6".3
H. D., -
G.M.T.,+
0\46
6". 3
91".98
1'32"
2^85
Corr., {j;
Dec, 22° 46' 42" N. (^"(^d to mean time.)
Corr., —
Eq.t., l'"26'. 0
+
7' 40"
t
d
14°
22
75
23
7
00' 00"
46 42
20 40
24 07 N.
02 30 N.
sec
tan
tan
.01310
9.62317
cosec
sin
sin
cos
.41210
h
9.63627
9.98563
9.59898
<f^
9.99671
Lat.
30
26 37 N.
Example: May 28, 1879, p. m., in Lat. 6° 20' S. by account. Long. 30° 21' 30" W.; chro. time,
7'' 35"" 10"; observed altitude of moon's upper limb, 75° 33' 00", bearing north and east; I. C, —3' 00";
height of eye, 26 feet; chro. fast of G. M. T., 1"" 37^5. Eequired the latitude.
Chro. t.,
C.C,
G. M. T.,
R. A. M. S.,
Red. (Tab. 9),
G. S. T.,
R. A. C.
H. A. from Gr.
Long.,
7h
35-
'10>
-
1
37.5
7
33
32.5
+ 4
22
37.3
+
1
14.5
11
57
24.3
-10
22
17
1
35
07
2
01
26
Obs. alt.'C.
S. D.,
Aug.,
dip,
I. C,
75° 33' 00"
15' 51"
0 16
5 00
3 00
24 07
R. A. C,
M. D.,
No. mill.,
Corr.,
R. A.,
lOh
21"
,. 07»
.78
+
28
.06
.54
-{
1'
69«.09
"09'
Dec,
M. D.,
No. mill.,
Corr.,
Dec,
6°49'52".4 N.
14".46
33"'.54
486"
05"
6° 41' 47"
-I '
I 8' I
N.
W.
\V.
Oh 26ni 19* E..
6° 34' 4.5"
Approx. alt., 75° 08' ,53"
p. (t-r.(Tab.24), + 14 37
h. 75 23 80
Hor. Par., 58' 03"
t
d
h
^"
9,'
Lat.
6° 34' 45"
6 41 47
75 23 30
6 44 26 N.
13 05 40 S.
6 21 14 S.
sec
tan
.00286
9.06973
tan 9.07259
sin
sin
.93324
9.98573
9.06959
cos 9.98856
Example: August 6, 1879, p. m., in Lat. 52° 47' S. by D. R., Long. 146° 32' E., observed altitude of
Achernar, near lower transit, 24° 01' 20" bearing south and west; watch time, 6'' 48"' 22"; C— AV, 9" 46"
27'; chro. corr. on G. M. T., + 1'" 57% height of eve, 18 feet; I. C. + 1' 00". Find the latitude.
Watch time,
c-w.
6" 48"'
+ 9 46
'22'
27
Obs. alt. y^,
Corr., —
I. c, +
dip, -
ref., —
Corr., —
24°
01' 20"
5 19
R.A. *, 1" 33-" 15'. 3
•Dec, 57° 50' 28" S.
Chro. t.,
C.C,
4
+
34
1
49
57
23
56 01
—
I'OO"
4' 09"
2 10
G. M. T., 5^
R. A. M. S.,
Red. (Tab. 9),
16
+ 8
36
54
2
46
39.8
43.7
G. S. T.,
R. A. *,
1
1
34
33
09.5
15.3
6 19
5' 19"
H. A. from Gr.
Long.,
,, 0
9
00
46
54 W.
. 08 E.
H. A.,
9
47
02 W.
t,
f 2"
I 83°
12"' 58'
' 14' 30"
t
d
33°
57
23
-<f/' 117
64
14' 30^'
50 28
56 01
44 18 S.
54 15 N.
LATITUDE.
sec .07760
tan .20153
coeec
sin
sin
cos
. 07233
h
180°-
tan .27913
9. 60818
9. 94699
'P'
9. 62750
Lat.
52
50 03 S.
101
BY THE POLE STAR.
340. This method, confined to northern latitudes, is available when the star Polaris and the hori-
zon are distinctly visible, the time of the observation being noted at the moment the altitude is measured.
Two methods will be given. The first is sufficiently precise for nautical purposes, involving the
computation of the formula:
L =^h — p cos t,
in which,
h = true altitude, deduced from the observed altitude;
p = polar distance = 90° — d, the apparent declination being taken from the Nautical Almanac
for the date; "
t = star's hour angle.
Find the right ascension and declination of Polaris from the Nautical Almanac; then find the hour
angle in the usual way.
To the log cosine of the hour angle add the logarithm of the polar distance in minutes; the number
corresponding to the resulting logarithm will be a correction in minutes to be subtracted from the star's
true altitude to find the latitude.
Attention must be paid to the sign of the correction p cos t. If t is more than 6*' and less than 18'',
the sign of cos / is — ; hence the formula becomes arithmetically:
L = /( + p cos t.
Example: June 11, 1879, from an observed altitude of Polaris the true altitude was found to be
29° 5' 55''. The time noted by a Greenwich chronometer was 13'' 41'" 26^^; chro. corr. — 2"' 22'; Long.
5h25.n42» W.
h, 29° 05' 55" R. A. *, 1" 14"' 04»
p cos t, + 1 19 54
Dec, 88° 39' 47" N.
Chro. time,
C. C,
13" 41" 26'
- 2 22
G; M. T., ll^
R.A.M.S.,
Red. (Tab. 9) ,
13
+ 5
+
39 04
17 49
2 15
G.S.T.,
R. A. *,
18
- 1
69 08
14 04
H. A. from Gr.
Long.,
, 17
5
45 04 W.
25 42 W.
H. A.,
t.
^2 19 22 W.
r 11" 40'" 38' E.
\175°09' 30"
Lat., 30 25 49 N.
° 20' 13"
^' I 80'. 2
p, 80'. 2 log 1. 90417
t, 175° m' 30" cos ( -) 9. 99845
pcosr, ^1019/54//
341. The second method is more rigorous, and should be employed when greater accuracy is
sought. It is embodied in Table 28.
Reduce the observed altitude of the star to the true altitude. Find from the Nautical Almanac the
apparent right ascension and declination of the star at the time of observation. Find the hour angle in
the usual manner.
With the hour angle take out the first correction, A, from Table 28, giving to it the sign — when the
hour angle is numerically less than 6"; the sign + when the hour angle is greater than 6".
With the hour angle and altitude take out the second correction, B, from Table 28. The sign of this
correction is always -j-. (If the altitude is greater than 60°, this correction may be found by taking
that for 45° and multiplying it by the tangent of the altitude; adding, if desirable, the second term in
the expression for B, viz: + 0".0076 sin* t tan' /(. )
With B and the declination take out the third correction, C, from Table 28, giving it the sign f
when the declination is less than 88° 48'; — when the declination is greater than 88° 48'.
With A and the declination take out the fourth correction, D, from Table 28, giving it the same sign
as that of A when the declination is less than 88° 48'; the opposite sign when the declination is greater
than 88° 48'.
Combine these corrections with the true altitude according to their signs; the result is the latitude
of the place of observation.
If, when several sights are taken, great precision is required, or the intervals are great, it will be
necessary to take out the first and second (corrections for each observation separately; in other cases the
102 LATITUDE.
mean of the times may be used. The means of these two corrections may always he used for finding
the third and fourth corrections; and these four quantities may be combined with the mean of the
altitudes.
If the nearest W^ suffices for each, the corrections may be taken out for the nearest arguments
without interpolation, and all but the first may thus be taken out when a precision of ^''is required. If
a precision of V is sufljcient for each correction, as is ordinarily the case at sea, an hour angle within
3™ will suffice for A; C and D may be neglected, and B used only when the altitude exceeds 47°.
Example: January 1, 1903, about 9 p. m.. Longitude 79° 54'' 07'^ W., observed doul)le altitude
of Polaris with artificial horizon, 81° 57^ 20^''; chro. time 1'' 55" 12^ chro. corr. on G. M. T. + 1'" 07';
I. C. —O'SO". (The necessary quantities, taken from the Nautical Almanac for 1903, are given
below.) Required the latitude.
Chro. time, li^ 55™ 12' Obs. 2 alt. *, 81° 57' 20" R. A. *, 1" 24"' 33».3
C. C, + 1 07
Dec, 88° 47' 42'' N.
G. M. T., 13 56 19
R. A. M. S., +18 39 50.9
Red. (Tab. 9), + 2 17.4
G. S. T.,
R. A. *,
8
1
38
24
27.3
33.3
H. A. froniGr.,
Long.,
7
5
13
19
54 W.
37 W.
H. A., 1 54 17 W.
Obs. 2 alt.
*,
81°
57'
20"
LC,
—
0
50
2)81
56
30
40
58
15
ref.,
—
1
07
h,
40
57
08
A,
— 1
03
13.9
B,
+
08.9
0,
00.0
D,
—
15.7
Lat,
39
53
47 N.
LONGITUDE. 103
CHAPTER XIII.
LONGITUDE.
342. The longitude of a position on the earth's surface is measured by the arc of the equator
intercepted between the j^rime meridian and the meridian passing through the place, or by the angle
at the pole between those two meridians.
Meridians are great circles of the terrestrial sphere passing through the poles.
The prhne meridian is that one assumed as the origin, passing through the location of some principal
observatory, such as Greenwich, Paris, or Washington. That of Greenwich is the prime meridian not
only for English but also for American navigators, and those of many other nations.
Secondari/ meridians are those connected with the primary meridian, directly or indirectly, by
exchange of telegraphic time signals.
Tertiary meridians are those connected with secondaries by carrying time in the most careful manner
with all possible corrections.
Longitude is found by taking the ■difference between the hour angle of a celestial body from the
prime meridian and its hour angle, at the same instant, from the local meridian. In determinations
ashore the hour angle from the prime meridian may be found either from chronometers or from
telegraphic signals; the local hour angle may ])e found by transit instruments or by sextant. In
determinations at sea the chronometer and sextant give the only means available.
DETERMINATION ASHORE.
343. Telegraphic Determination of Secondary Meridians. — In order to locate with accuracy
the positions of prominent points on the coasts, it is necessary to refer them, by chronometric measure-
ments, to secondary meridians of longitude which have been determined with the utmost degree of care.
Before the establishment of telegraphic cables, this was attempted principally through the observa-
tion of moon culminations, which seemed always to carry with them unavoidable errors, or by trans-
porting to and fro a large number of chronometers between the principal observatory and the position
to be located; and in this method it can be conceived that errors would be involved, no matter how
thorough the theoretical compensation for error of the instruments.
By the aid of the electric telegraph, differences of longitude are determined with great accuracy,
and an ever-increasing number of secondary meridional positions are thus established over the world;
these afford the necessary bases in carrying on the surveys to map correctly the various coast lines, and
render possible the publication of reliable and accurate navigators' charts.
344. To determine telegraphically the difference of longitude between two points, a small observa-
tory containing a transit instrument, chronograph, break-circuit sidereal chronometer, and a set of
telegraph instruments is established at each of the two points, and, being connected by a temporary
wire with the cable or land line at each place, the two observatories are placed in telegraphic com-
munication with each other.
By means of transit observations of stars, the error of the chronometer at each place on its own local
sidereal time is well determined, and the chronometers are then accurately compared by signals sent
first one way and then the other, the times of sending and receiving being very exactly noted at the
respective stations. The error of each chronometer on local sidereal time being applied to its reading,
the difference between the local times of the two places may be found, and consequently the difference
of longitude. The time of transmission over the telegraph line is eliminated by sending signals both
ways. By the employment of chronometers keeping sidereal time, the computation is simplified,
though mean-time chronometers may be used.
345. Establishment of Tertiary Meridians. — Let it be supposed that the meridional distance
between A and B is to be measured, of which A is a secondary meridional position accurately deter-
mined, and B a tertiary meridional position to be determined.
If possible, two sets of observations should be taken at A to ascertain the e' irs and rates of the chro-
nometers. The run is then made to B, and observations made to determine i time, and hence the
difference of longitude; and on the same spot altitudes of the sun, or of a nu ^r of pairs of stars, or
both, should be taken to determine the latitude. ~
Now, if chronometer rates could be relied on to })e uniform, this measurement would suffice, but
since variations may always arise, the run Ijack to A should be made, or to another secondary meridio-
nal position, C, and new rates there obtained. Finally, the errors of the chronometers on the day when
the observations were made at the tertiary position should be corrected for the loss or gain in rate, and
for the difference of the errors as thus determined.
When opportunity does not permit obtaining a rate at the secondary meridional station or stations,
both before and after the observations at B, the navigator may obtain the errors only, and assume that
the rate has been uniform between those errors.
A modification of the foregoing method that may sometimes prove convenient is to make the first and
third sets of observations at the position of the tertiary meridian, and the intermediate one at the second-
ary meridian; in this case the error will be obtained at the secondary station, and the rate at the tertiary.
104
LONGITUDE.
Example: A vessel at a station A, of known longitude, obtained chronometer eirors as follows:
May 27, noon, ehro. slow, 7'» 18^9,
June 3, noon, chro. slovv, 7 12 .7;
then proceeding to a station B a series of observations for longitude was taken on June 17: after which
returning to A, the following errors were obtained: '
July 3, noon, chro. slow, 7"" 00\7,
July 10, noon, chro. slow, 6 59 .8.
Required the correct error on June 17.
May 27, -7» 18^9 July 3, -7"' 00«.7
June 3, —7 12.7 July 10, —6 59,8
Change, + 6.2 Change, + 0 .9
Daily rate, + 0'.89 Daily rate, + 0M3
Therefore, assuming that these rates were correct at the middle of the periods for which thev were
determmed, we have, j -^
May 30, Midnight, Rate, +0\89
July 6, Midnight, Rate, -f 0 .13
Change of rate, 37 days, —0 .76
Daily change of rate, — 0*.021
Change of rate for 3J days, — 0^07; rate June 3, noon, +0^89— 0\07=+0* 82
Change of rate for 17| days, —0^37; rate June 17, noon, +0 .89—0 .37=+0 .52
Mean daily rate, June 3 to 17, ' -fO .67
Total change of error, June 3 to 17, -f 0"' 09".38
Error, June 3, _7 12.7
Error, June 17, —7 03 .3
346. Single Altitudes.— The determination of longitudes ashore by single altitudes of a celestial
body IS identical in principle with the determination at sea by that method, which will be explained
hereafter (art. 349). It may be remarked, however, that by 'taking observations on opposite sides of
the meridian, at altitudes as nearly equal as possible, a means is afforded, which is not available at sea
of eliminating certain constant errors of observation. '
34T. Equal Altitudes.— The method of equal altitudes, explained in article 321, Chapter XI is
available for the determination of longitudes as well as for chronometer error. In the case of the sun
the sight ^ives the chronometer time of L. A. noon or midnight; applying the chronometer correction
and equation of time (the latter with its sign for mean time), we obtain the G. A. T., which equals the
longitude, if west, or 24" minus the longitude, if east. For any other body, the sight gives the chro-
nometer time of transit; apply the chronometer correctfon and there results G. M. T., which may be
reduced to G. S. T.; the difference between the latter and the R. A. of the bodv (this being L 8 T^
is the longitude. j \ ^ ■ • '■•),
Example: April 20 p. m. and April 21 a. m., 1879, in Lat. 30° 25' N., Long, (approx.) 81° 26' \V
chro. corr. ~3"' U'A, observed times and equal altitudes of the sun as stated below; C — W for p m'
sights, 5" 31™ 58".5, and for a. m. sights, S" 32™ 01'. Required the longitude.
Dec, 11° 29' 17".l N. H. D. (20th), +5I".45
H. D. (21st), ,+50 .97
WATCH,
, P. M.
ALTS.
2>'51»
>40»
90° 0'
52
a5
89 60
52
30
40
52
55
30
53
20
20
Mean, W. T., P. M., 2h Si-"
'30«.0
Mean, W. T.
C-W,- ■ +5 31
58 .5
C - W,
P. M. Chro. T., 8 24
r
A.M. Chro.:
V'ATCH
, A.
M.
8h 59"
'00'
58
34
.5
58
09
.5
57
40
.0
57
20
.0
H.D.atMid.,+ .51".10
Long. H-12h, 17'>.43 DiflF. 24^, -0.48
A. M. Chro., T. +12'', 26 30 1
2)10 54 39 .5 Klapsed Time,
M., 8h 58"
+ 5 32
'10"
01
L21', 26
8
30
24
11 .0
28 .5
18
05
42 ,5
1"
04 '.9
+
0'.54
17''.43
+
9».4
Dec, 11° 44' 08" N.
f 890".7 Diflf. Ih, _ 0".02
114' .51" — —
DiflF. I'^AS, - 0".a5
H. D. at Mid., +.51".10
Mid. Chro. T., 5 27 19 .75
Eq. eq. alt., + 19.35 Eq. t.. 1"04».9 Tab. 37 log A ( + )9.9364 logB(-)9.7912
H.D.+51".101og (+)1.7084 log ( + )1.7084
Chro.t.L.A.Mid., 6 27 39.1 H. D., + 0'.54 Lat. 30° 25' ten ( + )9.7687 ri+ll°44'tan ( + )9.3175
Eq. t., + 1 14 .3 Long. + 12!>,
1st Part 4-25'.911og( + )1.4135
Chro. t.,L.M. Mid., 6 28 53.4 Corr., + 9».4 2d Part - 6 .56 log (-)0.8171
C. C. , - 3 11 .4
Eq.t, lml4.».3 *^%^^- }+19 .35
Lop„ -yy f Sh 25" 42 '.0 {Plus to mean time.)
" l81°25' 30"
LONGITUDE.
105
348. In the same example the equation of equal altitudes may be found by the less exact method
heretofore given (art. 324), as follows:
Change in declination between sights = H. D. X Elapsed time = 51'''.10 X IS*".! = 925^''.
Change in altitude due to 100'^ declination (Tab. 25) = + 53^^
h' = +
V = +
53 X925,
100 X 60
2''53'"20«-
= + 8M9.
2" 51"' 40^ ^ ^ 100' ,
90° 00^ - - 89° 20^ ' 40''
Eq. eq. alt. = + 8.19 X 2'.5 = i 20'.5.
: + 2'.5.
DETERMINATION AT SEA.
349. The Time Sight. — The method of determining longitude at sea which is employed almost to
the exclusion of all others is that of the lime sight, sometimes called the chronometer method. The altitude
of the body above the sea horizon is measured with a sextant and the chronometer time noted; the
hour angle of the body is then found by the process described in article 316, Chapter XI.
If the sun is observed, the hour angle is equal to the local apparent time; the Greenwich apparent
time may be determined by applying the equation of time to the Greenwich mean time as shown by the
chronometer; the longitude is then equal to the difference between the local and the Greenwich appar-
ent times, being east when the local time is the later, and west when it is the earlier of the two.
If any other celestial body is employed, the hour angle from the local meridian, found from the
sight, is compared with the hour angle from the Greenwich meridian to obtain the longitude; the
Greenwich hour angle is found by converting the Greenwich mean time into Greenwich sidereal time
in the usual manner, and then taking the difference between the latter and the right ascension of the
body, the remainder being marked east or west, according as the (xreenwich sidereal time is the lesser
or greater of the two quantities; and as the local hour angle may be marked east or west according to
the side of the meridian upon which it was observed, the name of the longitude will be indicated in
combining the (juantities.
350. As has been stated, the most favorable position of the celestial body for tinding the hour
angle from its altitude is when nearest the prime vertical, provided the altitude is not so small as to be
seriously affected by refraction.
351. In determining the longitude at sea by this method, it is necessary to employ the latitude
by account. This is seldom exactly correct, and a chance of error is therefore introduced in the result-
ing hour angle; the magnitude of such an error depends upon the position of the body relatively to the
observer. The employment of the Sumner line, which is to be explained in a later chapter, insures the
navigator against being misled from this cause, and its importance is to be estimated accordingly.
Example: At sea, May 18, 1879, a. m.; Lat. 41° 33' N.; Long. 33° 30' W., by D. K., the following
altitudes of the sun's lower limb were observed, and times noted by a watch compared with the Green-
wich chronometer. Chro. corr., -f 4'" 59''.2; I. C, — 30^'; height of the eye, 23 feet; C- W, 2" 17'" 06".
Required the true longitude.
Eq. t., 3"' 47 -.68
VV. T.,
7"
20^15'
20 47
21 14
-h
A.
A.
Obs. alt. 0
Mean,
Corp.,
h,
.S. D.,
dip,
p. A r.,
I.e.,
Corr.,
29°
41
70
, 29° 35'
41
46
30"
20
10
Dec,
H. D
G. M.
Corr.,
Dec,
P,
19° 32'
01".S X.
+
T., -
33".09
2h.3
Mean,
C-W,
7
+ 2
20
17
4.5.3
06
29
+
41
9
00
05
19° 30'
76". 1
16"
46" N.
Ohro. t.,
C. C,
9
+
37
4
51.3
59.2
29
50
05
+
+
50'
33
29
1.5'
51"
G. M. T.,
Eq. t.,
17'>, 21
+
42
3
50.5
47.9
70° 29'
sec
cosec
cos
sin
sin i t
14"
4'
1
0
42"
34
30
G. A. T.,
21
46
38.4
h
L
P
8
S-
G.
L.
6
46
9'
05''
00
14
05"
.12588
.02569
2)141
70
41
52
56
06
19
09
04
9.51406
9.81782
T. 21^
T. 19
46™
32
38'
07
2)19.48345
9.74172
H. D., - 0«.09
G. M.T., - 2';.3
Corr., + 0".21
Eq. t., 3">47».9
{Plun to mean time.)
Long. {32: 14; ^i;}w.
106 LONGITUDE.
Example: At sea, April 16, 1879, p. m., in T.at. 11° 47' S., Long. 0° 20' E., by D. R., observed au
altitude of the star Aldebaran, west of the meridian, 23° 13' 20"; chronometer time, e*" 56'" 32"; chro-
nometer fast of G. M. T., 2"' 27"; I. C. —2' 00"; height of eye, 26 feet. What was the longitude?
Chro. t., 6" 56'" 32"
C. C, - 2 27
«
G. M. T., 6 54 05
R. A. M. S., +1 37 01.9
Red. (Tab. 9),+ 1 08.0
G. S. T., 8 32 14.9
R. A. *, 4 28 59. 6
Obs.alt.*,
23° 13' 20"
R. A. 5+:, 4" 28°' 59^6
Corr.,
- 9 16
Dec, 16° 15' 59" IS
'',
23 04 04
p, 106° 15' 59"
I.e.,
- 2' 00"
dip.
- 5 00
ref.,
- 2 16
H.A.fromGr., 4 03 15 W.
Corr., - 9 16
/( 23° 04' 04"
L 11 47 00 sec .00925
p 106 15 59 cosec .01774
2)141 07 03
s 70 33 32 cos 9.52223
s—h Al 29 28 sin 9.86757
2)19.41679
Gr.H.A. 4'' 03'" 15^ W.
H. A. 4 05 50 W. sin \ t 9. 70839
rO" 02™ 35n,
.ong. Iqo 38, 45,/|i
Example: At sea, April 17, 1879, a. m., in Lat. 25° 12' S., Long. 31° 32' W., by D. R., observed an
altitude of the planet Jupiter, east of the meridian, 45° 40'; watch time, 5*' 48"" 02'; C — W, 2" 05"" 42';
C. C, +2'» 18^; I. C, +1' 30"; height of eye, 18 feet. Required the longitude.
W. T., 5h 48°> 02- Obs. alt. *,
C— \V, 2 05 42 Corr.,
Chro. t., 7 53 44 /(,
C.C, + 2 18
G.M.T.,16«, 19 56 02
R. A. M.S., OS +1 37 01.9
Red. (Tab. 9), + 3 16.5
I.e.,
dip,
ref.,
45°
40'
3
00"
36
45
36
24
+
1'
30"
-
4'
0
09"
57
_
5
06
R. A. (17'
10''),
221' 27°
>19».0
Dec. (mOk),
H.D.,
G.M.T.,
Corr..
Dec,
P,
, 10° 36' 28".l S.
H.D.,
G.M.T.,
Corr..
+
1».8
4t'.l
7'. 4
+
10".0
4«'.l
41".
R.A.,
22h 27"
' 11^6
10° 37'
■ 09" S.
79° 22'
51"
G.S.T.,
21 36 20.4
22 27 11.6
Corr.,
h
L
P
8
8—
Gr
H.
h
.H
A.
- 3' 36"
45° 36' 24"
25 12 00
79 22 51
sec
cosec
cos
sin
sin J /
H.A.fromGr.,
0 50 51 E.
. 04343
.00750
2)150 11 15
75 05 38
29 29 14
9.41032
9. 69217
\
. A. 0" 50'"51'E.
2 57 21 E.
2)19.15342
■ 9. 57671
T^.,„ / 2"06'"30nT^
Long. |3io37,3o//|W.
LONGITUDE. 107
Exami'lk: At sea, June 26, 1879, p. m., in Lat. 49° 50' N., Long. 6° 16' W., by account, observed an
altitude of the moon's lower limb 21° 18' 10", the body bearing east; chronometer time, 2" 26'" 58»;
chronometer slow of G. M. T., 42*; I. C., — 1' 45"; height "of eye, 22 feet. Find the longitude.
Chro. t, 2" 26-58 •
C. C, + 42
G.
M
. T.,
2
27
40
R.
A.
M. S.,
+ 6
16
57.5
E<
S.
(Tab. 9),
T.,
+
0
24.3
G.
8
45
01.8
R.
A.
^C-
11
38
39.3
H. A. from Gr., 2 53 37- E.
Ote. alt,
•i.
, alt
rab.
2)"
1
21° 18' 10"
R. A.,
M. D., +
No. min.,
Corr., +
R. A.,
Hor. par.,
sec
cosec
cos
sin
sin i t
llh 37'° 41'.96
Dec,
M. D.,
No. min.,
Corr.,
Dec. ,
P.
2° 35' 36".4 S.
S. D.,
Aug.,
+ 15' 59"
+ 6
2».07
27'". 7
15". 1
27°'. 7
+ 16 05
57'.34
_f 419".3
I 6' 59".3
2° 42' 36" S.
dip,
I.e.,
- 4' 36"
- 1 45
llh 38-" 39^.3
58' 35"
.19043
.00049
9.11923
9.93799
- 6 21
92° 42' 36"
1st corr.
+ 9' 44"
Approx,
p.&r. (1
21° 27' 54"
24), + 52 06
h
L
P
22 20 00
22° 20' 00"
49 50 00
92 42 36
8
s—h
164 52 36
82 26 18
60 06 18
Gr. H. .
H. A.
2" 53™ 37' E.
3 19 04 E.
2)19.24814
9.62407
Long.
0" 25- 27'-!^
6° 21' 45"/"^-
352. Equal Altitudes. — The method of finding the longitude at sea by observation of equal alti-
tude.'! of a heavenly body is one that may be conveniently employed when applicable, though the limits
of apj)licability are narrow.
If, on board a vessel which is either stationary in position or moving at a uniform rate of speed in a
true east or west direction, equal altitudes of the sun, a planet, or a star be observed before and after
transit, and the times noted by chronometer or watch, the interval from meridian being not greater than
ten minutes of time and the altitude not less than 75°, the mean of the times will be the time (by the
chronometer or watch used) of the meridian passage of the body; from this may be found the Green-
wich mean time of transit and thence the longitude.
If (the limits of time and altitude remaining as stated) observations be taken when the body bears
not less than 80° from the meridian, the time of meridian passage may with accurracy be regarded as
equal to the mean of the times of observation, no matter what course may have been steered by tb<
vessel in the interval.
But if the azimuth of the body is less than 80° from the north or south point of the horizon the
method is not available for vessels making a material amount of northing or southing; and if the hour
angle is greater than 10™ or the altitude less than 75°, it can not be accurately employed by any vessel,
no matter what course is steered. The navigator .«hould not yield to the temptation offered by the
simplicity of this method to follow it beyond the limits within which it may properly be considered
to apply.
353. To deduce the longitude by this method take the mean of the watch times before and after
transit, which will give the watch time of transit; correct this watch time in the usual manner for
C— W and chronometer correction, from which is derived the Greenwich mean time of transit.
In the case of the sun, apply to the Greenwich mean time the equation of time, giving it its sign of
application to mean time; the result is the Greenwich apparent time of transit, which is equal to the
longitude if the latter is west, or to 24'' mhiii.^ the longitude if east.
For other bodies, convert Greenwich mean time into Greenwich sidereal time by the usual method;
the body being on the meridian, the local sidereal time is equal to the body's right ascension; the
difference between Greenwich and local sidereal times is the longitude — east if the local time is greater,
and west if it is less.
108 LONGITUDE.
Example: April 2, 1879, in Lat. 3° 30' X., Long. 86° 00' E., by D. R., observed equal altitudes of
Q before and afternoon, using same sextant and same height of eve. Watch: a. m.. 11'' 52°' 37"; p.m.,
12" 07"" 22"; C - W, 6" 17" 48'; C. C, + 2™ 32'. Vessel steering west' between sights. Required the longi-
tude at noon.
W. T., A. M., 11" 52-" 37» Eq. t., 3"' 42\5
W. T., P. M., 12 07 22
« H. D., - 0^.75
G. M.T., - 5".7
W. T.,L. A.,noon, 11 59 59.5 Corr., + 4».3
C-W,
Eq. t., 3'" 46^8
Chro. t., L. A.,noon, 6 17 47.5 ( /S'u6<rad from mcaji time.)
c. c, ~ -
G. M. T., L. A., noon, 1 J,
Eq. t,
G. A. T.,L. A., noon,
T 4. A f 5" 43-" 27" ) r?
Longitude, | g^o ^y 45// 1 E.
Example: August 6, 1879, p. m., in Lat. 25° 55' S., by obs., and Long. 36° 58' W., by account,
observed equal altitudes of the star Antares, the chronometer times before and after passage being
gh 42m 38s and 10*" 00'" 26', and the true azimuths S. 81° E. and S. 81° W., respectively; chro. fast of
G, M. T., 1'" 27". The ship was steaming on a course SSW. What was the longitude?
Chro. time before, 9*' 42"' 38"
Chro. time after, 10 00 26
Chro. time passage,
C. C,
G. M. T. passage,
R. A. M. S.,
Red. (Tab. 9),
2)23
59
59
11
+ 6
59
17
59.5
48
6
17
2
47.5
32
18
20
3
19.5
46.8
18
16
33
G. S. T. passage,
L. 8. T. passage (R. A
Longitude, {gfo o|/' ^^,/}w.
2)19 43
04
9 51
- 1
32
27
9 50
+ 8 58
+ 1
05
36.3
36.9
18 50
, 16 22
18.2
03.4
AZIMUTH. 109
chaptp:r XIV.
AZIMUTH.
354. The azimuth of a body has been defined (art. 223, Chap. VII) as the arc of the horizon
interceptea between the meridian and the vertical circle passing through the body; and the amplitude
(art. 224) as the arc measured between the position of the body when its true altitude i.s zero and the
east or west point of the horizon. The amplitude is measured from the east point at rising and the west
point at setting, and, if added to or subtracted from 90°, will agree with the azimuth of the body when
in the true horizon. The azimuth is usually measured from the north point of the horizon in north
latitude, and from the south point in south latitude, through 180° to the east or west; thus, if a body
bore N. by E., its azimuth would l)e named N. 1^° E. in north, or S. 168J° PI in south latitude.
The determination of the azimuth of a celestial body is an operation of frequent necessity. At
sea, the comparison of the true bearing with a bearing by compass affords the only means of ascertain-
ing the error of the compass due to variation and deviation; on shore, the azimuth is required in order
to furnish a knowledge of the variation, and is further essential in all surveying operations, the true
direction of the base line being thus obtained.
355. There are various methods of obtaining the true azimuth of a celestial body, which will be
described as follows: ('/) Amplitudes, (h) Time Azimuths, (c) Altitude Azimuths, (d) Time and Altitude
Azimidlis. A further method, by means of the Sumner line, will be explained later (Chap. XV).
Still another operation jjertains to this subject, namely: {e) The determination of the Tme Bearing of a
Terrestrial Object.
AMPLITUDES.
356. The method of obtaining the compass error by amplitudes consists in observing the compass
bearing of the sun or other celestial body when its center is in the true horizon, the true bearing, under
such conditions, being obtained by a short calculation. Since the true horizon is not marked by any
visible line (differing as it does from the visible horizon by reason of the effects of refraction, parallax,
and dip), allowance may be made for the difference by an estimate of the eye, or else the observation
may be made in the visible horizon and a correction applied.
357. When the center of the sun is at a distance above the horizon equal to its own diameter it
is almost exactly in the true horizon; at such a time, note its bearing by compass, and also note (as in
all observations for determining compass error) the ship's head by compass, and the angle and direction
of the ship's heel.
Or, note the bearing at the instant at which the center of the body is in the visible horizon; in the
case of the sun and moon, the correct bearing at that time mav be most accurately ascertained by taking
the mean of the bearings when the upper and the lower limbs of the disk are just appearing or disap-
pearing.
35§. To find the true amplitude hij computation there are given the latitude, I^, and declination, d.
The quantities are connected by the fornuila,
sin Amp. =sec L sin d,
from a solution of which the amplitude is obtained.
To find the true amplitude hy inspection enter Table 39 with the declination at the top and the lati-
tude in the side column; under the former and opposite the latter will be given the true amplitude.
To obtain accurate results, interpolate for minutes of latitude and declination.
To reduce tJte observed atnplitude when taken in the visilile horizon to what it would have been if
taken in the true horizon, enter Table 40 with the latitude and declination to the nearest degree and
apply the correction there found to the observed amplitude; the result will be the corrected amplitude
by compass, which, l)y comjiarison with the true amplitude, gives the compass error. When the body
observed is the sun, a star, or a ])lanet, apply the correction, at rising in north latitude or at setting in
south latitude, to the right, and at setting in north latitude or at rising in south latitude, to the left.
For the moon, apjjly half the correction in a contrary direction.
Example: At sea, in Lat. 11° 29' N., the observed bearing of the sun, at the time of rising when its
center was estimated to be one diameter above the visible horizon, was E. 31° N. ; corrected declination
22° 32' N. Required the compass error.
By computation. By inspection ( Table S9).
L 11° 29^ sec .00878 L, 11°.5N.1t, ., ooo a at
d 22 32 sin 9. 58345 d, 22 . 5 N.} Trueamp. E. 23°. 0 N.
Obsd. amp. E. 31 .ON.
True amp. E. 23° 01' N. sin 9. 59223
Obsd. amp. E. 31 00 N. Error, 8°. 0 E.
Error, 7° 59' E.
110 AZIMUTH.
Example: At sea, in Lat. 25° 03'' S., the observed bearing of Venus when in the visible horizon at
rising was E. 18° 30^ N., its declination being 21° 44' N. Kequired the compass error.
By compuiation. By inspection ( Table S9).
L 25° 03' sec .04290 L, 25°.0S.lrp v o.o i xt
d 2144. sin 9.56854 d, 31 . 7 N.[ ^^^ ^"^1^- >- 24°. 1 N.
Obsd. amp. E. 18°. 5 N. j ^ v 1 q c xr
True amp. E. 24° 08' N. sin 9.61144 Corr. (Tab. 40) 0. 3 left.J ''^'"P* '^'"P- ^^- ^^ ' ^ ^•
Comp.amp.E. 18 48 N.
Error, 5° 20' W.
Error, 5°. 3 W.
Example: At sea, in Lat. 40° 27' N., the mean of the observed bearings of the upper and lower
limbs of the moon when in contact with the visible horizon at setting was W. 17° S. ; declination,
21° 12' S. What was the error of the compass?
By computation. By inspection ( Table 39).
L 40° 27' sec .11863 L, "^"^"-^ ^-j True amn W 28° 4 S
d 21 12 sin 9.55826 d, 21 . 2 S.j ^™^ '""P- ^^•^^•'if'-
Obsd. amp. AV. 17°.0S. ) p ait i^ 7 c
True amp. W. 28° 22' S. sin 9.67689 Corr. (Tab. 40) 0.3 right. f <^omp.amp. w. lb ./ b.
Comp. amp.W. 16 42 S.
Error, 11°. 7 W.
Error, 11° 40' W.
TIME AZIMUTHS.
359. In this method are given the hour angle at time of observation, t, the polar distance, p, and
the latitude, L; to find the azimuth, Z.
Any celestial body bright enough to be observed with the azimuth circle may be employed for
observation; the conditions are, however, most favorable for solution when the altitude is low.
360. Take a bearing of the object, bisecting it if it has an appreciable disk, and note the time with
a watch of known error. Record, as usual, the ship's head by compass and the amount of heel. If
preferred, a series of bearings may l)e taken with their corresponding times, and the means taken.
361. First prepare the data as follows:
(a) Find the Greenwich time corresponding to the local time of observation.
{h) Take out the declination of the body from the Nautical Almanac; if the method of computation
is employed the polar distance and the co-latitude should be noted.
(c) Find the hour angle of the body by rules heretofore given.
This having been done, the true azimuth may be determined either by Time Azimuth Tables, by the
graphic method of an Azimuth Diagram, or by Solution of the Astronomical Triangle. Owing to the pos-
sibility of more expeditious working, either of the first-named two is to be considered preferable to the
last, and the navigator is recommended to supply himself with a copy of a book of Azimuth Tables, or
with an Azimuth Diagram ; an explanation of the method of use accompanies each of these.
362. To solve the triangle:
Let S = ^ sum of polar distance and co-Lat.
D = I difference of polar distance and co-Lat.
ht = h hour angle.
Z = true azimuth.
Then, tan X = sin D cosec S cot ^ t;
tan Y = cos D sec S cot ^ t;
Z = X + Y, or X ~ Y.
First Case. — If the half-sum of the polar distance and co-Lat. is less than 90° : take the sum of the
angles X and Y if the polar distance is greater than the co-Lat. ; take the difference if the polar distance
is less than the co-Lat.
Second Ca^e. — If the half-sum of the polar distance and co-Lat. is greater than 90°: always take the
difference of X and Y, which subtract from 180°, and the result will be the true azimuth.
In either case, mark the true azimuth N. or S. according to the latitude, and E. or W. according
to the hour angle. It may sometimes be convenient to use the supplement of the true*azimuth, by
subtracting it from 180° and reversing the prefix N. or S., in order to make it correspond to the compass
azimuth when the latter is less than 90°.
The cotangent of half the hour angle may be found from Tal)le 44 abreast the whole hour angle in
the column headed "Hour P. M."
AZIMUTH.
Ill
Examplk: December 3, 1879, a. m., in Lat. 30° 25' X., Long. 5" 25™ 42^ W., the observed bearing of
BUn's center was N. 135° 30' E., and the Greenwich mean time, December 3, 2^ 36'" IP. The corrected
decUnation of the sun was 22° 07' S.; the equation of time (additive to mean time), 10™ 03'. Required
the error of the compass.
G.M.T. (Dec.3),
Long.,
2h 36m lis
5 25 42
co-Lat., 59° 35'
p, 112 07
L.M.T. (Dec.2), 21 10 29
Eq.t, + 10 03
L.A.T., 21 20 32
t, 2" 39"' 28"
p+co-L, 171 42
S, 85 51
p-co-L, 52° 32' X+Y 139 03
D, 26 16
True azimuth, N. 139° 03' E.
Comp. azimuth, N. 135 30 E.
t
s
D
2" 39"'
85° 51'
26 16
50 44
88 19
28"
cot J( .44051
cosec .00114
sin 9.64596
cot it .44051
sec 1.14045
cos 9.95267
X
Y
tan .08761
tan 1.53363
Compass error,
3 33 E.
Example: April 9, 1879, in Lat. 2° 16' N., the observed bearing of the sun's center was N. 85° 15' E;
sun's hour angle, 3'' 44" 16% and its declination, 7° 38' N. Required the compass error.
co-Lat., 87°
p, 82
44'
22
t
S
D
X
Y
Y-X
True a;
Comp.
Com pa
3" 44"' 16"
85° 03'
2 41
5 03
87 22
cot it .27372
cosec .00162
sin 8. 67039
cot it
sec
cos
tan
. 27372
1. 06406
9. 99952
p+co-L, 170
06
tan 8. 94573
82° 19' E.
85 15 E.
8, .85
03
1. 33730
co-L—p, 5°
22'
:82 19
zimuth, N.
azimuth, N.
88 error,
D, 2
41
2 56 W.
Example: April 26, 1879, Lat. 16° 32' S., observed bearing of Venus 56° 00' W., its hour angle
being 4'' 27"' 31", and its declination 23° 12' N. What was the error of the compass?
co-Lat. ,
P,
73° 28'
113 12
t
S
D
X
Y
Y-
Z
-X
4h 27n>
93° 20'
19 52
27 16
87 40
31"
cot it . 18022
cosec . 00074
sin 9.53126
cot i I
sec
cos
tan
: .18022
1.23549
9. 97335
p+co-L,
186 40
tan 9. 71222
s,
93 20
. 39° 44'
1. 38906
p — co-L,
(iO 24
119° 36'
D,
19 52
True azimuth, S. 119° 36' W.
Comp. azimuth, S. 124 00 W,
4 24 W.
ALTITUDE AZIMUTHS.
363. This method is employed when the altitude of the body is observed at the same time as tiie
azimuth; in such a case the hour angle need not be known, though the time of observation should be
recorded with sufficient accuracy for the correction of the declination of the sun, moon, or a planet.
There ace given the altitude, /(, the polar distance, p, and the latitude, L; to find the azimuth, Z.
364. Take a bearing of the body by compass, bisecting it if the disk is of appreciable diameter, and
simultaneously measure the altitude; note the time approximately. Observe also the ship's heading
(by compass) and the heel.
Or a series of azimuths, with corresponding altitudes, may be observed, and the mean employed.
365. Calculate the true altitude and declination from the observed altitude and the time. Then
compute the true azimuth from the following formula:
cos i Z =v/ooH s cos (.s— />) sec L sec h,
in which s = i (/i + L -fp)- The resulting azimuth is to be reckoned from the north in north latitude
and from the south in south latitude.
112 AZIMUTH.
It may occur that the term (s— ; ) will have a negative value, but since the cosine of a negative angle
less than 90° is positive, the result will not be affected thereby.
Example: December 3, 1879, in Lat. 30° 25' N., the observed l)earing of the sun's center was
N. 135° 30' E., and its corrected altitude 24° 59'; the approximate G. M. T. was 2''.6, the declination at
that time being 22° 07' S. Required the compass error.
h
L
P
•24°
30
112
59'
25
07
sec
sec
. 04267
. 06431
2)167
31
s
8-p
83
-28
45
22
cos
cos
2
9. 03690
9. 94445
) 19. 08833
z
69
139
30
00
cos
9. 54416
True azimuth, N. 139° 00' E.
Comp. azimuth, N. 135 30 E.
Compass error, 3 30 E.
/ 39° 52'
(I 22 07
/( 24 59
sin 9. 80686
cos 9. 96681
sec .04267
Z S. 40° 56' E.
sin 9. 81634
TIME AND ALTITUDE AZIMUTHS.
366. AVhen, at the time of observing the compass bearing of a celestial body, the altitude is meas-
ured and the exact time noted, the true azimuth may be very expeditiously determined, a knowledge
of the latitude being unnecessary.
In view of the simplicity of the computation this method strongly commends itself to observers not
provided with an azimuth table or diagram.
SeT. The observation is identical with that of the altitude azimuth (art. 364), with the exception
that the times of observation must be exactly instead of approximately noted.
36§. Ascertain the declination of the body at time of sight, and correct the observed altitude; com-
I^ute the hour angle. We then have :
sin Z=sin t cos d sec h,
from which the azimuth may be found.
This method has a defect in that there is nothing to indicate whether the resulting azimuth is
measured from the north or the south point of the horizon; but as the approximate azimuth is always
known, cases are rare when the solution will be in question.
Example: December 3, 1879, in Lat. 30° 25' N., Long. 5*' 25™ 42* W., the observed bearing of the
sun's center was N. 135° 30' E. ; its altitude at the time was 24° 59'; hour angle, 2" 39™ 28» (39° 52'), and
declination 22° 07' S. Find the compass error. (See example under Altitude Azimuths and first
example under Time Azimuths. )
True azimuth, N. 139° 04' E.
Comp. azimuth, N. 135 30 E.
3 34 E.
TRUE BEARING OF A TERRESTRIAL OBJECT.
369. Thus far, sea observations for combined variation and deviation have been discussed, but if it
becomes necessary, as in surveying, to ascertain the Tnie Bearing of a Terrestriid Ofijed, or to find the
variation at a shore station, more accurate methods than the foregoing must be resorted to.
The most reliable method is that by an Asitronomical Bearing. This consists in finding the true
bearing of some well-defined object by taking the angle between it and the sun or other celestial body
with a sextant or a theodolite, and simultaneously noting the time by chronometer, or measuring the
altitude, or observing both time and altitude. It should always be noted whether the object is right
or left of the sun.
370. By Sexiant. — Measure the angular distance between the object and the sun's limb; and if there
is a second observer, measure the altitude of the sun at the same moment and note the time. In the
absence of an as.sistant, first measure the altitude of the sun; next, the angular distance between the
sun and the object; then, a second altitude of the sun, noting the time of each observation. Also
measure the altitude of the defined point above the sea or shore horizon.
By Tlieodolite. — This instrument is far more convenient than the sextant, for, being leveled, the
horizontal angle between the sun and the object is at once given, no matter what may be the altitudes of
the oljjects. In case the altitude of the sun is needed, it may be read accurately enough from the vertical
circle, although not as finely graduated as the limb of the sextant. The error in altitude nmst, how-
ever, be found by the level attached to the telescope, since it will usually be found to differ from the
levels of the horizontal circle. If, in directing the telescope to the sun, there is no colored eye-piece, an
image of the sun may be cast on a piece of white paper held at a little distance from the eye-piece, and
by adjusting the focus the shadow of the cross-wires will be seen.
It should be understood that any celestial body may be used as well as the sun, and there are, in
fact, certain advantages in the use of the stars; the sun is chosen for illustration, because it will usually
be found most convenient to emi)loy that body.
AZIMUTH.
113
371. Find the true azimuth of the celestial body by any one of the methods previously explained
in this chapter and applj' to it the azimuth difference, or horizontal angle between the celestial and the
terrestrial body, having regard to the direction of one from the other.
To find the azimuth difference from sextant observations, change the observed altitudes of the
bodies into apparent altitudes by correcting them for index error of the sextant, dip, and semidiameter;
change the observed angular distance into apparent angular distance, by correcting for index error and
semidiameter. Then if S = J (App. Dist. + App. Alt. Q -f- App. Alt. Object) , we have:
cos I Az. Diff. = v/sec App. Alt. 0 sec App. Alt. Object cos S cos (S — App. Dist. ),
whence the azimuth difference is deduced.
When the theodolite is used, the horizontal angle is given directly. If only one limb of the sun is
observed, it will be necessary^ to apply the semidiameter, but it is usual to eliminate this correction by
taking the mean of observations of both limbs.
Example: Decemlier 10, 1879, a. m., in Lat. 30° 25' 24'' N., Long. 81° 25' 24" W., made observa-
tions with a sextant and obtained the following data for finding the true bearing of a station:
Watch time, 11" 22-" 36' Obs. Ang. Dist. 0, 117° 07' Left.
C-W, 5 21 18 Obs. 2Q, 71° 37' 20"
Chro. corr., + 2 16 Obs. alt. Station, 20'
I. C, zero.
Dec. S., 22° 56' 27"
Eq. t., + 7°' 00^
S. D., 16' 17"
Required the true bearing of the object.
2 0,
W. T.,
C-W,
Chro. t.,
C. C,
G.M.T.,Dec. 10,
Eq. t.,
G. A. T.,
Long.,
L. A. T.,
11" 22"' 36'
5 21 18
4 43
+ 2
54
16
4 46
-]-' 7
10
00
4 53
- 5 25
10
42
23 27
28
S. D.
71° 37' 20"
35 48 40
16 17
8° 08' 00"
22 56 27
36 03 37
App. Alt., 36 04 57
;). &r., — 1 13
,/ S. 9° 17' E.
IN. 170 43 E.
sin 9.15069
cos 9.96422
sec .09239
sin 9.20730
36 03 44
t,
fO" 32"'
32"
\8°08' 00"
Obs. Ang. Dist.,
117° 07' 00"
App. Dist.
117° 23'
True bearing 0, N. 170° 43' E.
0'sS. D.,
+ 16 17
App. Alt. 0
36 05
sec 0.092.50
Az. Diff., 125 00 Left.
App. Alt. Object
20
2)153 48
sec 0.00001
Api>. Ang. Dist.,
117 23 17
True bearing object, X. 45° 43' E.
S
76 54
cos 9.35536
S — App. Dist.
-40 29
cos 9.88115
2)19.32902
k Az. Diff.
62° 30'
cos 9.6&151
Az. Diflf.
125 00
Example: Same date and place and same objects as in the preceding example; measurement made
with a theodolite, angular distance C{), 123° 17'; object left of sun. AVatcli time, ll"" 16"" 34''.5; watch slow
of L. A. T., 4"' 53^5. Dec. 0, 22° 56' S. Required the true bearing.
W.T., ll''16"'34\5
W. slow, + 4 53.5
L. A. T., 23 21 28 .0
t, 0 38 32
co-Lat., 59° .35'
/>, 112 56
p-i
- co-L,
- co-L,
172
31
S,
86
15
P-
53
21
t
S
D
0" 38"'
86° 15'
26 41
79° 24'
89 39
32»
cot h t 1.07435
cosec .00093
sin 9.65230
cot J<
sec
cos
tan
1.07435
1.18440
9.95110
X
tan .72758
Y
2.20985
X + Y169 03
D,
26 41
True bearing 0,
Az. Diff.,
N. 169° 03' E.
123 17 Left.
Trtie bearing object, X. 45 46 E.
22489—03-
114
THE SUMNEE LINE.
CHAPTER XV.
THE SUMNEE LINE.
DESCRIPTION OF THE LINE.
372. The method of navigation involving the use of the Sumner Hue takes its name from Capt.
Thomas H. Sumner, an American shipmaster, who discovered it and published it to the world. As a
proof of its value, the incident which led to its discovery may be related:
" Having sailed from Charleston, S. C, 25th November, 1837, bound for Greenock, a series of heavy
gales from the westward promised a quick passage; after pansing the Azores the wind prevailed from
the southward, with thick weather; after passing .longitude 21° W. no observation was had vmtil near
the land, but soundings were had not far, as was supposed, from the bank. The weather was now more
boisterous, and very thick, and the wind still southerly; arriving about midnight, ITth December,
within 40 miles, by dead reckoning, of Tuskar light, the wind hauled SE. true, making the Irish coast
a lee shore; the ship was then kept close to the wind and several tacks made to preserve her position
as nearly as possible until daylight, when, nothing being in sight, she was kept on ENE. under short
sail with heavy gales. At about 10 a. m. an altitude of the sun was observed, and the chronometer time
noted; but, having run so far without oliservation, it was plain the latitude by dead reckoning was liable
to error and could not be entirely relied upon."
The longitude by chronometer was determined, using this uncertain latitude, and it was found to
be 15' E. of the position by dead reckoning; a second latitude was then assumed 10' north of that l)y
dead reckoning, and toward the danger, giving a position 27 miles ENPl of the former position; a third
latitude was assumed 10' farther north, and still toward the danger, giving a third position ENE. of the
second 27 miles. Upon plotting these three positions on the chart, they were seen to be in a straight
line, and this line passed through Smalls light.
" It then at once appeared that the observed altitude must have happened at all the three i>oints
and at Smalls light and at the ship at the same instant."
Then followed the conclusion that, although the absolute position of the ship was uncertain,' she
must be somewhere on that line. The ship was kept on the course EN?]., and in less than an hour
Smalls light was made, bearing ENE. ^ E. and close aboard.
The latitude by dead reckoning was found to be 8' in error, and if the ]wsition given by that latitude
had been assumed "correct the error Avould have been 8 miles too far S. and 81' 30" of longitude too far
W., and the result to the ship might have been disastrous had this wrong position been adopted. This
represents one of the ijractical applications of the Sumner line.
The properf.es of the line thus found will now be explained.
373. C'iRCLKs OF EQr.\L Altitude. — In figure 43, if EE'E" represent the earth projected upon the
horizon of a point A, and if it be assumed that, at some particular instant of time, a celestial body is in
the zenith of that point, then the true altitude of
the body as observed at A will be 90°. In such a
case the great circle EE'E", which forms the hori-
zon of A, will divide the earth into two hemi-
spheres, and from any point on the surface of one
of those hemispheres the body will be visible, while
over the whole of the other hemisphere it will be
invisible. The great circle EE'E", from the fact
of its marking the limit of illumination of the botly,
is termed the circle of illniiiuuition, and from any
point on its circumference the true altitude of the
center of the body will be zero. If, now, we con-
sider any si'nall circle of the sphere, BB'B", CC'C",
DD'D", whose plane is parallel to the plane of the
circle of illumination and which lies within the
hemisphere throughout which the body is visible,
it will be apparent that the true altitude of the
body at any point of one of these circles is equal
to its true altitude at any otiier point of the same
circle; thus, the altitude of the body at B is equal
to its altitude at B' or B", and its altitude at D is
the same as at D' or D".
It therefore follows that at any instant of time
there is a series of positions on the earth at wliich
a celestial bodv appears at the same given altitude,
and these positions lie in the circumference of a
circle described upon the earth's surface whose
center is at that position which has the body in the zenith, and whose radius depends upon the zenith
distance, or — what is the same thing — upon the altitude. Such circles are termed circles of etjnal altittuk.
Fig. 43.
THE SUMNER LINE. 115
374. The data for an astronomical s-i^ht comprise merely the time, declination, and altitude. The
first two fix the position of the body and may be regarded a^ giving the latitude and longitude of that
point on the earth in whose zenith thel)ody is found; the zenith distance (the complement of the altitude)
indicates the distance of the observer's zenith from that point; but there is nothing to show at which
of the numerous positions fulfilling the required conditions the observation may have been taken. A
number of navigators may measure the same altitude of a l)ody at the same instant of time, at places
thousands of miles apart;' and each proceeds to work out his position with identical data, so far as this
eight is concerned. It is therefore clear that a single observation is not enough, in itself, to locate the
point occupied by the observer, and it becomes necessary, in order to fix the position, to employ a
second circle, which may be either that of another celestial body or that of the same body given by an
observation when it is in the zenith of some other point than when first taken; knowing that the point
of observation lies upon each of two circles, it is only possible that it can be at one of their two points
of intersection ; and since the position of the ship is
always known within fairly close limits, it is easy to
choose the proper one of the two. Figure 44 shows
the plotting of observations of two bodies vertically
over the points A and A' upon the earth, the zenith
distances corresponding respectively to the radii A()
and A^O.
375. The Sumxer Line. — In practice, under
the conditions existing at sea, it is never necessary
to determine the whole of a circle of equal altitude,
as a very small portion of it will suffice for the pur-
poses of navigation; the position is always known
within a distance which will seldom exceed thirty
miles under the most unfavorable conditions, and
which is usually very much less; in the narrow linuts
thus required, the arc of the circle will practically
coincide with the tangent at its middle point, and
may be regarded as a straight line. Such a line, pj^. 44
comprising so much of the circle of etjual altitude as
covers the probable limits of po.«ition of the ol)Ferver, is called a Sumner line or Lii^e of position.
376. Since the direction of a circle at any point — that is, the direction of the tangent — must be
perpendicular to the radius at tliat point, it follows that the Sumner line always lies in a direction at
right angles to that in which the body bears from the oliserver. Thus, in figure 44, it may be seen that
m n/ an(l n 1/, the extended Sunmer lines corresponding to the Ijodies at A and A^, are respectively
perpendiculur to the bearings of the bodies OA and OA''. This fact has a most important application
m the employment of the Sumner line.
377. I'sEs OK THE SiMXER LiNE. — The Sumner line is valuable because it gives to the navigator'
a knowledge of all of the probable positions of his vessel, while a sight worked with a single assumed
latitude or lorgitude gives but one of tlie probable positions; it must be recognized that, in the nature
of things, an error in the assumed coordinate will almost invariably exist, and its possible effect should
betaken into consideration; the line of position reveals the difference of longitude due to an error in
the latitude, or the reverse.
Since the Sumner line is at right angles to the bearing, it may be seen that when the body bears
east or west — that is, when it is on the prime vertical — the resulting line runs north and south, coincid-
ing with a meridian; if, in this case, two latitudes are assumed, the deduced longitudes will be the same.
When the body bears north or south, or is on the meridian, the line runs east and west and becomes
identical with a parallel of latitude; in such a case, two assumed longitudes will give the same latitude.
Any intermediate bearing gives a Sunnier line inclined to both meridians and parallels; if the line
agrees in direction more nearly with the meridian, latitude should generally be assumed and the longi-
tude worked; if it is nearer a parallel, the reverse course is usually preferable. The values of the
assumed coordinates may vary from 10' to 1°, according to circumstances.
37S. Tlie greatest l)enelit to be derived from the Sumner method is when two lines are worked
and their intersections found. The two lines may be given liy different bodies, which is generally
preferable, or two different lines may be obtained from the same IkhIv from observations taken at
different times. The position given by the intersection of two lines is more accurate the more nearly
the lines are at right angles to each other, as an error in one line thus produces less effect upon the
result. When two observations of the same body are taken, the i)osition of the ship at the time of first
eight must be brought forward to that at the second in considering the intersection; if, for example, a
certain line is determined, and the ship then runs NW. 27 miles, it is evident that her new position is
on a line jiarallel with the first and 27 miles to the NW. of it; a second line being obtained, the inter-
section of this with the first line, as corrected for the run, gives the ship's position.
Besides the employment of two lines for intersections with each other, a single line may be made
to serve various useful purposes for the navigator. These are described in article 400, Chapter XVI.
METHODS OF DETERMINATION.
379. Any line may be defined in either of two way^ — by two of its points, or by one point and the
direction. Tliere are thus two methods by which a Sumner line may be determined:
(a) Assume two values of one coordinate and find the corresponding values of the other. Two
values of the latitude may be assumed and the longitudes determined, as was done by Captain Sumner
on the occasion that led to the discovery of the method; or else two values of the longitude may be
assumed and the latitudes determined. Two points are fixed in this way, and the line joining them is
the line of position.
(6) Assume either one latitude or one longitude and determine the corresponding coordinate. This
gives one point of the line. The azimuth of the body is then ascertained, and a line is drawn through
116
THE SUMNER LINE.
the determined point at right angles to the direction in which the body bore at the time of sight. This
will be the line of position.
3§0. It follows that if the Sumner line be located by the first method and its direction thus
defined, the azimuth of the observed body maybe determined by finding the angle made by the line
with the meridian and adding or substracting 90°.
Example: At sea April 17, 1879, A. M., in Lat. 25° 12' S., Long. 31° 32' W., by D. R., observed an
altitude of the planet Jupiter, east of the meridian, 45° 40'; watch time, 5" 48'° 02'; C — W, 2'> 05'" 42»;
C. C, + 2™ 18'; I. C, -t- r 30"; height of eye, 18 feet. Required the Sumner line.
From a solution of this same problem'for a single longitude (art. 351, Chap. XIII), the following
were found: H. A. from Gr., 0"50'" 51' E.; /*, 45° 36' 24"; ]>, 79° 22' 51". Assume values of Lat. 25° 02'
and 25° 22' S.
h
P
45'
25
36' 24"
02 00
22 51
sec
cosec
.04278
.00750
Lj 25° 22' 00"
sec
cosec
.04403
.00750
Gr. H
H. A
2)150
01
15
cos 9.41282
sin 9.69105
82 75
.tj— 7t 29
10 38
34 14
«! 75
81— /t29
00
24
38
14
cos 9.40794
sin 9.69328
i. A. 0"
2
50"
57
• 51' E.
30 E.
2)19.15415
sin i ^ 9.57708
Gr. H. A. 0"
H. A.., 2
50"' 51'
57 12
2)19.15275
sin 1 1, 9.57638
Lony
/ 2" 06'"39'\
•1 \31° 39' 45"/
^W.
, r 2" 06™21'\„.
Lon^-^ \31° 35' 15"r^
It should be observed that s.^ and s-^ — h can be obtained, respectively, from ^-j and s^—h by adding
half the difference between Lj and L,^; also that log cosec p is the same for both hour angles. The
determination of the second hour angle is thus considerably simplified.
A comparison of these results with those obtained by the solution with a single latitude shows that
the hour angle, and consequently the longitude, corresponding to the latitude 25° 12' S. are the means
of those corresponding to the latitudes here used; and therefore that the assumption that the Sumner
line is a straight line is accurate.
The line of the same sight might also have been found as follows:
Working with the single latitude 25° 12' S., it was found that the corresponding longitude was
31° 37' 30" \V. Now by referring to an azimuth table or azimuth diagram, the azimuth corresponding
to Lat., 25°. 2 8., Dec, i0°.6 S., H. A., 2^ 57'". 3 E. is S. 101° 24' E.; therefore the Sumner line extends
S. 11° 24' E.
The line may therefore be defined in either of two ways, thus:
A
Or,
/25° 02' 00" S.
H31 39 45 W.
25° 12' 00" S.
31 37 30 W.
^{:
. /25° 22' 00" S.
^^ \31 35 15 W.
Line runs S. 11° 24' E.
By inspection of the coordinates of Aj and A^ it may l)e seen that —
+ 20' diff. lat. makes — 4'.5 diff. long.; or,
+ 20 miles diff. lat. makes — 4.1 miles departure.
Therefore by reference to Table 2 it appears that the line runs about S. 11^° E., and the azimuth
of the bodv is S.' 101^" E. ; thus the results obtained by the two methods agree.
Example: At sea, Mav 18, 1879, A. M., Lat. 41° 33' N., Long. 33° 30' W., by D. R., the mean of a
series of observed altitudes of the sun's lower limb was 29° 35' 30"; the mean watch time, 7" 20"" 45'.3;
C. C., + 4'" 59'.2; I. C, — 30"; height of the eye, 23 feet; C — AV, 2^ 17'" 06'. Required the Sumner line.
From a solution of this same problem for a single longitude (art. 351, Chap. XIII) the following
were found: G. A. T., 21" 46'" 38'; h, 29° 50' 05"; p, 70° 29' 14". Assume values of the latitude 41° 03'
and 42° 03' X.
P
29° 50' 05"
41 03 00
70 29 14
sec
cosec
. 12255
. 02569
L,
42° 03' 00"
sec
cosec:
12927
. 02569
2)141 22 19
70 41 09
40 51 04
cos 9. 51950
sin 9. 81564
s-i 71
.*.,—/( 41
11
21
09
04
cos
sin
sin
9. 50852
9. 81999
21" 46™ 38'
2)19.48338
■
sin i /i 9. 74169
G. A.T. 21"
L. A.T.., 19
46"
32
'38' ,
06
2)19.48347
19 32 08
i <j 9. 74174
G. A. T.
21" 46™ 38'
L. A. T.,
19 32 08
Ix)ng.i|
2" 14" 30»\^
33° 37' 30"/^-
A.{
41° 03' 00" N.
33 37 30 W.
J r 2" 14"' 32' \,,r
l-ong.2 J33038/ 00"/^^ •
. /42° 03' 00" N.
^i'\33 38 00 W.
+ 60' diff. lat. makes + 0'.5 long.
+ 60 miles diff. lat. makes + 0.4 mile departure.
Line runs, X. ^ W. Azimuth, X. 89i° E.
THE SUMNER LINE.
117
The same sight worked with a single latitude, 41° 33' X., ais was <lone in tlie original example, with
azimuth taken from tables or diagram, gives:
. /41° 33' 00" N.
^133
133 37 45 W.
Azimuth, N. 89° 38' E.
Line runs, N. 0° 22' W.
This example illustrates the case in which an observation is taken practically on the prime vertical;
the azimuth shows the bearing to be within 0° 22' of true East, and the Sumner line is therefore within
U° 22' of the meridian; a variation of 30' in either direction from the dead reckoning latitude makes a
difference of only 15" in the longitude.
Example: May 28, 1879, in Lat. 6° 20' S. by account, Long. 30° 21' 30" W.; chro. time, 7'' 35'" 10";
observed altitude of moon's upper limb, 75° 33' 00", bearing north and east; I. C., — 3' 00"; height of
eye, 26 feet; chro. fast of (1. M. T., 1™ 37^5. Required the Sumner line.
From a solution of the same problem with a single longitude (art. 339, Chap. XII), the following
values were obtained: H. A. from Greenwich, 1" 35'" 07'' W.; h, 75° 23' 30"; d, 6° 41' 47" N. Assume
the longitudes 30° 10' and 30° 30' W.
Gr. H. A. 1" 35"' 07^ W.
Long., 2 00 40 W.
Gr. H. A. 1" 35"' 07"
lvong.2 2 02 00
<1
d
6^
6
75
6
13
' 23' 15"
41 47
23 30
44 17 N.
11 20 S.
, JO" 25'" 33'
^i\6°23' 15"
sec .00270
tan 9.06973
^2\6°
cosec .93324
sin 9.98573
sin 9.06942
26'" 53'
43' 15"
'^ > \.30
A /«°
^^H30
\
h
tan 9.07243
sec .00299
tan 9.06973
27' 03" S.
10 00 W.
9\
cos 9.98839
cosec .93324
sin 9.98573
sin 9.06972
Lat.,
d
1 fi
6°
6
75
6
13
27
43'
41
23
44
01
03 S.
15"
47
30
33
00
h
tan 9.07272
16' 27" S.
30 00 W.
¥.
cos 9.98869
Lat. J 6 16 27 S.
Working by the other method, and finding the azimuth, we have:
. / 6° 21' 14" S. T • V- ,.oo Av
130 21 30 W Lnie runs >. . b2° W.
It might be shown that the results check with each other, as in previous cases.
Example: At sea, July 12, 1879, in Lat. 50° N., Long. 40° W., observed circum-meridian altitude
of the sun's lower limb, the time by a chronometer regulated to Greenwich mean time being ^ 41'" 39";
chro. corr., — 2'" 30^; I. C, — 3' 0"; height of the eye, 15 feet. Find the Sumner line.
From the solution of the same problem for a single latitude (art. 338, Chap. XII) the following
values were obtained: G. A. T., 2" 33'" 50'; /;, 61° 57' 01"; d, 21° 59' 27" N.; a (Tab. 26), 2" .5.
Assume longitudes 39° 45' and 40° 15' W.
Gr. H. A.
Long. 1
2" 33" 50'
2 39 00
k
5 10
h
61°
+ .
57' 01"
1 06
Hx
61
58 07
2l
d
28
21
01 53 N.
59 27 N.
Gr. H.
Long. .
A. 2>'33'"50'
i -2 41 00
h
7 10
h
at./
61° 57' 01"
+ 2 08
H,
61 59 09
22
d
28 00 51
21 59 27
Li 50 01 20 N.
The line given by these coordinates is then :
. r50° 01'
'■^'\39 45
20" N.
00 AV.
■'{
50 00 18 N.
50° 00' 18" N.
40 15 00 W.
118 THE sumnp:r line.
This shows that the Sumner Hne lies so nearly in a due east-and-west direction that a difference of
longitude of 30' makes a difference of latitude of only 1''.
From an azimuth table or diagram, it is found that the azimuth of the sun corresponding to Lat. 50°
N. Dec. 22° N. and H. A. 6"' 10' E., is N. 177° E. Therefore, using the values given by the earlier
solution, the line is defined as follows:
50° OO' 5V' N. T • XT O-O 17
40 00 00 N. LmerunsN. 8/°E.
The direction of the line thus given and the one found from the double coordinates mav )>e shown
to agree as in examples before given.
FINDING THE INTERSECTION OF SUMNER LINES.
3§1. The intersection of Sumner lines may be found either graphically or by computation.
3S2. Graphic Methods. — Each line may be plotted upon the chart of the locality in which the
ship is being navigated and the intersection thus found. The details of the plotting will be obvious,
whether the line is defined by two of its points, or by one point and its direction. This plan will com-
mend itself especially when the vessel is near shore, as the chart in use will then jn-obably be one of
conveniently large scale, and it will be an advantage to see where the position falls with reference to
soundings and landmarks.
3§3. When clear of the land it is often inconvenient to follow this plan; a large scale chart may
not be at hand, it may not be desired to deface the chart with numerous lines, or the necessary space for
chart work may not be available. In such a case, the following method « is recommended, as it obviates
the disadvantages of the other.
To understand the principle of this method, suppose that the lines are defined ])y the latitude and
longitude of two points of each, and consider that they are plotted on a chart which is constructed upon
a sheet of elastic rubber. It i.s evident that if, while holding it fast in the direction of the meridians,
we stretch this rubber along the lines of the parallels in a uniform manner until the length of each
minute of longitude is made to equal a minute of latitude, the chart, while losing its accuracy as por-
traying actual conditions on the earth's surface, still correctly represents the jiositions of the various
points in terms of the new coordinates which have been created, namely, those in which a minute of
latitude is equal to a minute of longitude. Thus, if on the true chart a point is m minutes north and n
minutes east of another, on the stretched one it will still be vi minutes north and n minutes east, the
only difference being that the minutes of longitude will now be of a different length; and if on the orig-
inal chart the two Summer lines intersect at a point ?« minutes north and 7i minutes east (on the
original scale) of some definite point of one of the lines, the intersection on the stretched chart will lie
m minutes north and n minutes (of the new scale) to the east of the same point.
A stricter mathematical conception of the stretched chart and its properties may perhaps be
obtained by considering the chart of the locality to be projected (with the eye at the zenith) upon a
plane Avhich passes through one of the meridians and makes an angle with tbe plane of the horizon
which is equal to the latitude; each minute of longitude will then be increased by multiplying it by the
secant of the latitude, and thus becomes equal to a minute of latitude.
From a consideration of the properties of this hypothetical chart it may be seen that the following
rule may be laid down: If two or more Sumner lines be plotted by their latitude and longitude upon
any sheet of paper, using a scale whereon latitude and longitude are equal regardless of the latitude of
the locality, the intersection of those lines, measured by coordinates on the scale employed, correctly
represents the intersection of the lines as it would be measured upon a true chart.
It follows from this that we may plot Sumner lines upon any piece of paper, measuring the coordi-
nates with an ordinary scale ruler, and assigning any convenient length for the mile; the larger the
scale the more accurate will be the determination. Or, what is even more convenient, we may employ
"profile paper," whereon lines are ruled at right angles to each other and at equal distances apart, in
which case no scale ruler is needed.
One caution must be observed in using this method; all longitudes employed on the paper for any
purpose must be those of the scale, namely, one minute of longitude equals one minute of latitude.
For instance, if the two Sunmer lines be taken at different times, in bringing the first up to the iX)sition
of the second by the intermediate run, that run must be laid down to scale; that is, the easting or
westing must appear as so many minutes of longitude, not so many miles. To do this enter the traverse
table with course and distance run, and pick out latitude and departure; then, by means of the middle
latitude, convert departure into minutes of longitude and bring the first line to the second by laying off
so many minutes of latitude north or south, and so many of longitude east or west.
In the case where the Sumner is defined by one position and its line of direction, it is not correct to
lay down the angle to the meridian on the hypothetical chart, for all angles are distorted thereon. The
best way is to find another position on the line by assuming a second latitude ten or twenty miles
removed from that of the point given, entering the traverse tal)le with the angle that the line makes with
the meridian as a course, and abreast the latitude taking out the departure; (convert departure into differ-
ence of longitude, and plot the second point by its coordinates from the first.
Example: Let it be required to find the intersection, by each of the methods, of the following lines:
. /40° 00' N. . f40° 20' N.
^1163 15 W. ^463 07 W.
T./40 05 N. „r40 15 N.
^i\63 03 W. ^4^3 12 W.
1 Suggested by Lieut. G. W. Logan, U. 8. Navy.
THE SUMNER LINE.
119
Figure 45 shows the intersection, (1) by Mercator chart, (2) by scale, and (3) on profile paper,
as follows:
20'
f^
/
/ :
A,
III''
LrrA
1 1 1 1.| 1 III, y
20'
J 40"' >^
63° L5' 12' 10' err' 03' 63'<'"
1 -prtilft = .06in.cK
Fig. 45.
Ai,
y
: .:_ z t
: ---JL. -Z-- - -
23:__L
\ ': :
__ S_ -
;.;_::L.:i
: J I "
_ ::._ A z :^L--
:_::.::2 __ ...5,
:l 5:_-
"":::.:::::_;:
- -_ Z - --*L
::: :i:: _. .: '
zz-.A ±
^o'
10'
63'
iH>*
r40° 12' 8 N
Intersection :|g3- 09 ig W .
Suppose, in the example just given, the first line had been defined as follows: •
A|g^° 15^ W ^^"^ '■""^ ^'- ^''° ^•
To find a second coordinate bv which to plot it, proceed as follows:
In Table 2, for 17°: Lat. 20' X., Dep. 6.1 m. E. For Mid. Lat.: 40°, Dep.'6.1 m., diff. long. 8'.0 E.
Hence, as jjreviously given:
/40° 00' X.
''iteS 15 W
. /40° 20^ N.
^463 07 W.
3§4. Methods by Computation." — The finding of the intersection of two Sumner lines by compu-
tation may l)e divided into two cases:
Case I. When one line lies in a XP].-S'\V. direction, and the other in a XW.-SE. direction.
Case II. When l)oth lie in a XE.-.S\V., or both in a XW.-SE. direction.
Suppose, first, that the lines are defined by the latitude and longitude of two points of each, and for
the simplification of the problem consider the lines projected on a plane passing through one of the
meridians and making an angle with the i^lane of the horizon equal to the latitude, the properties of
which were explained under the graphic method, (art. 383); this saves the necessity ot converting
minutes of longitude into miles of departure before the solution and converting them back again after-
wards; as all points are thus projected in corresponding relative
J)08itions, the results are as exact as if the longer method be
oUowed of dealing with minutes of latitude and longitude of
unequal length.
3§5. Cfw I One line NE.-SW., and the other NW.-SE.—
Suppose the two lines, projected as described, are as shown in
figure 46, Aj A;^ and Bj Bj; for the present assume that the two
Soints, Aj and B,, have a common latitude. Drop the perpen-
icular PO from the intersection; then the latitude of the inter-
section will be a distance OP above the conmion latitude of Aj
and Bi, and its longitude will be a distance XyO to the right of
Ai and BjO to the left of Bi.
Find the angles <r and fi from the traverse table (Table 2),
they being taken out with the difference of latitude between the
two points of the same line in the column Lat. and the differ- A,'
ence of longitude in the column Dep. (Do not overlook the
fact that we are dealing now with the plane of projection and }!u.t. 46. ;
that a and (i are not the angles made by the Sumner line with
meridians on the earth's surface. ) The solution may now be accomplished by either of two methods:
(o) Observe that the case is the same as if a ship were steaming along the line A^ Bj and took the
first bearing of the point P when at A,, at an angle from the course equal to 90°— n-, and the second
bearing when at B,, at an angle from the course equal to 90°+/i, with an intervening run equal to the
difference of longitude Aj B,; or, she may be considered as steaming from Bj to Aj, in which case the
first angle is 90°—/? and the second 90°-r«. Picking out of Table 5 B, corresponding to the angles
given, the quantity in the second column, we shall have the ratio of the distance of passing abeam, OP,
to the distance Aj B,; multiply the difference of longitude by this ratio, and we shall have the actual
length of OP. Then entering the traverse table with this as a latitude and a as a course, we find in the
departure column the distance AjO by which the longitude of OP is defined; it is recommended also
to pick out BjO, using the angle fi, which affords a proof of the correctness of all work done after the
finding of a and f3.
««Suj?jrested by Lieut. G. W. Logan, r. S. Navy.
120
THE SUMNER LINE.
{b) The second method is to find by trial and error some latitude such that its departure correspond-
ing to a, plus its departure corresponding to fi, equals the difference of longitude Aj Bj; then the point
will be defined by the latitude, and by its longitude from Aj and Bj, the agreement of the longitude as
established from the different points furnishing a check upon the operation.
Example: Find the intersection of the following Sumner lines:
^^4 6 55.3 W.
/SO
L-A 7
50° 0(K N.
20.0 W.
+20^
+24.7
lat.
long.
'.{
49
40 N.
32.5 W.
B,{%
00 N.
11.3 W.
+20 lat.
—21.2 long.
Line runs NW.-SE.
(i-=51°.
Line runs NE.-SW.
/i=47°.
Longitude A^ B,=22
Fig. 47.
Hence, intersection:
First draw a rough sketch (fig. 47) to illustrate the direction
of coordinates.
Notice that A, is west of Bj. The line through Aj runs
NW.-SE. That through B„ NE.-SW. The intersection is
therefore south of both, east of Aj, and west of Bj.
(a) To solve by Table 5 B: First bearing (90°— a) =39°;
second bearing (90° -^/J) = 137°. Corresponding ratio, 0.43, mul-
tiplied by 22^8 = 9'. 8 lat. (The angles 90° - /i and 90°— a would
have given the same ratio, 0.43. ) Then (Table 2) with a = 51°,
lat. =9'.8, dep. =12M; and with /i = 47°, lat. =9^8, dep. =
10^5.
9^8 S. of lat. 49° 40' N. =49=
12 .1 E. of long. 6 55.3 W. = 6'
10 .5 W. of long. 6 32.5 W. = 6'
(b) To solve by Table 2:
Assuming lat y
Dep. for 51° 6.2
Dep. for 47° 5.3
Hence, intersection:
Sum
.11.5
9.7
8.5
18.2
30'
;° 43
;° 43.
10'
12.3
10.7
23.0
,2N.
0 YV. n^^*^^'
9'.9
12.2
10.6
22.8
9'.9 S.
12 .2 E.
10 .6 W.
of 49° 40'
of 6 55.3
of 6 32.5
= 49° 30'. 1.
= 6 43 .11
= 6 43 .1/
check.
It may be seen that the results by the two methods substantially agree.
396. Case II. Both lines XE.-SW., or both XW.-SE. — Consider the lines as drawn in figure 48, and
continue the assumption that Aj and B, have a common
latitude. The differences from the first case by both
methods simply involve a change of signs.
(o) If the ship is steaming from Aj toward B,, the
first angle from the keel line is 90° — a, and the second,
90° —/i] if steaming from Bi toward A,, the first angle is
90° + /i, and the second 90°^ a; in other words, either
add both angles to 90° or subtract both from 90° and
enter with the smaller angle as the first bearing.
{h ) It may be seen that 0 Aj ~ OBj = Aj Bj ; in other
words, to solve by the second method, the values must
be so found that the difference of the corresponding depar-
tures equals the difference of longitude, instead of their
sums, as before.
Fig. 48.
Example: Find the intersection of the Sumner lines defined V)elow;
i / 49° 30' N. . f 49° 50'
^U 5 24.8 W. -^n 5 21.5
T, /49 30 N. „ 149 50
■^H 5 25.8 W. ^4 4 52.1
Ai Bi=l'.0.
+20' lat.
—3.3 long.
+20 lat.
—33.7 long.
Line runs NE.-SW.
<r=9°.
Line runs NE.-SW.
/i=59°.
In this case (fig. 49) B, is west of A,, the lines
both run NE.-SW., and fi is the greater angle; there-
fore intersection lies to the north and east of both points.
(a) By Table 5 B: First course (90° + a) = 99°;
second course (90° + /3)= 149°; ratio 0.67X^.0 =
0'.7; or, first course (90° — /if) = 31°; second course
(90° — a) = 81°; ratio = 0.67, as before.
Fig. 49.
= 9°, lat. =0'.7, dep. =0'.l; and (i--
:59°, lat. =0'.7, dep. =1'.2.
THE SUMNER LINE.
121
Hence, intersection:
(b) By Table 2:
.7 N. of 49° 3(y N. =49° 30^7 N.
.1 E. of 5 24 .8 W. = 5 24
.2 E. of 5 25 .8 AV. = 5
6 w! } check.
Assuming lat 2^.0
Dep. for 9° 0.3
Dep. for 59° 3 .3
Difference 3.0
24.6
0^5 0^6
0.1
0.9
0.8
0.1
1 .1
1 .0
Hence, intersection:
0^.6 N. of 49° 30'
0 .1 E. of 5 24
1 .1 E. of 5 25
= 49° 30^6
;= 5 24.7
1= 5 24
- j- check.
387. In discussing these cases, we have assumed that there was a point of one Une which had a
common latitude with a point of the other line; this would be the case if two lines were worked from
time sights taken at the same time. It may occur, however, either that they have not a common lati-
tude, but do have a common longitude, as in the case of two lines
worked from <p' q/^ (latitude) sights taken at the same time; or that
they have neither a common latitude nor a common longitude, as
with one time sight and one
latitude sight, or with two
sights taken at different
times.
In case there is a com-
mon longitude (fig. 50),
which will be rather a rare
one, the problem is worked
with OP as a longitude co-
ordinate; the modification
of the other method will
B, suggest itself, the principal
change rendered necessary being due to the fact that the
angles from the course in Table 5 B will be complementary
to what they were before, as we are now dealing with angles
to the meridian instead of angles to the parallel.
When there is no common coordinate of either latitude
or longitude, the simplest way of solving is first to find some
point on one line which corresponds in latitude with one of
the points on the other line, then solve as before.
Thus, in figure 51, given A, A.^ and Bj B.^, find ix and p, and
thence the longitude of a point A3 corresponding to the difference of latitude between Aj and By on the
course a; then find intersection of A3 A.^ and Bj Bj in the usual way.
Example: Let it be required to find the intersection of Sumner lines as follows:
/ 25° 50^ S. +20' lat. Line runs SE.-NW.
•
\
%
\
<("
/A3
0
~^^/
a /
Fig. 51.
. / 25° 30^ S.
^H115 22 E.
T, / 25 15 S.
^M115 37 E.
*\115 40 E. +18 long. a=42°.
B,
25 35 S.
nil5 30 E.
-20 lat.
- 7 long.
Line runs NE.-SW.
/i=19°
Find where Bj B.^ crosses parallel 25° 30' S.
/i=19°, lat. = +15', dep. = — 5'.1. Hence, the line B3 Bj, becomes:
f 25° 30' S. ^ c _„, o Line runs NE.-SW.
Ii= 19°.
B.
=9'. 9
Ullo 31.9 E. '"^1 ^=*
The directions of the lines (fig. 52) require us to follow Case I. Aj is west of B3. The line through
, runs SE.-NW., and that through Bg.SW.-NE. Therefore, A o
A, runs bh^.-.n vv ., ana tnat tnrougn Ug, s vv .-> Ji. ineretore, /\
the intersection is south of Ai and B3, east of Aj, and west
ofBj.
(o) By Table 5 B. (90°-a)=48°, (90°4-/i)=109°. Ratio
0.81X9'.9=8'.0 lat.; a=42°, lat.=8'.0, dep.=7'.2. /i=19°;
lat. =8'.0, dep.=2'.7.
Hence, intersection:
(6) By Table 2:
8' S. of 25° 30' S. = 25° 38' S.
7.2 E. of 115 22 E.=115 29.2 E.\ , ,
2.7W.ofll5 31.9E.=115 29.2 E.r^^^'^"
Assuming lat 6' 8'
Dep. for 42° 5.5 7.2
Dep. for 19° 2.1 2.7
Sum 7.G 9.9
122
THE SUMNEE LINE.
Intersection:
8^ S. of 25° 30' = 25° 38'
7.2 E. of 115 22 =115 29.2\ , ,
2.7 W. of 115 31.9=115 29.2r"^"^-
3§§. The foUow^jpg is a summary of the method when lines are given by coordinates of two
points of each:
(a) By Tables B.
1. Write down hnes; find a and /?.
2. If there are no points which have a common
latitude, reduce one point of one line to latitude of
some given point of the other.
3. Write down difference of longitude.
4. Draw rough sketch to illustrate direction of
point of intersection.
5. Enter Table 5 B:
Case I, angles (90° - a) and (90° + /3) or (90° -
fi) and (90° + a).
Case II, angles (90° + a) and (90° + ft) or (90° —
fi) and (90° -a).
Take out ratio from second column, and multiply
by difference of longitude; this gives difference of
latitude of intersection from the common latitude.
6. Find departure corresponding respectively to
cc and ft with latitude; this gives differences, of
longitude to the point of intersection from the re-
spective points or common latitude.
(6) By Table 2.
1. Write down lines; find a and ft.
2. If there are no points which have a common
latitude, reduce one point of one line to latitude of
some given point of the other.
3. Write down difference of longitude.
4. Draw rough sketch to illustrate direction of
point of intersection.
5. Enter Table 2, at pages a and ft; find by trial
some latitude at which —
Case I, the sum of the corresponding departures
equals the total difference of longitude;
Case II, the difference of the corresponding de-
partures equals the total difference of longitude.
These give differences of latitude and longitude
to the point of intersection from the respective
points of common latitude.
3§9. If the lines, instead of being defined by coordinates of two points, are defined by the coordi-
nates of one point of each with its direction as deduced from the azimuth of the body, it will be better
not to consider the projection on the fictitious plane through the meridian, as there will then be no
advantage in so doing. In this case, consider the angles of the lines with the meridian, as given, a and
ft; reduce the difference of longitude Aj Bi to departure, and use this in miles instead of the Ai B, in
minutes; and when AjO and BjO are found, being in miles of departure, they must be reduced to min-
utes of longitude l)efore being applied to the longitude of A, and Bj.
Example: The Sumner lines of the last example being expressed by a single point and the direction,
as given below, find the intersection.
f 25° 40^
1115 31
B
ill
25 25 S.
115 33.5 E.
Line runs (a =) N. 39° W.
Line runs {ft =) N. 18° E.
First bring second line up to Lat. 25° 40^8. ft = 18°; lat. = + 15'; dep. = — 4.9 m. ; diff. long. =
— 5^.4; hence we have:
40' S.
28.1 E.
Line runs {ft = ) N. 18° E.
Fig. 53.
Intersection:
AB' = 2'.9 = 2.6 miles.
B' Ijeing west of A ( fig. 53) , and the lines through the two
points running respectively NE. and NW., the intersection is north
of both, east of B', and west of A.
(a) By Table 5 B. (90° - a) =51°; (90° +^) = 108°. Ratio
0.88 X 2.6 = 2'.3 lat. a = 39°, lat. = 2'.3, dep. = 1.8 m., diff. long. =
2.0. ft = 18°, lat. = 2'.3, dep. = 0.7 m., diff. long. = 0.8.
2'.3N. of 25° 40' S. = 25° 37'. 7 S.
2 .0 W. of 115 31 E. = 115 29 K-Lheck.
0 .8 E. of 115 28.1 E. = 115 28
(ft) By Table 2:
Assuminglat 1-4' 2' 2'.3
Dep. for 39° 3.2 1.6 1.9 = 2'.l
Dep.forl8° 1.3 0.7 0.7=0.8
Sum 4.5 2.3 2.6 = 2.9
Intersection:
= 25° 37' 7
2 .IW. of 115 31 =115 28:9|^heck.
2'.3 N. of 25° 40
2 .1 W. ol
0.8E. of 115 28.1 = 115 28
THE SUMNEE LINE.
123
The followinjj; Hiimmary gives the various steps when the lines are each given Ity tlie coordinates of
one point with the direction:
(«) By Tables B.
1. Write down lines as given.
2. If the points have not a common latitude,
reduce one point to latitude of the other.
3. Write down difference of longitude and con-
vert it to departure.
4. Draw rough sketch to illustrate direction of
point of intersection.
5. Enter Table 5 B:
Case I, angles (90°-a) and (90°! /i) or (90° -/i)
and (90°+<:r).
Vase IT, angles (90°4-^0 and (90°+/i) or (90°-/i)
and (90°— ct).
Take out ratio from second column, and multiply
by departure between the two points; this gives
difference of latitude of intersection from common
latitude.
6. Find departure corresponding respectively to
a and fi with this difierence of latitude, and con-
vert to difference of longitude; this gives differences
of longitude to the point of intersection from the
respective points of common latitude.
{b) By Tabled.
1. Write down lines as given.
2. If the points have not a common latitude,
reduce one jjoint to latitude of the other.
3. Write down difference of longitude and con-
vert it to departure.
4. Draw rough sketch to illustrate direction of
point of intersection.
5. Enter Table 2 at pages cc and fi; find ])y trial
some latitude at which —
Case I, the sum of the corresponding departures
equals the departure between the two points;
Case II, the difference of the corresponding
departures equals the departure between the two
points.
This difference of latitude, and these departures
(converted into difference of longitude) give dis-
tance of point of intersection in latitude and
longitude from the respective points of common
latitude.
390. The modification of the methods for finding the intersection of two Sumner lines, where there
is a run between the observations from which they are deduced, will be readily apparent. It is known
that at the time of taking a sight the vessel is at one of the points of the Sumner line, but which of the
various points represents her precise position must remain in doubt until further data are acquired.
Sujipose, now, that after an observation the ves.«el sails a given distance in a given direction; it is clear
that while her exact position is still undetermined it must be at one of the series of points comprised in
a line parallel to the Sumner line and at a distance and direction therefrom corresponding to the course
and distance made good; hence, if a second sight is then taken, the position of the vessel may be found
from the intersection of two lines — one, the Sumner line given by the second observation, and the other
a. line parallel to the first Sumner but removed from it by the amount of the intervening run.
Positions may be brought forward graphically on a chart by taking the course from the compass
rose with parallel rulers, and the distance by scale with dividers. If the method given in article 383 be
employed, runs in latitude and longitude must each be applied on their own scales, as explained in the
description of the method. If one of the methods by computation be adopted, the point or points of
the first line are brought forward by the traverse tables, using middle latitude sailing. The direction of
a Sumner line as determined from the azimuth of the body always remains the same, whatever shift
may be made in the position of the point by which the line is further defined.
124 THE PEACTICE OF NAVIGATION AT SEA.
• CHAPTER XVI.
THE PEACTICE OF NAViaATION AT SEA.
391. Having set forth in previous chapters the methods of working dead reckoning and of solv-
ing problems to find the latitude, longitude, chronometer correction, and azinuith from astronomical
observations, it will be the aim of the present chapter to describe the conditions which govern the
choice and employment of the various problems, together with certain considerations by which the
navigator may be guided in his practical work at sea.
392. Departire and Dead Reckoning. — On beginning a voyage, a good departure must be taken
while landmarks are still in view and favorably located for the purpose; this becomes the origin of the
dead reckoning, which, with frequent new departures from positions by observation, is kept up to the
completion of the voyage, thus enabling the mariner to know, with a fair degree of accuracy, the posi-
tion of his vessel at any instant.
At the moment of taking the departure, the reading of the patent log (which should have been
put over at least long enough previously to be regularly running) must be recorded, and thereafter at
the time of taking each sight and at every other time when a position is required for any purpose, the
log reading must also be noted. It is likewise well to read the log each hour, for general information as
to the speed of the vessel as well as to observe that it is in proper running order and that the rotator
has not been fouled by seaweed or by refuse thrown overboard froin the ship. It is a good plan to
record the time by ship's clock on each occasion that the log is read, as a supplementary means of arriv-
ing at the distance will thus be available in case of doubt. If a vessel does not use the patent log but
estimates her speed by the number of revolutions of the engines or the indications of the chip log, the
noting of the time becomes essential. A good sight is of no value unless one knows the point in the
ship's run at which it was taken, so that the position it gave may be brought forward with accuracy to
any later time.
393. Routine Day's Work. — The routine of a day's work at sea, no part of which should ever be
neglected unless cloudy weather renders it impossible to follow, consists in working the dead reckoning,
an a. m. time sight and azimuth taken when the sun is in its most favorable position for the purpose, a
meridian altitude of the sun (or, when clouds interfere at noon, a sight for latitude as near the meridian
as possible) , and a p. m. time sight and azimuth. This represents the minimum of work, and it may be
antplified as circumstances render expedient.
394. Morning Sights. — The morning time sight and azimuth should be observed, if possible, when
the sun is on the prime vertical. As the body bears east at that time, the resulting Sumner line is due
north and south, and the longitude will thus be obtained without an accurate knowledge of the latitude.
Another reason for so choosing the time is that near this point of the sun's apparent path the body is
changing most slowly in azimuth, and an error in noting the time will have the minimum effect in
its computed bearing. The time when the sun will be on the prime vertical — that is, when its azimuth
is 90° — may be found from the azinmth tables or the azimuth diagram. Speaking generally, during
half the year the sun does not rise until after having crossed the prime vertical, and is therefore never
visible on a bearing of east. In this case it is best to take the observation as soon as it has risen above
the altitude of uncertain atmospheric effects — between 10° and 15°.
A series of several altitudes should be taken, partly because the mean is more accurate than a single
sight, and partly because an error in the reading of the watch or sextant may easily occur when there
is no repetition. If the sextant is set in advance of the altitude on even five or ten minute divisions of
the arc, and the time marked at contacts, the method will be found to possess various advantages. As
the sight is being taken the patent log should be read and ship's time recorded. It is well, too, to make
a practice of noting the index correction of the sextant each time that the sextant is used. The bearing
of the sun by compass should immediately afterward be observed, and the heading by compass noted,
as also the time (by the same watch as was used for the sight).
Before working out the sight, the dead reckoning is brought up to the time of observation, and the
latitude thus found used as the approximate latitude at sight. It is strongly recommended that every
sight be worked for a Sumner line, either by assuming two latitudes, or by using one latitude and the azi-
muth, the advantages derived therefrom being always well worth the small additional labor expended.
The compass error is next obtained. From the time sight the navigator learns that his watch is a
certain amount fast or slow of L. A. T., and he need only apply this correction to the watch time of
azimuth to obtain the L. A. T. at which it was observed; thence he ascertains the sun's true bearing
from the azimuth tables or azimuth diagram, compares it with the compass bearing, and obtains the
compass error; he should subtract the variation by chart and note if the remainder, the deviation, agrees
with that given in his deviation table; but in working the next dead reckoning, if the Ship's course
does not change, the total compass error thus found may be used without separating it into its compo-
nent parts. It should be increased or decreased, however, as the ship proceeds, by the amount of any
change of the variation that the chart may show.
395. If there is any fear of the weather being cloudy at noon, the navigator should take the pre-
caution, when the sun has changed about 30° in azimuth, to observe a second altitude and to record
the appropriate data for another sight, though this need not actually be worked unless the meridian
THE PRACTICE OF NAVIGATION AT SEA. 125
observation is lost. If it is required, it may be worked for either a time sight or cp' cp" sight, according
to circumstances, a second Sumner line obtained, and the intersection of the earlier Sumner with it will
give the ship's position.
396. Noox SuiHTs. — Between 11 and 11.30 o'clock (allowing for gain or loss of time due to the
day's run) the ship's clocks should be set for the L. A. T. of the prospective noon position. The noon
longitude may be closely estimated from the morning sight and the probable run. The navigator
should also set his own watch for that time, to the nearest minute, and note exactly the number of
seconds that it is in error. lie may now compute the constant (art. 333, Chap. XII) for the meridian
altitude. The daily winding of the chronometer is a most important feature of the day's routine, and
may well be pei'formed at this hour. At a convenient time before noon, the observations for meridian
altitude are commenced and continued until the watch shows L. A. noon, at which time the meridian
altitude is measured and the latitude deduced.
If the weather is cloudy and there is doubt of the sun being visible on the meridian, an altitude
may be taken at any time Avithin a few minutes of noon, the time noted, and the interval from L. A.
noon found from the known error of the watch. It is then the work of less than a minute to take out
the a from Table 26, the of from Table 27, and apply the reduction to the observed altitude to obtain
the meridian altitude. Indeed, the method is so simple that it may be practiced every day and several
values of the meridian altitude thus obtained, instead of only one.
397. It now becomes necessary to find the longitude at noon. This may be done graphically by
a chart, or by computation. The former plan needs no explanation. There are a number of variations in
the methods of computation, one of which will l)e given as a type.
By the ship's run, work 1)ack the noon latitude to the latitude at a. m. time sight. If the Sumner
line was found from two assumed latitudes which differed + '« minutes, while the corresponding longi-
tudes differed zfc n minutes, then V difference of latitude causes ± — minutes difference of longitude. If
m
the true latitude at sight is rf: o- minutes from one of the assumed latitudes, then i .)-• X — is the corre-
m
sponding difference of longitude. If the Sumner line was found from one assumed latitude and an
azimuth, Z, it makes an angle with the meridian equal to 90° — Z. Enter the traverse table with this
as a course and with the difference between the true and assumed latitudes as a latitude, and the
departure will be found; convert this into difference of longitude at the latitude of observation, and
apply the result with its ])roper sign to the longitude corresponding to the assumed latitude. Having
thus the longitude at sight, the longitude at noon is worked forward for the run. If the sights show a
considerable current it should be allowed for, both in working back the latitude and in bringing uji the
longitude for the run between the sight and noon.
39§. CiKRENT AND EuN. — The current may be found by comparing the noon positions as obtained
by observation and by dead reckoning; and the day's run is calculated from the difference between the
day's noon position by observation and that of the preceding day. To "current" is usually attributed
all discrepancies between the dead reckoning and observations; but it is evident that this is not entirely
due to motion of the waters, as it includes errors due to faulty steering, improper allowance for the
compass error, and inaccurate estimate of the vessel's speed through the water.
The noon position by observation becomes the departure for the dead reckoning that follows.
399. Afterxoon SiciHTS. — The p. m. time sight and azimuth is similar to the morning observation.
400. Sumner Lines. — By performing the work that has just been described a good position is
obtained at noon each day, which, in a slow-moving vessel with plenty of sea room, may be considered
sufficient; but conditions are such at" times as to render it almost imj)eratively necessary that a more
frequent determination of the latitude and longitu<ie be made. If the vessel is near the land or in the
vicinity of off-lying dangers, if she is running a great circle course requiring frequent changes, if she is
making deep-sea soundings, if she has just come through a period of foggy or cloudy weather, or if the
indications are that she is about to enter upon such a period, it is obviously inexpedient to await the
coming of the next noon for a tix. The responsibilities resting upon the navigator require that he shall
earlier find his ship's position; and, generally speaking, the greater the speed made bj^ the vessel the
more absolute is this recjuirement.
The key to all such determinations will lie in the Sumner line, and a clear understanding of the
properties of such a line will greatly facilitate the solutions. The mariner must keep in mind two facts:
First, that a single observation of a heavenly body can never, by itself, give the point occupied by an
observer on the earth's surface; and second, that whenever any celestial body is visible, together with
enough of the horizon to permit the measuring of its altitude, an observer may thereby determine a Viue
which passes through his own position on the earth's surface in a direction at right angles to the bearing
of the body.
It may readily be seen that if two Sumner lines are determined the observer's position must be at
their intersection, and that that intersection will be most clearly marked when the angle between the
lines equals 90°; hence, if two heavenly bodies are in sight at the same time the position may be found
from the intersection of their Sumner lines, the angle of intersection being equal to the horizontal
angle between the bodies. If only one body is in sight, as is generally the case when the sun is shining,
one line of position may be gotten from an altitude taken at one time, and a second line from another
altitude takeii when it has changed some 30° in azinmth — usually, a couple of hours later. Bringing
forward the first line for the intervening run, the intersection may be found.
With the general principles of the Sumner line clearly before him, the navigator will find no diffi-
culty in making the choice of available bodies. If about to take a star sight, and sky and horizon are
equally good in all iiuarters, two bodies should be taken whose azimuths differ as nearly as possible by
90°. If one body can be taken on or near the meridian, its bearing being ])ractically north or south,
the resulting Sumner line will be east and west — that is, it may be said that whatever the longitude
(within its known limits) the latitude will be the same; the other sight may then be worked as a time
si^ht with this single latitude and time will thus be saved. The same is true if Polaris is observed, and
it is a very convenient practice to take an altitude of that star at dawn and obtain a latitude for working
126 THE PRACTICK OF NAVIGATION AT SEA.
the a. m. time sijiht of the sun. A similar c:ise arises when a both- is observed on the prime vertical;
its Sumner line then runs north and south and coincides with a meridian; if the other body is favorably
located for a ip' (p'' sijrht, it niav be worked with a single longitude and the latitude thus found directlv.
If it is not possible to obtain two lines and thus exactly locate the ship, the indications of a single
line may be of great value to the navigator. A Sumner line and a terrestrial bearing will give the ship's
position by their intersection in the same manner as two lines of position or two l)earing.<; or the posi-
tion of the ship on a line may be shown with more or le.«s accuracy by a sounding or a series of
soundings. If the body be observed when it bears in a direction at right angles to the trend of a
neighboring shore line, the resulting line will be parallel with the coast and thus show the mariner his
distance from the land, which may be? of great importance even if his exact position on the line remains
in doubt. If t'.ie bearing be ]>arallel to the coast line, then the Sumner line will point toward shore;
the value of a line thafc*!eads to the point that the vessel is trying to pick up is amply demonstrated by
the experience of Captain Sumner that led to the discovery of the method (art. 372, Chan. XV).
For especially accurate work three Sumner lines may be taken, varying in azimuth about 120°; if
they do not intersect in a point, the most probable position of the ship' is at the center of the triangle
that they form.
If two pairs of lines be determined, each pair based upon observation of two bodies l^earing in
nearly opposite directions and at about the same altitude, the mean positi(>n that results from the inter-
Bection of the four lines will be as nearly as possible free frf)m those errors of the instrument, of refrac-
tion, and of the observer, which can not otherwise be eliminated. This is fullv explained in article 451,
Chapter XVII.
401. Use of Staks, Planets, and Moox. — It may be judged that the employment in navigation
of other heavenly bodies than the sun is considered of the utmost imi»ortance, ancl mariners are urged
to familiarize themselves with the methods by which observations fif star.-;, planets, and the mofni may
be utilized to reveal to them the position of their vessels at frequent intervals throughout the twenty-
four hours.
It should be remembered, however, that in order to be of value these observations must be accu-
rate; and to measure an accurate altitude of the body above the horizon it is required not only that the
body be visible but also that the horizon be distinctly in view. Care should therefore be taken to make
the observations, if possible, at the time when the horizon is plainest — that is, during morning and
evening twilight. It may be urgently required to get a position during hours of darkness, and a dim
horizon line may sometimes be seen and an observation taken, using the star telescope of the sextant;
if the moon is shining, its light will be a material aid; but results ol)tained from such sights should be
regarded as questionable and used with caution. Altitudes measured, however, just before sunrise and
just after sunset are open to no such criticism; a fairly well-practiced observer who takes a series of sights
at such a time, setting the sextant for equal intervals of altitude, will find the regularity of the corre-
sponding time intervals" such as to assure him of accuracy.
402. Identification of Unknown Bodies. — On account of the very great value to be derived from
the use of stars and planets in navigation, it is stnjngly recommendetl that all navigators familiarize
themselves with the names and positions of those fixed stars whose magnitude renders possible their
employment for observations, and also with the general characteristics — magnitude and color — of the
three planets (Venus, Jupiter, and Mars) which are most frequently used. A study of the different
portions of the heavens, with the aid of any of the numerous charts and books which bear upon the
subject, W'ill enable the navigator to recognize the more important constellations and single stars by
their situation with relation to each other, and to the pole and the equator.
It may occur, however, that occa.«ion will arise for observing a body Avhose name is not known,
either because it has not been learned, or because the surrounding stars by which it is usually identified
are obscured by clouds or rendered invisible by moonlight or daylight. In such a case the observer
may estimate the hour angle and declination (the hour angle applied to local sidereal time giving the
right ascension), and the star or planet may thus be recognized from a chart or from an inspection of
the Nautical Almanac. This rough method will generally suffice when the body is the only one of its
magnitude within an extensive region of the heavens; but cases often arise where a much closer
approximation is necessary, and more exact data is required for identification.
403. If in doubt as to the name of the body at the time of taking the sight, it should be made an
invariable rule to observe its bearing by compass, whence the true azimuth may l)e approximately
deduced by applying the compass error. The method « to be descril)ed then affords a convenient n\eans
of identification. The quantities given are the corrected altitude of observation, /;, the (approximate)
true azimuth of the body, Z, and the latitude by dead reckoning, L; those to be determined are the
declination, d, and the hour angle, /. From the astronomical triangle we have:
sin Zsin t
~. r; or, sm Z cos /i=.«in t cos (/.
sin j) cos ft
The value of sin Z cos h (calculated from the given azimuth and altitude) must therefore equal
sin t cos (I, whatever the values of t and d mav prove to be.
From a given latitude, azimuth and declination, the hour angle may be found either by azimuth
tables or an azimuth diagram; or from a given latitude, azimuth and hour angle, the declination may
be found by the same means. If, therefore, some probable value of the declination be assumed, using
the known'latitude and azimuth, we may ascertain the corresponding hour angle; or, if the hour angle
be assumed, the corresponding declination is obtained; then the product of sin t cos d may be calculated,
and if it agrees substantially with sin Z cos /(, the trial values of the hour angle and declination are the
correct ones; if not, other trials mav be made until the correct ones are found. It may be remembered
that absolutely exact results are not sought, and in practice the operation may be made very short; the
n Suggested by Lieut. G. W. Logan, U. 8. Navy.
THE PRACTICE OF NAVIGATIOlSr AT SEA.
127
values of the quantities may be taken in even degrees and the logarithms need not be carried beyond
the third place; the sum of the logarithms will suffice and the corresponding numbers do not have to be
taken out. The possibility that the observed body may have been a planet must always be kept in
mind in looking it up in the star table or chart.
Example: May 16, 1879, in Lat. 5° N., Long. 2'* 53"" W. by I). R., a star is observed whose corrected
altitude is 38°, and true azimuth N. 107° E. The Greenwich sidereal time (as computed for use in the
regular working of the sight) is 12'' 53'". Let it be required to identify the body.
First find the logarithm of sin Z cos //.
Z 107° sin 9. 981
h 38° cos 9. 897
sin Z cos h log 9. 878
Now suppose the observer estimates from the position of the body that its declination is 3° S. Look
in the azimuth table on the page of latitude 5° (declination contrary name to latitude), and find the hour
angle (p. m.) corresponding to Dec. 3° and Az. 107°; this is about 1'' 40"'; then with fZ==3°, ^=1'' 40'",
find sin t cos d. (Sin t may be obtained either by converting time into arc and taking from the table in
the usual way, or by multiplying by 2 and finding it from the column headed "Hour P. M." Thus in
the present case find the sine of 25° 00' or of 3'' 20"'. In using the time column be careful to take the
name from the foot of the page when the double angle exceeds 6''. )
t P
d
40"
3°
sin 9. 626
cos 9. 999
sin t cos d log 9. 625
As this logarithm should equal 9.878, it is seen that the assumj)tion is incorrect. Try a value of the
declination 5° farther south — that is, 8° S. The corresponding hour angle is 2'' 50"'.
t 2^ 50"' sin 9. 830
d 8° cos 9. 996
sin t cos '/ log 9. 826
The logarithm is not yet (juite large enough; assume <leclination 10° S. ; the hour angle is 3'' 20'".
t 3" 20'" sin 9. 884
d 10° cos 9. 993
gin t cos d log 9. 877
This is practically identical with the logarithm of sin Z cos /*, and the correct values are, therefore,
t=Z^ 20"', d=\Q° S.
We now have:
G. S. T. 12" oS-"
Long. J 53 W.
L. S. T. 10 00
H. A. _3 20 E.
R. A. 13 20
From the Nautical Almanac it is found that the right ascension of Spica is 13'' 19"" and the decli-
nation 10° 32'' S. This is therefore the body observed.
Example: March 18, 1879, in Lat. 26° S.. Long. 5" 42"' E., by D. R., the altitude of a body is 41°
and its azimuth S. 84° E. , the Greenwich sidereal time being 10" 52™. Required the name of the body.
Z 84° sin 9.998
h 41° cos 9^78
sin Z cos h log 9.876
Assume first an hour angle of 3'' 00'". The corresponding declination is 23° (same name as lati-
tude).
< 3" 00™ sin 9.849
d 23° cos 9.964
sin t cos d log 9.813
Next assume an hour angle of 3" 30™. The declination is tiien 21° S.
t 3" 30"' sin 9.899
d 21° cos 9.970
sin t cos d log 9.869
128 THE PRACTICE OF NAVIGATION AT SEA.
Assume hour angle 3'' 35"'. Declination is gtill nearest to 21° S
t '6^ 35'" 8in 9.907
(/ 21° cos 9.970
sin/ cos(/ log 9.877
The last assumption, is therefore correct.
We then have:
G. 8. T. 10" 52"'
Long. 5 42 E.
• L. S^ T. 16 34
H. A. _3 35 K
R. A. 20 09
As there is no fixed star corresponding to these coordinates the tables for the planets should be
consulted. On [March 18, 1879, the right ascension of Mars is 20" 09"', and the declination 21° 06^ S.
This is therefore the body that was observed.
404. The following is a summary of the method employed:
1. Reduce time of observation to Greenwich sidereal time and find the true altitude to the nearest
degree. (These operations must be performed before any sight can be worked; they are, therefore, not
Btrictly a part of the ]>rocess of identification.)
2. Correct the observed azimuth for deviation and variation.
3. Find the logarithm of sin Z cos h to the third place.
4. Assume a declination and find the corresponding hour angle that will produce the given azimuth
at the given latitude; orassuine an hour angle and find the corresponding declination. ( Use an azimuth
table or diagram for the purpose.)
5. Find the logarithm of sin t cos (/ to the third place.
0. Observe whether this agrees with the logarithm of sin Z cos /;, and if it does not, repeat trials
until an agreement is found.
7. Having found the hour angle and declination, convert the Greenwich sidereal time into local
sidereal time and subtract the hour angle if west, or add it if east; the result is the ri^ht ascension of
the observed l)ody, by which, with the declination and magnitude, the identification is accomplished.
405. The exactness with which the comparison of logarithms is carried out will depend upon the
possibility of errors of identification in the region of the heavens involved. It will not usually be
necessary to find the correspondence as closely as has been done in the examples given, and the cases
will be rare when, with a fair estimate of hour angle or declination at beginning, a sufficiently accurate
knowle<lge of the values can not be arrived at after the second approximation; and frequently the first
will suffice for identificaton.
406. Value of the Moon in Observations. — Next to the sun, the most conspicuous body in the
heavens is the moon, and it may therefore frequently be employed by the mariner with advantage.
Owing to its nearness to the earth and the rapidity'with which it changes right ascension and declina-
tion, the various corrections entailed render observations of this body somewhat longer to work out,
with consequent increased chances of error; and errors in certain parts of the work will have more
serious results than with other bodies; the navigator will therefore usually pass the moon by if a choice
of celestial bodies is offered for a determination of position; but so many occasions present themselves
when there is no available substitute for the moon that the extra time and care necessary to devote to
it are well repaid. During hours of daylight it is often clearly visible, and its line of position may cut
with that of the sun at a favorable angle, giving a good fix from two observations taken at the same
time, when the only other method of finding the position would be to take two sights of the sun sepa-
rated by a time interval in which an imperfect allowance for the true run intervening would affect the
accuracy of the result, or a clouding-over of the heavens would prevent any definite result whatever being
reached; and during the night, the gleam upon the water directly below the moon may define the
horizon and give opportunity for an altitude of that body when it is impossible to take an observation
of any other. Navigators are therefore recommended to make use of the moon with complete confidence
whenever it will serve their purposes. It has been the purpose of this work to point out the features of
the various sights wherein the practice with the moon differs from that of the sun, stars, or planets;
care and intelligent consideration will render these quite clear.
Besides its availability for determining Sumner lines of position, which it shares with other bodies,
the moon affords a means for ascertaining the Greenwich meantime independently of the chronometer,
thus rendering it possible to deduce the longitude and chronometer error. This is accomplished by the
method of lunar distances, which is fully explained in Appendix V. If the Greenwich time given by
an observation of lunar distance could be relied upon for accuracy, the methoti would be a great boon
to the navigator; but this is not the case. The jnost practiced observer can not be sure of obtaining
results as close as modern navigation demands, and the errors to which the method is subject are larger
than the errors that may be expected in the chronometer, even when the instrument is only a moder-
ately good one and its rate is carried forward from a long voyage. The method is not, therefore, recom-
mended for use except Avhere the chronometer is disabled or where it is known to have acquired some
extraordinary error; and when lunar distances are resorted to care must be taken to navigate with due
allowance for possible inaccuracy of the results. In this connection it is appropriate to say that the
best safeguard against the dire consequences that may result from a disabled or unreliable chronometer
is for every vessel to carry two — or, far better, three — of those instruments, the advantages of which
plan are stated in article 265, Chapter VIII.
40T. Employment of Bodies nKPEXOEXT upon their Po.sition. — The practical navigator will soon
observe that there are certain conditions in which bodies are especially well adapted for the finding of
latitude, and others where the longitude is obtained most readily.
THE PRACTICE OF NAVIGATION AT SEA. 129
Taking the sun for an example, when a vessel is on the equator and the declination is zero, that
body will rise due east of the observer and continue on the same bearing until noon, when for an instant
it will be directly overhead, with a true altitude of 90°, and will then change to a bearing of west, which it
will maintain until its setting. In such a case any observation taken throughout the day -will give a true
north-and-south Sumner line, defining longitude perfectly, but giving no determination of the latitude,
excepting for a moment only when the body is on the meridian. With the exception noted, all efforts
to determine the latitude will fail. The reduction to the meridian takes the form ^ , becoming inde-
terminate, and in the q/ q/' sight the cosine of cf/ will assume a value that corresponds alike to any
angle within certain wide limits — the limits within which the circle of equal altitude has practically a
north-and-south direction. In conditions approximating to this we may obtain a longitude position
more easily than one for latitude, even within a few minutes of noon.
As the latitude and declination separate, conditions become more favorable for finding latitude and
less so for longitude; the intermediate cases cover a wide range, wherein longitude may be well determined
by observations three to five hours from the meridian, and latitude by those within two hours of
meridian passage. As extreme conditions are approached the accuracy of longitude determinations con-
tinues to decrease; at a point in 60° north latitude, when the sim is near the southern solstice, its bear-
ing differs only 39° from the meridian at rising; or, in other words, even if observed at the most
favorable position, the resulting Sumner line is such that V in latitude makes a difference of 1.3 miles of
departure, or 2^.6 of longitude, and is far better for a latitude determination than for longitude. And in
higher latitudes still this condition is even more marked.
Having grasped these general facts, the navigator must adapt his time for taking sights to the cir-
cumstances that prevail, and when the sun does not serve for an accurate determination of either
latitude or longitude the ability to utilize the stars, planets, and moon as a substitute will be of the
greatest advantage.
40§. Use of Various Sights. — Having taken a sight, the navigator may sometimes be in doubt as
to the best method. of working it. No rigorous rules can be laid down, and experience alone must be
his guide. In a general way it may be well, when the body is nearer to the prime vertical than to the
meridian, to work it for longitude, assuming latitude, and using the time sight; and when nearer the
meridian to work it for latitude, assuming longitude, by the q/ q/' method. The time sight is more
generally used than the other, it has wider limits of accurate application and is probably a little quicker;
but as the meridian is approached and the hour angle decreases small errors in the terms make large
ones in the results. The q/ q/' or latitude method should not ordinarily be employed beyond three
hours from the meridian, and only then when the body is within 45° or azimuth from the meridian;
when the hour angle is six hours (90°) its secant becomes infinity and the method is not available; nor,
as has been noted (art. 339, Chap. XII), does it give definite results when the azimuth is 90° or there-
abouts.
When the body is close enough to the meridian for the method of reduction to the meridian to be
applicable, that method is to be preferred because of its quickness and facility. It should be noted,
however, that, though close enough to employ the reduction, it may not be suflSciently correct to
assume that the body bears due north or south, and the sight should be worked with two longitudes,
or the Sumner line determined by the azimuth, unless the bearing nearly coincides with the direction
of the meridian.
In cases where a body transits near the zenith, a good fix both in latitude and longitude may be
obtained by sights, a few minutes apart, near its meridian passage. Various special methods have
been devised for doing this, but it seems simpler to treat the problem as an ordinary one for Sumner
lines, except where it falls within the narrow limits of application of the equal altitude method (art.
352, Chap. XIII). The solution is possible, because in the condition where it is available (that of a high
transit) the body makes a very rapid change of azimuth (from nearly east to nearly west) in a short
space of time, and two observations separated by a short interval give Sumntr lines that cut sPt a
favorable angle. The time sight or latitude sight may be used according as the body's bearing is
greater or less than 45° from the meridian. If one observation be taken when the bearing is about SE.
and the other when it is about SW., the intersection, allowing for intervening run, will not only give
the longitude, but will also afford a good check upon the meridian observation for latitude, which, in
the case of high transits, it is difficult to make with perfect accuracy.
409. Working to Seconds and Accuracy op Determinations. — The beginner who seeks counsel
from the more experienced in matters pertaining to navigation will find that he receives conflicting
advice as to whether it is more expedient to carry out the terms to seconds of arc, or to disregard seconds
and work with the nearest whole minute.
It is a well -recognized fact that exact results are not attainable in navigation at sea; the chro-
nometer error, sextant error, error of refraction, and error of observation are all uncertain; it is impos-
sible to make absolutely correct allowance for them, and the uncertainty increases if the position is
obtained by two observations taken at different times, in which case an exactly correct allowance for
the intervening run of the ship is an essential to the correctness of the determination. "No navigator
should ever assume that his position is not liable to be in error to some extent, the precise amount
depending upon various factors, such as the age of the chronometer rate, the quality of the various
instruments, the reliability of the observer, and the conditions at the time the sight was taken; perhaps
a fair allowance for this possible error, under favorable circumstances, will be 2 miles; therefore,
instead of plotting a position upon the chart, and proceeding with absolute confidence in the belief that
the ship's position is on the exact point, one may describe, around the point as a center, a circle whose
radius is 2 miles — if we accept that as the value of the possible error — and shape the future courses
with the knowledge that the ship's position may be anywhere within the circle.
It is on account of this recognized inexactness of the determination of position that some navigators
assume that the odd seconds may be neglected in dealing with the different terms of a sight; the average
possible error due to this course is probably about one minute, though under certain conditions it may
22489—03 9
180 THE PRACTICE OF NAVIGATION AT SEA.
be considerably more. It is possible that, in a particular case, the error thus introduced through one
term would be offset by that from others, and the result would be the same as if the seconds had been
taken into account; but that does not affect the general fact that the neglect of seconds as a regular
thing renders any determination liable to be in error about one minute. Those that omit the seconds
argue, however, that since, in the nature of things, any sight may be in error two minutes, it is imma-
terial if we introduce an additional possibihty of error of one minute, because the new error is as liable
to decrease the old one as to increase it; but the fallacy of the argument will be apparent when w'e return
to the circle drawn around our plotted point. The eccentricity of the sextant may exactly offset the
improper allowance for refraction, and the mistake in the chronometer error may offset the observer's
J)ersonal error, but unless we know that such is the case — which we never can — we have no justification
or doing otherwise than assume that the ship may be any place within the 2-mile circle. If, now,
we increase the possible trror by 1 mile, our radius of uncertainty must be increased to 3 miles, and the
diameter of the circle, representing the range of uncertainty in any given direction, is thereby increased
from 4 to 6 miles.
It is deemed to be the duty of the navigator to put forth every effort to obtain the mod probable
position of the shiji, which requires that he shall eliminate possible errors as completely as it lies
within his power to do. By neglecting seconds he introduces a source of error that might with small ,
trouble be avoided. This becomes of still more importance since modern instruments and modern
methods constantly tend to decrease the probability of error in the observation, and to place it within
the power of the navigator to determine his ship's position with greater accuracy.
410. There is a more exact way of defining the area of the ship's possible position than that of
describing a circle around the most probable point, as mentioned irt the preceding article, and that is to
draw a line on each side of each of the Sumner lines by which the position is defined, and at a uniform
distance therefrom equal to the po.ssible error that the navigator believes it most reasonable to assume
under existing conditions; the parallelogram f( rmed by these four auxiliary lines marks the limit to be
a.«signed for the shiji's position; this method takes account of the errors due to poor intersections, and
warns the navigator of the direction in which his position is lea.«t clearly fixed and in which he must
therefore make extra allowance for the uncertainty of his determination.
It must be remembered in this connection that no position can ever be obtained except from the
intersection of two Sumner lines, whether or not the lines are actually plotted; thus, a meridian altitude
gives a Sumner line that extends due east and west, and a sight on the prime vertical a line that extends
north and south, though it may not have been considered necessary to work the former with two
longitudes or the latter with two latitudes.
411. The "Work Book and.Fobms for Sights. — The navigation- work book, or sight book, being
the official record of all that pertains to the navigation of the ship when not running by bearings of the
land, should be neatly and legibly kept, so that it will be intelligible not only to the person who per-
formed the work, but also to any other who may have reason to refer to it.
Each day's work should be begun on a new page, the date set forth clearly at the top, and prefer-
ably, also, a brief statement of the voyage upon which the ship is engaged. It is a good plan to have
the dead reckoning begin the space allotted for the day, and then have the sights follow in the order in
which taken. The page should be large enough to permit the whole of any one sight to be contained
thereon without the necessity of carrying it forward to a second page. No work should be commenced
at the bottom of a page if there is not room to complete it. Every operation pertaining to the working
of the sights shoula appear in the book, and all irrelevant matter should be excluded.
It is well to observe a systematic form of work for each sight, always writing the different terms in
the same position on the page; this practice will conduce to rapidity and lessen the chances of error.
In order to facilitate the adoption of such a method, there are appended to this work (Appendix II)
a series of forms that are recommended for dead reckoning, and for time sights, meridian altitudes, and
latitude sights (both by cp' q^' formula and method of reduction to the meridian), for the sun, stars,
planets, and moon, respectively. For beginners, these are deemed of especial importance, and it is
recommended that, until perfect familiarity with the different sights is acquired, the first step in work-
ing out an observation be to Avrite down a copy of the appropriate blank form, indicating the proper
sign of application of each quantity (for which the notes will be a guide), and not to put in any figures
until the scheme has been completely outlined; then the reinainder of the work will consist m writing
down the various quantities in their proper places and performing the operations indicated.
MARINE SURVEYING.
131
CHAPTER XVII.
MAEINE SUEVEYING.
412. Definitions. — Surveying is the art of representing upon paper the .surface of the earth, giving
its characteristic features, such as, on land, the position of prominent objects, heights, and depressions,
and on water, the depth, character of bottom, and position of shoals.
Topographical Surrrgiiig delineates the land, and Ifi/c/rographlc Surveying, the water.
GmdeKy is a higher kind of surveying, which takes into account the curvature of the earth. To
points determined by a geodetic survey other surveys are referred.
It is not deemed appropriate to include in this Avork a complete treatise on Marine Surveying. The
scope of this chapter will be to set forth such general information regarding the principles of surveying
and the instruments therein employed as will give the navigator an intelligent understanding of the
subject sufficient to enable him to comprehend the methods by which marine charts are made, and, if
occasion should arise, to conduct a survey with such accuracy as the instruments ordinarily at hand on
shipboard may permit. For a more detailed discussion of Marine Surveying, the student is referred to
the various publications which treat the subject exhaustively.
INSTRUMENTS EMPLOYED IN MARINE SURVEYING.
413. The Theodolite
AND Transit. — The Theodo-
lite (fig. 54) is an instrument
for the accurate measure-
ment of horizontal and ver-
tical angles. While these
instruments vary in detail
as to methods of construc-
tion, the essential principles
are always identical.
A telescope carrying cross-
hairs in the common focus
of the object-glass and eye-
piece is so mounted as to
have motion about two axes
at right angles to one an-
other; graduated circles and
verniers are provided by
which angular motion in
azimuth and (usually) in
altitude may be measured;
and the instrument is capa-
ble of such adjustment by
levels that the planes of mo-
tion about the respective
axes will (iorrespond exactly
with the horizontal and the
vertical.
The telescope is carried
in appropriate supports
upon a horizontal plate
which lias, immovably at-
tached to it, one or more
verniers, and which revolves
just over a graduated circle
that is marked upon the
periphery of a second hori-
zontal i)late, a means of
measuring the motion of
the upper plate relatively to
the lower one being thus
provided. Thumb- screws
are fitted by which the up-
per plate may be clamped
to the lower, and (except-
ing in some simpler forms of
the instrument) others by
which the lower plate may
be made immovable in azi-
muth, or allowed free mo-
tion, at will; all clamping ^^^'- ^'*-
arrangements include slow-motion tangent-screws for finer control.
132 MARINE SURVEYING.
A vertical graduated circle, or arc, with a vernier, clamps, and tangent-screws, is fitted to most
theodolites, for the measurement of the angular motion of the telescope iii altitude.
The theodolite usually carries a magnetic needle, with a graduated circle an(l vernier for compass
bearings. The instrument is mounted upon a tripod, and levels and leveling-screws afford a means of
bringing the instrument to a truly horizontal position.
The Transit used in surveying is a modified form of the theodolite, and is generally employed where
less accuracy is required; it takes its name from the fact that the telescope may be turned completely
about its horizontal axis, or transited, without removal from its supports.
414. The line of collimation of a telescope is an imaginary line passing through the optical center of
the object-glass in a direction at right angles to that of its axis of rotation. This is also called the axis
of collimation. The line of sight i?, sm imaginarv line passing through the optical center of the object-
glass and the point of intersection of the cross-hairs.
A theodolite or transit, before it can be used for the accurate measurement of angles, must be in
adjustment in the following respects: (a) The vertical axes of revolution of the upper and lower hori-
zontal plates must be coincident; (h) the axis must be vertical and the plates horizontal when the
bubbles of the levels are in their central positions; (c) the vertical cross hair must be perpenclicular
to the horizontal axis of the telescope; {d) the line of collimation must coincide with the line of sight;
(e) the horizontal axis of the telescope must be perpendicular to the vertical axis of the instrument;
(/) the bubble of the telescope level must stand at the middle of its scale, and the vertical circle must
read zero, when the line of collimation is horizontal.
The last-named condition may be disregarded if vertical angles are not to be measured.
415. The instrument being in adjustment, to observe angles it should be set up, leveled, and
focused. This involves placing the tripod so that a plumb bob from the center of the instrument shall
hang directly over the spot at which the measurement is to be made. The legs of the tripod should be
firmly placed in Such manner that the height shall be convenient for the observer and the instrument
shall be nearly level. Then the horizontal plates are brought to a true level by means of the leveling
screws and bubbles. The telescope should next be focused by moving the object glass and eyepiece in
such manner that the object sighted and the cross hairs may be plainly seen and that the object will
not appear to have motion relatively to the cross hairs as the eye is moved to the right or left in front
of the eyepiece. This last condition insures the cross hairs being at the common focus of the eyepiece
and objective.
To observe a horizontal angle with a theodolite or transit, clamp the upper plate to the lower at zero,
leaving the lower plate undamped; swing the telescope so that its vertical cross hair bisects one of the
objects, and clamp the lower plate; unclamp the upper plate and bring the telescope to bisect the other
object, and the reading of the vernier on the scale will give the required angle. (The final nice motion
by which the cross-hair is brought exactly upon a point is always given by the tangent screw. )
In taking a round of angles, this operation is repeated successively upon each object to be observed
about the horizon, the upper plate being always swung, while the lower is kept where set upon the
first object, or origin. The result will give the angular distance of each object from the origin, and, if
the observations have been accurately made, upon finally sighting back to the origin, the reading
should be zero.
To repeat an angle, having made the first measurement of it in the usual way, unclamp the lower
circle and swing back the telescope until it again points to the first object, and clamp it; then unclamp
the upper circle, swing to the second object, and clamp. The scale-reading should now be double that
of the first angle. Kepeat as often as the importance of the angle requires, and the accepted value will
be the final reading divided by the number of measurements. All angles of the main triangulation,
and others of importance in the survey, are repeated.
Defects in adjustment of the instrument may be eliminated by taking one series of angles with
the telescope direct and another with the telescope reversed. To reverse the telescope, revolve it about its
horizontal axis through 180°, then swing it about its vertical axis through 180° — in other words,
invert it.
Vertical angles are measured on the same principle as that described for horizontal ones.
The process of setting up the instrument at a station and observing the angles between the various
objects that are visible is called occupying the station.
416. The Plane Table. — This is an instrument by which positions are plotted in the field directly
upon a working sheet. It consists (fig. 55) of a drawing board mounted upon a tripod in such manner
as to be capable of motion in azimuth, and with facilities for being brought to a perfect level; in con-
nection with it is employed an alidade, consisting of a straightedge ruler, upon which is mounted a
telescope with cross-hairs whose line of sight is exactly parallel to the vertical plane through the edge
of the rule. It is evident that if a sheet representing a chart be placed upon such a board and turned
so that the true meridians, as portrayed thereon, lie in the direction of the earth's meridian at that
place, then all lines of bearings on the chart will coincide with the corresponding lines on the earth's
surface; from which it follows that if the alidade be so placed that its rule passes through the spot
on the chart representing the position of the observer, while the telescope is directed to some visible
object, the position of that object on the chart lies somewhere upon the line drawn along the edge of
the rule. Upon this general principle depend the various applications of the plane table.
The drawing board is usually made of several pieces of well-seasoned wood, tongued and grooved
together, with the grain running in different directions to prevent warping; about its edge are several
metal clips for securing the paper in place. It is supported upon three strong brass arms, to which it is
attached by screws, thus permitting its removal at will. The arms are attached to a horizontal plate
which revolves upon a second horizontal plate lying immediately below it; a clamp and tangent screw
are fitted, by which the upper plate, and with it the drawing board, may be secured to the lower plate,
or may be given a fine motion in azimuth. Three equidistant lugs of brass, grooved on the under side,
project down from the lower plate, resting on screws in the top of the tripod, by which the instrument
IS leveled; when adjusted in this respect it is firmly clamped in position, and, aa the tripod is made
unusually large, the adjustment is not easily deranged.
MARINE SURVEYING.
133
The alidade is a metal straightedge with a vertical column at its center, at the top of which are the
supports which carry the telescope; a vertical arc and vernier are provided for measuring the motion of
the telescope in altitude. The telescope is usually so fitted that it may he revolved in azimuth through
an arc of exactly 180°, for the purpose of adjusting the line of collimation. On top of the rule near its
center is the level — sometimes replaced by two levels at right angles — by means of which it may be seen
when the table is in a true horizontal position.
A magnetic needle mounted in a rectangular metal box, whose outer straightedge is parallel to the
zero line of a graduated scale over which the needle swings, is provided for drawing the north-and-south
line on the chart; this is called a dedinatoire.
417. To be in correct adju.«tment, a plane table must comply with the following conditions:
(«) The fiducial edge of the rule must be perfectly straight, {b) The level must have the bubble in
its central position when the table is truly horizontal, (c) The vertical cross hair must be perpendic-
ular to the horizontal axis of the telescope, (d) The line of collimation must coincide with the line of
sight, {e) The horizontal axis of the telescope must be parallel to the plane of the table. (/) The
vertical circle should read zero when the line of collimation is horizontal.
418. The results derived from the use of the plane table, like all others dependent upon graphic
methods, must be regarded as less accurate than those deduced by computation, and even less accurate
than those derived from the careful plotting of theodolite angles. Hence it is that, in a careful marine
survey, this instrument would be employed only for the topography and shore line.
For whatever purpose used, the plane table would not ordinarily be called into requisition until the
survey had so far progressed that a chart could be furnished the observer showing certain stations
whose positions were already established; with this chart, the first step would be to occupy one of the
determined points. The table must be set up with the point on the chart directly over the center of the
station; it must then be leveled and the telescope focused as described for the theodolite or transit; and
finally it must be oriented, that is, so turned in azimuth that all lines of the chart are parallel to similar
lines of the earth's surface. To orient, unclamp the table and swing it until the north-and-south lineof the
chart is approximately parallel to that of the earth, one means of doing which is afforded by the decli-
natoire; place the alidade so that the edge of the rule passes through the points on the chart representing
the station occupied and some second station which is clearly in view; then, sighting through the tele-
scope, per/ect the adjustment of the table by swinging it until the second station is exactly bisected by
the vertical cross hair, the final slow motion being obtained by clamping the table and working the
tangent screw. If the adjustment has been correctly made, the rule may be laid along the line joming
the station occupied and any other on the chart, and the telescope will point exactly to that other station.
Being properly oriented, if the alidade be so placed that the edge of the rule pass through the station
occupied, and the telescope point directly to some unknown object whose position is to be determined.
134 MARINE SURVEYING.
then a line drawn along the rule will contain the ])oint which represents the position of that object.
If, now, the plane table l)e set np at a second station, oriented for its new position, and a line be simi-
larly drawn from that station toward the one to be established, it will intersect the first line in the
required point. This is the method of determining positions by prosection. Actually, the surveyor does
not regard the point as well established until the intersection is checked by a line from a third station.
In practical work, of course, each station is not occupied separately for the determination of each
point; tlie instrument is set up at a station, lines are drawn to all required points in view, and each line
is a]>proi)riately marked; then a second station is occupied, and the operation repeateii, and so on, the
various intei-sections being marked as the work proceeds.
A second method of establishing positions is that of resection; in this the first line is drawn from
some known station, as in the preceding method, and the observer next proceeds to the place whose
position is required ana occupies it; the plane table is there oriented by means of the line already
drawn, placing the edge of the rule along the line, sighting back toward the first station, and swinging
the table until that station is in the line of sight of the telescope; then choose some other established
station as nearly as possible at right angles to the direction of the first; i:>lace the edge of the rule upon,
the plotted position of this station and swing the alidade (the rule always being kept on the plotted
point) until the object is bisected by the telescope cross-hairs; draw this line, and its interse(!tion with
the first will give the required point, the accuracy of which can be checked from some other plotted
station.
A third method of locating a point is by means of a single bearing from a known station, with the
distance from the occupied station to the required one, the process of plotting being self-evident.
A fourth method is given by occupying an luidetermined position from which three established
stations are in view; the point occupied by the observer is then plotted by an application of the "three-
point problem."
419. It may be seen that where the greatest accuracy is not essential the plane table may be
employed for plotting all the points of a survey. In such a case it would only be necessary to begin
with the two base stations, plotted on the sheet on any relative bearing whatsoever and at a distance
apart eijual to the length of the base line (reduced t ) scale), as measured by the most accurate means
available. The work of plotting might even proceed before the base line had been measured, the two
stations being laid off at any convenient distance apart; when, later, the base line wa^ measured, the
scale of the chart would be determined, being eciual to the distance on the chart between base stations
divided by the length of the base line.
420. A plane table could be improvised on shipboard which would greatly facilitate the operation of
any, surveying work that a vessel not equipped with instruments might be called upon to perform. A
drawing board could be mounted upon a tripod (as, for example, the tripod supplied for compass work
on shore) in such manner as to be capable of motion in azimuth; it could be brought nearly to the
horizontal, if no better means offered, by moving the tripod legs, and this adjustment could be proved
by any small spirit level; sight vanes could be erected upon an ordinary ruler to take the place of the
alidade; in case there was difficulty in observing any object with such an alidade, because of its altitude
or for other reasons, a horizontal angle might be observed with a sextant and plotted with a pro-
tractor. By this means work could be done which, even if it should lack complete accuracy, might be
of great value.
421. The Telemeter and Stadia. — Any telescope fitted with a pair of horizontal cross-hairs at
the focus may be used as a telemeter, and v/hen accompanied by a graduated staff, called a stadia, affords
a means of measuring distance (up to certain limits) with a close degree of accuracy; the method con-
sists in observing the number of divisions of the scale subtended by the hairs when the stadia is held
up vertically and perpendicular to the line of sight of the teles -ope, it being evident that the closer the
distance the fewer divisions will appear between them. The facility with whicli distances can be
measured by this method makes it most important that all telescopes of theodolites, transits, and plane
tables be fitted as telen^eters, and that stadia rods be provided for all surveying work.
Speaking api)roximately, it may be .said that the number of divisions intercepted between the cross-
hairs will vary directly as the distance of the stadia rod. This would be exactly true if we looked at the
object through an empty tube, directly between the hairs. Since, however, the rays from the stadia are
refracted by the object glass before they are intercepted by the wires, the statement, to be absolutely
exact, must be slightly modified; but for j^ractical surveying work it may be accepted as given.
422. There are two methods of installing the telemeter cross-hairs — the first, in which they are
immovably secured in the telescope and always remain at the same distance apart, and the second, in
which the distance of the cross hairs is made variable, being under the control of the observer. The
former is generally regarded as the preferable method, and when it is employed it is evident that the
subtended height of the stadia bear3 a constant ratio to the distance of the staff from the telescope. It
proves mf)st convenient in i)ractice to space the hairs so that this constant ratio is some even multiple
of 10, for facility in converting scale readings into distance; it is also advantageous to mark the stadia
. in the unit of the chart scale and decimals thereof; for example, if the ratio of stadia height to distance
were 100, and the stadia were marked in meters and decimals, a reading of 2.07 would at once be con-
verted into a distance of 207 meters. Any units and any ratio may, however, be employed, and for any
given setting of cross-hairs it is very easy to graduate a stadia, by experiment, for any desired units; for
example, if it is required to mark the stadia in feet, set up and level the telescope, measure off a distance
of exactly 100 feet from it, hold up an unmarked staff and mark upon it the points intersected by the
cross hairs; the interval between these marks will represent 100 feet of the scale; divide this length into
100 parts, each of which will represent a distance of one foot, and mark the whole staff on the same scale;
then if the stadia be held up at any distance, the cross-hairs will intercept a number of divisions corre-
sponding to the r. umber of feet of distance.
MARINE SUEVEYING. 135
When the cross-hairs are movable the ratio becomes variable, but the principle of measuring
remains the same — namely, the distance of the staff from the telescope is equal to the existing ratio
multiplied by the distance intercepted on the scale.
4S3. The stadia is made of a light, narrow piece of wood and is usually hinged for convenience in
transporting. Ordinarily the background of the scale is painted white, while the main divisions are
marked in red, with minor divisions in black, and geometrical figures are employed to facilitate the
reading of fractional parts of the scale. Devices are furnished by which the man holding the stadia
may know when it is at right angles to the line of sight of the telescope — an essential condition for
accuracy of measurements.
424. Tlie use of the telemeter and stadia for measuring distances is limited to the distance at
which the scale divisions can be accurately read through the telescope. For fairly close work and with
the class of telescope usually supplied with surveying instruments, 400 meters represents about the
greatest distance at which it can be employed. With this limitation, the character of the survey
determines the nature of its employment. In a careful survey its greatest use would be in connection
with the theodolite or plane table in putting in shore lines, contour lines, and topography generally.
In a survey where only approximate results are sought it might afford the best means for the measure-
ment of the base.
425. If the telemeter be applied to a theodolite, transit, or plane table which is fitted with a
graduated vertical arc or circle, it is possible to measure the distance to the stadia not only in a horizontal
but also in a vertical direction. In this case the vertical angle must be observed as well as the stadia
reading. Tables are computed giving the solution of the triangles involved.
426. In making a survey with the ordinary resources of a ship, the principle of the telemeter and
stadia may be profitably employed, using a sextant and improvised staff. In this case it is usual to have
the stadia of some convenient flxed length, as, for example, 10 feet, and of slight width and thickness;
this is held at right angles to the line of sight from the observer, who notes the angle subtended by the
total length; tables are prepared by which the distance corresponding to each angle is given.
427. TiiK Skxtant. — This instrument is of the greatest value in hydrographic surveying. It is
fully described elsewhere in this work and its adjustment explained (Chap. VIII).
Sextants are manufactured of a form especially adapted to surveying work; they are smaller and
lighter than those usually employed in astronomical observations, but have a longer limb, by which
angles may be measured up to 135° ; the vernier is marked for quick reading and has no finer graduation
than half minutes; the telescope has a large field.
This instrument is principally employed in measuring the horizontal angles by means of which
soundings are plotted. It may, however, be put to various uses when making an approximate survey,
as has already been explained. It should be remembered, in measuring terrestrial angles with a sextant,
that rigorous methods require a reduction to the horizontal if either of the objects has material altitude
above the horizon.
42S. The Level. — This is an instrument for the accurate measure of differences of elevation. It
consists of a telescoi)e, carried in a Y-shaped rest, which is mounted upon a tripod and leveled in a man-
ner similar to a theodolite; but it differs from that instrument in that the telescope is not capable of
motion about a horizontal axis, and in having no graduated circle for ' measurements of altitude and
azimuth. The principle of its use contemplates placing the line of collimation of the telescope in a truly
horizontal plane and keeping it so fixed.
429. It is principally employed in marine surveying to determine heights and contour lines — the
latter being lines of equal elevation above the sea level — and for locating bench marks for tidal ob.serva-
tions (Chap. XX). In connection with it is used a graduated staff called a leveling rod, carrying a con-
spicuous mark, adjustable in height, called a target. To ascertain the difference of level between any
two points, set up the level with the telescope horizontal at some place between them; let an assistant
take the leveling rod to one of the jioints, and, while holding it on the ground in a truly vertical posi-
tion, move the target, under the dire(!tion of the observer at the telescope, to a point where it is exactly
bisected by the horizontal cross-hair; the height of the target on the staff — that is, the height of the cross-
hair above the level of tlie first point — is then accurately read with a vernier; now, without moving the
level, shift the rod to the second point and again adjust the target and read it. It is evident that a com-
parison of the reading at the first position with that at the second will give the difference of height at
the two points. The difference that can be read from one location of the instrument is limited by the
length of the rod; but by making a sufficient luimber of shifts any difference may be mea.sured.
The work of the level may be performed equally well by a theodolite whose telescope is adjusted
to the true horizontal.
430. Heliotrope and HELioGRAPn.-^These are instruments sometimes employed in surveying, by
means of which the sun's rays may be reflected in any given direction; the object of their use is to
render conspicuous a station which is to be observed at a distance and which would not otherwise jje
distinguishable. The instruments vary widely in form of construction and, in the absence of those
made for the purpose, substitutes may easily be devised.
4tJl. Astro xoMicAL Transit Ixhtrumexts. — Various instruments are employed for the astronom-
ical determinations necessary in a marine survey. Among these are the zenith telescope and portable
transit. While differing in detail they consist essentially of a telescope mounted upon a horizontal
axis that is placed truly in the prime vertical, thus insuring the revolution of the line of collimation in
the meridian; a vertical graduated circle and vernier are supplied, affording a measure of altitude; in
the focus are a number of equidistant vertical cross-hairs or lines; a small lamp is so placed that its
rays illuminate the cross-hairs and render possible observations at night. Latitude is obtained by
observing the meridian altitude of stars; hour angle (and thence longitude) by observing the times of
their meridian transit, which is taken from the mean of the times of passing all of the vertical cross-hairs.
Excepting in surveys of a most accurate nature, the astronomical determination of position by the
sextant and artificial horizon is regarded as satisfactory.
136
MARINE SURVEYING.
432. The Three- Armed Protractor, or Station' Pointer. — This is an instrument whereby posi-
tions are plotted on the principle of the "three-point problem," of which an explanation is given in
article 152, Chapter IV. It consists (tig.
56) of a graduated circle with three arms
pivoted at the center; each arm has one
edge that is a true rule, the direction of
which always passes through the center
of the circle. The middle arm is immov-
ably fixed at the zero of the scale; the
right and left arms each revolve about the
center on their own side^ and are ])ro-
vided with verniers giving the angular
distance from the middle arm. The pro-
tractor being set for the right and left
angles, it is so moved that the three arms
pass through the respective stations, when
the center marks the position of the ob-
server. Center pieces of vari-jus forms
are provided, being cylindrical plugs
made to fit into a socket at the pivot, and
by employing one or the other of them
the true center may be pricked with a
needle, dotted with a pencil, or its position
indicated by cross-hairs. Adjustable arms
are provided which can be fitted to the
ends of the ordinary arms when working
with distant signals.
The most valuable use of the three-
armed protractor is in plotting the posi-
tions of soundings taken in boats, where
sextant angles between signals are ob-
served. It may occur, however, that
certain shore stations will be located by
its use.
433. In default of a three-armed
protractor, a piece of tracing paper may
be made to answer its purpose. To use
the tracing paper, draw a line, making a
dot on it to represent the center station,
and with the center of an ordinary pro-
tractor on the dot, lay off the two observed
angles right and left of the line; then,
laying this on the plan, move it about till
the three lines pass exactly through the
three stations observed. The dot from
which thev were laid off will be on the
Fu;. 56.
position of the observer, and must be pricked lightly through or marked underneath in pencil.
434. The Beam Compass. — This instrument (fig. 57) is employed in chart drafting and performs
the functions of compasses and dividers when the dis-
tance that must be spanned is beyond the limits of
those instruments in their ordinary form. It consists
of an angular bar of wood or metal upon which two
instruments termed beam heads are fitted in such a
manner that the bar may slide easily through them.
A clamping screw attached to one side of the beam
head will fix it in any jmrt of its course along the
beam. Upon each head a socket is constructed to
carry a plain point, exchangeable for an ink or a
pencil point. For exact purposes the beam head
placed at the end of the beam has a fine adjustment,
which moves the point a short distance to correct
any error in the first rough setting of the instrument.
This adjustment generally consists of a milled-head
screw, which jjasses through a nut fixed upon the
end of the beam head, which it carries with its
motion.
435. Proportional Dividers. — These are prin-
cipally employed for reducing or enlarging drawings
in any given proportion. They consist (fig. 58) of
two narrow flat pieces of metal called legs^, which
turn upon a pivot whose position is movable in the
direction of their length. The ends of both legs are shaped into points like those of ordinary dividers.
When the pivot is fixed at the middle of the legs, any distance measured by the points at one end is
just equal to that measured by those at the other; for any other location of the pivot, however, the
Fig. 57
MARINE SURVEYING.
137
distances thus measured will not be equal, but with a given setting of the pivot any distance measured
by one end bears a fixed ratio to that measured by the other. The path of travel of the pivot is gradu-
ated so that the ratio may he given any desired value. Being adjusted in this respect, if a distance is
taken off a chart with the legs at one end of the instrument, then those at the other
end will show the same distance on the scale of a chart enlarged or reduced in the pro-
portion represented by the ratio for which the pivot was set.
METHODS EMPLOYED IN A HYDROGRAPHIC SURVEY.
436. A geodetic survey has for its object the determination, with the greatest
attainable accuracy, of points on the surface of the earth, by the employment of a pro-
cess of triangulation, all positions being located either trigonometrically or astronomic-
ally, and the curvature of the earth being taken into account.
Before commencing a survey a general inspection of the field is made; a base line
is located and its extremities marked by Klgnah; certain other positions, known as inahi
tricmgvlatlon points, are selected and also marked with signals, being so chosen that,
starting with the base and proceeding thence from one to another of these points, a
series of well-conditioned triangles or quadrilaterals may cover the field of survey. The
base line is measured with the greatest degree of accuracy which the resources of the
survey render possible. Each extremity of the base line and each other main tri-
angulation point is occupied by an observer with a theodolite, who measures the angles
at each station between all the other stations which are in sight. An astronomical
determination is made of the latitude and longitude of some point of the survey (fre-
quently one of the extremities of the base) and of the true azimuth of some known line
(frequently the base line) . Data is now at hand for the location upon the chart of the
base line and main triangulation points.
If the survey is one of considerable extent it is expedient to measure a check haM'
near the end of the triangulatif)n, a comparison between the measured and the computed
distance between any two stations showing the accuracy of the work and affording a
means of reconciling discrepancies. The position of a second observation spot may be
determined for a similar purpose.
The primary triangulation gives a skeleton of the field, but the points thus deter-
mined are not usually close enough together to afford a basis for all the detail work
that must be done. A second system of points is therefore selected and signals erected
thereon, and the position of these points is determined by a series of angles from the
main triangulation points and from each other. This is known as the secondary tri-
angulation. The yjoints thus located are used in the plotting of the topography and hydro-
graphy. It is not essential that their determination be as accurate as that of main
triangulation points.
The topography is put in, and includes the delineation of the features of the land —
shore line, light-houses, beacons, contour lines, peaks, buildings, and, in short, every-
thing that may be recognized by the navigator and utilized by him in locating the ship's pxG. 58.
position.
The hydrographic work is taken up and the depth of water and character of bottom determined as
accurately as possible for the complete water area, especial care being taken to develop all shoals and
dangers to navigation and to locate all aids to navigation, such as buoys, light-ships, and beacons.
One or more tidal .'Stations are established where observations are taken, continually and at frequent
intervals, of the height of the tide and direction and velocity of the tidal and other currents, whence
data is derived for the reduction of all soundings to the plane of reference and for the information aVjout
tides and currents which is to appear upon the chart.
Observations are made to determine the magnetic A'ariation and dip, and the intensity of the earth's
magnetic force.
437. The foregoing represent, in outline, the various steps that must be taken in the accumulation
of the data necessary for the construction of a complete hydrograpliic chart. In the following para-
graphs the details of the various operations will be more fully set forth.
The navigator who is called upon to conduct a marine survey without having available the time,
instruments, and general facilities necessary for the most thorough performance of the work must
exercise his discretion as to the modifications of method that he will make, and call upon his ingenuity
to adapt his means to the particular work in hand, x
'838. The Base Line. — As the base line is the foundation for all distances on the chart, the cor-
rectness of the results of the survey will depend largely upon the degree of accuracy with which it is
measured. The triangulation merely affords a measure of the various distances as compared with the
distances between the two initial points from which it began; if that initial distance is 1,000 feet, we
have certain values for the sides of the various triangles; if the same base line is 2,000 feet, th^ value
of each side becomes twice as great as it was before; with the same triangulation, therefore, distances
vary directly with the length of the base line; it may thus be seen that if an error exists in measurement
which is only a small fraction of the total length, the error will become much more material as the
more distant points of the survey are reached. In a base line 1,000 feet long, if a mistake of 10 feet be
made, all distances measured upon the chart will be in error 1 per cent, And a point plotted by trian-
gulation 10 miles from the observation spot (the point at which plotting begins), would be out of its
correct position one-tenth of a mile.
It is important that the base line should be as long as possible, as an error in measurement will
thus constitute a smaller percentage of the total length and will not accumulate so rapidly as the work
proceeds. The position of the line must be such as to afford favorably conditioned triangles and quadri-
138 MARINE SURVEYING.
laterals with adjoining main triangulation points, and its extremities must be visible from those points
and from each other. The character of the ground and the facility for measuring will of course form an
important consideration in the choice.
.439. In measuring a base by tape, chain, or similar means, a number of successive fleets are made
with the measure, wliatever its nature, the distance traversed l^eing appropriately marked after each
fleet, while an observer, with a theodolite or transit, insures the measurement b?nig made accurately
along the line.
440. The most careful measurements are made by a steel tape 100 feet long, stretched along a series
of battens which are supported by metal crutches and made exactly horizontal by a level. The tape is
stretched to a uniform tens^ion by a spring balance; its exact length at that tension is known from compar-
ison with some standard; a correction for temperature is applied. The ends of the fleets are marked by
driving into the grouncfa peg carrying in its top a tack; the exact end of the tape is marked by a score
filed on the head of the tack at a point marked by a plumb bob from the tape, and this score becomes the
origin for the next fleet. An assistant precedes the measuring party before each shift of the battens, and
is accurately aligned by the theodolite to mark the true direction of the base line. The result of this
method of measurement gives the horizontal distance between the points. It can be depended upon for
the greatest degree of accuracy of any method, excepting that with a special hasc-measurmg apparatus,
which is seldom employed in marine surveys.
441. A second method of })ase measurement is with the surveyor's chain. This depends for accu-
racy upon the surface traversed being plane and level, a condition that is well fulfilled on a sandy
beach, where the chain is nearly as accurate as the tape and much more rapid. A surveyor's chain is
usiially 100 feet long; the exact value of its length must be obtained by comparison with a standard,
and a correction applied for expansion or contraction due to temperature. The ends of the fleets are
marked by steel pnis driven into the ground; the alignment is kept by the theodolite.
442. Where neither chain nor ttipe is available substitutes may be improvised from sounding
wire taken from the deep-sea sounding machine, or, failing this, from well-stretched cod line.
443. Measurements made by the telemeter and stadia afford a close approximation to the true
result, and if these instruments are not at hand the sextant angle of a rod of fixed length can be employed.
The masthead height of the vessel may be used in determining the length of base line on this principle,
either by making the ship itself mark one of the extremities and observing the masthead angle from
the other extremity, or by simultaneously observing the masthead angle from both ends of a shore
base, and also the three horizontal angles of the triangle formed by the ship and the two base stations.
The latter plan is far preferable where accuracy is sought, as, if the angles are all taken by different
observers at the same instant (which can be marked by the hauling down of a flag), the error arising
from the motion of the ship about her anchor is eliminated, and, moreover, the data furnished offers a
double solution of the triangle and the mean may be taken as giving a closer result.
444. A crude method of measuring a base is by means of the velocity of sound, though this would
never be used where close results are expected. Fire a gun at one end of the base and at the other
note by the most accurate means available the time between seeing the flash and hearing the report.
Eepeat several times in each direction. The mean number of seconds and tenths of a second multiplied
by the velocity of sound per second at the temperature of observation (art. 314, Chap. XI) gives the
approximate length of base line.
445. When for any reason the existing conditions do not permit of a direct measurement being
made along the line between the two base stations, recourse must be had to a broken base, that is, one
in which the length of the base is obtained by reduction from the measured length of two or more
auxiliary lines. Necessity for resorting to a broken base arises frequently when the two stations are
situated on a curving shore line and the straight line between them passes across water, or where wooded
or unfavorable country intervenes, or where a stream must be crossed. The most common form of
broken base is that in which the auxiliary lines run from each extremity of the base at an acute angle
and intersect; in addition to measuring each of these lines, the angles of the triangle formed by them
with the base line must be observed and the true length of the base deduced by solution of the triangle.
The form that is most frequently used where only a short section of the base is incapable of measure-
ment (as is the case where a deep stream flows across) is that of an auxiliary right triangle whose base
is the required distance along the base line and altitude a distance measured along a line perpendicular
thereto to some convenient point; by this measured distance and the angles which are observed, the
triangle is solved and the length of the unmeasured section determined.
446. In a survey of considerable extent, where good means are at hand for the correct determina-
tion of latitude and longitude, a base line actually measured upon the earth may be dispensed with,
and, instead of that, the jtositions of the two stations which are most widely separated may be deter-
mined astronomically and plotted; the triangulation is then plotted upon any assumed scale, and when
it has been brought up to connect the two stations the true value of the scale is ascertained. This is
called the method of an astronomical base.
447. Signals. — All points in the survey whose positions are to be located from other stations,' or
from which other ])ositions are to be located, must be marked by signals of such character as will render
them distinguishable at the distance from which they are observed. The methods of constructing signals
are of a wi(le variety. "
A vessel regularly fitted out for surveying would carry scantlings, lumber, bolts, nuts, nails, white-
wash, and sheeting for the erection of signals; however meager the equipment, the whitewash and
sheeting (or some substitute for sheeting, preferably half of it white and half dark in color, ) should he
provided, if possible, before l)eginning any surveying work. Regular tripod signals, which are quickly
erected and are visible, under favorable circumstances, for many miles, are almost invariably employed
to mark the main triangulation stations; among other advantages the tripod form permits the occupation
with the theodolite of the exact center of the station, and avoids the necessity for the reduction which must
otherwise be applied. Signals on secondary stations take an innumerable variety of forms, the require-
MARINE SURVEYING. 139
ment being only that they shall be seen throughout the area over which they are to be made use of;
a whitewashed spot on a rock, a whitewashed trunk of a tree, a whitewashed cairn of stones, a sheeting
flag, a piece of sheeting wrapped about a bush or hung, with stones attached, over a cliff, or a white-
washed barrel or box filled with rocks or earth and surmounted by a flag, suggest some of the secondary
signals that may be employed; sometimes objects are found that are sufiiciently distinct in themselves
to be used as signals without further marking, as a cupola or tower, a hut, a lone tree, or a bowlder; but
it is seldom that an object is not rendered more conspicuous by the flutter of a flag above it, or by the
dead-white ray reflected from a daub of whitewash.
For convenience, each signal is given some short name by which it is designated in the records.
448. The Main Triangulatiox. — ^The points selected as stations for the main triangulation mark
in outline the whole area to be surveyed; they are close enough together to afford an accurate means
of plotting all intermediate stations of the secondary triangulation; and they are so placed with relation
to one another that the triangles or quadrilaterals derived from them are well conditioned. The points
are generally so chosen that small angles will be avoided. In order to fulfill the other conditions, it
frequently becomes necessary to carry forward the triangulation by means of stations located on points
a considerable distance inland, suclii as mountain peaks, which would not otherwise be regarded as
properly within the limits of the surv^ey.
Great care should be taken in observing all angles upon which the main triangulation is based; the
best available instrument should be employed; angles taken with a theodolite or transit should be
repeated, and observed with telescope direct and reversed, and the mean result taken; if the sextant is
used, a number of separate observations of each angle should be taken and averaged for the most prob-
able value. It must be remembered that while, in any other part of the work, an error in an angle
affects only the results in its immediate vicinity, a mistake in the main triangulation goes forward
through all the plotting that comes after it.
It frequently occurs that the purposes of the survey are sufficiently well fulfilled by a graphic plot-
ting of the main triangulation, but where more rigorous methods prevail, the results are obtained by
calculation. The sum of the angles of each triangle is taken, and if it does not exactly equal 180° the
values are adjusted to make them comply with this condition. The lengths of the various sides are
then computed, regarding the stations, usually, as forming a series of quadrilaterals, and allowing for
the curvature of the earth where the sides are sufficiently long to render it expedient to do so.
449. The Secondary Triangulation. — The points of the secondary triangulation are located, as
far as possible, by angles from the main triangulation stations; these angles, having less dependent upon
them, need not be repeated. A graphic plotting of these stations, without calculation, will suffice.
450. Astronomical Work. — This comprises the determination of the correct latitude and longitude
of some point of the survey, which is the first position plotted, and of the true direction of some other
point from the observation spot, which is the first line to be laid down on the chart; it is evident that
these determinations form the origin of all positions and of all directions, without which the chart
could not be constructed.
The methods of finding latitude, longitude, and the true bearing of a terrestrial object are fully set
forth in previous chapters. The feature that distinguishes such work in surveying from that of deter-
mining the position of a ship at sea lies in the greater care that is taken to eliminate possible errors.
At sea, results of absolute exactness are recognized as unattainable and are not required; but in a careful
survey no step which will contribute to accuracy should be neglected.
Tlie results should therefore be based upon a very large number of observations, employing the
best instruments that are available, and the various sights being so taken that probable errors are offset
in reckoning the mean.
4.51. By taking a number of sights the observer arrives at the most probable result of which his
instruments and his own faculties render him capable; but this result is liable to an error whose amount
is indeterminate and which is etiual to the algebraic sum of a number of small errors due, respectively,
to his instruments (which must always lack perfection in some details), to an improper allowance for
refraction under existing atmospheric conditions, and to his own personal error. Assuming, as we
may, that the personal error is approximately constant, these three causes give rise to an error by which
all altitudes appear too great or too small by a uniform but unknown amount. Let us assume', for an
illustration, that this error has the effect of making all altitudes appear 30'^ too great; if an observer
attempted to work his latitude from the meridian altitude of a star bearing south, the result of this
unknown error would give a latitude 30''' south of the true latitude; if another star to the southward
were observed, this mistake would be repeated; but if a star to the north were taken, the resulting
latitude would be 30'^ to the north. It is evident, therefore, that the true latitude will be the mean of
the results of observation of the northern and the southern star, or the mean of the average of several
northern stars and the average of several southern stars. A similar process of reasoning will show that
errors in the determination of hour angle are offset by taking the mean of altitudes of objects respectively
east and west of the meridian.
452. It must be remembered that the uniformity of the unknown error only exists where the
altitude remains approximately the same, as instrumental and refraction errors may vary with the
altitude; another condition of uniformity requires that the instrument and the observer remain the same,
and that all observations be taken about the same time, in order that atmospheric conditions remain
unchanged; to preserve uniformity, if the artificial horizon is used, the same end of the roof should
always be the near one to the observer; in taking the sun, however, as the personal error may not be
the same for approaching as for separating limbs, every series of obsers^ations should be made up of an
equal number of sights taken under each condition.
453. With all of this in mind, we arrive at the general rule that astronomical determinations
shall be based upon the mean of observations, under similar conditions, of l)odies whose respective dis-
tances from the zenith are nearly equal, and which bear in opposite directions therefrom.
140 MARINE SURVEYING.
454. This condition eliminates the sun from availability for observations for latitude, though it
properly admits the use of that body for longitude where equal altitudes or single a. m. and p. m. sights
are taken. Opposite stars of approximately equal zenith distance should always be used for latitude,
circum-meridian altitudes being observed during a few minutes before and after transit; excellent results
are also obtained from stellar observations for longitude; but very low stars should be avoided, on
account of the uncertainty of refraction, and likewise very high ones, as the reflection from the index
mirror of the sextant may not be perfectly distinct when tne ray strikes at an acute angle.
455. If there is telegraphic communication, an endeavor should be made to obtain a time signal
from a reliable source, instead of depending upon the chronometers.
456. Topography. — The plane-table, with telemeter and stadia, affords the most expeditious means
of plotting the topograijhy, and should be employed when available. Points on shore may also be
plotted by sextant angled, using the three-point problem, or by any other reliable method.
457. Hydrography. — The correct delineation of the hydrographic features being one of the most
important objects of the survey, great care should be devoted to this part of the work. Soundings are
run in one or more series of parallel lines, the direction and spacing oi which depend upon the scope of
the survey. It is usual for one series of lines to extend in a direction normal to the general trend of the
shore line. In most cases a second series runs perpendicular to the first, and in surveys of important
bodies of water still other series of lines cross the system diagonally. In developing rocks, shoals, or
dangers the direction of the lines is so chosen as will best illustrate the features of the bottom. When
lines cross, the agreement of the reduced soundings at their intersection affords a test of the accuracy of
the work.
As the depth of water increases, if there is no reason to suspect dangers, the interval between lines
may be increased.
Lines are run by the ship or boat in such manner as to follow as closely as possible the scheme of
sounding that has been laid out. The position is located by angles at the beginning of each line, at each
change of course, at frequent intervals along the line, and at the point where each line is finished.
Soundings taken between positions are plotted by the time interval or patent-log distances.
458. There are a number of methods for determining positions while sounding, which may be
described briefly as follows:
By tico sextant angles. — Two observers with sextants measure simultaneously the angles between
three objects of known position, and the position is located by the three-point problem. This is the
method most commonly employed in boat work, and has the great advantage that the results may be
plotted at once on the working sheet in the boat and the lines as run thus kept nearly in coincidence
with those laid out in the scheme. A study of the three-point problem (art. 153, Chap. IV) will give
the considerations that must govern in the selection of objects.
By two theodolite angles. — Two stations on shore are occupied by observers with theodolites, and at
certain instants, indicated by a signal from the ship or boat, they observe the angular distance thereof
from some known point. The intersection of the direction lines thus given is at the required position.
This method is expeditious where the signals are small or not numerous. Its disadvantage is that the
plotting can not be kept up as the work proceeds.
By one sextant and one theodolite angle. — An observer ashore occupies a station with a theodolite and
cuts in the ship or boat, while one on board takes a sextant angle between two objects, of which one
should preferably be the occupied station. It is plotted by laying off the direction line from the theodo-
lite and finding with a three-armed protractor or piece of tracing paper what point of that line subtends
the observed angle between the objects. Its advantages and disadvantages are the same as those of the
preceding method.
In running lines of soundings offshore, where signals are lost sight of, the best method is to get an
accurate departure, before dropping the land, by the best means that offers, keeping careful note of the
the dead reckoning, and on running in again, to get a position as soon as possible, note the drift and
reconcile the plotting of intermediate soundings accordingly. Where circumstances require, the position
may be located by astronomical observations as usually taken at sea.
459. A careful record of soundings must be kept, showing the time of each (so that proper tidal
correction may be applied), the depth, the character of bottom, and such data as may be required to
locate the position.
460. Tidal Observations. — These should begin as early as practicable and continue throughout
the survey, it being most important that they shall, if possible, cover the period of a lunar month. In
the chapter on Tides (Chap. XX) the nature of the data to be obtained is explained.
461. Magnetic Observations. — The feature of the earth's magnetism with which the navigator is
most concerned is the variation, which is set forth on the chart, and upon the determination of which
will depend the correctness of all courses and bearings on shipboard. It is usually obtained by noting
the compass direction from the observation spot of the object whose true bearing is known by calcula-
tion, and comparing the true and compass bearings; or it may be observed by mounting the ship's com-
pass in a place on shore free from foreign magnetic influence, and finding the compass error as it is found
on board. Observations for dip and intensity are also made when the proper instruments are at hand.
462. Running Survey. — Where time and opportunity permit only a superficial examination of a
coast line or water area, or where the interests of navigation require no more, recourse is had to a Run-
ning Surrey, in which shore positions are determined and soundings are made while the ship steams
along the coast stopping only occasionally to fix her position, and in which the assistance of boat or
shore parties may or may not be employed.
In this method the ship starts at one end of the field from a known position, fixed either by astro-
nomical observations or by angles or bearings of terrestrial objects having a determined location. Care-
ful compass bearings or sextant angles are taken from this position to all objects ashore which can be
recognized, and a series of direction lines is thus obtained. The ship then steams along the coast, at a
convenient distance therefrom, keeping accurate account of her run by compass courses and patent log.
MARINE SURVEYING. 141
From time to time other series of bearings or angles are taken upon those objects ashore which are to be
located, the direction lines plotted from the estimated position of the ship, and the various objects located
by the intersections with their other direction lines. During all the time that the ship is under way,
soundings are taken at regular intervals and plotted from the dead reckoning. As frequently as circum-
stances permit, the ship is stopped and her position located by the best available means, and the inter-
vening dead reckoning reconciled for any current that may be found.
If a steam launch can be employed in connection with a running survey, it is usually sent to run a
second line inshore of the ship. The boat's position is obtained by bearings of objects ashore which are
located by the ship, or by bearings and mast-head angles of the ship, or by such other means as offer.
The duty of the boat is to take a series of soundings, and to collect data for shore line and topography.
If circumstances allow the landing of a shore party, its most important duty is to mark the various
objects on shore by some sort of signals which will render them unmistakable. Beyond this, it can
perform such of the duties assigned to shore parties in a regular survey as opportunity permits.
142 WINDS.
CHAPTER XVIIL
WINDS.
463. Wind is air in approximately horizontal motion. Observations of the wind should include
its true direction, and its force or velocity. The direction of the wind is designated by the point of the
compass from which it proceeds. The force of the wind is at sea ordinarily expressed in terms of
the Beaufort Scale, each degree of this scale corresponding to a certain velocity in miles per hour, as
explained in article 67, Chapter II.
464. The Caise of the Wind. — Winds are produced by differences of atmospheric pressure, which
are themselves ultimately, and in the main, attributable to differences of temperature.
To undei-stand how the air can be set in motion by these differences of pressure it is necessary to
have a clear conception of the nature of the air itself.
The atmosphere which completely envelops the earth may be considered as a fluid sea at the
bottom of which we live, and which extends upward to a considerable height, probably 200 miles,
constantly diminishing in density as the altitude increases.
The air, or material of which this atmosphere is composed, is a transparent gas, which, like all
other gases, is perfectly elastic and highly compressible. Although extremely light, it has a perfectly
definite weight, a cubic foot of air at ordinary pressure and temperature weighing 1.22 ouncres, or about
one seven hundred and seventieth part of the weight of an equal volume of water. In consequence of
this weight it exerts a certain pressure upon the surface of the earth, amounting on the average to 15
pounds for each square inch. To accurately measure this pressure, which is constantly undergoing ■
slight changes, we ordinarily employ a mercurial barometer (art. 48, Chap. II), an instrument in which
the weight of a column of air of given cross section is balanced against that of a column of mercury
having an equal cross section; and instead of saying that the pressure of the atmosphere is a certain
number of pounds on each square inch, we say that it is a certain number of inches of mercury, meaning
thereby that it is equivalent to the pressure of a column of mercury that many inches in height, and
one square inch in cross section.
All gases, air included, are highly sensitive to the action of heat, expanding or increasing in volume
as the temperature rises, contracting or diminishing in volume as the temperature falls. Suppose
now that the atmosphere over any considerable region of the earth's surface is maintained at a
higher temperature than that of its surroundings. The warmed air will expand, and its upper layers
will flow off to the surrounding regions, cooling as they go. The atmospheric pressure at sea level
throughout the heated areas Mill thus be diminished, while that over the circumjacent cooler areas will
be correspondingly increased. As the result of this difference of pressure, there will be movement of
the surface air away from the region of high pressure and towards the region of low, somewhat similar
to the flow of water which takes place through the connecting bottom sluice as soon as we attempt to
fill one compartment of a divided vessel to a slightly higher level than that found in the other.
A difference of atmospheric pressure at sea level is thus immediatelj' followed by a movement of
the surface air, or by winds; and these differences of pressure have their origin in differences of tempera-
ture. If the atmosphere were everywhere of uniform temperature it would lie at rest on the earth's
surface — sluggish, torpid and oppressive — and there would be no winds. This, however, is fortunately
not the case. The temperature of the atmosphere is continually or periodically higher in one region
than in another, and the chief variations in the distribution of temperature are systematically repeated
year after year, giving rise to like systematic variations in the distribution of pressure.
465. The Normal Distkibittion of Pressure. — The winds, while thus due primarily to differences
of temperature, stand in more direct relation to differences of pressure, and it is from this point of view
that they are ordinarily studied.
In order to furnish a comprehensive view of the distribution of atmospheric pressure over the
earth's surface, charts have been prepared showing the average reading of the barometer for any given
period, whether a month, a season, or a year, and covering as far as possible the entire globe. These
are known as isobaric charts, from the fact that all points at which the barometer has the same reading
are joined by a continuous line or isobar.
The isobaric chart for the year (fig. 59) shows in each hemisphere a well-defined belt of high
pressure (30.20 inches) completely encircling the globe, that in the northern hemisphere having its
middle line about in latitude 35° North, that in the southern hemisphere about in latitude 30° South,
these constituting the so-called meteorological tropics. From the summit or ridge of each of these belts
the pressure fails off alike toward the equator and toward the pole, although much less rapidly in the
former direction than in the latter. The equator itself is encircled by a belt of somewhat diminished
pressure (29.90 inches), the middle line of which is ordinarily found in northern latitudes. In the
northern hemisphere the diminution of pressure on the poleward slope is much less marked and much
less regular than in the southern hemisphere, minima (29.70 inches) occurring in the North Atlantic
Ocean near Iceland, and in the North Pacific Ocean near the Aleutian Islands, beyond which the
pressure increases. In the southern hemisphere no such minima are apparent, the pressure continuing
to diminish uninterruptedly as higher and higher latitudes are attained. Along the sixtieth parallel of
south latitude the average barometric reading is 29.30 inches.
WIlN'DS.
143
Fig. 59.
144 WINDS.
466. Seasoxal Variatioks of Pressurk. — As might be expected from its close relation to the
temperature, the whole system of pressure distribution exhibits a tendency to follow the sun's motion
in declination, the barometric equator occupying in July a position slightly to the northward of its
position in January. In either hemisphere, moreover, the pressure over the land during the winter
season is decidedly above the annual average, during the summer season decidedly below it; the
extreme variations occurring in the case of continental Asia, where the mean monthly pressure ranges
from 30.50 inches during January to 29.50 inches during July. Over the northern ocean, on the other
hand, conditions are reversed, the summer pressures being here somewhat the higher. Thus, in January
the Icelandic and the Aleutian minima increase in depth to 29.50 inches, while in July these minima
fill up and are well-nigh obliterated, a fact which has much to do with the strength and frequency of
the winter gales in high northern latitudes and the absence of these gales during the summer. Over
the southern ocean, m keeping with its slight contrast between winter and summer temperatures,
similar variations of pressure do not exist.
467. The Prevailing Winds. — As a result of the distribution of pressure just described, there is
in either hemisphere a continual motion of the surface air away from the meteorological tropic — on one
side towards the equator, on the other side towards the pole, the first constituting in each case the
trade winds, the second the prevailing winds of higher latitudes. Upon a stationary earth the direction
of this motion would be immediately from the region of high towards the region of low barometer, the
moving air steadily following the barometric slope or gradient, increasing in force to a gale where these
gradients are steep, decreasing to a light breeze where they are gentle, sinking to a calm where they
are absent. The earth, however, is in rapid rotation, and this rotation gives rise to a force which
exercises a material influence over all horizontal motions upon its surface, whatever their direction,
serving constantly to divert them to the right in the northern hemisphere, to the left in the southern.
The air set in motion by the difference of pressure is thus constantly turned aside from its natural
course down the barometric gradient or slope, and the direction of the wind at any point, instead of
being identical with that of the gradient at that point, is deflected by a certain amount, crossing the
latter at an angle which in practice varies between 45° and 90° (4 to 8 compass points), the wind in
the latter case blowing parallel to the isobars. As a consequence of this deflection the northerly winds
which one would naturally expect to find on the equatorial slope of the belt of high pressure in the
northern hemisphere become northeasterly, — the NE. trade; the southerly winds of the polar slope
become southwesterly, — the prevailing westerly winds of northern latitudes. So, too, for the southern
hemisphere, the southerly winds of the equatorial slope here becoming southeasterly, — the SE. trades;
the northerly winds of the polar slope northwesterly, — the prevailing westerly winds ti southern
latitudes.
46§. The relation here described as existing between the distribution of atmospheric pressure and
the direction of the wind is of the greatest importance. It may be briefly. stated as follows:
In the northern hemisphere stand with the back to the wind; in this position the region of high
barometer lies on your right hand and somewhat behind you; the region of low barometer on your left
hand and somewhat in front of you.
In the southern hemisphere stand with the back to the wind; in this position the region of high
barometer lies on your left hand and somewhat behind you; the region of low barometer on your right
hand and somewhat in front of you.
This relation holds absolutely, not only in the case of the general distribution of pressure and cir-
culation of the atmosphere, but also in the case of the special conditions of high and low pressure which
usually accompany severe gales.
469. The Trade Winds. — The Trade Winds blow from the tropical belts of high pressure towards
the equatorial belt of low pressure — in the northern hemisphere from the northeast, in the southern
hemisphere from the southeast. Over the eastern half of each of the great oceans they extend consid-
erably farther from the line and their original direction inclines more towards the pole than in mid-
ocean, where the latter is almost easterly. They are ordinarily looked upon as the most constant of
winds, but while they may blow for days or even for weeks with slight variation in direction or
strength, their uniformity should not be exaggerated. There are times when the trade winds weaken
or shift. There are regions where their steady course is deformed, notably among the island groups of
the South Pacific, where the trades during January and February are practically nonexistent. They
attain their highest development in the South Atlantic and in the South Indian Ocean, and are every-
where fresher during the winter than during the summer season. They are rarely disturbed by cyclonic
storms, the occurrence of the latter within the limits of the trade wind region being furthermore con-
fined in point of time to the late summer and autumn months of the resijective hemispheres, and in
scene of action to the western portion of the several oceans. The South Atlantic Ocean alone, however,
enjoys complete immunity from tropical cyclonic storms.
470. The Doldrums. — The equatorial girdle of low pressure occupies a position between the high-
pressure belt of the northern and the similar belt of the southern hemisphere. Throughout the extent
of this barometric trough the pressure, save for the slight diurnal oscillation, is practically uniform, and
decided barometric gradients do not exist. Here, accordingly, the winds sink to stagnation, or rise at
most only to the strength of fitful breezes, coming first from one point of the compass, then from another,
with cloudy, rainy sky and frequent thunderstorms. The region 'throughout which these conditions
prevail consists of a wedge-shaped area, the base of the wedge resting in the case of the Atlantic Ocean
on the coast of Africa, and in the case of the Pacific Ocean on the coast of America, the axis extending
westward. The position and extent of the belt vary somewhat with the season. Throughout February
and March it is found immediately north of the equator and is of inappreciable width, vessels following
the usual sailing routes frequently passing from trade to trade without interruption in both the Atlantic
and the Pacific Oceans. In July and August it has migrated to the northward, the axis extending east
and west along the parallel of 7° north, and the belt itself covering several degrees of latitude, even at
its narrowest point. At this season of the year, also, the southeast trades blow with diminished fresh-
ness across the equator and well into the northern hemisphere, being here diverted, however, by the
effect of the earth's rotation, into southerly and southwesterly winds, the so-called southwest monsoon
of the African and Central American coasts.
WINDS. 145
471. The Horse jlatitudes. — On the outer margin of the trades, corresponding vaguely with the
summit of the tropical ridge of high pressure in either hemisphere, is a second region throughout which
the barometric gradients are faint and undecided, and the prevailing winds correspondingly light and
variable, the so-called hor^e latitudes, or calms of Cancer and of Capricorn. Unlike the doldrums, how-
ever, the weather is here clear and fresh, and the periods of stagnation are intermittent rather than
continuous, showing none of the persistency which is so characteristic of the equatorial region. The
explanation of this difference will Ijecome obvious as soon as we come to study the nature of the daily
barometric changes of pressure in the respective regions, these in the one case being marked by the
uniformity of the torrid zone, in the other sharing to a limited extent in the wide and rapid variations
of the temperate.
472. The Prevailing Westerly Winds. — On the exterior or polar side of the tropical maxima
the pressure again diminishes, the barometric gradients being now directed towards the pole; and the
currents of air set in motion along these gradients, diverted to the right and left of their natural course
by the earth's rotation, appear in the northern hemisphere as southwesterly winds, in the southern
hemisphere as northwesterly — the prevailing westerly winds of the temperate zone.
Only in the southern hemisphere do these winds exhibit anything approaching the persistency of
the trades, their course in the northern hemisphere being subject to frequent local interruption by
periods of winds from the eastern semicircle. Thus the tabulated results show that throughout the
portion of the North Atlantic included between the parallels 40°-50° North, and the meridians 10°-50°
West, the winds from the western semicircle (South — NNW.) comprise about 74 per cent of the whole
number of observations, the relative frequency being somewhat higher in winter, somewhat lower in
summer. The average force, on the other hand, decreases from force 6 to force 4 Beaufort scale, with
the change of season. Over the sea in the southern hemisphere such variations are not apparent; here
the westerlies blow through the entire year with a steadiness little less than that of the trades them-
selves, and with a force which, though fitful, is very much greater, their boisterous nature giving the
name of the " Roaring Forties" to the latitudes in which they are most frequently observed.
The exi)lanation of this striking difference in the extra-tropical winds of the two halves of the globe
is found in the distribution of atmospheric pressure, and in the variations which this latter undergoes in
different parts of the world. In the landless southern hemisphere the atmospheric pressure after cross-
ing the parallel of 30° South diminishes almost uniformly towards the pole, and is rarely disturbed by
those large and irregular fluctuations which form so important a factor in the daily weather of the
northern hemisphere. Here, accordingly, a system of polar gradients exists quite comparable in
stability with the equatorial gradients which give rise to the trades; and the poleward movement of the
air in obedience to these gradients, constantly diverted to the left by the effect of the earth's rotation,
constitutes the steady westerly winds of the south temperate zone.
473. The Monsoon Winds. — Theairover the land is warmer in summer and colder in winter than
that over the adjacent oceans. During the former season the continents thus become the seat of areas
of relatively low pressure; during the latter of relatively high. Pressure gradients, directed outward
during the winter, inward during the summer, are thus established between the land and the sea, which
exercise the greatest influence over the winds prevailing in the region adjacent to the coast. Thus, off
the Atlantic seaboard of the United States southwesterly winds are most frequent in summer, north-
westerly winds in winter; while on the Pacific coast the reverse is true, the wind here changing from
northwest to southwest with the advance of the colder season.
The most striking illustration of winds of this class is presented by the monsoons {Mausum, season)
of the China Sea and of the Indian Ocean. In January abnormally low temperatures and high pressure
obtain over the Asiatic plateau, high temperatures and low pressure over Australia and the nearby
portion of the Indian Ocean. As a result of the baric gradients thus established, the southern and
eastern coast of the vast Asiatic continent and the seas adjacent thereto are swept by an outflowing
current of air, which, diverted to the right of the gradient by the earth's rotation, appears as a north-
east Avind, covering the China Sea and the northern Indian Ocean. Upon entering the southern
hemisphere, however, the same force which hitherto deflected the moving air to the right of the
gradient now serves to deflect it to the left; and here, accordingly, we have the monsoon appearing as
a northwest wind, covering the Indian Ocean as far south as 10°, the Arafura Sea, and the northern
coast of Australia.
In July these conditions are precisely reversed. Asia is now the seat of high temperature and
correspondingly low pressure, Australia of low temperature and high pressure, although the departure
from the annual average is by no means so pronounced in the case of the latter as in that of the former.
The baric gradients thus lead across the equator and are addressed toward the interior of the greater
continent, giving rise to a system of winds whose direction is southeast in the southern hemisphere,
southwest in the northern.
The mtrtheast (winter) monsoon blows in the China Sea from October to April, the southwest
(summer) monsoon from May to September. The former is marked by all the steadiness of the trades,
often attaining the force of a moderate gale; the latter appears as a light breeze, unsteady in direction,
and often sinking to a calm. Its prevalence is frequently interrupted by tropical cyclonic storms,
locally known as t;/phoons, although the occurrence of these latter may extend well into the season of
the winter monsoon.
474. Land and Sea Breezes. — Corresponding with the seasonal contrast of temperature and
pressure overland and water, there is likewise a diurnal contrast which exercises a similar though more
local effect. In summer particularly, the land over its whole area is warmer than the sea by day, colder
than the sea by night, the variations of pressure thus established, although insignificant, sufficing to
evoke a system of littoral breezes directed landward during the daytime, seaward during the night,
which, in general, do not penetrate to a distance greater than 30 miles on and off shore, and extend but
a few hundred feet into the depths of the atmosphere.
The sea breeze begins in the morning hours — from 9 to 11 o'clock — as the land warms. In the late
afternoon it dies away. In the evening the land breeze springs up, and blows gently out to sea until
22489—03 10
1 46 WINDS.
morning. In the tropics this process is repeated day after day with great regularity. In our own
latitudes, the land and sea breezes are often masked by winds of cyclonic origin.
475. A single important effect of the seasonal variation of temperature and pressure over the land
remains to be described. If there were no land areas to break the even water surface of the globe, the
trades and westerlies of the terrestrial circulation would be developed in the fullest simplicity, with
linear divisions along latitude circles between the several members — a condition nearly approached in
the land-barren southern hemisphere during the entire year, and in the northern hemisphere during the
winter season. In the summer season, however, the tropical belt of high pressure is broken where it
crosses the warm land, and the air shouldered off from the continents accumulates over the adjacent
oceans, particularly in the northern or land hemisphere. This tends to create over each of the oceans a
circular or elliptical area St high pressure, from the center of which the baric gradients radiate in all
directions, giving rise to an outflowing system of winds, which by the effect of the earth's rotation is
converted into an outflowing spiral eddy or aniicydonic whirl. The sharp lines of demarcation which
would otherwise exist between the several members of the general circulation are thus obliterated,
the southwesterly winds of the middle northern latitudes becoming successively northwesterly, northerly,
and northeasterly, as we approach the equator and round the area of high pressure by the east; the
northeast trade becoming successively southeasterly, southerly, and southwesterly, as we recede from the
equator and round this area by the west; similarly for the other hemisphere.
147
chaptp:r XIX.
OYCLONIO STOEMS.
476. Variations of the Atmospheric Pressure. — The distribution of the atmospheric pressure
previously described (Chap. XV^III) and the attendant circulation of the winds are those which become
evident after the effects of many disturbing causes have been eliminated by the process of averaging, or
embracing in the summation observations covering an extended period of time. The distribution of
pressure and the system of winds which actually exist at a given instant will in general agree with
these in its main features, but may differ from them materially in detail.
Confining our attention for the time being to the subject of atmospheric pressure, it may be said
that this, at any given point on the earth's surface, is in a constant state of change, the mercury rarely
becoming stationarv, and then only for a few hours in succession. The variations which the pressure
undergoes may be divided into two classes; viz, periodic, or those which are continuously in operation,
repeating themselves within fixed intervals of time, long or short; and non-periodic or accidental, which
occur irregularly, and are of varying duration and extent.
477. Periodic Variations. — Of the former class of changes the most important are the seasonal,
which have been already to some extent described, and the diurnal. The latter consists of the daily
occurrence of two barometric maxima, or points of highest pressure, with two intervening minima.
Under ordinary circumstances, with the atmosphere free from disturbances, the barometer each day
attains its first minimum about 4 a. ra. As the day advances the pressure increases, and a maximum,
or point of greatest pressure, is reached about 10 a. m. From this time the pressure diminishes, and
a second minimum is reached about 4 p. m., after which the mercury again rises, reaching its second
maximum about 10 p. m. The range of this diurnal oscillation is greatest at the equator, where it
amounts to ten hundredths (0.10) of an inch. It diminishes with increased latitude, and near the poles
it seems to vanish entirely. In middle latitudes it is much more apparent in summer than in winter.
478. Non-periodic Variations. — The equatorial slope of the tropical belt of high pressure which
encircles the globe in either hemisphere is characterized by the marked uniformity of its meteorological
conditions, the temperature, wind, and weather changes proper to any given season repeating them-
selves as day succeeds day with almost monotonous regularity. Here the diurnal oscillation of the
barometer constitutes the main variation to which the atmospheric pressure is subjected. On the polar
slope of these belts conditions the reverse of these obtain, the elements which go to make up the daily
weather here passing from phase to phase without regularity, with the result that no two days are pre-
cisely alike; and as regards atmospheric pressure, it may be said that in marked contrast with the
uniformity of the torrid zone, the barometer in the temperate zone is constantly subjected to non-periodic
or accidental fluctuations of such extent that the periodic diurnal variation is scarcely apparent, the
mercury at a given station frequently rising or falling several tenths of an inch in twenty-four hours.
479. Progressive Areas of High and Low Pressure. — The explanation of this rapid change of
conditions is found in the approach and passage of extensive areas of alternately high and low pressure,
which affect alike, although to a different degree, all the barometers coming within their scope. The
general direction of motion of these areas is that of the prevailing winds; eastward, therefore, in the
latitudes which are under consideration.
Taken in conjunction, these areas of high and low pressure exercise a controlling influence over the
weather changes of the temperate zones. As the low area draws near, the sky becomes overclouded,
the prevailing westerly wind falls away, and is succeeded by a wind from some easterly direction, faint
at first, but increasing as the pressure continues to diminish; the lowest pressure having been reached,
the wind again goes to the westward, the glass starts to rise, and the weather clears; all marking the
eastward recession of the low area and the approach of the subsequent high.
The first stage in the development of the low is a slight diminution of the atmospheric pressure,
amounting in general to not more than one or two hundredths of an inch, throughout an area covering
a more or less extensive portion of the earth's surface, either land or water, but far more frequently
over the former than over the latter. Shortly after the advent of this initiatory fall the decrease of pres-
sure throughout some small region within the larger area assumes a more decided character, the mercury
here standing at a lower level than elsewhere and reading successively higher as we go outward, the
region thus becoming, as it were, the center of the whole barometric depression. A system of baro-
metric gradients is by this means established, all directed radially inward, and in obedience to these
gradients there is a movement of the surface air towards the center or point of lowest barometer. The
air once in motion, however, the effect of the earth's rotation is brought into play precisely as in the
case of the larger movements of the atmosphere, with the result that the several currents, instead of
following the natural course along these gradients, are deflected from them, in the northern hemisphere
to the right hand, in the southern hemisphere to the left, the extent of the deflection being from 4 to 8
compass points.
4§0. Cyclones and Cyclonic Circulations. — A central area of low barometer will thus be sur-
rounded by a system of winds which constantly draw in towards the center but at the same time circulate
about it, the whole forming an inflowing spiral; the direction of this circulation being in the southern
hemisphere with the motion of the hands of a watch, in the northern hemisphere opposed to this
1.48
CYCLONIC STORMS.
motion. Where the barometric gradients are steep, these winds are apt to be strong; where they are
gentle, the winds are apt to be weak; where they are absent, as is the case at the center or bottom of
the depression, cahns are apt to prevail.
Around the center of the area of high pressure a similar system of wind will be found, but l)lowmg
in a contrary direction. Here the barometric gradients are directed radially outward, with the result
that in place of the inflowing, we have an outflowing spiral, the circulatory motion being right handed
or with the hands of a watch in the northern hemisphere, left handed or against the hands of a watch
in the southern.
All of these features are shown in the accompanying diagrams (fig. 60), which exhibit the general
character of cyclonic (around the low) and anticy clonic (around the high) circulations in the northern
An'icyclonic. northern hemisphekk. Otielnnir.
Aiiticyclonic.
Cyclonic.
SOl'THERN HEMISPHERE.
Fig. 60.
The light arrows .show the direction of the gradients; the heavy arrows the direction of the winds.
and the southern hemisphere, respectively. The closed curves represent the isobars, or lines along
Avhich the barometric pressure is the same; the short arrows show the direction of the gradients, which
are everywhere at right angles to the isobars; the long arrows give the direction of the winds, deflected
by the earth's rotation to the right of the gradients in the northern hemisphere, to the left in the
southern.
4§1. Features op Cyclonic and Anticyclonic Regions. — Certain features of the two areas may
here be contrasted. In the anticyclonic, the successive isobars are as a rule far apart, showing weak
gradients and consequently light winds; the areas themselves are of relatively great extent, and their
rate of progression is sIoav. During the summer they originate as extensions into higher latitudes of
the margins of the tropical belts of high pressure; during the winter, as offshoots of the strong anticy-
clone which covers the land throughout that season. Their approach and presence is accompanied by
polar or westerly winds, temperature below the seasonal average, fair weather, and clear skies. In the
cyclonic area the successive isobars are crowded together, showing steep gradients and strong winds;
they may appear either as trough-like extensions into the temperate zone of the polar belt of low pres-
sure, in which case the easterly winds proper to their polar side are nonexistent, or (in lower latitudes)
as independent areas, sometimes, indeed, as detached portions of the equatorial low-pressure belt, which
move eastward and poleward across the temperate zone, and are ultimately merged into the great
cyclonic area surrounding the pole. The progress of these independent areas is invariably attended by
the strong and steadily shifting winds, foul weather, and other features which make up the ordinary
storm at sea. In the trough-like depressions of higher latitudes these features may or may not be
observed, their presence depending upon the depths of the barometric trough and the steepness of its
slopes. In these, moreover, the cyclonic circulation is never completely developed, the storm winds
having rather the character of right line gales, blowing from an equatorial or easterly direction until the
axis of the trough is at hand, and as this passes shifting by the west at one bound to a polar direction.
482. Cyclonic Storms. — Strong winds are the result of steep barometric gradients. These may
occur with cyclonic or with anticyclonic areas, the latter being exemplified in the case of the northers
in the Gulf of Mexico and the northwesterly winter gales along the Atlantic coast of the United States,
which are almost invariably accompanied by barometers above the average. They are, however, so
much more frequent in the case of areas of low pressure and consequent cyclonic circulations, wnth their
attendant foul weather characteristics, that the latter are generally known as cyclonic storms, i. e.,
storms in which the wind circulation is cyclonic.
Cyclonic storms may with convenience be divided into two classes; viz, tropical, or those which
originate near but not on the equator; and extra-tropical, or those which first appear in higher
latitudes.
4§3. Tropical Cyclonic Storms. — The occurrence of tropical cyclonic storms is confined to the
summer and autumn months of the respective hemispheres, and to the w^estern part of the several
oceans, the North Atlantic, the North Pacific, the South Pacific, and the Indian Ocean. They are
unknown in the South Atlantic Ocean.
The Arabian Sea and the Bay of Bengal are also visited by cyclonic storms, the season of their
occurrence extending from May to October.
4§4. Motion of the Storm Center. — In the case of tropical cyclonic storms there is always a
tendency for the barometric depression, impelled by the general motion of the atmosphere in the
CYCLONIC STORMS.
149
trade wind region, to follow a path which tends at once westward and away from the equator. This
motion conthmes until the limits of the trades are reached, where the path ordinarily recurves, and
the subsequent motion of the depression is eastward and towards the pole, the disturbance at the same
time assuming the features of the extra-tropical cyclonic storm.
4§5. Rate of Progress op the Stor.^i Center. — Within the tropics (in the northern hemisphere)
the average velocity of the storm center along the track is about 17 miles per hour; in the latitudes of
recurvature this drops to 8 miles per hour, the center at the time frequently becoming stationary; in
higher latitudes it again increases, rising to 20 or even to 30 miles per hour.
In the southern hemisphere the average velocity of progress as far as determined is somewhat less
than in the northern, but shows about the same relation in different parts of the track.
The general path of the tropical cj-clonic storm in either hemisphere and the cyclonic circulation of
the wind about the storm center are given in figures 61 and 62; that for the northern hemisphere
applying to the West India hurricane; that for ^
the southern hemisphere to the hurricanes of ,„ ,, ^P° ^ .,.,.■. . ,'i i— i >""^ hi/iiT
the South Pacific Ocean. ■' ' ' '^ '^^ ^ . . , . . . i ^^^
486. Character of Tropical Cycloxic
Storms. — Within the tropics the storm area is
small, the region covered by violent winds ex-
tending in general not more than 150 miles from
the center. The barometric gradients are, how-
ever, exceedingly steep, instances having been
recorded in which the difference of pressure for
this distance amounted to 2 inches. In the
typhoons of the North Pacific Ocean gradients
of one inch in 60 miles are not infrequent. The
successive isobars are almost circular. As a
consequence of this distribution of pressure the
winds on the slopes of the depression are fre-
quently of great violence, and in the matter of
direction they are more symmetrically disposed
about the center than is the case with the larger
and less regularly shaped depressions of higher
latitudes. In these low latitudes the average
values of the deflection of the wind from the
barometric gradient is in the neighborhood of
six compass points, — to the right in the northern
hemisphere, to the left in the southern.
4§7. To Fix the Bearing of the Storm
Center from the Vessel. — On this assumption,
the following rules will enable an observer to
fix the bearing of the storm center from his
vessel : —
In the northern hemisphere, stand with the
back to the wind; the storm center will bear six
points to the observer's left.
In the southern hemisphere, stand with the
back to the wind; the storm center will bear six
points to the observer's right.
On the basis of these rules the tables here-
after given (art. 492) show the bearing of the
center corresponding to a wind of any direction.
488. To Fix the Distance of the Storm Center from the Vessel. — The following table, taken
from Piddington's "Sailor's Horn Book," may prove of some assistance in estimating the distance of the
storm center from the vessel:
Fig. 61.
Average fall of the barometer
per hour.
From 0.02 to 0.06 in.
From 0.06 to 0.08 in.
From 0.08 to 0.12 in.
From 0.12 to 0.15 in.
Distance from the storm center.
From 250 to 150 miles.
From 150 to 100 miles.
From 100 to 80 miles.
From 80 to 50 miles.
The table assumes that the vessel is hove-to in front of the storm, and that the latter is advancing
directly toward it.
489. To Avoid the Center of the Storm. — In the immediate neighborhood of the center itself
the winds attain full hurricane force, the sea is exceedingly turbulent, and there is danger of being
struck aback. Every effort should therefore be made to avoid this region,' either by running or by
heaving-to; and if recourse is had to the latter maneuver, much depends upon the selection of the
proper tack; this being in every case the tack which will cause the wind to draw aft with each successive
shift.
A vessel hovo-to in advance of a tropical cyclonic storm will experience a long heavj' swell, a falling
barometer with torrents of rain, and winds of steadily increasing force. The shifts of wind will depend
upon the position of the vessel with respect to the path followed by the storm center. Immediately upon
the path, the wind will hold steady in direction until the passage of the central calm, the ''eye of
the storm," after which the gale will renew itself, but from a direction opposite to that which it previ-
150
CYCLONIC STOEMS.
ously had. To the right of the path, or in the right-hand semicircle of the stomi (the observer being
supposed to face along the track ), the wind, as the center advances and i)asses the vessel, will constantly
shift to the right, the rate at which the successive shifts follow each other increasing with the prox-
imity to the center; in this semicircle, then, in order that the wind shall draw aft with each shift, the
vessel must be hove-to on the starboard tack; similarly, in the left-hand semicircle, the wind will con-
stantly shift to the left, and here the vessel must l)e hove-to on the port tack.
These rules hold alike for both hemispheres and for cyclonic sti)rms in all latitudes.
The above shifts of the wind are based upon the supposition that the vessel is lying-to. A vessel in
rapid westerly motion may, in low latitudes, readily overtake the storm center, in which case the
observed shifts will be just the reverse of those here described.
490. Dangerois and Navigable Semicircles. — Prior to recurving, the winds in that semicircle
of the storm which is more remote from the equator (the right-hand semicircle in the northern hemi-
sphere, the left-hand semicircle in the
180° 170° southern ) are liable to be more severe than
those of the opposite semicircle. A vessel
hove-to in the semicircle adjacent to the
equator has also the advantage of immu-
nity from bec(jming involved in the actual
center itself, inasmuch as there is a distinct
tendency on tiie part of the latter to move
away from the equator. For these reasons
the more remote semicircle has been called
the dangerouK; the less remote, ihenavigable.
491. Maneuvering. — A vessel sus-
l^ecting the dangerous proximity of a trop-
ical cyclonic storm should lie-to for a time
on the starboard tack to locate the center
by observing shifts of the wind and the
behavior of the barometer. If the former
holds steady and increases in force, while
the latter falls rapidly, say at a greater rate
than 0.03 of an inch per liour, the vessel
is probably on the track of the storm and
in advance of the center. In this position
the proper step (providing, of course, that
sea room permits) is to run, keeping the
wind, in the northern hemisphere, at all
times well on the starboard quarter; in the
1^ southern hemisphere, well on the port; and
thus constantly increasing the distance to
the storm center. The same rule holds good
if the observation places the vessel at but
a scant distance within the forward quad-
rant of the dangerous semicircle. Here,
too, the natural course will be to seek the
navigable semicircle of the storm, even
though such a course involves crossing the
track in advance of the center, always ex-
ercising due caution to keep the wind frotn
drawing too far aft.
The critical case is that of a vessel
— which finds herself in the forward quad-
rant of the dangerous semicircle and at a
considerable distance from the track, for
here the shifts of the wind are sluggish and
the indications of the barometer are unde-
cided, both causes conspiring to render the
bearing of the center doubtful. If, upon
heaving-to, the barometer becomes station-
ary, the position should be maintained
until indications of a rise are apparent, upon which the course may be resumed with safety and held as
long as the rise continues. If, however, the barometer falls, a steamer should make a run to the NNE.
or NE. (southern hemisphere, SSE. orSE. ), keeping the wind and sea a little on the.port (southern
hemisphere, starboard) bow, and using such speed as will at least keep the mercury stationary. Such
a step will in general be attended with the assurance that the present weather conditions will in any
case grow no worse. For a sailing vessel, unable to stand closer to the wind than six points, the last
maneuver will be impossible, and driven to leeward bj'^ wind, sea, and current, she may be compelled
to cross the track immediately in advance of the center, or may even become involved in the center
itself. In this extremity the path of the storm center during the past twenty-four hours should be laid
down on a diagram as accurately as the observations permit, and the line prolonged for some distance
beyond the present position of the center. Having assumed an average rate of progress for the center,
its probable position on the line should be frequently and carefully plotted, and the handling of the
vessel should be in accordance with the diagram.
492. Summary of Rules. — The following summary comprises the rules for maneuvering in the
Northern Hemisphere, so far as they may be made general: —
Fig. 62.
CYCLONIC STORMS.
151
In the Right Semicircle: Haul by the wind on the starboard tack and carry sail as long as possible;
if obliged to heave-to, do so on starboard tack.
In the Left Semicircle: Bring the wind on the starboard quarter, note course and keep it; if obliged
to heave-to, do so on port tack.
In Front of Center: Bring wind two points on starboard quarter, note course and keep it; if obliged
to heave-to, do so on port tack.
In Rear of Center: Run out with wind on starboard quarter; if obliged to heave-to, do so on star-
board tack.
The application of these rules for the various directions of the wind is shown in the following
table: —
Storm Table, Northern Hemisphere.
If wind
1
Direcyon
Direction
shifts to-
If wind shifts towards the
If wind steady with falling
If wind steady with rising
of wind.
of center.
wards the
left.
barometer.
barometer.
right.
North.
ESE.
a
Run SSW.
K ■
Run SSW.
K
Run SSW.
a
NNE.
NE.
ENE.
SE.
SSE.
South.
aul b>
and cs
ble; il
on sta
Run SW.
Run WSW.
Run West.
old CO
if obli
port ti
Run SW.
Run AVSW.
Run West.
old course
obliged to
port tack.
Run SW.
RunAVSW.
Run West.
old coi
if obli
starbo
East.
ESE.
SSW.
SW.
' wind
irry sa
oblige
rboard
RunWNW.
Run NW.
arse
ged
ick.
RunWNW.
Run NW.
RunWNW.
Run NW.
P5 ||I^ ^
"1 ^ 7i
SE.
WSW.
Run NNW.
f-i- a
Run NNW.
fo
_^ao
Run NNW.
1^:
SSE.
West.
on SI
il as 1
dtoh
tack.
Run North.
Run North.
ffi O
Run North.
r ET ^
South.
WNW.
Run NNE.
2 o
Run NNE.
^1
Run NNE.
^o-
ssw.
NW.
Run NE.
< D
Run NE.
Run NE.
< D
SW.
NNW.
1%^
Run ENE.
Run ENE.
Run ENE.
WSW.
North.
t^ g
Run East.
p m
Run East.
t3
ClO
Run East.
P §
West.
NNE.
?^S S
Run ESE.
S'o
Run ESE.
ogg
Run ESE.
Cu^c
WNW.
NE.
d ta
pos
), do
Run SE.
Run SE.
g E
Run SE.
CD 00
NW.
ENE.
Run SSE.
° 5-'
Run SSE.
° a
Run SSE.
o :f
NNW.
East.
00 ^^ rt
Run South.
2Jf
Run South.
o
Run South.
Dif
a Courses given are for wind two points on starboard quarter, but it is preferable to take wind broad on quarter if possible.
Similarly, the following rules and table apply for the Southern Hemisphere: —
In the Right Semicircle: Bring the wind on the port quarter, note course and keep it; if obliged to
heave-to, do so on starboard tack.
In the Left Semicircle: Haul by the wind on the port tack and carry sail as long as possible; if
obliged to heave-to, do so on port tack.
In Front of Center: Bring wind two points on port quarter, note course and keep it; if obliged to
heave-to, do so on starboard tack.
In Rear of Center: Run out with wind on port quarter; if obliged to heave-to, do so on port tack.
Storm Table, Southern Hemisphere.
If wind
1
Direction
Direction
If wind shifts towards the
shifts to-
If wind steady with falling
If wind steady with rising
of wind.
of center.
right.
wards the
left.
barometer.
barometer.
North.
WSW.
Run SSE.
a
a
Run SSE.
W
Run SSE.
a
NNE.
NE.
West.
WNW.
Run South.
Run SSW.
old CO
if obli
starbo
aul
carr
obli
port
Run South.
Run SSW.
old
obli
star
Run South.
Run SSW.
old cour
if oblige
port tacl
ENE.
NW.
Run SW.
te 2 -». "^
Run SW.
o rti o
Run SW.
East.
NNW.
Run WSW.
S5 aq —
5 2?^
O 03 D-
Run WSW.
iirse
d to
ard
Run WSAV.
ESE.
North.
Run West.
CLP.^
Run West.
Run West.
Kl p^ CO
SE.
SSE.
NNE.
NE.
Run WNW.
Run NW.
fS o o
Run WNW.
Run NW.
1^^
Run WNW.
RunNW.
o a
p-i
South.
ENE.
Run NNW.
S o
<S. §
Run NNW.
% §
Run NNW\
S o'
SSW.
East.
Run North.
?^
por
t as
e-tb.
Run North.
OGR
Run North.
II
SW.
ESE.
Run NNE.
k
Run NNE.
o S
Run NNE.
#1
WSW.
SE.
Run NE.
° g
Run NE.
a^
Run NE.
West.
SSE.
Run ENE.
o g
o ^ f
Run ENE.
o gg
Run ENE.
%^
WNW.
South.
Run East.
!» §0
00 O"?^
Run East.
OD O'
Run East.
m gg
NW.
SSW.
Run ESE.
C
Run ESE.
Run ESE.
Z e!
NNW.
SV7.
Run SE.
gir
O „ D
Run SE.
o
Run SE.
pif
a Courses given are for wind two points on port quarter, but it is preferable to take wind broad on quarter, if possible.
/
152
CYCLONIC STORMS.
493. Extra-Tropical Cyclonic Storms. — On turning to the cyclones oi temperate latitudes, we
find many features in which they resemble those of the torrid zone, but certain other features in which
they differ. Their fundamental resemblance to tropical cyclones is seen in their incurving winds, form-
ing an inflowing left-handed spiral about the center of low pressure in the northern hemisphere, an
inflowing right-handed spiral in the southern. The intensity of these winds varies with the depth of
the barometric depression. The depression itself, however, in place of covering a few miles, as is the
case in the tropics, will frequently have a diameter of several hundred or even a thousand miles, and for
some distance around the center the gradients will have a tolerably strong value. For this reason there
is less concentration of violence close to the center, and the calm and clear central space, or "eye," is
seldom sharply develop^l, although it is not uncommon to discover a gradual weakening or failing of
the winds, and sometimes even an imperfect breaking away of the clouds as the central area passes over
the observer. The form of tropical cyclones as defined by their isobaric lines is nearly circular.
Extra-tropical cyclones are as a rule less symmetrical, and their isobars are often elongated into an oval
form, the longer axis of the oval trending (in the northern hemisphere) between north and east —
about, therefore, in the direction of progression. The steepest gradients, and consequently the s'trongest
winds, are apt to be found on the equatorial and westerly sides of the depression.
Extra-tropical cyclones generally follow^ an easterly course, inclining somewhat towards the pole;
but they occasionally turn to one side or the other, become stationary, or even move backward. The
velocity of progression varies from 15 to 40 miles an hour. If they exist as independent barometric
depressions, with strong upward gradients on all sides of the center, the cyclonic circulation will be
complete, the wind shifting with the sun for an observer situated in the equatorial semicircle of the
storm, against the sun for an observer situated in the polar semicircle.
494. Storms Along the Transatlantic Steamship Koutes. — The storms which are so frequently
met during the winter season along the steamshii:) routes between America and Europe are not, as a
rule, due to central barometric depressions, but
to depressions having a trough or V shape, which
extend southerly from the extensive permanent
area of low pressure having its center in the
vicinity of Iceland. They are not attended by
complete cyclonic circulations, inasmucn Jis the
polar gradients which would otherwise give rise
to easterly winds on this polar side are lacking.
Their approach is heralded by a gradual hauling
of the wind to southward, which is later fol-
lowed (at the time of passage of the central line
of the trough ) by a change to NW. , accompanied
by heavy rain squalls and a rapid increase in
force. The general distribution of pressure and
the surrounding winds are showii m figure 63.
The changes in wind and pressure ensue much more rapidly in the case of a westward-bound vessel than
in that of one eastward bound, the rate at which the observer and the depression approach each other
being in the former case the sum of his own westward velocity and the eastward velocity of the trough,
in the latter case, the difference of these velocities.
TIDES. 153
CPIAPTER XX.
TIDES.
495. Definitions. — Tidal phenomena present themselves to the observer nnder two aspects — as
alternate elevations and depressions of the sea, and as recurrent inflows and outflows of streams. The
word tidr, in common and general usage, is made to refer without distinction to both the vertical and
horizontal motions of the sea, and confusion has sometimes arisen from this double application of the
term; in its strict sense, this word may be used only with reference to the changes of elevation, while
the recurrent streams are jjroperly distinguished as tidal cumnds.
The tide rises until it reaches a maximum height called high water or high tide, and then falls to a
minimum level called low imter or low tide; that period at high or low water marking the transition
between the tides, during which no vertical change can be detected, is called Hland.
Of the tidal currents, that which arises from a movement of the water in a direction, generally
speaking, from the sea toward the land, is called Jlood, and that arising from an opposite movement,
ebb; the intermediate period between the currents, during which there is no horizontal motion, is dis-
tinguished as slack-. Set and drift are terms applicable to the tidal currents, the first referring to the
direction and the second to the velocity.
Care should be taken to avoid confusing the terms relating to tides with those which relate to tidal
currents.
496. Causk. — The cause of the tides is the unequal attraction of the sun and moon upon different
parts of the earth. These bodies attract the parts of the earth's surface which are nearer to them with
greater force than they do its center, and attract its center more than they do its opposite surface; to
restore equilibrium the waters take a spheroidal figure, whose longer axis lies in the direction of the
attracting body. The mean force of the moon in raising the tides is two and a half times as great as
that of the sun, for though the mass of the sun is vastlj- greater than the mass of the moon, the sun's
distance is so great that it attracts the different parts of tlie earth with nearly equal force. Theory is
not sufficiently advanced to render possible a prediction of tides or tidal changes from a mere knowledge
of the positions of the sun and moon, but by theory, supplemented by observation of actual tidal condi-
tions during a certain period of time, very accurate predictions may be arrived at.
497. EsT.VBLisHMKNT. — High and low water occur, on the average of the twenty-eight days com-
prising a lunar month, at about the same intervals after the transit of the moon over the meridian.
These nearly constant intervals, expressed in hours and minutes, are known respectively as the Jiigh
water litrritidal interval and low water lunitidal interval.
The interval between the moon's meridian passage at any place and the time of the next succeeding
high water, as observed on the days when the moon is at full or change, is called the vvlgar (or common)
establi.'ilnnent of that place, or, sometimes, simply the establislmient. This interval is frequently spoken
of as the time of Jiigh water on full and cliange days (abbreviated "H. W. F. & C."); for since, on such days,
the moon's two transits (upper and lower) over the meridian occur about noon and midnight, the vul-
gar estaV^lishment then corresponds closely with the local times of high water. When more extended
observations have been made, the average of all the high water lunitidal intervals for at least a lunar
month is taken to obtain what is termed, in distinction to the vulgar establishment, the corrected estab-
lishmeiit of the port, or mean high water lunitidal interval. In defining the tidal characteristics of a place
some authorities give the corrected establishment, and others the vulgar establishment, or "high water,
full and change;" calculations based upon the former will more accurately represent average conditions,
though the two intervals seldom differ ])v a large amount.
Having determined the time of high water by applying the establishment to the time of moon's transit,
the navigator may ol.)tain the time of low water with a fair degree of apjiroximation by adding or
subtractings'' 13'" (one-fourth of a mean lunar day); but a closer result will be given by applying to
the time of transit the mean low leater lunitidal interval, which occupies the same relation to the time of
low water as the mean high water lunitidal interval, or corrected establishment, does to the time of
high water.
498. Range. — The range of the tide is the difference in height between low water and high water.
This term is often applied to the difference existing under average conditions, and may in such a case
be designated as the mean range or mean rise and fall to distinguish it from the spring range or neap range,
which are the ranges at spring and neap tides, respectively.
499. Spring and Neap Tides. — At the times of new and full moon the relative positions of sun
and moon are such that the high water produced by one of those bodies occurs at the same time as that
produced by the other, and so also with the low waters; the tides then occurring, called spring tides,
have a greater range than any others of the lunar month, and at such times the highest high tides as
well as the lowest low tides are experienced, the tidal range being then at its maximum. At the first
and third cjuarters of the moon the positions are such that the high tide due to one body occurs at the
time of the low tide due to the other, so that the two actions are opposed; this causes the neap tides,
which are those of minimum range, the high waters being lower and the low waters higher than at
other periods of the month.
154
TIDES.
Since the horizontal motion of the water depends directly upon the rise and fall of the tides, it follows
that the currents will be greatest at springs and least at neaps.
The effect of the moon's being at full or change is not felt at once in all parts of the world, and the
greatest range of tides does not generallj' occur until one or two days thereafter; thus, on the Atlantic
coast of North America, the highest tides are experienced one day, and on the AtJantic coast of Europe,
two days afterwar4, though on the Pacific coast of North America they occur nearly at full and change.
500. The nearer the moon is to the earth the stronger is its attraction, and as it is nearest in perigee,
the tides will be larger then on that account, and consequently less in apogee. For a like reason, the
tides will be increased by the sun's action when the earth is near its perihelion, about the 1st of January,
and decreased when near its aphelion, about the 1st of July.
501 . The height ^f the tides at any place .may undergo modification on account of strong prevailing
winds or abnormal barometric conditions, a wind blowing off the shore or a high barometer tending to
reduce the tides, and the reverse. The effect of atmospheric jiressure is to create a difference of about
2 inches in the height of tide for every tenth of an inch of difference in the barometer.
502. Priming and Lagging. — The tidal day is the varial)le interval, averaging 24'' 50"', between two
alternate high or low waters. The amount by which corresponding tides grow later day by day — that
is, the amount by which the tidal day exceeds 24'' — is called the daily retardation. When the sun's tidal
effect is such as to shorten the lunitidal intervals, thus reducing the length of the tidal day and causing
the tides to occur earlier than usual, there is said to be a jyriming of the tide; when, from similar causes,
the interval is lengthened, there is said to be a lagging.
503. Types of Tidks. — The observed tide is not a simple wave; it is a compound of several elemen-
tarj^ undulations, rising and falling from the same conmion plane, of which two can be distinguished and
separated by a simple grouping of the data. These two waves are known as the semi-diurnal and the
diurnal tides, because the first, if alone, would give two high and two low waters in a day, while the
second would give but one high and one low water in an equivalent period of time. In nearly all ports
these two tides coexist, but the proportion between them varies remarkably for different seas. The
effect of the coml)ination of these two types of tide is to produce a diurnal inequality, both in the height
of two consecutive high or low waters, and in the intervals of time between their occurrence. The
height of the diurnal wave may be regarded as reaching a maximum fortnightly, soon after the moon
attains its extreme declination and is therefore near one of the tropics. The tides that then occur are
denominated tropic tides.
In undertaking to investigate the tides of a port it is important to ascertain as early as possible the
form of the tide; that is, whether it resembles the semi-diurnal, the diurnal, or the mixed type; because
not only may this information be of scientific value, but the knowledge thus gained at the outset will
enable the observer to fix upon the best method of keeping his record.
304. The type forms referred to are
illustrated in the diagram in figure 64,
where the waves are plotted in curves,
using the times as abscissa? and the
heights as ordinates. In this diagram,
the curve traced in the full line is a tide-
wave of the semi-diurnal type; that
traced by the dotted line one of the di-
urnal; while the broken line is one of the
mixed type, in this case the compound
of the two others. _
In order to determine the type to
which the tide of any port belongs, it is
usually only necessary to make hourly
observations for a day or two at the date
of the moon's maximum declination, and
to repeat the series about a week later,
when the moon crosses the equator.
The reported irregularities of the rise
and fall at any place should not deter
persons from careful investigation.
When analyzed, even the most compli-
cated of tides are found to follow some
general law'.
505. Tidal, Currents. — It should
be clearly borne in mind by the naviga-
tor that the jieriods of flood and ebb currents do not necessarily coincide with those of rising and falling
tides, and that, paradoxical though it may seem at first thought, the inward set of the surface current
does not always cease when the water has attained its maximum height, nor the outward set when a
minimum height has been reached. Tinder some circumstances it may occur that stand and slack will
be simultaneous, while other conditions may produce a maximum current at stand, with a maximum
rate of rise or fall at slack water.
The varying effects which will be produced according to local conditions may be considered by the
comparison of two tidal basins, to one of which the tide-wave has access from the sea by a channel of
ample capacity, while the other has an entrance that is narrow and constricted. In the first case, the
process of filling or emptying the basin keeps pace with the change of level in the sea and is practically
completed as soon as the height without becomes stationary; in this case slack and stand occur nearly
at the same time, as do flood and rise and ebb and fall. In the second case, the limited capacity of the
entrance will not permit the basin to fill or empty as rapidly as the tide changes its level without;
(
) 1 2 3 "4 5 6 7 8 9 10 H 12 33 14 15 16 17 18 19 20 21 22 23 24 |
Ff
1
1
3
2
1
D
1.
2
S
a
<<r
-.,
1
\
,A~
s
,'
•-'
■■"
•->.
,'
^
N
I
/
,'
V
f\
/I
/
■**
/
v
/
/
\
\
,'
' -
-.^
^
/
/
\'l
/'
'\
/
^'
''\
\
^
^^^
/
/
1
,-
'''
\
"
/
^
/
/ L'l
\
/
K
--j-
7
/
/
r*'
\
/
4-'
\^
V
-
V
^
r i7
"Vrr
/I
—
V
L U'1
■ Semi-diurnal.
diurnal.
Fig. 64.
• mixed.
TIDES. 155
hence there is still a difference of level to produce a current when the vertical motion in either direction
has ceased on the outside, and for a considerable time after motion in the reverse direction has been in
progress; under extreme conditions it may even occur that a common level will not be established
until mid-tide, and therefore the surface current at some places will ebb until three hours after low
water and flow until three hours after high water.
Localities that partake of the nature of the first case are those upon open coasts and wide-mouthed
bights. Examples of the latter class will be found in narrow bays and long channels.
TIMES OF HIGH AND LOW WATER.
506. Tide Tablks. — The most expeditious, as well as most exact, method of ascertaining the times
of high and low water and other features of the tides will be by reference to a Tide Table, and every
navigator is recommended to provide himself with such a publication. The United States Coast and
Geodetic Survey pubUshes annually, in advance, tables giving, for every day in the year, the predicted
time and height of the tides at certain principal porta of the world, and from these, by a simple reduc-
tion, the times and heights at a multitude of other ports may readily be obtained; data for ascertaining
the tidal currents in certain important regions are also provided. General tide tables are also published
by the governments of other maritime nations, and special tables are to be had for many particular
localities.
507. Where no tide tables are available, the method of calculation by applying the lunitidal inter-
val to the time of the moon's meridian passage must be resorted to.
To do this, find first the time of the moon's meridian passage, upper or lower, as may be required.
The Greenwich mean time of upper transit at Greenwich is given in the Nautical Almanac (page IV of
the month) ; the corresponding time of lower transit is most easily found by taking the mean of the two
adjacent upper transits; to the Greenwich time of Greenwich transit apply the correction for longitude
given in Table 11 (using the daily variation of the moon's meridian passage shown in the Almanac),
adding in west and subtracting in east longitude; the result is the local mean time of local transit.
Add to this the high-water or low-water lunitidal interval of the port from Appendix IV, according as
the time of high or low water may be required. The result is the time sought.
• The astronomical date must be strictly adhered to, and in so doing it may be found necessary to
employ the time of a lower transit, or the transit of a preceding day, to find the time of the tide in
question.
Appendix IV contains, besides the geographical positions of all the more important positions in the
world, a series of tidal data relating to many of those places. In such data are comprised the mean
lunitidal intervals for high and low water; also, for places where the semi-diurnal type of tide prevails,
the tidal range at spring and at neap tides, and for those where the tide is of the diurnal type, the tropic
range. An alphabetical index is appended to this table.
The corrected establishment taken from the charts may be substituted for the high-water lunitidal
interval of the table; or, with only slight variation in the results, the vulgar establishment (H. W. F.
& C. ) may be employed.
Example: Find the times of the high and low waters at the New York navy yard, occurring next
after noon on April 22, 1879.
G. M. T. of Gr. transit, 22'» 0" 32™. 2
Corr. for + 74° Long. (Tab. 11) , + 10
L. M. T. of local transit, 22 0 42
Transit, 22'i O"- 42'" Transit, 22^ O** 42'"
H.W.Lun. Int. (App. IV), 8 44 L. W. Lun. Int. (App. IV), 2 49
L.M.T.,H.W., {iyi22!9.26p.m. L. M. T., L. W., • {'^J,2f,3.Sl^. rn.
Example: Find the time of high water at the Presidio, San Francisco, Cal., on the afternoon of
May 7, 1879.
G. M. T. of Gr. transit, 6'' 12" Se^.G
Corr. for + 122° Long. (Tab. 11), -f- 22
L. M. T. of local transit, 6 12 59
H. W. Lun. Int. (App. IV), + 11 43
L. M. T., H. W., I L ^T ^-Fo Ao
' ' \ May 7, 12.42 p. m.
Example: Find the time of low water at Singapore on the night of May 28, 1879.
G. M. T. of Gr. transit, 28^ 5'> 55™. 3
Corr. for —104° Long. (Tab. 11), — 13
G. M. T. of local transit, 28 5 42
L. W. Lxm. Int. (App. IV), -f 4 02
L. M. T., L. W., j?J ^oQ"^n^.
' ' \ May 28, 9.44 p. m.
156 TIDES.
Example: Find the time of morning high water and afternoon low water at GibraUar on June 26,
1879.
G. INI. T. of Gr. upper transit, 25'' 4" 40'».l
G. M. T. of Gr. upper transit, 26 5 27 .0
2)51 10 07 .1
G. M. T. of Gr. lower transit, 25 ] 7 04
Corr. for -f 5° Long. (Tab. 11 ), -[- 01
L. M. T. of local lower trans., 25 17 05
Transit, 25'M7''05"" Transit, 25'^! 7** 05™
H.W.Lun.Int. (App. TV), 185 L. W. Lun. Int. (App. IV), 7 55
L AI T H W P^ ^^ ^^ I M T T W f 26 1 00
L. 31. i., n. W., I j^^^ 26, 6.40 a. m. ^- ^^- ^^ ^- ^^ - { June 26, 1 p. m.
TIDAL OBSERVATIONS.
508. Since navigators will frequently have opportunity to observe tidal conditions, either in con-
nection with a hydrographic survey or otherwise, at places where existing knowledge of the tides is
incomplete, an understanding of the methods employed in tidal observations may be important.
_509. Tides. — For the proper study of tides, frequent and continuous observations are necessary;
it will not suffice to observe the heights of the high and low waters only, even if they present them-
selves as distinct phases, but the whole tidal curve for each day should be develoi^ed by recording the
height of water at intervals, which, preferably, should not exceed thirty minutes. Observations, to be
complete, must cover a whole lunar month ; or, if it be impracticable to observe the tides at night, the
day tides of two lunar months may be substituted.
510. When made for the purposes of a hydrographic survey the tidal observations are used to
correct the soundings, and care must be taken to make sure that the gauge is placed in a situation visited
by the same form of tide as that which occurs at the place where soundings are being made. It will not
answer, for instance, to correct the soundings upon an inlet-bar liy tidal observations made within the
lagoon with which this inlet communicates, because the range of the tide within the lagoon is less than
upon the outside coast. A partial obstruction, like a bridge, or a natural contraction of the channel
section, while it may not reduce the total range of the tide or materially affect the time of high or low
tides, will alter the relative heights above and below at intermediate stages, so that the hydrographer
must be careful to see that no such obstruction intervenes between his field of work and the gauge.
511. Tidal Currents. — Observations for tidal currents should be made with the same regularity
as for tides; the intervals need not ordinarily be more frequent than once in every half hour. They
should always be made at the same point or points, which should be far enough from shore to be repre-
sentative of the conditions prevailing in the navigable waters. The ordinary log may be employed for
measuring the current, but it is better to replace the chip by a pole weighted to float upright at a depth
of about fifteen feet; the line should be a very light one, and buoyed at intervals by cork floats to keep it
from sinking; the set of the current should be noted by a compass bearing of the direction of the pole
at the end of the observation.
512. Record. — The record of observations should be kept clearly and in complete form. It should
include a description of the locality of observation, the nature of gauge and of instruments used for
measuring currents, and the exact position of both tidal and current stations, together with situation
and height of bench mark. The time of making each observation should be shown, and data given for
reduction to some standard time. In extended tidal observations the meteorological conditions should
be carefully recorded, the instruments used for the observations being properly compared with standards.
51 3. There are freciuently remarkable facts in reference to tides and currents to be obtained from
persons having local knowledge; these should be examined and recorded. The date and circumstances
of the highest and lowest tides ever known form important items of information.
514. Planes of Keference. — The plane of reference is the plane to which soundings and tidal data
are referred. One of the principal objects of observing tides when making a survey is to furnish the
means for reducing the soundings to this plane. Four planes of reference are used; namely, mean low
water, mean low water springs, mean lower low waters, and the harmonic or Indian tide plane.
Mean low water is a plane whose depression below mean sea level corresponds with half the mean
semi-diurnal range, while the depression of mean low-water springs corresponds with half tlie mean range
of spring tide; mean lower loiv water depends upon the diurnal inequality in high and low water; the
harmonic or Indian tide plane was adopted as a convenient means of expressing something of an approxi-
mation to the level of low water of ordinary spring tides, but where there is a large diurnal inequality
in low waters it falls considerably below the true mean of such tides.
As these planes may differ considerably, it is important to ascertain which plane of reference is
adopted before making use of any chart or considering data concerning the tides.
515. The tides are subject to so many variations dependent upon the movements of the sun and
moon, and to so many irregularities due to the action of winds and river outflows, that a very long series
of observations would be necessary to fix any natural plane. In consideration of this, and keeping in
view the possibilities of repetitions of the surveys or subsequent discoveries within the field of work, it
is necessary to define the position of the plane of reference which has resulted from any series of obser-
vations. This is done by leveling from the tide gauge to a permanent bench, precisely as if the adopted
plane were arbitrary.
516. Bench ]\!ark. — The plinth of a light-house, the water table of a substantial building, the
base of a monument, and the like, are proper l^enches; and when these are not within reach, a mark
TIDES. 157
may be made on a rock not likely to be moved or started by the frost, or, if no rock naturally exists in
the neighborhood, a block of stone buried l)elow the reach of frost and plowshare should be the resort.
When a bench is made on shore, it should be marked by a circle of 2 or 3 inches diameter with a cross
in the center, iudicating the reference point. The levelings between this point and the gauge should be
be run over twice and the details recorded. A bench made upon a wharf or other perishable structure
is of little value, but in the absence of- permanent objects it is better than nothing. The marks should
be cut in, if on stone, and if on wood, copper nails should be used. The bench must be sketched and
carefully described, and its location marked on the hydrographic sheet, with a statement of the relative
position of the plane of reference.
517. The leveling from the bench mark to the tide gauge may be done, when a leveling instrument
is not available, by measuring the difference of height of a number of intermediate points' by means of
a long straight-edged board, held horizontal by the aid of a carpenter's spirit level, or even a plummet
square, taking care to repeat each step with the level inverted end for end. A line of sight to the sea
horizon, when it can be seen from the bench acrot^s the tide staff, will afford a level line of sufficient
accuracy, especially when observed with the telescope. It may often be convenient to combine these
methods.
518. Tide Gauges. — The Staff Gauge is the simplest device for measuring the heights of tides, and
in perfectly sheltered localities it is the best. It consists of a vertical staff graduated upward in feet and
tenths, and so placed that its zero shall lie below the lowest tides. The same gauge may also be used
where the surface is rough, if a glass tube with a float inside is secured alongside of the staff, care being
taken to practically close the lower end of the tube so as to exclude undulations; readings may also be
made by noting the point midway between the crest and trough of the waves.
A staff gauge should always be erected for careful tidal observations, even where other classes of
gauge are to be employed, as it furnishes a standard for comparison of absolute heights, and also serves
to detect any defects in the mechanical details upon which all other gauges are to a greater or less extent
dependent.
519. Where there is considerable swell, and where, from the situation of the gauge or the great
range of the tide (makiBg it inconvenient for the observer to see the figures in certain positions) the
staff gauge can not be used, recourse must be had to the Box Gauge. This gauge consists of a vertical
box, closed at the bottom, with a few small holes in the lower part which admit sufficient water to keep
the level within equal to the mean level without, but which do not permit the admission of water with
sufficient rapidity to be affected by the waves. Within the box is a copper float; in some cases this
float carries a graduated vertical rod whose position with reference to a fixed point,of the box affords a
measure for the height of the water; in other gauges of this class the float is attaclied to a wire or cord
which passes over ])ulleys and terminates in a counterpoise whose position on a vertical graduated scale
shows the height of tide.
520. An Automatic Gauge requires a box and float such as has just been described. The motion of
the float in rising and falling with the tide is communicated to a pencil which rests upon a moving
sheet of paper; uniform motion is imparted to the paper by the revolution of a cylinder driven by clock-
work; the motion of the pencil due to the tide is in a direction perpendicular to the direction of motion
of the paper, and a curve is thus traced, of which one coordinate is time, and the other height. The
paper, which is usually of sufficient length to contain a month's record, is paid out from one cylinder,
passes over a second whereon it receives the record, and is rolled upon a third cylinder, which thus
contains the completed tidal sheet.
This gauge, besides giving a perfectly continuous record, has the further merit of requiring but
little of the observer's time. But its indications, both of time and heights, should be checked by
occasional comparisons with the standard clock and tlie staff gauge, the readings of which should be
noted by hand at api^ropriate jioints of the graphic record.
158 OCEAN CURRENTS.
CHAPTER XXL
OCEAN OUKRENTS.
521. An ocenn current is a progressive horizontal motion of the water occurring throughout a
region of the ocean, as a result of which all bodies floating therein are carried with the stream.
The set of a current is the direction toward which it flows, and its drift, the velocity of the flow.
522. Cause. — The principal cause of ocean currents is the wind. Every breeze sets in motion, by
its friction, the surface particles of the water over which it blows; this motion of the upper stratum is
imparted to the stratum next beneath, and thus the general movement is communicated, each layer of
particles acting upon the one below it, until a current is established. The direction, depth, strength,
and permanence of such a current will depend upon the direction, steadiness, and force of the wind;
all, however, subject to modification on account of extraneous causes, such as the intervention of land
or shoals and the meeting of conflicting currents.
A minor cause in the generation of ocean currents is the difference in density of the sea water in
different regions, as a result of which a set is produced from the more dense toward the less dense, in
the effort to establish equilibrium of pressure; the difference of density may be due to temperature, the
warmer water near the equator being less dense than the colder water of higher latitudes; or it may be
created by a difference in the amount of contained saline matter, resulting from evaporation, freezing,
or other causes. Another minor factor that may have influence upon ocean currents is the difference of
pressure exerted by the atmosphere upon the water in different regions. But neither of the last-
mentioned causes may be regarded as of great importance when compared with the influence, direct
and indirect, of the wind.
523. Drift and Stream Currents. — Ocean currents may be divided into two classes: Ihnfl and
Stream Currents.
A Drift Current is one which arises from the effect of wind upon the surface water, impelling the
particles to leeward. Such currents reach only to shallow depths, except in regions where caused by
winds whose prevalence is almost unbroken, and where, in consequence, motion is communicated stratum
by stratum, during a long series of years, until the influence is felt at great depths.
A Stream Current is one which arises when the water carried forward by a drift current encounters
an obstacle which prevents a further flow in the direction which it has been following, and the particles
are forced to acquire a new motion which takes such direction as may be imposed by the conditions
existing in the locality.
Some currents are compounded of both drift and stream ; for a stream already formed may pass
through the region of a prevalent wind in such direction that it will receive an accelerating effect due to
the wmd.
524. Submarine Currents. — In any scientific investigation of the circulation of ocean waters it is
necessary to take account of the submarine currents as well as those encountered upon the surface; but
for the practical purposes of the navigator the surface currents alone are of interest.
525. Methods of Determination. — The methods of determining the existence of a current, with
its set and drift, may be divided into three classes; namely, (a) by observations from a vessel occupying
a stationary position not affected by the current; (6) by comparison of the position of avessel under way
as given by observation with that given by dead reckoning; and (c) by the drift of objects abandoned
to the current in one locality and reappearing in another.
526. Of these methods, the first named, by observations from a vessel at anchor, is by far the most
accurate and reliable, but being possible only under special circumstances is not often available. The
most valuable information about ocean currents being that which pertains to conditions in the open sea,
the great depths there existing usually preclude the possibility of anchoring a vessel; ships especially
fitted for the purpose have at times, however, carried out current observations with excellent results;
the most notable achievements in this direction are those of the survey of the Gulf Stream, made by
United States naval officers acting under the Coast and Geodetic Survey, during which the vessel was
anchored and observations were made in positions where the depth reached to upward of 2,000 fathoms.
527. The method of determining current from a comparison of positions obtained, respectively,
by observation and by dead reckoning is the one upon which our knowledge must largely depend.
This method is, however, always subject to some inaccuracy, and the results are frequently quite
erroneous, for the so-called current is thus made to embrace not only the real set and drift, but also
the errors of observation and dead reckoning. In the case of a modern steamer accurately steered and
equipped with good instruments for determining the speed through the water as well as the position by
astronomical observations, the current may be arrived at by this method with a fairly close degree of
accuracy. It is not always possible, however, to keep an exact reckoning, and this is especially true
in sailing vessels, where the conditions render it difficult to determine correctly the position by account;
this source of error may be combined with faulty instrumental determinations, giving apparent currents
differing widely from those that really exist.
528. Much useful knowledge regarding ocean currents has been derived from the observed drift
of objects from one to another locality. This is true not only of the bottles thrown overboard from vessels
with the particular object of determining the currents, but also of derelicts, drifting buoys, and pieces
OCEAN CURRENTS. 159
of wreckage, which fulfill a similar mission. The deductions to be drawn from such drift are of a
general nature only. The point of departure, point of arrival, and elapsed time are all that are posi-
tively known. The route followed and the set and drift of current at different points are not indicated,
and in the case of objects floating otherwise than in a completely submerged condition account must
be taken of the fact that the drift is influenced l)y the wind. But even this general information is of
great value in researches as to ocean currents, and navigators who desire to aid in the work of investi-
gation may do so by throwing overboard, from time to time, sealed bottles containing a statement of
date and position at which they are launched.
529. Currents of the Atlantic Ocean. — A consideration of the currents of the Atlantic most
conveniently begins with a description of the Equatorial Currents. The effect of the northeast and
southeast trade winds is to form two great drift currents, setting in a westerly direction across the
Atlantic from Africa toward the American continent, whose combined width covers at times upward
of fifty degrees of latitude. These are distinguished as the Northern or Southern Equatorial Currents,
according as they arise from the trade winds of the northern or southern hemisphere.
Of the two, the Southern Equatorial Current is the more extensive. It has its origin off the conti-
nent of Africa south of the Guinea coast, and begins its flow with a daily velocity that averages about
15 miles; it maintains a general set of west, the portion near the equator acquiring later, however, a
northerly component, while the drift steadily increases until, on arriving off the South American coast,
a rate of 60 miles is not uncommon. AttCape San Roque the current bifurcates, the main or equatorial
branch flowing along the Guiana coast, while the other branch is deflected to the southward.
The Northern Equatorial Current originates to the northward of the Cape Verde Islands and sets
across the ocean in a direction that averages due west; though parallel to the corresponding southern
drift, its velocity is not so high.
330. Between the Northern and Southern Equatorial Currents is found the Equatorial Counter
Current, which sets to the eastward, being apparently a flowing back, in the region of equatorial calms,
of water carried westward by the trade drifts. The extent and strength of this current varies with the
season, a maximum being attained in July or August, when its effect is apparent to ths westward of
the flftieth meridian of west longitude, while at its minimum, in November or December, its influence is
but slight and prevails over a limited area only.
531. To the westward of the region of the Equatorial Counter Current the North and the South
Equatorial Currents unite. A large part of the combmed stream flows into the Caribbean Sea through
the various passages between the Windward Islands, takes up a course first to the westward and then
to the northward and westward, finally arriving off the extremity of the peninsula of Yucatan; from
here some of the water follows the shore line of the Gulf of Mexico, while another portion passes
directly toward the north Cuban coast; by the reuniting of these two branches in the Sti-aitsof Florida
there is formed the most remarkable of all ocean currents — the Gulf Stream.
From that portion of the combined equatorial currents which fails to find entrance to the Caribbean
Sea a current of moderate strength and volume takes its course along the north coasts of Porto Rico,
Haiti, and Cuba, flows between the last-named island and the Bahamas, and enters the Gulf Stream off
the Florida coast, thus adding its waters to those of the main branch of the equatorial current which
have arrived at the same point by way of the Caribbean, the Yucatan Passage, and the Gulf.
532. The Gulf Stream, which has its origin, as has been described, in the Straits of Florida, and
receives an accession from a branch of the Equatorial Current off the Bahamas, flows in a direction that
averages true north as far as the parallel of 31°, then curves sharply to ENE. until reaching the latitude
of 32°, when a direction a little to the north of NE. is assumed and maintained as far as Cape Hatteras;
at this point its axis is about 40 miles, while its inner edge is in the neighborhood of 20 miles off the
shore. Thus far in its flow the average position of the maximum current is from 11 to 20 miles outside
the 100-fathom curve, disregarding the irregularities of the latter, and the width of the stream — about
40 miles — is nearly uniform. From off Hatteras the stream broadens rapidly and curves more to the
eastw^ard, seeking deeper water; its northern limit may be stated to be 60 to 80 miles off Nantucket
Shoals and 120 to 150 miles to the southward of Nova Scotia, in which latter place it has expanded to
a width of about 250 miles. Further on, its identity as the Gulf Stream is lost, but its general direction
is preserved in a current to be described later.
The water of the Gulf Stream is of a deep indigo-blue color, and its junction with ordinary sea
water may be plainly recognized; in moderate weather the edges of the stream are marked by ripples;
in cool regions the evaporation from its surface, due to difference of temperature between air and water,
is apparent to the eye; the stream carries with it a quantity of weed known as "gulf weed," which is
familiar to all who have navigated its waters.
In its progress from the tropics to higher latitudes the transit is so rapid that time is not given for
more than a partial cooling of the water, and it is therefore found that the Gulf Stream is very much
warmer than the neighboring waters of the seas through which it flows. This warm water is, however,
divided by bands of markedly cooler water which extend in a direction parallel to the axis and are
usually found near the edges of the stream of warm water. The most abrupt change from warm to cold
water occurs on the inshore side, where the name of the Cold Wall has been given to that band which
has appeared to some oceanographers to form the northern and western boundary of the stream.
The investigations of Pillsbury tend to prove that the thermometer is only an approximate guide to
the direction and velocity of the current. Though it indicates the limits of the stream in a general way,
it must not be assumed that the greatest velocity of flow coincides with the highest temperature, nor
that the northeasterly set will be lost when the thermometer shows a region of cold sea water.
The same authority has also demonstrated that in the vicinity of the land there is a marked varia-
tion in the velocity of current at different hours of the day, which may amount to upward of 2 knots,
and which is due to the elevation and depression of the sea as a result of tidal influences, the maximum
current being encountered at a period which averages about three hours after the moon's transit. Another
effect noted is that at those times when the moon is near the equator the current presents a narrow
front with very hi^h vel >city in the axis of maximum strength, while at periods of great northerly or
160 OCEAN CUREENTS.
southerly declination the front broadens, the current decreasing at the axis and increasing at the edges.
These tidal effects are not, however, obi-erved in the open sea.
The velocity of the Gulf Stream varits with the seasons, following the variation in the intensity of
the trade winds, to which it largely owes its origin. The drift of the current under average conditions
may be stated as follows:
' Between Key West and Habana: Mean surface velocity in axis of maximum current, 2\ knots;
allowance to be made by a vessel crossing the entire width of the stream, 1.1 knots per hour.
Off Fowey Rocks: Mean surface velocity in axis, 3.5 knots; allowance in crossing, 2} knots per hour.
Off Cape Hatteras: Mean surface velocity in axis, upward of 2 knots; allowance in crossing the
stream, IJ knot,s jser hour between the lOC-fathora curve and a point 40 miles outside that curve.
533. After passin|: beyond the longitude of the easternmost portions of North America, it is gen-
erally regarded that the Gulf Stream, as such, ceases to exist; but by reason of the prevalence of westerly
winds the direction of the set toward Europe is continued until the continental shores are approached,
when the current divides, one branch going to the northeastward and entering the Arctic regions and
the other running off toward the south and east in the direction of the African coa.st. These currents
have received, respectively, the designations of the Easterly, Nortiwasf, and Southeast Drift Currents.
534. The effect of the currents thus far described is to create a general circulation of the surface
waters of the North Atlantic, in a direction coinciding with that of the hands of a Avatch, about the
periphery of a huge ellipse, whose limits of latitude maybe considered as 10° N. and 45° N., and which
IS bounded in longitude by the P^astern and Western continents. The central space thus inclosed, in
which no av ell-marked currents are observed, and in the waters of which great quantities of the Sargasso
or gulf weed are encountered, is known as the Sargasso Sea.
535. The Southeast Drift Current carries its waters to the northwest coast of Africa, whence they
follow the general trend of the land from Cape Spartel to Cape ^"erde. From this point a large part of
the current is deflected to the eastward close along the upper Guinea coast. The steam thus formed,
greatly augmented at certain seasons by the prevailing monsoon and by the waters carried eastward
with the Equatorial Counter Current, is called the Guinea Current. A remarkable characteristic of this
current is the fact that its southern limit is only slightly removed from the northern edge of the west-
moving Equatorial Current, the effect being that the two currents flow side by side in close proximity,
but in diametrically opposite directions.
536. The Arctic or Labrador Current sets out of Davis Strait, flows southward down the coasts of
Labrador and Newfoundland, and thence south westward past Nova Scotia and the coast of the United
States, being found inshore of the Gulf Stream. It brings with it the ice so frequently met at certain
seasons off Newfoundland.
537. RennelVs Current is a temporary but extensive stream, which sets at times from the Bay of
Biscay toward the west and northwest, across the entrance to the English Channel and to the westward
of Cape Clear.
538. Of the two branches of the Southern Equatorial Current which are formed by its bifurcation
off Cape San Roque, the northern one, setting along the coasts of northeastern Brazil and of Guiana and
contributing to the formation of the Gulf Stream, has already been described; the other, known as the
Brazil Current, flows to south and west, along the southeastern coast of Brazil, as far as the neighborhood
of the island of Trinidad; here it divides, one part continuing down the coast and having some slight
influence as far as the latitude of 45° S., and the other curving around toward east.
539. The last-mentioned branch of the Brazil Current is called the Soutlieryi Connecting Cm-rent and
flows toward the African coast in about the latitude of Tristan d'Acunha. It then joins its waters with
these of the general northerly current that sets out of the Antarctic region, forming a current which
flows to the northward along the southwest African coast and eventually connects with the Southern
Equatorial Current, thus completing the surface circulation of the South Atlantic.
540. There are two other currents whose effects are felt in the Atlantic, one originating in the
Indian Ocean and flowing around the Cape of Good Hope, the other originating in the Pacific and flow-
ing around Cape Horn. They will be described under the currents of the oceans in which they first
appear.
541. Currents of the Pacific Ocean. — As in the Atlantic, the waters of the Pacific Ocean, in
the region between the tropics, have a general drift toward the westward, due to the effect of the trade
Avinds, the currents produced in the two hemispheres being denominated, respectively, the Nortltern and
the Southern Equatorial Currents. These are separated, as also in the case of the Atlantic, by an ea.st-
setting stream, about 300 miles wide, whose mean position is a few degrees north of the equator, and
which receives the name of the Equatorial Counter Current.
542. The major portion of the Northern Equatorial Current, after having passed the Mariana
Islands, flows toward the eastern coast of Formosa in a WNW. direction, whence it is deflected north-
ward, forming a current which is sometimes called the Jajmn Stream, but which more frequently
receives its Japanese name of A'ttro >S'm'o, or "black stream." This current, the waters of which are
dark in color and contain a variety of seaweed similar to "gulf Aveed," carries the Avarm tropical water
at a rapid rate to the northward and eastward along the coasts of Asia and its offlying islands, presenting
many analogies to the Gulf Stream of the Atlantic.
The limits and volume of the Kuro Siwo A'ary according to the monsoon, being augmented during
the season of southwesterly Avinds and diminished during the prevalence of those from northeast. The
current sets to the north along the east coast of Formosa, and in about latitude 26° N. changes its course
to northeast, arriving at the extreme south Avestern point of Japan by a route to westward of the Meiaco-
sima and Loo-choo islands. A branch makes off from the main stream to follow northAvard along the
west coast of Japan, entering the Sea of Japan by the Korea Channel; but the principal current bends
toward the east, floAvs through Van Diemen Strait and the passages betAveen the Linschoten Isles, and
runs parallel to the general trend of the south shores of the Japanese islands of Kiushu, Sikok, and
Nipon, attaining its greatest velocity l>etween Bungo and Kii channels, where its average drift is
between 2 and 3 knots per hour. Continuing beyond the southeastern extremity of Nipon, the direction
^ . I
OCEAN CURRENTS. 161
of the stream ))ecomes somewhat more northerlj-, and its width increases, with consequent loss of
velocity. In the Knro Siwo, as in the Gulf Stream, the temperature of the sea water is an approximate,
though not an exact, guide as to the existence of the current.
543. Near 146° or 147° E. and north of the fortieth parallel the Kuro Siwo divides into two parts.
One of these, called the Kamchatka Current, flows to the northeast in the direction of the Aleutian
Islands, and its influence is felt to a high latitude. The second branch continues as the main stream,
and maintains a general easterly direction to the 180th meridian, where it is merged into the north and
northeast drift currents which are generally encountered in this region.
544. A cold counter current to the Kamchatka Current sets out of Bering Sea and flows to the
south and west close to the shores of the Kuril Islands, Yezo and Nipon, sometimes, like the Labrador
Current in the Atlantic, bringing with it quantities of Arctic ice. This is often called by its Japanese
name of 0//a Sivo.
545. On the Pacific coast of North America, from about 50° N. to the mouth of the Gulf of
California, 23° N., a cold current, 200 or 300 miles wide, flows with a mean speed of three-quarters of a
knot, being generally stronger near the land than at sea. It follows the trend of the land (nearly SSE. )
as far as Point Concepcion (south of Monterey), Avhen it begins to bend toward SSW., and then to WSW,,
off Capes San Bias and San Lucas, ultimately joining the great northern equatorial drift.
On the coast of Mexico, from Cape Corrientes (20° N.) to Cape Blanco (Gulf of Nicoya), there are
alternate currents extending over a space of more than 300 miles in width, whicli appear to be produced
by the prevailing winds. During the dry season — January, February, and ^larch — the currents generally
set toward southeast; during the rainy season — from ]\Iay to October — especially in July, August, and
September, the currents set to northwest, particularly from Cosas Island and the Gulf of Nicova to the
parallel of 15°.
546. The Southern Equatorial Current prevails between limits of latitude that may be approxi-
mately given as 4° N. and 10° S., in a broad region extending from the American continent almost to
the one hundred and eightieth meridian, setting always to the west and with slowly increasing velocity.
In the neighborhood of the Fiji Islands this current divides; one part, known as the Ronsel Cwn-enf, con-
tinues to the westward, following a route marked by the various passages between the islands, and later
acquiring a northerly component and setting through Torres Strait and along the north coast of New
Guinea; the other part, called the Australia Cui-revt, sets toward south and west, arriving off the east
coast of Australia, along Avhich it flows southward to about latitude 35° S., whence it bends toward
southeast and east and is soon after lost in the currents due to the prevailing wind.
547. The general drift current that sets to the north out of the Antarctic regions is deflected until,
upon gaining the regions to the southwest of Patagonia, it has acquired a nearly easterly set; in striking
the shores of the South American continent it is divided into two branches.
The first, known as the Cape Horn Cnrrcnt, maintains the general easterly direction, and its influence
is felt, where not modified by winds and tidal currents, throughout the vicinity of Cape Horn, and, in
the Atlantic Ocean, off the Falkland Islands and eastern Patagonia.
The second branch flows northeast in the direction of Valdivia and Valparaiso, follows generailj'
the direction of the coast lines of Chile and Peru (though at times setting directly toward the shore iia
such manner as to constitute a great danger to the navigator), and forms the important current which
has been called variously the Peruvian, Chilean, or Humboldt Current, the last name having been given
for the distinguished scientist who first noted its existence. The principal characteristic of the Peru-
vian Current is its relatively low temperature. The direction of the waters between Pisco and Payta is
between north and northwest; near Cape Blanco the current leaves the coast of America and bears
toward the Galapagos Islands, passing them on both the northern and southern sides; here it sets toward
AVNW. and west; beyond the meridian of the Galapagos it widens rapidly, and thecuiTent is lost in the
equatorial current, near 108° W. As often happens in similar cases, the existence of a counter-current
has been proved on different occasions; this sets toward the south, is very irregular, and extends only a
little distance from shore.
54§. CiRRENTs OF THE IxDiAN OcEAN. — In this occau the currents to the north of the equator
are-very irregular; the periodical winds, the alternating breezes, and the changes of monsoon produce
currents of a variable nature, their direction depending upon that of the wind which produces them,
upon the form of neighboring coasts, or, at times, upon causes which can not be satisfactorily explained.
549. There is, in the Indian Ocean south of the equator, a regular Equatorial Current which, by
reason of owing its source to the southeast trade winds, corresponds with the Southern Equatorial Currents
of the Atlantic and Pacific. The limits of this west-moving current vary with the longitude as well as
with the season. Ui)on reaching about the meridian of Rodriguez Island, a l)ranch makes off toward
the south and west, flowing past Mauritius, then to the south of Madagascar (on the meridian of which
it is 480 miles broad) , and thereafter, rapidly diminishing its breadth, forming jiart of the Agulhas Cur-
rent a little to the south of Port Natal.
The main equatorial current continues westward until passing the north end of Madagascar, where,
encountering the obstruction presented by the African continent, it divides, one branch following the
coast in a northerly, the other in a southerly, direction. The former, in the season of the south-nest
monsoon, is merged into the general easterly and northeasterly drift that prevails throughout the
ocean from the northern limit of the Equatorial Current on the .'■'outh, as far as India and the adjacent
Asiatic shores on the north; but during the northeast monsoon, when there exists in the northern
regions of the Indian Ocean a westerly drift current analogous to the Northern Equatorial Currents
produced in the Atlantic and Pacific by' the northeast trades, there is formed an east-setting Equatorial
Counter Current, which occupies a narrow area near the equator and is made up of the waters accumu-
lated at the Avestern continental boundary of the ocean by the drift currents of both hemispheres.
550. The southern branch of the Equatorial Current flows to the south and west down the
Mozambique channel, and, being joined in the neighborhood of Port Natal by the stream which
arrives from the open ocean, there is formed the warm Agulhas Current, which possesses many of the
characteristics of the Gulf and Japan streams. This current skirts the east coast of South Africa and
22489—03 11
162 OCEAN CUERENTS.
attains considerable velocity over that part between Port Xatal and Algoa Bay. During the summer
months its effects are felt farther to the westward; during the winter it diminishes in force and extent.
The meeting of the Agulhas Current with the cold water of higher latitudes is frequently denoted by a
broken and confused sea.
Upon arriving at the southern side of the Agulhas Bank, the major part of the current is deflected
to the south, and then curves toward east, flowing back into the Indian Ocean with diminished strength
and temperature, on about the fortieth parallel of south latitude, where its influence is felt as far as the
eightieth meridian. A small part of the stream which reaches Agulhas Bank continues across the
southern edge of that bank, then turns to the northwest along the west coast of the continent until it
is united with the waters of the Southern Connecting Current of the Atlantic.
551. Along the fortieth parallel of south latitude, between Africa and Australia, there is a general
easterly set, due to the branch of the Agulhas current already described, to the continuation of the drift
current from the Atlantic which passes to southward of the Cape of Good Hope, and to the westerly
winds which largely prevail in this region. At Cape Leeuwin, the southwestern extremity of Australia,
this east-setting current is divided into two branches; one, going north along the west coast of Australia,
blends with the Equatorial current nearly in the latitude of the Tropic of Capricorn; the other preserves
the direction of the original current and has the effect of producing an easterly set along the south coast
of Australia.
552. As in the other oceans, a general northerly current is observed to set into the Indian Ocean
from the Antarctic regions.
EXTRACTS FROM NAUTICAL ALMANAC.
163
APPENDIX I.
EXTEAOTS FEOM THE AMEKIOAN EPHEMEEIS AND NAUTICAL ALMA-
NAC, FOE THE YEAE 1879, WHICH HAVE EEFEEENCE TO THE
EXAMPLES FOE THAT YEAE GIVEN IN THIS WOEK.
[Extracts: Page I.]
AT GREENWICH APPARENT NOON.
THE sun's
Apparent
Right Ascension.
Diff. for
1 hour.
Apparent
Dewination.
Diff. for
1 hour.
Semi-
diameter.
Sidereal
Time of
the Semi-
diameter
passing
the
Meridian
Equation of
Time, to be
added to
suhtraxied
from Appar-
ent Time.
Diff. for
1 hour.
JANUARY.
Sun.
19
Mon.
20
Tues.
21
20 4 60. 17
10. 626
20 9 14.84
10.595
20 13 28. 75
10.564
20 21 9. 0
+31.54
20 8 20.4
32.49
19 55 9. 1
-1-33.43
16 17.58
16 17.48
16 17.38
69.72
69.61
69. 51
10 56. 68
11 14. 74
11 32.05
0.769
0.738
0.706
APRIL.
Tues.
1
Wed.
2
Thur.
3
Sun.
13
Mon.
14
Tues.
15
Wed.
16
Thur.
17
Frid.
18
Sat.
19
Sun.
20
Mon.
21
0 41
0 45
0 49
1 25
1 29
1 33
54.87
9.096
33.24
9.100
11.70
9.106
47.34
9.206
28.45
9.219
9.91
9.234
51.74
9.250
33.95
9.268
16.56
9.285
59.58
9.302
43.01
9.320
26.87
9.337
N.
N.
4 30 43. 2
+57.85 '
4 53 49. 1
57.64 t
5 16 49. 8
.57.41
9 0 54. 1
.54.40
9 22 35.4
M.03 ;
9 44 7.5
53.64
10 5 29.9
53.23
10 26 42. 3
52.80
10 47 44. 7
62.37
11 8 36.4
61.92
11 29 17.1
.51. 46
11 49 46.4
+50.97
16 2.16
64.51
16 1. 89
64.53
16 1.61
64.55
15 58. 86
64.89
15 58. 59
64.94
15 58. 31
64.99
65.04
15 58. 04
15 57. 77
65.09
15 57. 50
65.15
15 57. 24
65.21
15 56. 98
65. 27
15 56. 72
65. 33
4 0.
3 42.
3 24.
0 35.
0 19.
0 4.
0 10.
0 24.
0 38.
0 51.
1 4.
1 17.
0.758
0.754
0.748
0.649
0.635
0.620
0.604
0.587
0.570
0.553
0.536
0.518
MAY.
Mon.
5
Tues.
6
Sat.
10
Sun.
11
Thur.
15
Frid.
16
Sat.
17
Sun.
18
48 30. 72
9.626
52 22. 03
9.650
7 53. 03
9.747
11 47.27
9.771
27 30. 07
9.871
31 27. 26
9.895
35 25. 03
9.919
39 23. 37
9.942
N. 16 13 40. 4
16 30 40. 4
17 35 53. 8
17 51 29. 1
18 50 48. 5
19 4 51.6
19 18 35.5
N. 19 31 59. 8
+42.86
42.17
39.33
38.59
35.52
34.72
33.91
+33.06
15 53. 36
66.37
15 53. 14
66.45
15 52. 25
66.78
15 52. 03
66.86
15 51. 20
67.19
15 51.00
67.27
15 50. 80
67.35
15 50.61
67. 43
3 25. 18
3 30. 40
3 45.58
3 47.90
3 51.32
3 50.68
3 49. 47
3 47.69
0.229
0.206
0.109
0.084
0.014
0.039
0.062
0.086
Note.— Mean Time of the Semidiameter i)assing may be found by substracting 0".18 from the Sidereal Time.
+ prefixed to the hourly change of declination indicates that north declinations are increasing and south
declinations are decreasing; — indicates that north declinations are decreasing and south declinations
increasing.
164
EXTRACTS FROM NAUTICAL ALMANAC.
[Extracts: Page I.]
AT GREENWICH APPARENT NOON— Continued.
THE SUN'S
Apparent
Right Ascension.
Diff. for
1 hour.
Apparent
Declination.
DifE. for
1 hour.
Semi-
diameter.
Sidereal
Time of
the Semi-
dinmeter
passing
^he
Meridian.
Erjuation of
Time, to be \
subtracted
from
atlfled to
Apparent
Time.
Diff. for
1 hour.
JUNE.
Sat.
7
Tues.
10
Wed.
11
Frid.
13
Sat.
14
Frid.
20
Sat.
21
Wed.
25
Thur.
26
Frid.
27
0
12
17
25
29
54
58
15
6 19
6 23
33.74
10. 312
57.61
10. 348
6.09
10. 3.^8
23.73
10. 376
32. 85
10.383
30. 05
10. 402
39.75
10. 402
18.00
10. 389
27.29
10.383
36.42
10.376
22 45 9.5
+ 14.64
23 0 55. 9
11.63
23 5 22.9
10.62
23 13 3.8
8.58
23 16 17.4
7.55
23 27 0. 3
1.36
23 27 20.5
-f 0.32
23 24 33. 1
- 3.78
23 22 49. 5
4.81
23 20 41. 3
- 5.84
15
15
15
15
15
15
15
15
15
15
47.63
47.30
47.20
47.00
46.91
46.48
46.43
46.27
46.24
46.22
68. 70
68. 81
68.84
68.90
68.92
68.98
68.98
68.94
68.93
68.91
1 28.86
0 54. 76
0 42. 87
0 18.42
0 5.89
1 11.75
1 24.86
2 16.72
2 29.42
2 41.97
0. 4-V)
0.490
0.500
0. 518
0. 525
0. .546
0.546
0.532
0.526
0. 519
JULY.
Frid.
11
Sat.
12
Tues.
22
Wed.
23
Thur.
24
7
21 16.72
10.197
7
25 21. 24
10. 179
8
^ 39. 82
9.%4
8
9 38. 68
9.939
8
13 36. 94
9.914
N. 22 8 29. 2
22 0 23. 2
20 19 8.9
20 7 5.2
X. 19 54 41.3
-19. 76
20.71
29. 72
30.57
-31.41
15 46. 30
68.30
15 46.33
68.24
15 46. 94
67.51
15 47. 03
67.43
15 47. 13
67.35
5 10.04
5 17.99
6 10. 85
6 13. 15
6 14.84
0. 339
0.321
0.108
0.083
0.059
SEPTEMBER.
Tobesubtract-
edfrom A])-
2Mrent Time.
Wed.
Thur.
11 13 33.93
11 17 9.68
8.993
8.988
4 59 24.2
-56.90
15 55. 81
4 36 36. 2
-57.10
15 56.06
64.12
64.10
3 1.29
3 22.03
0.862
0.867
DECEMBER.
Mon.
Tues.
18
18
1 24. 12
5 50. 72
11. 108
11.107
S. 23 27 17. 3
S. 23 26 54. 3
+ 0.37
16 18. 13
71. 30
+ 1.55
16 18. 18
71.30
1 16.61
0 46. 64
1.248
1.246
Note. — Mean Time of the Semidiameter pas.sing may be found by subtracting 0'.18 from the Sidereal Time.
-(- prefixed to the hourly change of declination indicates that north declinations are increasing and south
declinations are decreasing ; — indicates that north declinations are decreasing and south declinations
increasing.
EXTRACTS FROM KAUTICAL ALMANAC.
165
[Extracts: Page II.J
AT GREEN^A^ICH MEAN NOON.
Day of
the
Week.
Day of
the
Month.
THE sun's
Apparent
Right Ascension.
h. m. s.
Diff. for
1 hour.
Apparc7it
Declination.
Diff. for
1 hour.
E(^uation of
Time, to be
sitbtractal from Diff. for
.. ,, '■- 1 hour.
added to Mean
Time.
JANUARY.
Sidereal Time
or Right As-
cension of
Mean Sun.
//. m.
Frid.
10
Rat.
11
Mon.
20
Tues.
21
19 26 16.08
10.866
19 30 36.59
10.842
20 9 12.84
10.593
20 13 26. 71
10.562
S.21 58 32.0
21 49 22. 7
20 8 26. 6
S. 19 55 15. 6
+ 22. 35
23.41
32. 48
+ 33.42
7
43. 42
1.010 [
8
7.37
0. 986 1
11
14.60
0.738 1
11
31.91
0. 706 1
19 18 32. 66
19 22 29. 22
19 57 58. 24
20 1 54.80
APRIL.
Tues.
1
Wed.
9
Tues.
8
Wed.
9
Tues.
15
Wed.
16
Thur.
17
Sun.
20
Mon.
21
Tues.
22
Wed.
23
Thur.
24
Frid.
25
Tues.
29
Wed.
30
0 41
0 45
1 7
11
33
36
40
51
55
59
2 2
2 6
2 10
2 25
2 29
54.27
9.098
32.68
9.102
26.22
9.146
5.87
9. 1.57
9.91
9.236
51.77
9.252
34.02
9.269
43.19
9.321
27.08
9.338
11.41
9.356
56.19
9.375
41.42
9.394
27.11
9.414
34.67
9.494
22.79
9.515
. 4 30
4 53
7 10
7 32
9 44
10 5
10 26
11 29
11 49
12 10
12 30
12 50
13 9
14 26
14 44
39.4
+ 57.86
45.6
57.65
20.3
66.08
42.8
55.77
7.4
53.65
63.24
30.1
42.8
62.81
18.1
61.46
47.6
50.98
5.4
50.48
11.2
49.97
4.7
49.46
45.4
48.92
14.5
46.65
46.7
+ 46.04
4 0.65
0.758
3 42. 50
0.754
1 56. 74
0.709
1 39.83
0.698
0 4.54
0.620
0.604
0 10. 15
0 24. 46
0.587
1 4.94
0.536
1 17.61
0.518
1 29.83
0.600
1 41. 61
0.481
1 52.93
0.462
2 3.80
0.442
2 42. 46
0.361
2 50. 89
0.340
0 37
0 41
2 32
53.62
50.16
29.48
26.04
5. 37
1.92
58.48
48.13
44.69
41.24
37. 80
34. 35
30.91
17.13
13.68
MAY.
Frid.
9
Sat.
10
Sun.
11
Mon.
12
Frid.
16
Sat.
17
Sun.
18
Wed.
28
Thur.
29
Frid.
30
Sat.
31
Sat.
7
Sun.
8
Wed.
11
Sat.
14
Sun.
15
Wed.
25
Thur.
26
Frid.
27
0.01
9. 723
53.65
9.747
47.89
9.771
42.71
9.7%
27.90
9.895
25.67
9.919
24.01
9.942
36.81
10.155
40.75
10. 173
45.12
10.190
49.91
10.207
17
17
17
18
19
N.17 20 3.5
35 56. 3
51 31.6
6 48.9
4 53.8
19 18 37.6
19 32 1. 8
21 27 5.9
21 36 37. 4
21 45 46. 5
N. 21 54 33. 0
JUNE.
5 0 34. GO
10. 311
5 4 41. 64
10. 324
5 17 6.22
10.357
5 29 32. 87
10.382
5 33 42. 11
10.388
6 15 17.60
10.888
6 19 26. 86
10.382
6 23 35. 96
10. 375
N. 22 45 9. 9
22 50 49. 3
23 5 23.0
23 16 17.4
23 19 6.4
23 24 33. 2
23 22 49. 7
N.23 20 41.6
+ 40.06
39.33
38.69
37.84
34. 72
33.91
33.09
24.28
23.34
22.40
+ 21. 45
+ 14. 64
13.64
10.62
7. 55
+ 6.52
-3.78
4.81
-5.84
3 42. 68
3 45. 59
3 47. 91
3 49.64
3 50. 68
3 49. 47
3 47. 68
3 0.46
2 53.08
2 4,5.26
2 37.03
To be added to
wbtrarted from
Mean Time.
1 28.85
1 17.77
0 42. 86
0 5.89
0 6.80
2 16. 70
2 29. 40
2 41. 95
0.134
0.109
0.084
0. 060
0.U39
0.062
0.086
0.297
0.315
0.334
0.3.51
3 7 42.69
3 11 39.24
3 15 35. 80
3 19 32. 35
3 35 18.58
3 39 15. 14
3 43 11.69
4 22 37. 27
4 26 33. 83
4 30 30. 38
4 34 26.94
0.456
0. 467
0.500
0. .525
0.532
0.532
0. 526
0.519
Note. — The Semidiameter for Mean Noon may be assumed the same as that for Apparent Noon.
+ prefixed to the hourly change of declination indicates that north declinations are
increasing and south declinations are decreasing; — indicates that noMh declinations are
decreasing and south declinations increasing.
5 2 2. 85
5 5 59. 41
5 17 49. 08
5 29 38. 76
5 33 35. 31
6 13 0.90
6 16 57. 46
6 20 54. 01
Diff. for 1 hour.
-^9».8565.
166
EXTRACTS FROM NAUTICAL ALMANAC.
[Extracts: I'age II.]
AT GREENWICH MEAN NOON— Continued.
Day of
the
Week.
Dav of
the
Month.
THE sun's
Apparent
Right Ascension.
h. m.
Difif. for
1 hour.
Appareiit
Declination.
Diff. for
1 hour.
Equation of
Time, to be
subtracted frovi
Mean Time.
Diff. for
1 hour.
Sidereal Time
or Ri^ht As-
cension of
Mean Sun.
AUGUST.
Tiies.
Wed.
0 27.45
4 17.82
9.610
9.586
N. 17 1 29. 2
N. 16 45 8. 6
-40.62
-41.20
SEPTEMBER.
Wed.
10
Thur.
11
11
13
3-1.
39
8. 995
11
17
10.
19
8.990
N. 4 59 21.3 -56.91
N. 4 36 32.9 i -57.12
5 47. 69
5 41.51
To be added to
Mean Time.
3 1.33
3 22.07
0.246
0.270
0. 862
0.867
8 54 39. 76
8 58 36. 31
11 16 35.72
11 20 32. 26
OCTOBER.
Wed.
15
Thur.
16
Frid.
17
Tues.
28
Wed.
29
13 20 28.07
9.309
13 24 11. 75
9.333
13 27 56. 01
9.357
14 9 44.78
9.662
14 13 37.03
9.693
S. 8 29 16. 2
8 51 28. 1
9 13 32.4
13 6 2.6
S. 13 26 4. 6
55.65
55.34
55.02
50.34
49. 82
14 7. 02
0.548
14 19.89
0. 524
14 32. 18
0..T00
16 5.51
0.195
16 9.82
0. 164
13 34 35.08
13 38 31. 64
13 42 28. 19
14 25 50. 29
14 29 46. 84
NOVEMBER.
Wed.
Thur.
12
13
15 9 14.01
15 13 18. 76
10.180
10.216
s. i;
s.i;
41 18.4
57 27.6
- 40. 77
-39.99
15 44. 60
15 36.41
0.323
0. 359
15 24 58. 61
15 28 55. 17
DECEMBER.
Wed.
3
Thur.
4
Mon.
8
Tues.
9
Wed.
10
Thur.
11
Mon.
22
Tues.
23
Wed.
24
16 37 40. 65
10.844
16 42 1. 22
10. 869
16 59 29. 19
10. 960
17 3 52.48
10. 979
17 8 16.23
10.998
17 12 40. 41
11.015
18 1 24.34
11.104
18 5 50. 85
11. 103
18 10 17.33
11. 101
S. 22 6 24. 6
22 14 43. 0
22 43 35. 6
22 49 42. 3
22 55 21.9
23 0 34. 3
23 27 17. 3
23 26 54. 3
S. 23 26 2. 9
- 21. 30
20. 23
15.83
14.71
13.58
- 12.45
0.37
1.55
2.73
+
+
5.66
41.65
59.91
33.18
5.99
6 38. 37
1 16.58
0 46. 63
0 16. 71
10
9
7
7
7
0.987
1.013
1.104
1.123
1.142
1.159
1.248
1.246
1.244
16 47 46, 31
16 51 42. 87
17 7 29. 10
17 11 25.66
17 15 22.22
17 19 18. 78
18 2 40. 92
18 6 37. 48
18 10 34.03
Note. — The Semidiameter for Mean Noon may be a.<«umed the same a.s that for Apparent Noon.
+ prefixed to the hourly change of declination indicates that north declinations are
increasing and south declinations are decreasing: — indicates that north declinations are
decreasing and south declinations increasing.
Difl. for 1 hour.
+ 9».a565
EXTRACTS FROM NAUTICAL ALMANAC.
167
[Extracts: Page III.]
AT GREENWICH MEAN NOON.
Day of
the
Month.
Day of
the
Year.
THE SUN'S
Logarithm of
the Radius
Vector of the
Earth.
Diff. for
1 hour.
Mean time of
Sidereal Oh.
Tvue LONGITUDE.
Diff. for
1 hour.
LATITUDE.
A.
A'
0 ' II 1 II
"
II
h. m. s.
APRIL.
21
22
Ill
112
30 60 16. 5
31 58 46. 1
59 47. 4
58 16.9
146.27
146. 19
+0.52
+0.52
0. 0023923
0. 0025087
+48.8
+48.3
21 59 38.53
21 55 42.62
[Extracts: Page IV.]
GREEN\VICH MEAN TIME,
THE MOON
SEMIDIAMETER.
Noon.
Midnight.
HORIZONTAL PARALLAX.
Noon.
Diff. for
1 hour.
Midnight. Diff.J-
MERIDIAN PASSAGE.
Diff. for
1 hour.
Noon.
APRIL.
16
17
18
19
20
21
22
23
24
25
26
15 4.7
14 57.0
14 51.1
14 47.0
14 44. 5
14 43. 4
14 43. 8
14 45. 7
14 49.2
14 54.5
15 1. 6
15 0.6
14 53.
8
14 48. 9 1
14 45.
6
14 43.
t
14 43.
4
14 44.
6
14 47.
2
14 51.
6
14 57.
8
15 5.
9
55 13.6
-1.34
54 45.1
1.04
54 23.5
0.76
54 8.4
0.50
53 59. 1
0.27
53 55.3
-0.06
53 56. 7
+0.17
54 3.6
0.41
54 16.5
0.67
54 35. 8
0.94
55 2.1
+L24
54 58.5
-1.19
54 33. 5
0.90
54 15.2
0.63
54 3.1
0.38
53 56. 5
-0.16
53 55. 3
+0.06
53 59. 4
0.29
54 9.3
0.54
54 25. 3
0.80
54 48. 0
1.09
55 17.9
+1.39
21 3.8
1.71
21 44.3
1.67
22 24. 6
1.68
23 5.4
1.73
23 47. 7
1.81
6
0 32.2
1.90
1 19.0
2.01
2 8.2
2.10
2 59,3
2.15
3 51. 2
2.16
24.6
25.6
26.6
27.6
28.6
29.6
0.9
1.9
2,9
3,9
4.9
MAY.
28
29
16 44. 6
16
38.5
15
47.0
15
59.4
16 42. 1
16 33. 7
15 53. 2
16 5.6
61 20,1
-0..53
60 57. 8
-1.29
57 48, 8
+1.86
58 34,3
+1.90
61 11.3
-0.93
60 40. 2
-1.62
58 11.4
+ 1.90
58 57. 1
+L88
12 36, 6
2.66
13 41,2
2.69
5 55.3
1.95
6 42.5
1.98
14.9
15.9
7.3
8.3
25
26
27
15 49. 8
15 58. 7
16 7.2
JUNE.
15
54.3
16
3.0
16
11.1
57
59.1
1
37
58 31.7
1
34
59
3.0
1
25
58
15.5
1.36
58 47. 6
1.30
59
17.5
1.17
4 40.1
5 27.0
6 15.6
1.94
1.98
2.08
5.7
6.7
7. 7
168
EXTRACTS FROM NAUTICAL ALMANAC.
[Extracts: Pages V-XII.]
GREENWICH MEAN TIME.
THE MOOX'S RIGHT ASCENSION AND DECLINATION.
Hour.
Right Ascension. ' j^^^^^
1
Declination. j^^iff^
Hour.
Right Ascension. f»\«^
Declination.
Diff.
for 1 m.
■
I-*
h. m. #. s.
1
O 1 H II
h. m. s.
s.
o < "1 "1
THURSDAY, APRIL 10.
WEDNESDAY, MAY 28.
17
18
19
17 18 38.57 1 2.6448
17 21 17.16 i 2.6414
17 23 55.54 2.6379
S. 26 19 38. 3
26 19 41. 1
S. 26 19 33. 0
- 0.138
+ 0.044
+ 0.225
6
7
8
10 19 4.23
10 21 7. 78
10 23 11. 34
2.0.591
2.0592
2.0593
N. 7 4 18.5
6 49 52.4
N. 6 35 23. 4
-14.411
14. 459
-14.507
WEDNESDAY, APRIL 16.
THURSDAY, JUNE 26.
t
6
22 12 47. 08
22 14 39. 29
22 16 31. 30
1.8718
1.8685
1.86.53
S. 8 12 37.4
7 59 36. 1
S. 7 46 33.5
+13.010
13.032
+ 13.054
2
3
11
11 37 41.96
11 39 46.49
11 56 28. 42
2. 0743 i S. 2 35 36. 4
2.0767 i 2 50 44.4
2.0989 S. 4 51 36.5
-15.135
15. l;?3
-1.5.069
FRIDAY, APRIL 25.
:\rONDAY, DECEMBER 8.
16
17
18
5 41 33. 19
5 43 48. 55
5 46 3. 93 .
2. 2558
2.2562
2.2566
N. 26 5 43. 8
26 4 23. 5
N. 26 2 55. 2
- 1.272
1. 405
- 1.5.37
2
3
4
12 23 13.52 2.1615 S. 8 9 24.4
12 25 23.37 2.1668 8 23 44.9
12 27 3.'].54 ! 2.172-2 S. 8 38 3.8
14. 354
14.328
14.302
TUESDAY, APRIL 29.
11
12
13
9 2 56. 23 2. 1384
9 5 4.49 2.1369
9 7 12.66 2.13.56
X. 15 27 3. 6
15 14 52. 7
N. 15 2 36.3
-IJ.lSo
12. 227
-12.318
EXTRACTS FROM NAUTICAL ALMANAC.
[Extracts: Pages relating to Planets.]
GREENWICH MEAN TIME.
169
JXJPITKR.
VEJiTXJS.
April.
April.
Apparent
Right
Ascension.
Noon.
22 25 51.70
22 26 35.54
22 27 19.02
22 28 2.14
Var. of
R. A.
fori
Hour.
Noon.
Apparent
Declination.
Noon.
+1.834 —10 44 29.6
1.819 10 40 28.0
1-804! 10 36 28.1
+1.789, _io 32 30.0
Var. of
Pec.
fori
Hour.
Noon.
+10.10
10.03
9.9d
Meridian
Passage.
Apparent
Right
Ascension.
Var. of
R. A.
fori
Hour.
Noon.
Noon.
h. m.
20 50.0
20 46.8
20 43.6
+9.89 20 40.3
h. III. n. s.
4 19 14.43+12.686
4 24 19.28' 12.718
4 29 24.88+12.748
Day of the Month.
Polar Semidiameter
Horizontal Parallax
1st.
11th.
16.4
1.5
16.7
1.6
17.1
Day of the month.
17.5
1.6 1.6
Semidiameter
Hor. Parallax
1st.
6.0
Apparent
Declination.
Noon.
+22 40 33.2
22 55 4.9
4-23 8 59.5
Var. of
Dec.
fori
Hour.
Noon.
Meridian
Passage.
+37.08
35.55
+34.00
h. m.
2 10.7
2 11.9
2i3.0
6th.
6.2: 6.3
6.2
6.4
16th.
6.3
6.5
6.4
26th.
6.6
6.7 6.8
September.
M^RS.
Apparent
Right
Ascension.
Var. of
R. A.
fori
Hour.
Noon.
Noon.
h. m. s.
22 32 5.11
22 31 38.03
Apparent
Decimation.
Noon.
-1.134
-1.120
-10 44 20.5
-10 46 57.2
Var. of
Dec.
for 1
Hour.
-6.58
-6.47
March.
Meridian
h. m.
10 49.8
10 45.5
Day of Month.
Polar Semidiameter
Horizontal Parallax
23.6
2.2
nth.
21st.
II
II
23.5
23.2
2.2
2.2
Apparent
Right
Ascension.
h. ni. s.
20 5 56.83
20 9 1.27
20 12 5.45
Noon.
s.
+7.690
7.680
+7.669
Apparent
Declination.
Noon.
-21 13 58.1
21 5 40.4
-20 57 10.7
Var. of
Dec.
fori
Hour.
Noon.
+20.48
20.98
+21.48
Meridian
Passage:
h. m.
20 26.4
20 25.6
20 24.7
22.8
2.2
Note. — North declinations are marked +, south declinations — .
+ prefixed to the hourly change of declination, indicates that north declinations are increasing and south
declinations are decreasing; — indicates that north declinations are decreasing and south declinations
increasing.
170
EXTKACTS FROM NAUTICAL ALMANAC.
[Extracts: Pages relating to Fixed Stars.]
FIXED STARS.
MEAN PLACES FOR 1879.0. (J.\n. O+0.OI6, Washington.)
Star'»Name.
Magni-
tude.
Right Ascension. An. Variation.
Declination.
An. Varia-
tion.
•
(x Ursse Min. (Polanfi) *..
2
//. Vi. 8.
1 14 24.861
1 33 12.133
4 28 58.716
6 15 38.457
6 39 48.935
13 18 49.216
14 10 8.551
16 21 59.432
+21.485
+ 2.233
+ 3.437
+ 3.633
+ 2.645
+ 3.154
+ 2.735
+ 3.670
0 / ff
+88 39 49.92
—57 51 5.79
+16 15 53.35
+22 34 26.94
-16 33 4.30
-10 31 44.21
+19 48 48.59
-26 9 41.94
n
+19.00
+18.40
+ 7.59
- 1.48
- 4.68
—18.90
—18.87
- 8.34
orEridani {Acheriiar)
a Tauri {Aldebaran)
1
1
3
1
1
1
1.2
Jit Geminorum
a Canis Maj. {Sirius)
a Virginis { Spica )
cc Bootis {Arctui'ua)
a Seorpii (Antares)
* Circnmpolar Star.
APPARENT PLACES FOR THE UPPER TRANSIT AT WASHINGTON.
oUrsae
Minorls. {Polaris.)
a Erldani. ( Achertiar. )
a Tauri. ( Aldebaran. )
Mean Solar
Right
Declination
Mean Solar
Right Declination
Mean Solar Right
Declination
Date.
Ascension.
North.
Date.
Ascension.
South.
Date. Ascension.
North.
h. m.
0 1
h. m.
0 1
h. m.
0 1
1 13
+88 39
1 33
-57 50
4 28
+16 15
June 10.8
63.54
n
47.1
July 27. 7
14.91 +.47
II
28.6 +0.5
Apr. 9.1
59.66 -.10
58.7 -0.2
11.8
64.35
47.0
Aug. 6.7
15.37 +•«
28.3 0.0
19.1 59.57 .07
58.6 -0.1
12.8
65.21
46.9
29.1 59.52 -.02
58.5 0.0
aCani
s Majoris. (Si
rius.)
a Virginis. (Spica.)
a Bootis. ( Arcturus. )
Mean Solar
Right
Declination
Mean Solar
Right
Declination
Mean Solar
Right Declination 1
Date.
Ascension.
Soidh.
Date.
Ascension.
South.
Date.
Ascension.
North.
h. m.
0 ,
h. TO.
0 I
■ h. TO.
0 1
6 39
-16 32
13 18
-10 31
14 10
+19 48
(Dec. 30.5)
51'. 06 +.10
63.7 -2.5
Apr. 29.5
52^28 +.02 ! 64.6 -o.i
May 9.4
8. "
11.71 +.02
II
32 A +1-6
Jan. 9.5
51.14 +.05
66.1 -2.3
May 9.4
52.29 .00 ! 64.7 0.0
19.4
11.71 -.01 33.7 +1.6 1
Apr. 9.2
50.09 -18
76.2 +0.3
19.4
52.28 -.03
64.6 +0.1
1
19.2
49.92 -16
75.8 0.6
29.4
52.24 .04
64.4 0.3
29.2
49.77 -13
75.0 0.9
June 8.3
52.19 -.60
64.1 +0.4
May 9.2
49.65 -10
74.0 +1-1
•
aSC(
)rpli. (Antare
8.)
Mean Solar
Right
Declination
Date.
Ascension.
South.
h. m.
16 21
0 1
-26 9
May 9.5
63;il +19
II
53.8 -0.5
19.5
63.28 16
54.3 0.4
29.5
63.43 12
54.7 0.4
June 8.5
63.53 09
55.0 0.3
18.4
63.60 +-05
55.3 -0.3
1
July 28.3
63.49 -10
56.0 0.0
Aug. 7.3
63.38 -13
55.9 +0.1
17.3
63.24 -i-i
55.8 +0.2
FORMS FOR WORK.
171
APPENDIX II.
A COLLECTION OF FOEMS FOE WOEKING DEAD EECKONINa AND YAEI-
OUS ASTEONOMICAL SIGHTS, WITH NOTES EXPLAINING THEIE
APPLICATION UNDEE ALL CIECUMSTANCES.
(The figures in parenthesis refer to the Notes following these forms.)
FOKM FOK DAY'S WORK, DEAD BEUKOMNG.
Time.
Compass Course.
Var.
Dey.
Lee-
way.
Total
error.
True Course.
Patent
log.
Dist.
N.
S.
E.
W.
Diflf.(i)
Long.
'
Laliti
0
de.
Longiixidf.
Left at departure
(or noon)
. (S) N. or S.
. (2) E. or W
Run to
N. or S.
N. or S.
E. orW
ByD. R.at
E. or W
Run to
N. or S.
E. or W.
By D. R.at
N. or S.
E. or W.
FURM FOK TLVE SIGHT OF SUN'S LOWER LIMB (SIMNER LIKE).
h. m. s.
W. T.
C-W
Chro.
C.C.
(11) G. M. T
(T)Eq.t.
G. A. T.
Obs. alt. Q .
Corr. ±
(3) S. D.
i.*) L C.
dip
p. & r.
(MDec.
H.D.
G.M.T.
N.orS.
Corr. ± .
Dec.
(«)!>
N.orS.
(5) Eq. t.
H. D.
G. M. T.
Corr.
Eq. t.
Corr.
2).
h. m. s.
G.A.T. ..
L.A.T.I..
(h. m. S.I
(8) Long.Ji----,----„4E.orW.
sec
cosec
cos
sin
sin i ti
2).
DLo
(10)
So-ll
h. m. s.
G.A.T
L.A.T.,
Jll. 7)1. S.'
i"'T"„-\E.orW.
sec
cosec
cos
sin
sin i ti
2).
172 FORMS FOR WORK,
W. T,
C-W
Chro,
, t.
C. C.
(!•) G.M.
T.
R. A.
M.S.
Red.
(Tab. 9)
G. S.
T.
R. A.
*
FORM FOK TIME SIGHT OF A STAR (SUMKEB LIXE).
h. m. s. o , „ ^ ^ g_
Obs. alt. * R. A ,
+ Corr. ±
Dec N.orS.
+ .....«L.
+
(*).I.C. + («)p
dip
xef.
(IS) H. A. from Gr E. or VV.
Corr. ±
h ° ' "
Li sec (9) La sec
p cosec cosec
«1
si-h.
cos
sin
Gr. H. A.
(18) H. A.i
h.
m.
f:.
2
.. E.orW.
. E.orW. 8ini?i
h.
m.
f.
(14) Long.i
o
,
II
•'Ie.oj-W.
(1") «■> cos
sin
*)-/t
Gr. H. A.
li.
m.
s.
H. A.»
h.
m.
8.
Long.o
o
'
II
sin i U
>¥.. or W.
FORM FOB TIME SIGHT OF A PLANET (SUMNER LINE).
W. T.
C-W
S.
.b.9
h. m. s.
+
Chro. t.
C. C.
^..".\..
(11) G. M. T.
R. A. M.
Red. (Ta
+
) +
G. S. T.
R. A.*
(i2)H.A.fromGr E.orW.
Obs.
alt.
*
R. A.
Corr.
4-
h
H. D.
' II
G. M. T
(15) par.
+
(4) I. C.
+
Corr.
+
' //
R. A.
dip
-
ref.
-
' II
Corr.
i
h. m. .V. o ' "
Dec. N.orS.
h. TO. «.
H. D.
G. M. T.
Corr.
Dec. N.orS.
(«)p
7i.
/ //
o
' II
O ;
' II
For the remainder of the work, by which the hour angles and thence the longitudes are found, employ the method
given under " Form for Time Sight of a Star (Sumner Line)."
W. T.
C-W
S.
b.9
h. m. 8.
+
Chro. t.
C. C.
±
(")G. M. T.
R. A. M.
Red. (Ta
+
')+
G. S. T.
R. A. C
FORMS FOR WORK. 173
FORM FOR TIME SIGHT OF MOON'S LOWER LIMB (SUMXER LINE).
° ' " !i. m. 8. o I II
Obs.alt. C (i-)R. A. (i-)Dec. N.orS.
(i«)S. D. + M.I). + M. D.
Aug. + m.
(*)I. C. + No. mill. ± No. mill. ±.
^— — Corr. ± Corr.
dip — h. m. 8,
— — R. A. Dee.
/ //
(i2)H.A.fromGr E.orW. 1st corr. ± (6)p
O / fl
Approx. alt
p.ct-r.(Tab.24)+
For the remainder f)f the Wf)rk, by which the hour angles and thence the longitude.s are found, employ the method
given under " Form for Time Sight of a Star (Sumner Line)."
FORM FOR MERIIUAX ALTITIDE OF SIN'S L(MVER LIMB.
O I II I II O I II
Obs.alt.Q (3)S.D. + (") Dec N.orS.
Corr. ± (*)I. C. +
(18) c N.orS. dip —
rf N. or S. p.ii-r. —
Lat. N.orS.
H. D. 4-
Long. ±
h.
Corr. 4-
O 1 II
Dec
N.orS.
Corr. ±
FORM FOR MERIDIAN ALTITUDE OF A STAR.
O I II I II O I II
Obs.alt.* (<) I. C. + Dec N.orS.
dip -
ref. -
h
(18) Z
d
N.orS.
N.orS.
Lat.
N.orS.
Corr. ±
• FORM FOR MERIDIAN ALTITUDE OF A PLANET.
O I II I II ii^ „j o / //
Obs.alt. =)< (15) par. + G. M. T., Gr. trans Dec N.orS.
Corr. 4: (4)1. C. + Corr. for Long. + — ^—
L. M. T., local trans H. D. +
Long. ± h.
G.M.T
(18); N.orS. dip- G. M. T., local trans.
d N.orS. ref. -
Lat. N.orS. —
Corr. ±
Dec N.orS.
174
FORMS FOR WORK.
(IS);
FORM FOR MERIDIAN ALTITUDE 0¥ MOON'S LOWER LIMB.
° ' " h. VI.
O I II
Obs. alt. ^
N.orS. (W}S.D.
X.orS. Aujr.
(<)I.C.
Lat N.orS.
dip
G. M. T., Gr. trans.
■^-^— Corr. for Long.(Tab. 11) ±
+ L. M. T., local trans.
+ Long. + .
+
+ ..
G. M. T., local trans.
('■) Dec
II
M. D. ±...
m.
Xo. min. ± . . .
I II
Corr. + . . .
0
t II
Dec.
N.orS.
N.orS.
Ist corr.
Approx. Alt.
jj.<fcr. (Tab.24) +.
ALTERNATIVE FORM FOR MERIDIAN ALTITUDE OF A BODY. (»))
± 90° 00' 00" Jiules/or signs.
(M) Dec.
Corr.
Constant :
Obs. alt.
Lat.
Case I. Lat. & Dec. same name, Lat. greater -i- 90° + Dec. — Corr. — Alt-
Case II. Lat. & Dec. same name, Dec. greater —90° + Dec. + Corr. + Alt.
Case III. Lat. and Dec. opposite names + 90° — Dec. — Corr. — Alt.
Ca.se IV. Lower transit +90° — Dec. +Corr. + Alt.
N.orS.
FORM FOR LATITUDE SIGHTS OF SUN'S LOWER LIMB (SUMNER LINE).
W.T.
■i
h.
III. s.
Obs. alt.
Corr.
h
S.D.
LC.
C-W
Chro. t.
C.C. +
(")G.M.T.
(T) Eq.t.
4_
+
G.A.T.
Long. 1 ±
L.A.T.,
(«) Long, g rt
L.A.T.2
h. m. s.
dip
p. &r.
Corr.
(6) Dec.
H.D.
G. M. T.
Corr.
Dec.
N. or S.
(*) Eq. t
N. or S.
T
».
H.D. ± .
h.
G.M.T.
s.
Corr. ± .
m.
&
Ea.t.
h. m. s.
<!>' <t>" Method.
(s*)9>i" N.orS.
a> 1 ' N. or 8.
Lat. 1 N. or S.
h
«>j"
<Pi'
Lat. 2 N. or S.
sec.
tan .
sec.
tan .
sni.
sin.
sin.
sin.
(25) a
h
(20) fl < 1 2 rt
H,
d
Reduction to Meridian.
N. or S.
N. or S.
Lat. 1 N. or S.
h
atn^ ±
Lat.s N.orS.
W. T.
C-W
+
Chro. t.
0. C.
±
(") G. M. T.
R. A. M. S.
+
Red. (Tab. 9)
+
G. S. T.
R. A.*
FORMS FOR WORK 175
FORM FOB LATITUDE SKiHTS OF A STAR (SUMXER LINE).
h. m. 8. 0 1 It fi^ „j_ g^
R.A
(12) H.A.fromGr E. or W.
(!") Long.i E.orW.
(h. m. «.|
Ie. or W.
(«3) Long.2
f^. m. «.
Corr.
-t- ..
h
I.e.
+ ....
' "
dip
ref.
, „
Corr.
±
/ //
Dec. N. orS.
For the remainder of the work, by which the latitudes are found from either the <p' <p" formula or the reduction to the
meridian, employ the methods given under " Form for Latitude Sights of Sun's Lower Limb (Sumner Line)."
FORM FOR LATITUDE SItiHTS OF A PLACET (SUMNER LINE).
h. in. 8. ° '
W. T. Ob8.alt.5(< R.A. Dec. N. or S.
C-W + Corr.
Chro. t.
C. C.
(")G. M. T. (»6) par. +.
R. A. M.S. + (<) I.e. +.
Red. (Tab.9) +
G.S.T.
R.A.* ^jp _ R-A Dec N.orS.
R. A.
4;
h.
m.
8.
Dec.
H. D.
8.
H. D.
G. M. T.
G. M. T.
h.
Corr.
8.
Corr.
R.A.
h.
in.
8.
Dec.
(W) H.A.fromGr E.orW. reL
(«)Long., E.orW.
h. m. 8.
h. m. 8.
(58) Long.o
I h. in. 8.
Corr.
E. or W.
For the remainder of the work, by which the latitudes are found from either the <p' <p" formula or the reduction to the
meridian, employ the methods given under " Forms for Latitude Sights of Sun's Lower Limb (Sumner Line)."
176
FORMS FOR WORK.
FORM FOR LATITUDE SIGHTS OF MOOX'S LOWER LIMB (SUMXER LINE).
h. m. s.
W.T.
C-W
Chro. t.
C. C.
(11) G. M. T.
R. A. M. S.
+ .
Iljd. (Tab. 9) +
G. S. T.
R.A.C
(12) H. A. from Gr K.or W.
(«) Long.] E.orW.
Obs.alt.C
(16) S. D.
Aug.
(*)I-C.
dip
h. VI. g.
('■) R. A.
^E.orW.
1st Corr.
Approx. alt.
p. dr. (Tab. 24) +.
M. I>.
+ ...
«.
No. min.
-4- ..
«).
Corr.
-1-
*••
R. A.
/(.
m. i<.
(•■) Dec
^
^__
II
i\r
D.
4- ...
m.
No
.ram
■ dt- ■
Coi
rr.
1 II
_
De(
B.
0
1 II
N.orS.
N.orS.
Long.o
//. m. i.
h. m. s.
E.orW
For the remainder of the work, by which the latitudes are found from either the 9' q>" formula or the reduction to the
meridian, employ the method.s given under " Forms for Latitude Sights of Sun's Lower Limb (Sumner Line)."
FORM FOR CHRONOMETER CORRECTION BY EQUAL ALTITUDES OF SUN.
W. T., A. M.
h. m.
s. h. m. s.
W. T.,P. M
(28) Dec.
H. D. a
merid.
Long.
Corr.
Dec.
(31) Tab. 37
H. D.
L
1st pt.
2dpt.
Eq.eq.l
± .
±. ..
0
± . ..
±...
± - -.
0
1 II
N.orS.
H. D. (
noon;
H. D.
noon)
Diff. 24"
Diff. li>
Diff. for
H. D. at
0
.. d ±...
P'-e^-} ±
Wll.Ji
i 4-
n
+
C-W +
C-W
h.
A. M. Chro. t.
P. M. Chro. t
P. M. Chro. t.
+
A.M.Chro.t.-
2)
4- ,
■" —
Mid. Chro. t.
"
1 II
-1-..
Eq. eq. alt.
long. 4-
"
0
II
s.
N.orS.
]ogA(±)...
log (±)...
tan ( + )...
log (±)...
}
Chro. t. L. Ai
noon
C) Eq. t.
merid. ±
II
TO. S.
— (2'*)Eq. t.
logB( + ).
log (±).,
... tan (±)..
log (±)..
Chro. t. L. M.
noon
(29) Long.
}
S.
H. D. -4-
—
/j
]-
G. M. T.
Corr. ±
m. 8.
Eq. t.
\~..
~
FORM FOR FINDING THE TIME OF HIGH (OR LOW) WATER.
d. h. m.
G. M. T. of Greenwich transit
(32) Corr. for Long. (Tab. 11)
L. M. T. of local transit
' Lunitidal int. (App. IV)
L. M. T. of high (or low) water
FORMS FOR WORK. 177
NOTES KELATIXG TO THE FORMS.
1. It Is not necessary to convert departure into difference of longitude for eacli course; it will suffice to make one
conversion for the sum of all the departures used in bringing- forward the position to any particular time.
2. In D. R. it will be found convenient to worli Lat. and Long, in minutes and tenths, rather than in minutes and
seconds.
3. If upper limb is observed, the correction for S. D. should be negative, instead of positive.
4. A positive I. C. has been assumed for illustration throughout the forms; if negative, it should be included with the
minvs terms of the correction.
6. For time sights and 9' q>" sights, take Dee. and Eq. t. from Naut. Aim., p. II (G. M. noon).
0. To obtain p, subtract Dec. from 90° if of same name as Lat.: add to 90° if of opposite name.
7. Sign of Eq. t. that of application to mean time.
8. If G. A. T. is later than L. A. T., Long, is west; otherwise it is east.
P. If Lat. is exactly known, a second latitude need not be employed.
10. So and So— /( may be obtained by applying half the difference between Lj and L.^, with proper sign, to Sj andsj— ^,
respectively.
11. The G. M. T. must represent the proper number of hoiirs from noon, the beginning of the astronomical daj'; to obtain
this it may be necessary to add V2^ to the Chro. t.
12. H. A. from Greenwich is the difference between G. S. T. and R. A., and should be marked W. if the former is greater;
otherwise, E.
1;^. Local H. A. is marked E. or W., according as the body is east or west of the meridian at time of observation.
11. Subtract local hour angle from Greenwich hour angle to obtain longitude; that is, change name of local hour angle
and combine algebraically.
15. The forms include a correction for the parallax of a planet, but in most cases this is small, and may be omitted. When
used, take hor. par. from Kaut. Aim. and reduce to observed altitude by Table 17. The semidiameter of a planet may be
disregarded in sextant work if the center of the body is brought to the horizon line.
16. If upper limb is observed, the corrections for S. D. and Aug. should be negative, instead of positive.
17. R. A. and Dec. are to be picked out of Naut. Aim. for nearest hour of G. M. T., and to be corrected for the number
of minutes and tenths.
IS. Mark zenith di.stance N. or S. according as zenith is north or south of the body observed: mark Dec. according to its
name, subtracting it from 180° for cases of lower transit; then, in combining the two for Lat., have regard to their names.
19. For meridian altitudes, take Dec. from Naut. Aim., p. I (G. A. noon).
20. This form enables "Constant" to be worked up before sight is taken, and gives latitude directly on completion of
meridian observation. Longitude and altitude at transit must be known in advance with sufficient accuracy for correcting
terms.
21. The details of obtaining Dec. at transit and correction for altitude are shown in the meridian altitude forms for each
of the various bodies.
22. In an a. m. sight subtract L. A. T. from 24'' to obtain t; in a p. m. sight L. A. T. is equal to t.
23. If Long, is exactly known, a second longitude need not be employed.
24. Mark <p" N. or S. according to name of Dec, and subtract it from 180° when body is nearer to lower than to upper
transit; mark q>' N. or S. according as zenith is north or south of the body; then combine for Lat. having regard to the names.
25. Take a from Table 26 and at- from Table 27.
26. Add for upper, subtract for lower transits.
27. Subtract longitude from Greenwich hour angle to obtain local hour angle; that is, change name of longitude and
combine algebraically.
28. For equal altitude sights, take Dec. and Eq. t. from Naut. Aim., p. I (G. A. noon).
29. Add longitude if east; subtract if west.
80. If error is +, the chronometer is fast, and the correction is subtractive; and the reverse.
31. Mark log A and log B as indicated in Table 37; mark N. Lat., N. Dec, an<l H. D. toward the north +, and the
reverse. If, in combining the three logarithms for the respective parts of the equations, one or three of them should be
minus, the sign of that part is minus; otherwise, plus.
32 Add for west, subtract for east longitude.
22489—03 12
178
KULES AND PRINCIPLES OF MATHEMATICS.
APPENDIX III.
EXPLANATION OF OEETAIN EULES AND PRINCIPLES OF MATHEMATICS
OF USE IN THE SOLUTION OF PEOBLEMS IN NAVIGATION.
DECIMAL FRACTIONS.
Fractions, or Vulgar Fractions, are expressions for any assignable part of a unit; they are usaually
denoted by two numbers, placed one above the other, with a line between them; thus \ denotes the
fraction one-fourth, or one part out of four of some whole quantity, considered as divisible into four
equal parts. The lower number, 4, is called the denominator of the fraction, showing into how many
parts the whole is divided; and the upper number, 1, is called the numerator, and shows how many of
those equal parts are contained in the fraction. It is evident that if the numerator and denominator be
varied in the same ratio the value of the fraction will remain unaltered; thus, if both the numerator
and denominator of the fraction, \, be multiplied by 2, 3, 4, etc., the fractions arising will be f, -^t^, ^,
etc., all of which are evidently equal to \.
A Decimal Fraction is a fraction whose denominator is always a unit with some number of ciphers
annexed and the numerator any number whatever; as, -f^, yifjj, rMfft etc. And as the denominator of
a decimal is always one of the numbers 10, 100, 1000, etc., the necessity for writing the denominator
may be avoided by employing a point; thus, fV is written .3, and j^j^ is written .14; the mixed number
3tA> consisting of a whole number and a fractional one, is written 3. 14.
In setting down a decimal fraction the numerator must consist of as many places as there are
ciphers in the denominator; and if it has not so many figures the defect must be supplied by placing
ciphers before it; thus, yVV = -16, y^f (y = .016, xjyVVff = -0016, etc. And as ciphers on the right-hand side
of integers increase their value in a tenfold proportion, as 2, 20, 200, etc., so when set on the left hand
of decimal fractions they decrease their value in a tenfold proportion, .as .2, .02, .002, etc.; but ciphers
set on the right hand of these fractions make no alteration in their value; thus, .2 is the same as
.20 or .200. -"
The common arithmetical operations are performed the same way in decimals as they are in inte-
gers, regard being had only to the particular notation, to distinguish the integral from the fractional
part of a sum.
Addition of Decimals. — Addition of decimals is performed exactly like that of whole numbers,
placing the numbers of the same denomination under each other, in which case the separating decimal
points will range straight in one column.
Ex.\MPLES.
Add:
Sum:
Miles.
26.7
32.15
143.206
.003
202.059
Feet.
1.26
2.31
1.785
2.0
7.355
Inches.
272.3267
.0134
2.1576
31.4
305.8977
Subtraction of Decimals. — Subtraction of decimals is performed in the same manner as in whole
numbers, observing to set the figures of the same denomination and the separating points directly
under each other.
Examples.
From :
Take:
31.267
2.63
36.75
.026
1.254
.316
1364.2
25.163
Difference:
28.637
36.724
.938
1339.037
Multiplication of Decimals. — Multiply the numbers together as if they were whole numbers,
and point off as many decimals from the right hand as there are decimals in both factors together; and
when it happens that there are not so many figures in the product as there must be decimals, then
prefix such number of ciphers to the left hand as will supply the defect.
Example I.
Multiply 3.25 by 4.5.
3.25
4.5
1.625
13.00
Answer: 14.625
In one of the factors is one decimal, and in the
other two; their sum, 3, is the number of decimals
of the product.
Example II.
Multiply .17 by .06.
.17
.06
Answer:
.0102
In each of the factors are two decimals; the pro-
duct ought therefore to contain 4; and, there being
only three figures in the product, a cipher umst be
prefixed.
RULES AND PRINCIPLES OF MATHEMATICS.
179
Example III.
Multiply 0.5 by 0.7.
Answer:
0.5
0.7
0.35
Example IV.
Multiply .18 by 24.
.18
24
Answer:
72
36
4.32
Division of Decimals. — Division of decimals is performed in the same manner as in whole num-
bers. The number of decimals in the quotient must be equal to the excess of the number of decimals
of the dividend above those of the divisor; when the divisor contains more decimals than the dividend,
ciphers must be affixed to the right hand of the latter to make the number equal or exceed that of the
divisor.
Examplk I.
Divide 14.625 by 3.25.
3.25 ) 14.625 ( 4.5
1300
1625
1625
In this example there are two decimals in the
divisor and three in the dividend; hence, there is
one decimal in the quotient.
Example II.
Divide 3.1 by .0062.
Previous to the divishm affix three ciphers to
the right hand of 3.1, to make the numl)er of deci-
mals in the dividend equal the number in the
divisor.
.0062) 3.1000(500
310
Example III.
Divide 17.256 by 1.16.
1.16 ) 17.25600 ( 14.875
116
565
464
1016
928
880
812
680
580
100
000
Multiplication of Decimals by Contraction. — The operation of multiplication of decimal fractions
may be very much abbreviated when it is not required to retain any figures beyond a certain order or
place; this will constantly occur in reducing the elements taken from the Nautical Almanac from Green-
wich noon to later or earlier instants of time.
In multiplying by this method, omit writing down that part of the operation which involves decimal
places below the required order, but mental note should be made of the product of the first discarded
figure by the multiplying figure, and the proper number of tens should be carried over to insure accuracy
in the lowest decimal place sought.
Example: Required the reduction for the sun's declination for 7'".43, the hourly difference being
58^''. 18, where the product is required to the second decimal.
By ordinary method.
58'M8
7\43
By contraction
58'M8
7^43
17454
23272
40726
1.74
23.27
407.26
432^^2774, ^.
432.^^27
In the contracted method, for the multiplier .03 it is not necessary to record the product of any
figures in the multiplicand below units; for the multiplier .4, none below tenths; but in each case
observe the product of the left-hand one of the rejected figures and carry forward the number of tens.
180
RULES AND PRINCIPLES OF MATHEMATICS.
REDrcTioN OF Decimals. — To reduce a vulgar fraction to a decimal, add any number of ciphers to
the numerator and divide it by the denominator; the quotient will be the decimal fraction. The decimal
point must be so placed that there may be as many figures to the right hand of it as there were added
ciphers to the numerator. If there are not so many figures in the quotient place ciphers to the left hand
to make uj) the number.
Example I.
Reduce ^V to a decimal.
50)^.00
.02 Answer.
Example II.
Reduce | to a decimal.
8)3.000
.375 Answer.
Example III.
Reduce 3 inches to the decimal of a foot.
Since 12 inches = 1 foot this fraction is xi-
12)3.00
Example IV.
Reduce 15 minutes to the decimal of an hour.
Since 60"' = 1\ this fraction is f§.
60)15.00
.25 Answer.
Example V.
Reduce 1
7m
22' to the decimal of an hour
22»
22"'
= — =0'".37.
60
IT^.S?
iT'-.s:
= =0\289 Answer.
60
.25 Answer.
Any decimal may be reduced to lower denominations of the same quantity by multiplying it by the
number representing the relation Vjetween the respective denominations.
Example VI: Reduce 7.231 days to days, hours, minutes, and seconds.
01.231
24
924
462
5\544
0\544
60
32". 640
0™.640
60
38\400
Answer: 7* 5'' 32'» 38'. 4.
GEOMETRY.
Geometry is the science which treats of the description, properties, and relations of magnitudes, of
which there are three kinds; viz, a line, which has only length without either breadth or tnickness; a
surface, comprehended by length and breadth; and a solid, which has length, breadth, and thickness.
A point, considered mathematically, has neither length, breadth, nor thickness; it denotes position
simply.
A line has length without breadth or thickness.
A surface has length and breadth without thickness.
A solid has length, breadth, and thickness.
A straight or right line is the shortest distance between two points on a plane surface.
A plane surface is one in which, any two points being taken, the straight line between them lies
wholly within that surface.
Parallel lines are such as are in the same plane and if extended indefinitely never meet.
A circle is a plane figure bounded by a curve line of which every point is
equally distant from a point within called the center. The bounding curve of
the circle is called the circumference.
The radius of a circle, or semi-diameter, is a right line drawn from the
center to the circumference, as AC (fig. 65) ; its length is that distance which
is taken between the points of the compasses to describe the circle.
A diameter of a circle is a right line drawn through the center and termi-
nated at both ends by the circumference, as ACB, its length being twice that
of the radius. A diameter divides the circle and its circumference into two
equal parts.
An arc of a circle is any portion of the circumference, as DFE.
The chord of an arc is a straight line joining the ends of the arc. It divides
the circle into two unequal parts, called segmivti, and is a chord to them both;
thus, DE is the chord of the arcs DFE and DGE.
A semicircle, or half circle, is a figure contained between a diameter and the arc terminated by that
diameter, as AGB or AFB.
RULES AND PRINCIPLES OF MATHEMATICS. 181
Anypart of a circle contained between two radii and an arc is called a sector, as GCH.
A quadnmt is half a semicircle, or one-fourth part of a whole circle, as CAG.
All circles are supposed to have their circumferences divided into 360 equal parts, called degrees;
each degree is divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called
seconds; an arc is measured by the number of degrees, minutes, and seconds that it contains.
A aphere is a solid bounded by a surface of which every point is equally distant from a point within
which, as in the circle, is called the center. Substituting surface for circumference, the definitions of the
radius and diameter, as given for the circle, apply for the sphere.
An angle is the inclination of two intersecting lines, and is measured by the arc of a circle inter-
cepted between the two lines that form the angle, the center of the circle being the point of intersection.
A i-ig}tt angle is one that is measured by a quadrant, or 90°. An acute angle is one which is less than
a right angle. An obtuse angle is one which is greater than a right angle.
A plane triangle is a figure contained by three straight lines in the same plane.
When the three sides are equal, the triangle is called equilateral; when two of them are equal, it is
called isosceles. When one of the angles is 90°, the triangle is said to be right-angled. When each angle
is less than 90°, it is said to be acute-angled. When'one is greater than 90°, it is said to be obtuse-angled.
Triangles that are not right-angled are generally called oblique-angled.
A quadrilateral figure is one bounded by four sides. If the opposite sides are parallel, it is called a
parallelogram. A parallelogram having all its sides equal and its angles right angles is called a square.
When the angles are right angles and only the opposite sides equal, it is called a rectangle.
In a right-angled triangle the side opposite the right angle is called the hi/potenuse, one of the other
sides is called the base, and the third side is called the }>erjiendicular. In any oblique-angled triangle,
one side having been assumed as a base, the distance from the intersection of the other two sides to the
base or the base extended, measured at right angles to the latter, is the j)erpendicular. In a parallelo-
gram, one of the sides having been assumed as the base, the distance from its opposite side, measured
at right angles to its direction, is the perpendicular. The term altitude is sometimes substituted for
perpendicular in this sense.
Every section of a sphere made by a plane is a circle. A great circle of a sphere is a section of the
surface made by a plane which passes through its center. A small circle is a section by a plane which
intersects the sphere without j)assing through the center.
A great circle may be drawn through any two points on the surface of a sphere, and the arc of that
circle lying between those points is shorter than any other distance between them that can be measured
upon the surface. All great circles of a sphere have equal radii, and all bisect each other.
The extremities of that diameter of the sphere which is perpendicular to the plane of a circle are
called the poles of that circle. In the case of a small circle the poles are named the adjacent pole and
the remote pole. All circles of a sphere that are parallel have the same poles. All points in the circum-
ference of a circle are equidistant from the poles. In the case of a great circle, the poles are 90° distant
from every point of the circle.
Assuming any great circle as a primary, all great circles which pass through its poles are called its
secondaries. All secondaries cut the primary at right angles.
Useful Formll.e Derived from Geometry. — In these formulae the following abbreviations are
adopted:
h, base of triangle or parallelogram. r, radius of sphere or circle.
h, perpendicular of triangle or parallelogram. d, diameter of sphere or circle.
/, height of cylinder or cone. A, major axis of ellipse.
7t, ratio of diameter to circumference a, minor axis of ellipse.
( = 3.141593). s, side of a cube.
Area of parallelogram = bxh.
Area of triangle = ^ b X h.
Area of any right-lined figure = sum of the areas of the triangles into which it is divided.
Sum of three angles of any triangle = 180°.
Circumference of circle = 27tr, or Ttd.
Area of circle = TCr', or —j--
Angle subtended by arc equal to radius = 57°. 29578.
Volume of sphere = -^ •
Surface of sphere = 7td\ or 47rr*.
Area of ellipse = — r —
Volume of cube = s*.
Volume of cylinder = Area of base X I-
Volume of pyramid or cone = Area of base X "3 •
182
EULES AND PRINCIPLES OF MATHEMATICS.
TRIGONOMETRIC FUNCTIONS.
The trigonometric functions of the angle formed by any two lines
are the ratios existing between the sides of a right triangle formed by
letting fall a perpendicular from any point in one line upon the
other line; no matter what point is chosen for the perpendicular
nor which line, the ratios, and therefore the respective functions,
will be the same for any given angle.
Let ABC (lig. 66) be a plane right triangle in which C is the
right angle; A and B, the other angles; c, the hypotenuse; a and
b the sides opposite the angles A and B, respectively. In considering
the functions of the angle A, its opposite side, a, is regarded as the
perpendicular and adjacent side, b, as the base; for the angle B, b is
the perpendicular and a the base. Then the various ratios are
designated as follows:
perpendicular . „ , ^, . , , . , ,
hypotenuse ' ^^ called the sine of angle A, abbreviated sin A;
hvpotenuse' ^^ called the cosine of angle A, abbreviated cos A;
])erpendicular . ,, , ,
is called the tangent of the angle A, abbreviated tan A;
base
base
is called the cotangent of the angle A, abbreviated cot A;
a
c'
b
a
v
b
a'
c
F
c^
a'
1-
1 — sine A, is called the co-versed sine of A, abbreviated covers A.
The following relations may be seen to exist between the various functions:
c .
= - = cosec A;
> is called the secant of the angle A, abbreviated sec A;
perpendicular'
hypotenuse
base
hvpotenuse . ,, , , , , , . , , . ,
or rtprnendicular' ^^ called the cosecant of the angle A, abbreviated cosec A;
cosine A, is called the versed sine of A, abbreviated vers A.
= 1
cosA = l-^7=ft=^^«^'
!HLA^£_ii = «=tanA.
cos A c ' c h
Hence the cosecant is the reciprocal of the sine, the secant is the reciprocal of the cosine, the cotan-
gent is the reciprocal of the tangent, and the tangent equals the sine divided by the cosine.
The complement of an angle is equal to 90° minus that angle, and thus in the triangle ABC the
angle B is the complement of A. The supplement is equal to 180° minus the angle.
From the triangle ABC, regarding the angle B, we have:
8inB= — = cosA;
tan B = = cot A ;
sec B = — = cosec A.
RULES AND PRINCIPLES OF MATHEMATICS.
183
Fig. 67.
Hence it may be seen that the sine of an angle is the cosine of the complement of that angle; the
tangent of an angle is the cotangent of its complement, a
and the secant of an angle is the cosecant of its com-
plement.
The functions of angles vary in sign according to
the quadrant in which the angles are located.
Let AA^ and BB^ (fig. 67) be two lines at right
angles intersecting at the point O, and let that point
be the center about Avhich a radius revolves from an
initial position OB, successively passing the points
A, B', A'. In considering the angle made bv this
radius at any position, P^ P^^ V'^', V'^, with the line ,
OB, its position of origin, the functions will depend *
upon the ratios existing between the sides of a right
triangle whose base, h, will always lie within BB,^
and whose perpendicular, a, will always be parallel to
AA/', while its hypotenuse, c (of a constant length
equal to that of the radius), will depend upon tlie
position occupied by the radius. Now, if OB and OA
be regarded as the positive directions of the base and
perpendicular, respectively, and OB^ and OA^ as their
negative directions, the sign of the hypotenuse being
always positive, the sign of any function may be deter-
mine'd by the signs of the sides of the triangle upon
which it depends.
For example, the sine of the angle P^'OB is -, and since a is positive the quantity has a positive
value; its cosine is -, and as h is measure<l in a negative direction from O the cosine must therefore be
negative.
In the first quadrant, between 0° and 90°, all quantities being positive, all functions will also be
positive.
In the second quadrant, between 90° and 180°, sin A f = J is positive; cos A { =-- \ has a nega-
.tive value Wuse ,, i, negative; ,a„ A (=|) « al» negative because of .. The cosea>nt, recant, and
cotangent have, as in all cases, the same signs as the sine, cosine, and tangent, respectively, being the
reciprocals of those quantities.
In the third quadrant, between 180° and 270°, sin A { =- J and cos A f =7 J are both negative,
because both d and h have negative values; tan A f =r ) is positive for the same reason.
In the fourth quadrant, between 270° and 360°, sin A f =^ ) is negative, cos A f =- J is positive,
and tan A f =r J is also negative.
From a consideration of the signs in the manner that has been indicated the following relations
will appear:
sin A = sin (180°-A) = -sin (180° +A) = — sin (360° -A).
cos A = — cos (180°— A) = -co8 (180° + A) = co8 (360°— A).
tan A = - tan (180° -A) = tan (180° + A) = — tan (360° -A).
sin A = cos (90° — A) = - cos (90°+A) = -cos (270° -A) = cos (270°+ A).
Any similar relation may be deduced from the figure.
It is of great importance to have careful regard for the signs of the functions in all trigonometrical
solutions.
LOGARITHMS.
In order to abbreviate the tedious operations of multiplication and division with large numbers, a
series of numbers, called Logarithms, was invented by Lord Napier, by means of which the operation of
multiplication may be performed by addition, and that of division by subtraction. Numbers may be
involved to any power by simple multiplication and the root of any power extracted by simple division.
In Table 42 are given the logarithms of all numbers, from 1 to 9999; to each one must be prefixed
an index, with a period or dot to separate it from the other part, as in decimal fractions; the numbers
from 1 to 100 are given in that table with their indices; but from 100 to 9999 the index is left out for the
sake of brevity; it may be supplied, however, by the general rule that the index of the logarithm of any
184 RULES AND PRINCIPLES OF MATHEMATICS.
integer or mixed number is always one less than the number of integral places in the natural number.
Thus, the index of the logarithm of any number (integral or mixed) l)etween 10 and 100 is 1; from 100
to 1000 it is 2; from 1000 to 10000 it is 3, etc. ; the method of finding the logarithms from this table will
be evident from the rules that follow:
To find the logarithm of amj number less than 100, enter the first page of the table, and opposite the
given number will be found the logarithm with its index prefixed. Thus, opposite 71 is 1.85126, which
IS its logarithm.
To find the logarithm of any number between 100 and 1000, find the given number in the left-hand col-,
umn of the table of logarithms, and immediately under 0 in the next column is a number, to which must
be prefixed the number 2 as an index (because the number consists of three places of figures), and the
required logarithm willjae found. Thus, if the logarithm of 149 was required, this number being found
in the left-hand column, against it, in the column marked 0 at the toj) (or bottom) is found 17319, pre-
fixing to which the index 2, we have the logarithm of 149, 2.17319.
To find the logarithtn of any number between 1000 and 10000, find the three left-hand figures of the given
number in the left-hand column of the table of logarithms, opposite to which, in the column that is
marked at the top (or bottom) with the fourth figure, is to be found the required logarithm, to which
must be prefixed the index 3, because the number contains four places of figures. Thus, if the logarithm
of 1495 was required, opposite to 149, and in the column marked 5 at the top (or bottom) is 17464, to
which prefix the index 3, and we have the logarithm, 3.17464.
To find the logarithm of any number above 10000, find the first three figures of the given number in the
left-hand column of the table, and the fourth figure at the top or bottom, and takeout the corresponding
logarithm as in the preceding rule; take also the difference between this logarithm and the next greater,
and multiply it by the remaining figure or figures of the number whose logarithm is sought, pointing off
as many decimal places in the product as there are figures in the multiplier. To facilitate the calcula-
tion of the proportional parts several small tables are placed in the margin, which give the correction
corresponding to the difference, and to the fifth figure of the proposed number. Thus, if the logarithm
of 14957 was required, opposite to 149, and under 5, is 17464; the difference between this and the next
greater number, 17493, is 29; this multiplied by 7 (the last figure of the given number) gives 203;
pointing off the right-hand figure gives 20.3 (or 20) to be added to 17464, which makes 17484; to this,
Prefixing the index 4, we have the logarithm sought, 4.17484. This correction, 20, may also be found
y inspection in the small table in the margin, marked at the top 29; opposite to the fifth figure of the
number, 7, in the left-hand column, is the corresponding correction, 20, in the right-hand column.
Again, if the logarithm of 1495738 was required, the logarithm corresponding to 149 at the left, and
5 at the top, is, as in the last example, 17464; the difference between this and the next greater is 29;
multiplying this by 738 (the given number excluding the first four figures) gives 21402; crossing off the
three right-hand figures of this product (because the number 738 consists of three figures), we have the
correction 21 to be added to 17464; and the index to be prefixed is 6, because the given number consists
of 7 places of figures; therefore the required logarithm is 6.17485. This correction, 21, may be found as
above, by means of the marginal table marked at the top 29, taking at the side 7.38 (or 7^ nearly), to
which corresponds 21, as before.
To find the logarithm of any mixed decimal number, find the logarithm of the number, as if it Avere
an integer, by the preceding rules, to which prefix the index of the integral part of the given number.
Thus, if the logarithm of the mixed decimal 149.5738 was required, find the logarithm of 1495738, with-
out noticing the decimal point; this, in the last example, was found to be 17485; to this prefix the index
2, corresponding to the integral part 149; the logarithm sought will therefore be 2.17485.
lb find the logarithm of any decimal fraction less than unity, it must be observed that the index of the
logarithm of any number less than unity is negative; but, to avoid the mixture of positive and negative
quantities, it is common to borrow 10 in the index, which, in most cases, may afterwards be neglected
in summing them with other indices; thus, instead of writing the index — 1 it is written -|-9; instead
of — 2 we may write + 8; and so on. In this way we may find the logarithm of any decimal fraction
by the followmg rule: Find the logarithm of a fraction as if it were a whole number; see how many
ciphers precede the first figure of the decimal fraction, subtract that number from 9, and the remainder
will be the index of the given fraction. Thus the logarithm of 0.0391 is 8.59218 — 10; the logarithm of
0.25 is 9.39794 — 10; the logarithm of 0.0000025 is 4.39794 — 10, etc. In most cases the writing of — 10
after- the logarithm may be dispensed with, as it will be quite apparent whether the logarithm has a
positive or a negative index.
To find the number corresponding to any logarithm, seek in the column marked 0 at top and bottom
the next smallest logarithm, neglecting the index; write down the number in the side column abreast
which this is found and this will give the first three figures of the required number; carry the eye along
the line until the next smallest logarithm to the given one is found, and the fourth figure of the required
number will be at the top and bottom of the column in which this stands; take the difference between
this next smallest logarithm and the next larger one in the table, and also the difference between the
next smallest logarithm and the given one; entering the small marginal table which has for its heading
the first-named difference and finding in the right-hand column of that table the last-named difference,
there will appear abreast the latter, in the left-hand column, the fifth figure of the required number.
Where it is desired to determine figures beyond the fifth for the corresponding number, the difference
between the next lower logarithm and the given one may be divided by the difference between the
next lower and next higher ones, and the quotient (disregarding the decimal point, but retaining any
ciphers that may come between the decimal point and the significant figures) will be the fifth and suc-
ceeding figures of the number sought. Having found the figures of the corresponding number, point
off from the left a number of figures which shall be one greater than the index number, and there place
a decimal point. In this operation of placing the decimal point, proper account must be taken oi the
negative value of any index.
Thus, if the number corresponding to the logarithm 1.52634 were required, find 52634 in the column
marked 0 at the top or bottom, and opposite to it is 336; now, the index being 1, the required number
must consist of two integral places; therefore it is 33.6.
EULES AND PRINCIPLES OF MATHEMATICS.
185
If the number corresponding to the logarithm 2.57345 were required, look in the column 0 and find
in it, against the number 374, the logarithm 57287, and, guiding the eye along that line, find the given
logarithm, 57345, in the column marked 5; therefore the mixed number sought is 3745, and since the
index is 2, the integral part must consist of 3 places; therefore the number sought is 374.5. If the index
be 1 the number will be 37.45, and if the index be 0 the numljer Avill be 3.745. If the index be 8,
corresponding to a number less than unity, the number will be 0.03745.
Again, if the number corresponding to the logarithm 3.57811 were required, find, against 878 and
under 5, the logarithm 57807, the difference between this and the next greater logarithm, 57818, being
11, and the difference between 57807 and the given number, 57811, being 4: in the marginal table headed
11, find in the right hand column the number 4, and abreast the latter appears the figure 4, which is the
fifth figure of the required number; hence the figures are 37854; pointing off from the left 3 + 1 = 4
places, the number is 3785.4.
If the given logarithm were 5.57811, since the index 5 requires that there shall be six places in the
whole number, it is desirable to seek accuracy to the sixth figure. The logarithmic part being the
same as in the example immediateh' preceding, it is found as before that the first four figures are 3785,
the difference between the next lower and next greater logarithms is 11, and between the next lower
logarithm and the given one is 4; divide 4 by 11 and the quotient is .36; drop the decimal point, annex
and point off, and the number required is found to be 378536.
It may be remarked that in using five-place logarithm tables it is not generally to be expected that
results will be exact beyond the fifth figure.
To show, at one view, the indices corresponding to mixed and decimal numbers, the following
examples are given:
Mired number. Logarithms.
40943.0 Log. 4.61218
4094. 3 Log. 3. 61 21 8
409. 43 Log. 2. 61218
40.943 Log. 1.61218
4. 0943 Log. 0. 61218
Decimal nnmher. Logarithms.
0. 40943 Log. 9. 61218 — 10
0. 040943 Log. 8. 6121 8 — 1 0
0. 0040943 Log. 7. 61218 - 10
0. 00040943 Log. 6. 61218 — 10
0. 000040943 Log. 5. 61218 — 10
To perform multiplicaiitm hi/ logarithms, add the logarithms (jf the two numbers to be multiplied and
the sum will be the logarithm of their product.
Example I.
Multiply 25 by 35.
25 Log. 1. 39794
35 Log. 1.54407
Product, 875 Log. 2. 94201
Example II.
Multiply 22.4 by 1.8.
22.4 Log. 1.35025
1.8 Log. 0. 25527
Product, 40.32 Log. 1.60552
Example III.
Multiply 3.26 by 0.0025.
3. 26 Log. 0. 51322
0. 0025 Log. 7. 39794
Product, 0. 00815 Log. 7. 91 116
Example IV.
Multiply 0.25 by 0.(X)3.
0. 25 Log. 9. 39794
0. 003 Log. 7. 47712
Product, 0. 00075 Log. 6. 87506
In the last example, the sum of the two logarithms is really 16.87506 — 20; this is the same as
6.87506— 10, or, remembering that the quantity is less than unity, simply 6.87506.
To perform divivon hg logarithms, from the logarithm of the dividend subtract the logarithm of tlie
divisor; the remainder will be the logarithm of the quotient.
Example I.
Divide 875 by 25.
875 Log. 2. 94201
25 Log. 1 . 39794
Quotient, 35 Log. 1. 54407
Example II.
Divide 40.32 by 22.4.
40.32 Log. 1.60552
22.4 Log. 1.35025
Quotient, 1.8 Log. 0. 25527
Example III.
Divide 0.00815 by 0.0025.
0.00815 Log. 7.91116
0.0025 .Log. 7.39794
Quotient, 3.26 Log. 0. 51322
Example IV.
Divide 0.00075 by 0.025.
0.00075 Log. 6.87506
0.025 Lop:. 8. 39794
Quotient, 0.03 Log. 8.47712
In Example III both the divisor and dividend are fractions less than unity, and the divisor is the
lesser; consequently the quotient is greater than unity. In Example IV both fractions are less than
unity; and, since the divisor is the greater, its logarithm is greater than that of the dividend; forxthis
reason it is necessary to borrow 10 in the index before making the subtraction, that is, to regard the
logarithm of .00075 as 16.87506 — 20; hence the quotient is less than unity.
186
RULES AND PRINCIPLES OB' MATHEMATICS.
The arithmetical complement of a l>gan.thm is the difference between that logarithm and the loga-
rithm of unity (10.00000— 10, of 0.00000). It is therefore the logarithm of unity divided by that
num]>er which is the reciprocal of the number; and, since the effect of dividing by any number is the
same as that of multiplying by its reciprocal, it follows that, in performing division bv logarithms, we
may either subtract the logarithm of the divisor or add the arithmetical complement of that logarithm.
As the addition Of a number of quantities can be performed in a single operation, while in subtraction
the difference between only two quantities can lie taken at a time, it is frequently a convenience to deai
with the arithmetical complements rather than with the logarithms themselves.
Example I.
Divide 875 by 25.
875 Log. 2. 94201
25 Log. 1.39794.... Colog. 8.60206
Quotient, 85 Log. 1.54407
Ex.\MPI.E II.
Divide 0.00075 by 0.025.
0.00075 Log. 6. 87506
0.025 Log. 8.39794 Colog. 1.60206
Ex.\MPLE III.
Simplifv the expression, 40.32 X .00815
* ■ ^ ' 22.4 X. 0025
40.32 Log. 1. 60552
.00815 Log. 7.91116
22.4 Log. 1.35025 Colog. 8.64975
.0025 Log. 7.39794 Colog. 2.60206
Result, 5.868 Log. 0.76849
Quotient, 0.03 Log. 8.47712
To perform involution by logarithms, maltiply the logarithm of the given number by the index of the
power to which the quantity is to be raised; the product will be the logarithm of the power sought.
Example I.
Required the square of 18.
18 Log. 1.25527
2
Answer, 324 Log. 2.51054
Example II.
Required the square of 6.4.
6.4 Log. 0.80618
2
Answer, 40.96 Log. 1. 61236
Example III.
Required the cube of 13.
13 Log. 1.11394
3
Answer, 2197 Log. 3.34182
Example IV.
Required the cube of 0.25.
0.25 Log. 9.39794
3
Answer, 0.015625 Log. 8. 19382
In the last example, the full product of the multiplication of 9.39794—10 by 3 is 28.19382—30, Avhich
is equivalent to 8.19382—10.
To perform evolution by logarithms divide the logarithm of the number by the index of the power;
the quotient will be the logarithm of the root sought. If the number whose root is to be extracted is a
decimal fraction less than unity, increase the index of its logarithm by adding a number of tens which
shall Ije less by one than the index of the power before making the division.
Example I.
Required the square root of 324.
324 Log. 2) 2. 51055
Answer, 18 Log. 1,25527
Example II.
Required the cube root of 2197.
2197 Log.3)3.34183
Answer, 13 Log. 1.11394
Example III.
Required the square root of 40.96.
40.96 Log.2) 1.61236
Answer, 6.4 Log. 0.80618
Example IV.
Required the cube root of 0.015625.
0.015625 Log. 8.19382
Add 20 to the index 3)28. 19382
Answer, 0.25 Log. 9. 39794
In the last example the logarithm 8.19382—10 was converted into its equivalent form of 28.19382— 30i
which, divided by 3, gives 9.39794—10.
To find the loganthm of any function of an angle, Table 44 must be employed. This table is so
arrangeJl that on every page there appear the logarithms of all the functions of a certain angle A,
together with those of the angles 90°— A, 90° + A, and 180°— A; thus on each page may be found the
logarithms of the functions of four different angles. The number of degrees in the respective angles
are printed in bold-faced type, one in each corner of the page; the number of minutes corresponding
appear in one column at the left of the i)age and another at the right; the names of the functions
RULES AND PRINCIPLES OF MATHEMATICS. 187
to which the various logarithms correspond are printed at the top and bottom of the columns. The
invarial)le rule must be to take the name of the function from the top or the bottom of the page,
according as the number of degrees of the given angle is found at the top or bottom; and to take the
minutes from the right or left hand column, according as the number of degrees is found at the
right or left hand side of the page; or, more briefly, take names of functions and number of minutes,
respectively, from the line and column nearest in position to the number of degrees.
Taking, as an example, the thirty-first page of the table, it will be found that 30° appears at the
upper left-hand corner, 149° at the upper right-hand, 59° at the lower right-hand, and 120° at the lower
left-hand corner. Suppose that it is desired to find the log. sine of 30° 10'; following the rule given, we
find 10' in the left-hand column and Sine at the top of the page, and abreast one and below the other is
the required logarithm, 9.70115. But if the log. sine of 59° 10' were sought, as 59° appears below and at
the right of the page, the logarithm 9.93382 would be taken from the column marked Sine at the bottom
and abreast 10' on the right. It may also be seen that log. sin 30° 10'=log. cos 59° 50'=log. cos
120° 10'=log. sinl49° 50'=9.70115,theequality of the functions agreeingwith trigonometrical deductions;
(in this statement numerical values only are regarded, and not signs; the latter must, of course, be taken
into account in all operations).
Example I.
Required the log. sine, cosecant, tangent, cotan-
gent, secant, and cosine of 28° 37'.
Log. sin 9. 68029 Log. cot 10. 26313
Log. cosec 10. 31971 Log. sec 10. 05658
Log. tan 9. 73687 Log. cos 9. 94342
E.XAMPLE II.
Required the log. sine, cosecant, tangent, cotan-
gent, secant, and cosine of 75° 42'.
Log. sin 9. 98633 Log. cot 9. 40636
Log. cosec 10. 01367 Log. sec 10. 60730
Log. tan 10. 59364 Log. cos 9. 39270
When the angle of which the logarithmic function is required is given to seconds, it becomes
necessary to interpolate between the logarithms given for the even minutes next below and next above;
this may be done either by computation or (except in a few cases) by inspection of the table.
To interpolate by computation, let n represent the number of seconds, D the difference between the
logarithms of the next less and next greater even minute, and d the difference between the logarithm
of the next less even minute and that of the required angle. Then,
It should be noted when the number of seconds is 30, 20, 15, or some similar nimiber, permitting
the reduction of the fraction w^ to a simple value, such as i, J, J, as the interpolation by this method
may thus be made with greater facility.
Having obtained the difference of the logarithm from that of the next lower even minute, it must
be applied in the proper direction — that is, if the function is such that its logarithm increases as the
angle increases, the logarithmic difference must be added; but if it decreases, then that difference must
be subtracted.
For example, let it be required to find the log. sin and log. cosec of 30° 10' 19". The log. sin of
30° 10' is 9.70115; the difference between this logarithm and that of the sine of 30° 11' (9.70137) is + 22,
which is D. Hence,
d = ^X( + 22) = -|-7;
and the required logarithm is 9.70122. The log. cosec of 30° 10' is 10.29885; the difference, D, between
that and log. sin 30° 11' (10.29863) is — 22. In this case
rf = Wx(-22) = --;
therefore, log. cosec 30° 11' 19" = 10.29878.
The method of interpolating by inspection consists in entering that column marked "Diff." which
ia adjacent to the one from which the logarithmic function for the next lower minute is taken, and
finding, abreast the number in the left-hand minute column which corresponds to the seconds, the
required logarithmic difference; and the latter is to be added or subtracted according as the logarithms
increase or decrease with an increa.sed angle. Thus, if it be required to find log. sin 30° 10' 19", find as
before log. sin 30° 10' = 9.70115; then, in the adjacent column headed "Diff." and abreast the number
of seconds, 19, in the left-hand minute column will be found 7, the logarithmic difference; add this, as
the function is increasing, and we have the required logarithm 9.70122. If log. cosec 30° 10' 19" be
sought, find log. cosec 30° 10' = 10.29885; then in the adjacent difference column, which is the same as
was used for the sines, find as before the logarithmic difference, 7; and since this function decreases as
the angle increases, this must be subtracted; therefore, log. cosec 30° 10' 19" = 10.29878.
This method of interpolation by inspection is not available in that portion of the table where the
logarithmic differences vary so rapidly that no values will apply alike to all the angles on the same
page; on such pages the difference for one minute is given in a column headed "Diff. 1'," instead of
the usual difference for each second; in this case, the interpolation must be made by computation, the
given difference for one minute being D. In other parts of the table the interpolation by inspection
may be liable to slight error because of the variation in logarithmic difference for different angles on
the same page; but the tabulated values are sufficiently accurate for the usual calculations in navigation.
It will be evident that while the methods explained have contemplated entering the tables with a
smaller angle and interpolating ahead, it would be equally correct to enter with a greater angle and
interjwlate hack for the proper number of minutes, making the requisite change in the sign of the
correction.
188
RULES AND PRINCIPLES OF MATHEMATICS.
Example I.
Required the log. sine, cosine, and tangent of
42° 57' 06'''.
For 42° 57
For 42° 57' 06".
Log. sin
Log. cos
Log. tan
9.83338 I
9.86448
9.96890
9. 83339
9. 86447
9. 96893
EXAMIM.H II.
Required the log. secant, cosecant, and cotangent
of 175° 32' 36".
For 175° 32'
For 175° 32' 36"
Log. sec
Log. cosec
Log. cot
10. 00132
11. 10858
11. 10726
- 1
+97
4^8
10. 00131
11. 10955
11. 10824
It should be observed that, for uniformity and convenience, all logarithms given in Table 44 have
been increased by 10 in the index, and it is understood that —10 ought properly to be written after
each; thus all logarithms under 10.00000 represent functions whose value is less than unity, and all
over 10.00000 those greater than unity; for example, 11.10726 is the logarithm of a number in which
the decimal point should be placed after the second figure from the left.
To find the angle corresponding to anij logarithmic function, the process is the reverse of the one just
described. Find, in the column marked with the name of the function, either at top or bottom, the
two logarithms between which the given one falls; write down the degrees and minutes of the lesser of
the two corresponding angles, which will be the degrees and minutes of the angle required. Call the
difference between the two tabulated logarithms D, and the difference between the given logarithm and
that which corresponds to the lesser angle, d; then if n represent the number of seconds, we have:
n = p X 60.
Or, the same may be obtained by inspection (except where, as before explained, the differences
for seconds are not tabulated) byfinding, in the "Diff." column adjacent to that from which the logarithm
was taken, the logarithmic difference, d, and noting the number of seconds abreast which it stands in
the left-hand minute column.
Interpolation may be also made in the reverse direction from the next greater even minute.
Thus, if it be required to find the angle corresponding to log. sin 9.61400, we find log. sin 24° 16',
9.61382, and log. sin 24° 17', 9.61411; hence D = 29, and d = 18;
18 ,^
n = 29 X 60
37;
and the angle is 24° 16' 37". Or, in adjacent column headed "Diff.," 18 would be found abreast 38,
39, or 40 (seconds) in the left-hand minute column — a correspondence sufficiently close for navigation
work.
If the angle were known to be in the second quadrant, we find log. sin 155° 43', 9.61411, and log.
sin 155° 44', 9.61382; here, D = 29, and d = 11 ;
n = 29 X 60 = 23;
therefore, the angle is 155° 43' 23". Or, in adjacent "Diff." column find, abreast 11, 23 or 24 seconds.
Example I. Example II.
Find angles less than 90° corresponding to log.
cot 10..3.3621, log. sec 10.11579, and log. cos 8.70542.
Log. cot 10. 33621 24 45
Log. sec 10. 11579 40 00
Log. cos 8. 70542 87 05
4
116
15
22
28
Find angles in second quadrant corresponding to
log. tan 10.15593, log. sin 8.87926, and log. cosec
10.04944.
Log. tan 10. 15593
Log. sin 8. 87926
Log. cosec 10. 04944
0
'
d
II
124
55
19
42
175
39
69
25
116
49
3
27
The Hour Columns in Table 44 give the measure in time corresponding to twice the angular distance
given in arc. Thus, abreast the angle 13° 00' stands in the P. M. column l"" 44" 00", corresponding in
time to 2 X 13° 00', and in the A. M. column lO*" 16™ 00% which is the same subtracted from 12\ These
columns are of use in working the various formula? which involve functions of half the hour angle.
Interpolation for values intermediate to those given in the tables is made on the same principle as for
the angular measure; this operation may be performed by inspection by the use of the small tables at
the bottom of each page, where n, the number of seconds of time, is given in bold-faced type, and (/, the
logarithmic difference for the respective columns, appears below.
Example I.
Given t=V' 48'" 44% find log. cot J t.
For 1" 48'° 40", log. cot. i t 10. 61687
Diff. for 4% Col. B, - 28
For 1" 48'» 44',
log. cot J t 10. 61659
Example II.
Given log. sin § t 9.91394, find the Hour A. M.
corresponding.
For 9.91389, 4''39'°12»
Diff. for 5, Col. C, - 5
For 9.91394,
4 39 07
RULES AND PRINCIPLES OF MATHEMATICS.
189
jytlSCELLANEOUS TJSEFTJL DATA.
Earth's Polar radius =6, 356, 583. 8 meters.
Earth's Equatorial radius=6,378,206.4 meters.
Earth's Compression = ^qq Anh-
Earth's Eccentricity =^0.0824846
Number of feet in one statute mile=5280
Number of feet in one nautical mile=6080.27
Sine of 1^^=0.00000485
Sine of 1^=0.00029089
The Napierian base £=2.7182818
The modulus of common logarithms=0. 4342945
French meter in Enplish feet, 3.28087
French meter in En-^lish statute miles, 0.00062138
French meter in nautical miles, 0.00053959
1 pound Avoirdupois=7,000 grains Troy.
French gramme=0.00220606 Imperial pound Troy.
French kilogramme=0.0196969 English cwts.
Cubic inch of distilled water, in grains =252. 458.
Cubic foot of water, in ounces Troy =908. 8488.
Cubic foot of water, in pounds Troy=75.7374.
Cubic foot of water, in ounces Avoirdupois=997. 1366691.
Cubic foot of water, in pounds Avoirdupois =62. 3210606. J
Length of pendulum which vibrates second at Greenwich, 39.1393 inches.
log 8. 9163666.
log 3. 7226339.
log 3. 7839232.
log 4. 6855749.
log 6. 4637261.
log 0. 4342945.
log 9. 6377843.
log 0. 5159890.
log 6. 7933560.
log 6. 7320620.
Bar. 30.00 in. ; ther. 62° F.
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
The following table contains the latitude and longitude of a large number of places, together with
lunitidal intervals and tidal ranges at the more important ones. It is arranged geographically and
followed by an alphabetical index.
The geographical position generally relates to some specified exact location, and is based upon the
best available authority. The tidal data relate to the waters adjacent to the point whose latitude
and longitude are given, being abstracted from the Tide Tables published by the United States Coast and
Geodetic Survey for the year 1903.
The high water and low water lunitidal intervals represent the mean intervals between the moon's
transit and the time of next succeeding high and low waters throughout a lunar month. The spring
and neap ranges are the differences in height between high water and low water at spring and at neap
tides. For those places where the tide is chiefly of a diurnal type, and where there is usually but one
high and one low water during a lunar day, the tidal values are bracketed; in such cases the lunitidal
intervals are for the semi-diurnal part of the tide ( which, however, is only appreciable for a few days when
the moon is near the equator), and the range given in the column headed "Spg." does not, as in other
cases, apply to the spring tide, but to the greatest periodic daily range, which usually occurs a day or
two after the moon attains its extreme of declination, and is therefore near one of the tropics. As those
places where the diurnal type predominates seldom experience large tidal effects, the general data
furnished regarding such tides will suffice for the ordinary purpose of the navigator. The method
of finding the time of high or low water from this table is illustrated in article 507, Chapter XX.
190
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA.
[Page 191
Place.
Salisbury Island: E. pt
Nottingham Island : S. ] )t
Digges Island : W. extreme
Cape AVostenholme
Charles Island: E. pt
w. pt :....
Cape Weggs
Prince of Wales Sound : Center of ent
Cape of Hopes Advance
Akpatok Island: E. pt
Green Island : NE. pt
Button Islands: N. pt
Cape Chidleigh
Resolution Island: S. pt., Hutton h'dl'd
E. pt., C. Resolution
Black Head
Eclipse Harbor: E. side
Nachvack Bay: Islands off entrance
Saddle Island
Port Man vers : Entrance
Nain: Church
Hopedale Harbor: Hill to E'd
Aillick Harbor: Cape Mokkivik
Cape Harrison : N. extreme
Indian Harbor: Obs
Outer Gannet Island: Summit
Gready Harbor
Cartwright Harbor: Caribou Castle
Indian Tickle : Summit
Roundhill Island : Summit
Occasional Harbor: E. summit of Twin I.
Cape St. Lewis: SE. pt
Battle Islands: NE. extreme, SE. I
Table Head
Belle Isle; Light-house
Cape Bauld : Light-house
Bell Island : S. end
Cape St. John: Gull Island light
Tilt Cove, L^nion Copper
Mine
Funk Island: Summit
Offer Wadham : Light-house
Toulinguet Islands: Light-house
Seldom-come-by Harbor: Shiphill
Cape Freels : Gull I
Greenspond Island
Cape Bonavista: Light-house
Catalina Harbor: Green I. light-house ..
Bonaventure Head
Hearts Content: Light-house
Baccalieu Island : Light-house
Harbor Grace: Light-house on beach
Cape St. Francis: Light-house
St. Johns Harbor: Chain Rock Battery..
Cape Race: Light-house
Cape Pine: Light-house
Trepassey Harbor: Shingle Neck
Cape St. Mary : Light- house
Little Placentia Harbor: W. side Coopers
Cove
Burin Island : Light-house
Laun : Gr. Laun R. C. Church
St. Pierre: U. S. Coast Survey Station .. .
Brunet Island: Mercers Hd. light-house.
Boar Islands: Burgeo I. lijiht-house
Lat. N.
Long. W.
Liin.
Int.
Range.
H.W.
L. W.
Spg.
Neap.
o / //
63 27 00
O / II
76 30 00
77 50 00
78 08 00
77 33 00
74 00 00
75 20 00
74 03 00
72 25 00
70 02 00
67 05 00
67 50 00
64 40 00
64 12 00
65 00 00
64 30 00
64 28 00
64 07 15
63 20 00
61 20 00
62 07 00
61 40 13
60 12 34
59 08 01
57 56 40
57 12 40
56 31 31
56 23 00
56 59 50
55 58 39
55 35 48
55 44 29
55 38 08
55 32 20
55 41 00
55 22 10
55 25 12
55 35 30
55 21 33
55 37 17
53 10 56
53 45 00
54 47 35
54 12 00
53 25 12
53 37 45
53 04 42
53 02 40
53 23 35
53 23 20
52 47 42
53 08 11
52 47 20
52 40 54
53 04 30
53 31 55
53 22 10
54 11 42
53 58 43
55 08 49
55 32 00
56 10 36
55 51 40
57 36 52
h. m.
h. m.
ft.
ft.
63 06 00
62 37 00
8 58
2 46
13.5
6.1
62 35 00
62 48 00
62 50 00
62 30 00
62 07 00
61 18 00
60 10 00
60 40 00
60 52 00
60 33 00
61 21 00
61 40 00
60 00 00
59 48 00
59 07 00
57 35 00
'
i
8 00
7 00
1 48
0 48
5.0
5.2
2.0
2.1
57 00 00
1 ;
56 32 45
55 27 04
55 13 33
7.00
5 30
0 48
11 43
6.5
6.9
3.0
3.2
54 55 50
t 1
54 26 55
54 00 05
6 10
12 23
7.0
3.2
53 oO 00
53 42 37
53 34 25
53 26 00
52 40 07
52 21 16
52 15 36
52 06 00
51 53 00
51 38 48
50 42 10
49 59 54
49 53 00
6 27
0 15
6.0
2.8
6 38
6 30
0 26
0 18
5.0
3.5
2.3
L6
1
' i
1 '
49 45 29
1
49 35 40
1
49 41 20
; 1
49 36 50
49 15 20
49 04 20
48 42 01
48 30 15
48 16 55
47 53 10
48 08 58
47 42 45
47 48 30
47 34 02
46 39 24
46 37 04
46 43 20
46 49 34
47 17 55
47 00 26
46 56 30
46 46 51
47 15 30
47 35 13
i 1 1
1 ;
7 23
1 11
4.1
1.9
7 15
1 03
3.3
r.5
7 12
6 50
1 01
0 38
3.3
6.5
1.5
3.0
6 50
8 20
0 38
2 08
6.6
7.2
3.1
3.3
8 05
8 23
1 8 53
8 22
1 53
2 11
2 41
2 10
7.0
6.6
6.5
6.2
3.2
3.1
3.0
2.9
Page 192] APPENDIX IV.
MAKITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
al
0
Place.
Lat. N.
LaPoileBay: (ir. Espic Church
Cape Ray : Light-house
Codrov island: S. side Boat Harbor '
Cape St. George: Red I., SE. pt
Cow Head : N W. extreme '
Port Saunders: NE. point of entry
Rich Point: Light-house j
Ferolle Point: Cove Point, NE. extreme J
Flower Cove: Capstan Pt '
Green Island: 150 fms. from NE. end . . .|
Cape Norman : Light-house I
Chateau Bay: S. pt. Castle I
Amour Point : Light-house |
Wood Island: S. pt ;
Greenly Island : Light-house
Bradore Bav : Obs. Spot, Jones Pt i
Old Fort Island : Center
Great Mecatina Island : SE pt
Mecatina Harbor: S. point of Dead Cove.
Little Mecatina I. : S. pt. C. McKinnon. .
St. INIary Reefs
South Makers Ledge
Cape Whittle ,
Natashquan Point : S. edge ,
Clearwater Point: SW. extreme.
Carousel Island: Light-house
Point de Monts: Light-house
Quebec: Mann's Bastion, Citadel.
Montreal : Cathedral
Father Point : Light-house
Cape Chatte: Extreme
Cape iVIagdalen : Light- house
Cape Rosier: Light-house
Cape Gaspe : Light-house
Anticosti Island: Heath Pt. light-house
SW. pt. light-house . .
E. pt
Bonaventure Island:
Leander Shoal
Macquereau Point
Chaleur Bay : Carlisle
Dalhousie I
Miscou Island: NE. pt., Point Birch
Miramichi Bay: Portage I., N. pt...
Point Escumenac: Light-house
North Point: Light-house
Richmond Harbor: Royalty Pt..
East Point: Light-house
Charlottetown : Flag-staff on fort
47 39 50
47 37 00
47 52 30
48 33 48
49 55 20
50 38 30
50 41 39
51 02 10
51 17 25
51 24 10
51 38 00
51 58 00
51 27 35
51 22 45
51 22 35
51 27 30
51 21 40
50 47 30
50 46 44
50 31 40
50 14 00
50 09 30
50 11 00
50 06 00
50 12 27
50 05 40
49 19 35
46 48 17
45 30 24
48 31 25
49 06 00
49 15 40
48 51 37
48 45 15
49 05 20
49 23 45
48 29 30
48 24 00
48 12 00
48 01 00
48 04 24
48 01 00
47 14 00
47 05 00
47 03 46
46 34 00
46 27 15
46 13 55
Gt. Bird Rock : Light-house
East Island : E. extreme
Entry Island : Light-house
Amherst Hbr. : N. side of entrance
Deadman Rock: W. pt
St. Paul Island: Light-house, NE. end..
Light-house, SW. end..
Cape North : Light-house
St. Anns Harbor: K. pt. entrance
50 40
37 40
16 30
14 23
16 03
47 13 50
47 11 20
47 01 45
46 21 00
Sydney Harbor: Light-house 46 12 25
Long. \V.
58 24 10
59 18 00
59 23 40
69 13 10
57 50 00
57 17 07
57 24 20
57 02 40
56 44 45
56 33 40
55 53 52
55 50 20
56 51 05
57 08 00
57 10 50
57 14 12
57 46 00
58 51 00
58 59 20
59 20 00
59 45 00
59 57 00
60 08 00
61 44 00
63 27 03
66 22 44
67 21 55
71 12 19
73 33 04
68 27 40
66 46 00
65 19 30
64 12 00
64 09 35
61 42 30
63 35 46
64 08 00
64 18 00
64 46 30
65 19 00
66 22 10
64 29 00
65 02 00
64 47 33
63 59 19
63 43 00
61 58 05
63 07 23
61 08 32
61 24 30
61 41 20
61 49 38
62 12 25
60 08 32
60 09 50
60 23 27
60 27 00
60 12 50
Lun. Int.
Range.
H.W.
/*. m.
8 50
8 50
"9'46'
1 25
1 43
1 48
6 07
1 52
1 46
1 33
1 25
1 55
2 20
3 10
2 00
4 16
L. \v.
Spg.
h. VI.
2 38
6.0
2 32
"3*13'
4.3
'I'd
6 45
4.0
7 05
7 18
0 54
8.1
10.8
14.6
7 33
7 13
6 50
6 40
12.0
10.5
6.4
5.5
6 35
6 40
3.6
4.9
7 33
8 07
9 10
8 25
10 59
4.7
4.8
8.1
4.0
2.3
Neap.
4 20
5 15
8 17
11 07
8 30
8 35
8 25
8 10
11 00
11 55
2 20
4 23
2.4
1.8
1.4
6.4
2 12
2.7
2 17
2 13
2 05
3.1
6.0
5.0
ft.
2.8
2.1
"2."5
2.0
6.0
8.0
10.8
8.9
7.8
4.7
4.1
1.8
2.5
2.3
2.4
4.1
2.0
1.2
1.2
0.9
0.7
3.2
1.4
1.6
3.7
3.1
BSfl
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
[Page 193
Place.
Lat. N.
Scatary Island: Light-house, NE. pt
Louisburg: Light-house, NE. pt
Madame Island : S. pt
Port Hood : Just-au-corps I
Sable Island: Light- house, E. end
Pictou: Custom-house
Cape St. George
North Canso: Light-house, NW. entrance.
Arichat Harbor: R. C. Church steeple . .
Cape Canso: Cranberry I., light-house ..
White Head Island: Light- house
Green Island : Light-house
Wedge Island : Light-house
Halifax : Dock-yard ob.«ervatory
Sambro Island: Light-house
Margaret Bay : Shut-in I
Tancook Island
Lunenburg: Battery Pt. light
Cape Le Havre: Black Rock
Coffin Island : Light-house
Little Hope Island : Light-house
Shelburne Hbr.: Two lights, McNutts I
Cape Sable: Light-house
Seal Island : Light-house
Yarmouth : Cape Fourchu light
Cape St. Mary..
Bryer Island : Light-house
Annapolis Harbor: Prim Pt. light
Haute Island : Light-house
Cape Chignecto
Burntcoat Head : Light-house
Cape Enrag^: Light-house
Cape Quaco: Light-house
St. Johns: Partridge I. light
Cape Lepreau : Light- house
L'Etang Harbor: S. pt. tower
St. Andrew: S. pt. light
Campo Bello Island: Light-house, N. pt.
Grand Manan Island: Light-house, NE. pt.
GannetRock: Light-house, NE. pt
Machias Island: Light-house
46 02 15
45 54 34
45 28 00
46 00 00
43 58 14
45 40 50
45 52 00
45 41 42
45 30 48
45 19 49
45 11 58
45 06 15
45 00 35
44 39 38
44 26 10
44 34 00
44 29 00
44 21 45
44 12 00
44 02 00
43 48 30
43 37 15
43 23 19
43 23 34
43 47 28
44 05 20
44 14 57
44 41 34
45 14 55
45 19 00
45 18 40
45 35 34
45 19 30
45 14 20
45 03 40
45 04 00
45 04 06
44 57 40
44 45 52
44 30 38
44 30 07
Long. W.
Calais: Astronomical station 45 11
Eastport: Cong. Church 44 54
Quoddy Head: Light-house [ 44 48
Machias: Town Hall 44 43
Petit Manan Island : Light-house 44 22
Bakers Island : Light-house
Mount Desert Rock : Light-house
Bangor: Thomas Hill
Belfast: Methodist Church
Rockland : Episcopal Church
Matinicus Rock : Light-house
Monhegan Island : Light-house
Seguin Island : Light-house
Bath: Winter St. Church
Brunswick: College spire
Augusta: Baptist Churcli
Portland: Custom-house
Portland Head light-house . . .
Cape Elizabeth: Li^ht-house (west)
Wood Island : Light-house
Boon Island : Light-house
44 14
43 58
44 48
44 25
44 06
43 47
43 45
43 42
43 54
43 54
44 18
43 39
43 37
43 33
43 27
43 07
59 40 25
59 59 26
61 03 00
61 36 00
59 46 08
62 42
61 52
61 29
61 01
60 55
61 08
61 32
61 52
63 35
63 33
63 54
64 06
64 17
64 18
64 37
64 47
65 15
65 37
66 00
66 09
66 12
66 23
65 47
65 00
64 57
63 48
64 46 55
65 32 00
66 03 20
66 27 40
66 49 00
67 02 52
66 54 10
66 44 00
66 47 00
67 06 13
67 16
66 59
66 57
67 27
67 51
68 11
68 07
68 46
69 00
69 06
68 51
69 18
69 45
69 49
69 57
69 46
70 15
70 12
70 12
70 19
70 28
Lun. Int.
H. W.
h. TO.
7 45
7 55
9 05
9 34
9 20
9 26
7 55
7 43
7 45
7 34
'7'32
39
8 17
9 35
10 00
10 29
10 49
11 07
0 27
11 21
11 07
11 04
11 09
11 00
11 02
"io'si'
11 36
11 09
11 02
0 23
11 35
11 09
10 45
12 13
2 54
11 06
11 12
L. W.
h. m.
1 35
1 47
2 47
Range.
Spg. Neap.
ft.
5.0
5.0
3.5
3.9
2.8
3.1
5.0
6.5
1 46
1 30
'i"36'
2 05
3 23
3 41
4 36
4 41
5 27
7 27
5 21
'I'm
5 40
5 05
5.2
7.1
'7."6'
8.5
12.8
16.0
20.8
27.5
33.0
50.5
30.0
23.9
24.5
23.3
24.9
22.5
18.0
23.3
20.9
4 59 15.5
6 47
5 22
4 55
4 31
15.1
11.7
11.0
10.2
6 16
10 18
4 51
4.9
10.1
4 51
10.2
ft-
3.1
3.1
1.8
2.0
1.4
1.6
3.1
4.0
4.1
3.2
"4.' 4
"4.' 3
5.2
9.5
11.8
15. 4
20.4
24.4
37.4
22.2
17.7
18.2
17.1
18.2
16.7
13.2
17.1
15.2
11.3
11.0
8.6
8.1
7.5
5.8
3.6
7.3
22489—03-
-13
Page 194] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
Place.
Whale Back: Light-house
Portsmouth : Ntfvy-y ard flagstaff
Fort Constitution
Hampton: Baptist Church
Isles of Shoals: White I. light-house
Newburyport: Academy
Plum I. light-house
Ipswich : Light-house ( rear)
Annisquam Harbor: Light-house
Cape Ann: Thatchers I. light-house (N.) .
Gloucester: Universalist Church
Ten-pound I. light-house
Beverly : Hospital Pt. light-house
Salem : Derbys Wharf light-house
Marblehead : Light-house
Cambridge: Harvard Observatory
Boston : Navy-yard flagstaff
State house
Little Brewster I. light-house. . .
Minots Ledge: Light-house
Plymouth : Pier head
Gurnet light-house
Barnstable: Light-house
Cape Cod : Highlands light- house
Chatham : Light-house (south )
Monomoy Point: Light-house
Nantucket: South Church
Nantucket South shoal: Light ship
Sankaty Head : Light-house
Tarpaulin Cove: Light-house
Vineyard Haven: W. Chop light-house..
Gay Head: Light-house
Cuttyhunk: Light-house
New Bedford : Baptist Church
Sakonnet Point: Light-house
Beaver Tail: Light-house
Newport: Flagstaff, torpedo station
Bristol Ferry: Light-house
Providence: Unitarian Church
Point Judith : Light-house
Block Island: Light-house (SE)
Watch Hill Point: Light-house
Lat. N.
43 03 32
43 04 56
43 04 16
42 56 15
42 58 02
48 30
48 55
41 07
39 43
38 21
36 46
36 07
32 48
31 00
30 20
22 48
22 22
21 28
19 41
16 11
58 44
00 12
43 20
02 23
40 15
33 34
16 55
37 05
17 01
28 08
28 51
20 55
24 52
38 10
41 26 30
41 26 58
41 29 07
41 38 34
41 49 26
41 21 40
41 09 10
41 18 14
Montauk Point: Light-house 41
Stonington: Light-house 41
New London : (proton Monument 41
Little Gull Island : Light-house 41
Gardners Island: Light-house, N. pt 41
Plum Island: Light-house, W. pt 41
Say brook: Light-house, Lynde Pt 41
New Haven: Yale College spire (middle). 41
Bridgeport Harbor: Light-house ; 41
Norwalk Island: Light-house | 41
Shinnecock Bay : Light-house . .
Fire Island : Light-house
Albany: Dudley Observatory. ..
New York: Navy-vard flagstaff.
City Hall
40
40
42
40
40
Fort Wadsworth : Light-house ■ 40
04 16
19 31
21 16
12 23
08 29
10 25
16 17
18 28
09 24
02 56
51 03
37 57
39 50
42 02
42 44
36 20
Long. W.
70 41 49
70 44 22
70 42 34
70 50 12
70 37 25
70 52 28
70 49 10
70 46 00
70 40 55
70 34 31
70 39 59
70 39 58
70 51 23
70 53 03
70 50 03
71 07 43
71 03 05
71 03 50
70 53 26
70 45 35
70 39 12
70 36 04
70 16 52
70 03 40
60 57 01
60 59 39
70 05 57
69 36 33
69 57 57
70 45 29
70 36 01
70 50 08
70 57 01
70 55 36
71 13 30
71 24 00
71 19 40
71 15 39
71 24 19
71 28 55
71 33 08
71 51 32
71 51 27
71 54 49
72 04 47
72 06 26
72 08 44
72 12 43
72 20 37
72 55 45
73 10 49
73 25 11
72 30 16
73 13 08
73 44 56
73 58 51
74 00 24
74 03 15
Lun. Int.
H. W.
h. m.
"ii"23'
11 19
11 23
11 17
11 13
11 02
11 16
11 09
11 27
"ii'69'
11 23
11 36
12 11
12 00
0 04
7 51
11 34
7 31
7 86
7 57
7 40
7 40
7 48
7 53
8 12
7 32
7 33
8 49
8 20
9 09
9 26
9 26
9 40
10 29
11 08
11 09
11 03
7 48
7 19
5 13
8 44
7 41
L. W.
Range.
Spg.
h. m. ft.
'5"69 Tio.'s'
4 58
5 10
5 04
5 00
4 49
5 03
4 57
5 17
'4"56'
5 11
5 25
5 57
5 48
6 00
1 51
4 33
1 20
0 59
1 18
1 05
1 09
1 00
0 40
0 57
1 17
1 25
2 38
2 03
3 03
3 32
3 04
3 35
11
54
04
56
38
20
0 46
2 49
1 38
10.0
9.1
10.1
10.1
10.2
10.6
10.6
11.0
i6.*9"
10.8
11.6
4.6
4.3
3.8
2.8
2.0
3.7
4.3
5.2
4.5
4.7
4.4
5.2
5.4
3.8
3.7
3.2
2.3
3.2
2.9
3.0
2.5
4.3
7.0
8.4
8.2
3.0
2.2
2.8
5.3
5.4
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
[Page 195
Place.
Lat. N.
Sandy Hook: Light-house (rear)
Light-ship
Navesink Highlands: N. Hght-house
Barnegat Inlet: Light-house
Tuckers Beach : Light-house
Absecon Inlet: Light-house
Five Fathom Bank: Light-ship
Cape May : Light-house
Philadelphia, Pa. : Statehouse
Navy-yard flagstaff,
League I v .
Wilmington, Del. : Town hall
Cape Henlopen : Light-house
Assateague Island: Light-house
Hog Island: Light-house
Cape Charles: Light-house
Baltimore: Washington Monument
Annapolis: Naval Academy observatory.
Point Lookout: Light-house
Washington, D. C. : Navy-yard flagstaff .
Naval Observatory .
Capitol dome
Old Point Comfort: Light-house
Norfolk : Navy-yard flagstaff
Richmond, Va. : Capitol
Cape Henry : Light-house
Elizabeth City : Court-house . . .
Eden ton : Court-house
Currituck Beach : Light-house .
Bodie Island : Light-house
Cape Hatteras: Light-house
Ocracoke: Light-house
Newbern, Episcopal spire
Cape Lookout: Light-house ...
Beaufort, N. C. : Court-house . .
Frying- Pan Shoals: Light-ship
Georgetown : Episcopal Church
Light-house, North I
Cape Romain : Light-house
Charleston: Light-house, Morris I
St. Michael's Church
Beaufort, S. C. : Episcopal Church
Port Royal: Martins Industry light-ship.
Tybee Island : Light-house
Savannah : Exchange spire
Sapelo Island: Light-house
Darien : Winnowing House
St. Simon : Light-house
Brunswick: Academy
Amelia Island : Light-house
Fernandina: Astronomical station ..
St. Johns River: Light-house
Jacksonville: Methodist Church
St. Augustine: Presbyterian Church
Light-house
Cape Canaveral : Light-house
Jupiter Inlet: Light-house
Fowey Rocks: Light-house
Carysfort Reef: Light-house
40 27 42
40 28 15
40 23 48
39 45 52
39 30 22
39 21 59
38 47 20
38 65 59
39 56 53
39 53 14
39 44 27
38 46 42
37 54 40
37 23 46
37 07 22
39 17 48
38 58 53
38 02 19
38 52 30
38 53 39
38 53 20
37 00 06
36 49 33
37 32 16
36 55 35
36 17 58
36 03 24
36 22 36
35 49 07
35 15 17
35 06 32
35 06 21
34 37 22
34 43 05
33 34 26
33 22 08
33 13 21
33 01 06
32 41 43
32 46 34
32 26 02
32 05 33
32 01 20
32 04 52
31 23 28
31 21 54
31 08 02
31 08 51
30 40 23
30 40 18
30 23 36
30 19 43
29 53 20
29 53 07
28 27 37
26 56 54
25 35 25
25 13 17
Long. W.
74 00 09
73 50 09
73 59 10
74 06 24
74 17 08
74 24 52
74 34 36
74 57 39
75 09 03
75 10 32
75 33 03
75 05 03
75 21 23
75 41 59
75 54 24
76 36 59
76 29 08
76 19 20
76 59 45
77 03 06
77 00 36
76 18 24
76 17 46
77 26 04
76 00 27
76 13 23
76 36 31
75 49 51
75 33 49
75 31 16
75 59 11
77 02 24
76 31 29
76 39 48
77 49 12
79 16 49
79 10 55
79 22 19
79 52 54
79 55 49
80 40 27
80 33 15
80 50 37
81 05 26
81 17 01
81 25 39
81 23 30
81 29 26
81 26 26
81 27 47
81 25 27
81 39 14
81 18 41
81 17 12
80 32 30
80 04 48
80 05 41
80 12 40
Lun. Int.
Range.
H.W.
h. m.
7 30
7 50
7 48
9 59
8 16
1 28
0 53
12 00
8 17
8 03
6 34
4 39
0 31
7 42
8 44
9 05
4 30
7 53
7 37
7 00
6 29
7 21
8 39
"6"59'
7 20
8 10
8 00
7 39
7 36
8 12
8 00
8 00
8 20
8 21
L.W.
Spg.
h. TO.
1 23
1 43
1 42
3 57
1 47
8 58
8 02
6 40
1 50
2 19
0 44
10 53
6 52
1 56
2 17
2 47
11 55
1 43
1 26
0 45
0 20
1 08
3 38
"o'So'
1 10
2 06
1 31
1 33
ft.
5.6
2.7
4.2
4.7
5.6
6.2
7.0
6.7
5.4
3.0
1.4
1.0
1.7
3.5
3.0
3.2
4.3
3.2
3.4
2.2
4,4
3.3
4.3
'5.'9'
6.0
8.5
7.9
7.6
8.4
7.5
7.5
7.8
5.4
5.3
5.9
1.8
2.6
2.7
Neap.
ft.
3.6
1.7
2.7
3.0
3.6
4.4
5.2
4.9
3.5
2.0
1.0
0.8
1.1
2.5
2.0
2.1
2.8
2.1
2.2
1.5
3.0
2.3
2.9
"4.'i
4.2
5.9
5.5
5.3
5.8
5.2
5.3
5.4
4.8
3.7
3.6
4.0
1.2
1.3
1.4
Page 196] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
Place.
Alligator Reef: Light-house
Sombrero Key: ^ight-house
Sand Key : Light-house
Key West: Light-house
Loggerhead Key : Light-house
Sanibel Island: Light-house
Gasparilla Island: Light-house
Tampa Bay : Egmont Key light
Cedar Keys: Ast. station, Depot Key
Seahorse Key light
St. Marks: Fort St. Marks
Apalachicola: Flag-staff
Cape St. George: Light-house
Cape San Bias: Light-house
Pensacola: Light-house
Navy-yard chimney
Sand Island: Light-house (front)
Mobile Point: Light-house
Mobile: Episcopal Church
Horn Island : Light-house
East Pascagoula: Coast-Survey station. . .
Mississippi City: Coast-Survey station...
Ship Island : Light-house
Cat Island: Light-house
Chandeleur: Light-house
Mouth Mississippi River: Pass a 1' Outre
light
S. Pass light
(East Jetty)
SW. Pass light
New Orleans: United States Mint
Barataria Bay : Light-house
Timbalier Island : Light-house
Ship Shoal: Light-house
Southwest Reef: Light-house
Calcasieu Pass: Light-house
Sabine Pass: Light-house
Galveston: Cathedral, N. spire
Light-house, Bolivar Pt
Matagorda: Coast-Survey station
Light-house
Indianola: Coast-Survey station
Lavaca: Coast-Survey station
Aransas Pass: Light-house
Brazos Santiago: Light, S. end Padre I ..
Point Isabel : Light-house
Rio Grande del Norte: Obs. N. side of
entrance
San Fernando River: Entrance
Santander River: Entrance
Mount Mecate: Summit
Tampico: Light-house
Cape Roxo
Lobos Cay : Light-house
Tuspan Reefs: Middle islet
Mexico: National Observatory
Bernal Chico: Middle of islet
Zempoala Point: Extreme
Vera Cruz: San Juan d'Ulloa light
Sacrificios Island
Orizaba Mountain : 1 7, 400 feet
Cofre de Perote Mount: 14,000 feet
Al varado : E. side of entrance
Roca Partida: Summit
Tuxtla, volcano: Summit
Montepio: Landing place
Lat. N.
24 51 02
24 37 36
24 27 10
24 32 58
24 38 04
26 27 11
26 43 06
27 36 04
29 07 29
29 05 49^
30 09 03
29 43 32
29 35 18
29 40 00
30 20 47
30 20 49
30 11 19
30 13 44
30 41 26
30 13 23
30 20 42
30 22 54
30 12 53
30 13 57
30 02 58
29 11 30
28 59 28
28 58 22
29 57 46
29 16 30
29 02 49
28 54 56
29 23 36
29 46 55
29 43 04
29 18 17
29 22 05
28 41 29
28 20 18
28 32 28
28 37 36
27 51 53
26 04 16
26 04 36
25 57 22
25 23 40
23 46 20
22 38 40
22 15 50
21 35 00
21 28 12
21 03 00
19 26 01
19 39 50
19 27 26
19 12 29
19 10 10
19 04 00
19 29 30
18 49 00
18 44 00
18 29 00
18 40 00
Long. W.
80 37 08
81 06 40
81 52 40
81 48 04
82 55 42
82 00 43
82 15 34
82 45 40
83 01 57
83 03 58
84 12 42
84 59 12
85 02 54
85 21 30
87 18 32
87 16 06
88 03 02
88 01 26
88 02 28
88 31 39
88 32 45
89 01 57
88 57 56
89 09 41
88 52 19
89 02 28
89 08 08
89 23 30
90 03 28
89 56 43
90 21 25
91 04 15
91 30 14
93 20 43
93 51 00
94 47 26
94 46 00
95 57 26
96 25 28
96 31 01
96 37 21
97 03 23
97 10 00
97 12 28
97 08 57
97 21 25
97 46 55
98 04 55
97 49 55
97 22 00
97 13 00
97 13 35
99 06 39
96 24 39
96 20 22
96 07 57
9() 05 30
97 15 55
97 07 30
95 44 48
95 11 14
95 08 00
95 05 12
Lun. Int.
H. W.
h. m.
8 22
8 24
8 40
9 20
9 44
12 17
0 42
11 32
0 42
2 00
[12 10]
[11 10]
iii'28i
[11 25]
[1 35]
[12 00]
[0 20]
[0 23]
[11 53]
[11 15]
[10 55]
[10 54]
[11 00]
[11 50"
[0 18
[0 40
2 17
3 17
[4 18]
[4 07]
L.W.
00
05
20
36
21
6 10
6 19
5 07
7 13
Range.
Spg. Neap.
■ft
2.6
1.9
1.5
1.6
1.4
2.3
1.4
1.8
3.1
8 30 2. 6
[5 35] i [2.5]
[4 55]
[4 20]
[3 09]
[6 50]
[5 40]
[5 45]
[6 35]
[5 33]
[5 00]
[4 42]
[4 41]
[4 35]
[4 25]
[155]
4 47]
'5 38]
6 33]
6 56]
8 41
9 36
[10 33]
[10 23]
[10 47]
[10 35]
[8 03]
[1 06] [7 19]
[2 49] [8 38]
[2.1];
[1.7]
J. 5]
[2.1]
2.0]
2.3]
[2.1]
[1.8]
[1.6]
[1.7]
[1.9]
2.1]
2.0]
2.2]
2.0]
1.7
0.9
[1.4]
[1.6]
[1.6]
[1.6]
[1.4]
[1.3]
[2.4]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA,
EAST COAST OF NORTH AMERICA— Continued.
[Page 197
Place.
Zapotitlan Point: Light-house
San Juan Point: Light-house
Coatzacoalcos: Light-house
Santa Ana Lagoon: Entrance
Tupilco River: Entrance
Tabasco River: Light-house
Carmen Island : N E. pt
Laguna de Terminos: Vigia tower, W.
end Carmen I
Paypoton Mount: Summit
Lerma: Church
Campeche: Light-house
Fort San Jo^6
Point Palmas
Sisal : Fort light
Madagascar Reef: Center
Progreso: Light-house
Silan: Village
Lagartos: Milage
Cape Catoche: Light-house
Areas Cays: Light-house
Obispo Shoal : 16-foot spot
New Bank : Center
Triangles, E. reef: Beacon
Triangles, W. reef: Cay at SW. end
Bajo Nuevo Reef: Center
Arenas Cays: N W. Cay
Alacran Reef: Perez Cay
Con toy Island : Light-house
Mugeres Island : Light-house
Cancun Island: Nisuc Pt
Cozumel Island: N. pt. light-house
S. pt. light-house
Ascension Bay : Allen Pt
Chinchorro Bank: Cayo Lobos light
Half-Moon Cay: Light-house
Mauger Cav, NW. end: Light-house
Glover Ree'f : SW. Cay
English C^y : Light-house
St. Georges Cay : Center
Sand-Fly Cays": II ut, S. end
South Water Cay : Center
Belize: Fort George light
North Standing Creek: Entrance
Sittee Point: Cay
Cockscomb Mount: Summit, 4,000 feet..
Placentia Point: Huts on point
Icacos Point: S. extreme
Sarstoon River: Entrance
Dulce River: Entrance, W. side
Dulce Gulf: Fort St. Philip
Isabel
Hospital Bight: Hut, N. pt. of entrance.
Cape Three Points: NAV. extreme
Seal Cays: S. Cay
Omoa: Entrance
Cape Triunfo: Bluff pt
Congrehoy Peak: Summit, 8,040 feet
Truxillo: Fort
Utilla Island: S. Cay
Hog Islands: Highest hill on W. islet. . .
Roatan: Center of Coxen Cay
Port Royal, NW.pt. of GeorgeCay
Bonacca Island: Summit, 1,200 feet
Misteriosa Bank: S. Point
Swan Islands: NW. pt. of W. I
Lat. N.
Long. W.
Lun.
Int.
Range.
H. W.
L. W.
Spg.
Neap.
O 1 II
18 34 00
O 1 II
94 50 00
94 38 57
94 24 46
93 51 53
93 25 25
92 42 00
91 30 50
91 50 17
90 43 27
90 36 11
90 32 20
90 30 51
90 22 00
90 02 37
90 18 27
89 39 30
88 54 27
88 10 27
87 04 10
91 57 45
92 13 27
91 52 27
92 12 47
92 18 57
92 04 26
91 24 21
89 41 45
86 48 00
86 43 39
86 46 45
86 43 55
86 59 04
87 28 27
87 23 40
87 32 30
87 46 30
87 50 50
88 03 20
88 04 45
88 06 05
88 05 36
88 11 20
88 13 48
88 15 15
88 37 40
88 22 13
88 35 51
88 56 20
88 46 22
89 01 36
89 09 44
88 33 22
88 38 50
88 20 15
88 04 31
87 27 46
86 55 00
85 59 18
86 59 15
86 32 09
86 34 27
86 18 41
85 55 00
84 02 00
83 56 27
h. m.
h. m.
ft.
ft.
18 19 45
18 08 56
18 18 49
18 26 44
18 39 30
18 47 08
18 38 44
19 38 00
[12 16]
[6 00]
[1.6]
19 48 24
1
19 50 20
19 51 36
2 59
9 28
2.1 1.3
21 02 00
1
21 10 06
21 26 30
10 20
4 10
1.8 0.9
21 17 00
21 23 00
1
21 36 30
21 35 50
20 12 45
20 29 00
9 30
[12 06]
3 19
[5 50]
1.5
[1.6]
0.8
20 32 00
20 54 54
20 58 00
[12 00]
[5 45]
[1.6]
21 50 00
22 07 10
22 23 36
....
21 33 00
21 12 00
21 03 00
9 20
3 08
1.6
0.9
20 35 50
20 16 20
8 20
2 08
1.5
0.8
19 46 55
18 23 20
17 12 15
17 36 15
16 42 20
17 19 30
17 33 15
16 57 50
16 48 50
17 29 20
16 57 40
8 00
1 50
1.5
0.8
16 47 45
16 48 10
16 30 54
16 14 15
15 54 00
15 49 45
15 38 00
9 00
2 50
2.0
1.1
15 24 20
15 52 20
15 57 45
16 08 00
15 47 11
I
15 48 45
15 38 00
15 55 45
16 03 40
15 58 00
16 18 00
16 24 20
7 35
1 23
3.5
1.8
16 28 00
18 44 00
8 50
2 38
1.5
0.8
17 24 30
Page 198] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
o
s
« j
§2
8
•
s
«
■M
i
a
1
c
0
PS
!fi
S
0
5
Place.
L*t. N.
Long. W.
Lun. Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
•
Great Rock Head : Bluff extreme
Cape Camaron
o / «
15 53 00
16 00 00
15 51 50
15 48 50
15 23 40
15 00 00
16 03 30
o / //
85 27 10
85 03 00
84 38 33
84 17 10
83 42 36
83 10 00
83 08 20
82 23 27
82 18 07
82 42 08
82 20 00
82 45 57
80 51 27
79 50 53
80 15 20
81 08 21
81 07 21
80 05 05
81 21 26
81 43 06
81 27 53"
81 49 54
83 21 27
83 23 10
83 37 12
83 45 57
83 41 57
82 58 35
83 03 35
83 42 15
83 47 27
83 02 00
82 39 06
82 21 47
82 20 31
83 03 27
82 20 33
82 07 51
81 55 02
81 33 57
h. m.
h. m.
ft.
ft.
Brewers Lagoon: E. side of entrance
Patook River: E. side of entrance
Carataska Lagoon: E. side of entrance . .
Cape Gracias-d-Dios: Light-house
Caxones Reef: Great Hobby Islet
10 20
4 07
2.0
1.1
GordaBank: Gorda Cay ' 15 52 00
Farrall Rock: Center
15 51 00
Half-Moon Cay: Center
15 08 50
15 07 00
14 21 12
16 54 00
15 47 45
14 21 33
14 08 00
14 30 00
13 34 30
13 22 54
12 31 40
12 24 00
12 10 00
14 03 00
12 22 35
12 20 39
12 15 30
11 59 00
12 17 30
12 09 17
10 56 15
10 01 30
10 00 05
9 38 30
9 25 45
9 24 47
9 16 30
9 14 22
9 14 30
9 10 30
9 06 30
Alargate Reef: E. pt
Mosquito Cays: S. end
Rosalind Bank : N W. extreme
Serranilla Bank: Beacon Cay
4 00
4 00
10 13
10 13
2.0
2.0
1.1
1.1
Serrana Bank : Little Cay
Quita Sueno Bank: S. extreme of reef. . .
Spit at NW. end
Roncador Cay: S. pt
j
Old Providence: Isabel House
4 00
io 13 i.6
0.5
St. Andrews Island : SW. cove, Entrance I .
Courtown Cays: Middle Cay
1
Albuquerque Bank: Smith Cay
'
Brangmans Bluff: Extreme
Pearl Cays: Colombilla Cay
1 50
8 03
2.0
1.1
Pearl Cays Lagoon: Mosquito Pt
Cookra Hill : Summit
Bluefields: Schooner Pt
1 40
7 52
2.0
1.1
Little Corn Island : Gun Pt
Great Corn Island: Wells N. of Quin Bluff.
Greytown : Light-house
1 35
1 00
7 47
7 13
2.0
1.5
1.1
0.8
Mount Cartago: Peak, 11,100 feet
Port Limon: Grape Cay light
1 00
7 13
1.6
0.9
Carreta Point: Extreme
Tirby Point: Extreme
Columbus Island : Lime Pt
Blanco Peak: Summit, 11,740 feet
Shepherd Island: Hut on summit
Cobbler Rock: Center
Valiente Peak: Summit, 722 feet
Escudo de Veragua: W. pt. of island
1
........I .....
1
WEST COAST OF NORTH AMERICA.
•
1
Point Barrow: Highest lat. of U. S
Icy Cape: Extreme
71 23 30
70 16 00
68 52 00
67 09 00
66 14 30
66 32 00
65 35 30
65 33 30
65 16 40
65 00 00
64 26 00
63 26 00
63 34 30
61 40 00
63 16 00
63 50 00
60 18 00
60 13 00
60 25 22
58 48 31
156 27 00
161 47 30
166 06 00
163 34 00
161 45 00
163 36 00
168 40 00
168 00 00
166 46 30
168 02 00
165 05 00
162 02 30
162 42 30
166 15 00
168 41 00
171 31 00
172 02 00
172 36 00
166 08 30
160 50 00
11 41
5 33
0.6
0.2
Cape Lisburne: 849 feet
Cape Krusenstern : Extreme
Chamisso Island : Summit
7 45
1 50
2.0
0.6
Cape Espenberg: Extreme
Diomede Island: Fairway Rock
Cape Prince of Wales: W. pt
1 .
Port Clarence: Point Spencer
6 10
1 10
1.1 0.9
King Island: N. pt
Cape Nome: Extreme
[2 05]
;8 05]
rs 25]
r2.ni
St. Michael: Fort
[1 20]' [4.5]i 1
Stuart Island: W. pt
Cape Romanzof : Extreme
St. Lawrence Island : E. pt
NW.pt
1
St. Matthew Island: SE.pt
4 40
11 0 3. 1
1.6
Pinnacle Islet: Summit, 930 feet
Nunivak Island : Cape Etolin
Hagenmeister Islant
!
1
":r: r i
APPENDIX IV.
MAKITIME POSITIONS AND TIDAL DATA.
WEST COAST OF NORTH AMERICA— Continued.
[Page 199
Place.
Cape Menchikof : Extreme
Port Moller
St. George Island: S.
side
Lat. N.
Attu Island: Chichagof Harbor
Kiska Island : Kiska Harbor, Ast. sta . . .
Amchitka Island : Constantine Harbor . .
Adakh Island : Bay of Islands
Atka Island: Nazan Bay (church)
Pribilof Island: St. Paul I., village
Unalaska Island: C. S. station, Iliuliuk .
Sannakh Reefs: S. edge
Sannakh Island : NE. end
Unga Island
Popof Island : Humboldt I
Nagai Island : Sanborn Harbor
Koniushi Island: NW. harbor
NE. harbor
Simeonof Island : Simeonof Harbor
Cape Strogonof : Extreme
Chignik Bay : Anchorage
Anowik Island : S. end
Chiachi Islands
Light-House Rocks
Chirikof Island
Kodiak Island, St. Paul Harbor: Cove
N W. of village
Port Etches
Middleton Island
Mount St. Elias: Summit
Yakutat Bay: Port Mulgrave
Lituya Bay
Sitka: Middle of parade ground
Juneau
Wrangell: Ast. station
North Island: N. pt
Cape Knox : Extreme
Port Kuper: Sansum I
Forsyth Point: Extreme
St. James Cape: S. extreme
Cumshewa Harbor: N. side of entrance
Skidegate Bay : Rock on bar
Rose Spit Point: J^xtreine
Massett Harbor: Uttewas village
Cape Edenshaw : Extreme
Hecate Bay: Observatory Islet
Stamp Harbor: Observatory Islet...
Island Harbor: Observatory Islet...
Cape Beale: Light-house
Refuge Cove: Village on W. side . . .
Hesquiat Harbor: Boat Cove
Estevan Point: S. extreme
Nootka Sound : Friendly Cove
Port Langford: Colwood Islet
Esperanza Inlet: Observatory Rock.
Kyuquot Sound : Shingle Pomt
Nasparti Inlet: Head Beach
Cook Cape: Solander I
North Harbor: Observatory Rock. . .
57 30 24
55 54 59
56 34 23
52 56 01
51 59 04
51 23 39
51 49 18
52 10 36
57 07 19
53 52 54
54 13 30
54 26 12
55 20 45
55 19 17
55 07 36
55 03 17
54 58 25
54 55 30
56 48 00
56 19 20
56 05 13
55 51 58
55 45 24
55 48 22
57 47 57
60 20 43
59 27 22
60 20 45
59 33 42
58 36 57
57 02 52
58 18 00
56 27 00
54 15 00
54 10 30
52 56 31
52 09 07
51 54 00
53 02 00
53 22 20
54 13 00
54 01 40
54 04 30
49 15 22
49 13 46
48 54 41
48 47 23
49 20 50
49 27 31
49 22 07
49 35 31
49 47 20
49 52 45
49 59 55
50 11 21
50 06 31
50 29 25
Long. W.
157 58 30
160 34 54
169 39 50
Long. E.
J 73 12 24
177 30 00
179 12 06
Long. W.
176 52 00
174 15 18
170 17 52
166 31 44
162 38 00
162 18 00
160 38 39
160 31 14
159 56 06
159 23 05
159 22 18
159 15 03
158 46 00
158 24 24
156 39 19
159 05 24
157 27 04
155 42 51
152 21 21
146 37 38
146 18 45
141 00 12
139 46 16
137 40 06
135 19 31
134 24 00
132 23 00
132 56 20
132 57 50
132 09 06
131 03 20
131 01 26
131 31 00
131 51 00
131 34 00
132 10 00
132 20 56
125 55 43
124 50 07
125 16 54
125 13 14
126 16 06
126 24 53
126 31 58
126 36 58
126 56 31
126 59 21
127 08 56
127 37 24
127 56 46
128 03 05
Lun. Int.
H.W.
h. m.
3 35
3 30
3 25
4 17
3 50
12 13
2 40
2 20
1 45
0 16
0 50
0 34
0 06
0 45
0 30
0 00
0 07
12 15
0 45
12 20
12*65'
12 05
11 55
11 50
11 47
L. W.
h. m.
9 48
9 43
9 38
10 29
9 58
6 10
8 55
8 33
7 58
6 24
7 05
6 41
6 17
6 56
6 39
6 12
6 19
6 08
7 20
6 15
'5'56'
5 55
5 45
5 38
5 34
Range.
Spg.
ft.
5.7
5.2
5.0
2.7
2.9
5.7
8.2
7.5
8.1
9.0
10.1
9.5
9.9
18.6
17.7
11.5
12.8
10.0
12.4
9.9
io.'s'
9.7
9.3
9.3
Neap.
2.9
2.7
2.6
1.4
1.5
2.8
4.1
3.8
4.0
4.5
5.1
5.0
5.2
9.7
9.2
5.7
5.8
7.1
5.7
5.9
5.6
5.5
5.3
5.3
Page 200] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF NORTH AMERICA— Continued.
Place.
Lat. N.
Lun. Int.
Long. W.
H.W.
L.W.
Range.
Spg. Neap.
Koprino Harbor: Observatory Rock
Hecate Cove : Kitten Islet
Triangle Island : *NV. side
Cape Scott: Summit
Bull Harbor, Hope Island : N. pt. Indian I .
Port Alexander: Islet in center
Beaver Harbor: Shell Islet
Cormorant I.: Yellow Bluff in Alert Bay.
Baynes Sound : Beak Pt
Nanoose Harbor: Entrance Rock
Nanaimo: Light-house
Benson's House
Victoria: Light-house
Esquimalt: Fisgard I. light
Race Island : Light-house
Sooke Inlet : Secretary I
Port Sail Juan : Pinnacle Rock
Port Harvey : Tide Pole Islet
Port Neville: Robber's Nob
Knox Bay, Thurlow Island: Stream at
head of bay
Valdes Island: S. pt
Howe Sound: Plumper Cove
Atkinson Point: Light-house
Vancouver, Burrard Inlet: Govt. Re-
serve, English Bay
Eraser River: Garry Pt
New Westminster: Military barracks
Point Roberts: Parallel station
Semiamoo Bay : Parallel station
Admiralty Head : Light-house ,
Steilacoom: Methodist Church
Seattle: C. S. ast. station
Port Townsend : C. S. ast. station
Smith Island : Light-house
New Dungeness: Light-house
Port Angeles: Ediz Hook light-house
Cape Flattery : Light-house
Cape Shoalwater: Light-house
Cape Disappointment: Light-house ..
Kalama : Methodist Church
Bremerton : Navy-yard flagstaff
Tacoma: St. Luke Church
Astoria: Flagstaff
Yaquina Head : Light-house
Cape Arago, or Gregory: Light-house ..
Cape Blanco : Light-house
Crescent City: Light-house
Trinidad Head : Light-house
Eureka: Methodist Church
Humboldt: Light-house
Cape Mendocino: Light-house
Point Arena: Light-house
Point Reyes: Light-house
San Francisco: Coast Survey ast. station .
Presidio station .
Mare Island: Stone block, obs. station. .
Benicia: Church
Farallon Islet: Light-house
Santa Clara: Catholic Church
Mount Hamilton: Obs. peak
San Jos^: Spire
Pigeon Point: Light-house
50 30 00
50 32 26
50 51 53
50 46 41
50 54 47
50 50 49
50 42 36
50 35 02
49 36 29
49 15 43
49 12 50
49 10 1ft
48 25 26
48 25 50
48 17 53
48 19 .35
48 33 30
50 33 58
50 31 09
50 24 15
50 02 42
49 24 39
49 19 42
49 16 18
49 07 04
49 13 01
49 00 00
49 00 00
48 09 19
47 10 20
47 35 54
48 06 56
48 19 07
48 10 52
48 08 24
48 23 30
46 43 00
46 16 29
46 00 26
47 33 24
47 15 32
46 11 19
44 40 35
43 20 36
42 50 22
41 44 36
41 03 01
40 48 11
40 41 37
40 26 18
38 57 12
37 59 39
37 47 55
37 47 30
38 05 53
38 03 05
37 41 51
37 20 49
37 21 03
37 19 58
37 10 49
127 51 42
127 35 44
129 05 58
128 26 11
127 55 29
127 39 23
127 24 33
126 56 56
124 50 44
124 07 32
123 48 11
123 56 02
123 23 28
123 26 46
123 31 47
123 42 40
124 27 37
126 16 06
126 03 47
125 38 26
125 14 34
123 28 46
123 15 54
123 11 26
123 11 27
123 53 52
123 04 52
122 44 56
122 40 34
122 35 51
122 19 59
122 44 58
122 50 36
123 06 31
123 24 07
124 44 06
124 04 25
124 03 11
122 50 39
122 37 33
122 26 26
123 49 42
124 04 40
124 22 31
124 33 30
124 12 10
124 09 03
124 09 41
124 16 26
124 24 25
123 44 27
123 01 24
122 24 32
122 27 49
122 16 16
122 09 23
123 00 07
121 56 26
121 36 40
121 53 39
122 23 39
ft.
0 10
0 32
0 30
0 55
4 45
4 52
4 40
[2 17]
[2 00]
4 59
0 08
12 22
3 39
4 27
4 32
0 15
11 50
11 55
11 33
11 27
11 57
11 33
11 00
10 36
11 23
12 07
11 43
1 05
1 35
10 40
6 22
6 44
6 42
7 08
11 00
11 18
10.7
11.6
11.5
12.8
10.6
10.2
11 05
[8 31]
[8 14]
[5.7]
[5.8]
8 10
8 47
10 00
10 15
11 58
11 35
12 01
11 23
14.1
16.0
15.7
7.2
9.0
7.8
8.2
7.0
11 10
7.1
11 04
10 33
9 32
9 28
8 34
8 23
6 16
11.0
9.2
7.1
6 19
11 25
10 35
10 45
6 42
5 37
5 49
5 15
5 11
5 45
5 19
4 50
4 21
5 08
5 34
5 07
7 15
7 48
4 25
7.7
3.2
9.4
9.8
7.8
7.3
6.0
4.1
5.1
5.1
4.6
5.6
5.6
4.5
appp:ndix IV.
MARITIME POSITIONS AND TIDAL DATA.
* WEST COAST OF NORTH AMERICA— Continued.
[Page 201
1
Place.
Lat. N.
Long. W.
Lun.
Int.
Range.
H. W.
L. W.
Spg.
Neap.
•
£
u.
©
i
s
.0
u
0
Santa C niz : Warehouse flagstaff
Monterey: C. S. azimuth station
Point Pinos: Light-house
o / //
36 57 31
36 35 21
36 37 55
35 39 50
34 26 49
34 26 10
34 15 46
33 42 14
34 03 05
32 39 48
32 43 06
32 31 58
34 04 19
33 56 30
34 03 12
34 00 25
33 28 16
33 14 55
33 23 09
31 51 10
31 33 04
30 57 39
30 28 58
30 22 16
29 47 20
29 25 29
29 10 50
28 56 06
28 40 16
28 14 26
28 03 52
28 18 08
27 39 35
27 06 10
26 45 45
26 42 49
26 18 56
26 03 18
24 58 00
24 47 31
24 38 23
24 18 12
24 20 17
23 27 14
22 53 07
23 03 35
23 32 48
24 03 52
24 15 31
24 10 10
24 24 10
24 52 03
25 29 23
25 59 37
26 00 41
26 30 44
26 53 37
27 10 21
27 26 06
28 00 07
28 25 04
O / "
122 01 29
121 52 59
121 56 02
121 17 06
120 28 18
119 42 42
119 15 56
118 17 41
118 14 32
117 14 37
117 09 41
117 07 32
120 21 55
119 58 29
119 33 51
119 23 04
119 02 29
119 31 19
118 24 05
116 38 05
116 40 51
116 17 28
116 06 46
115 59 07
115 48 12
115 12 14
118 18 30
114 31 06
114 14 15
114 06 21
115 11 32
115 36 10
114 54 27
114 17 25
113 16 25
113 35 04
112 41 44
112 17 52
115 51 54
112 18 25
112 08 54
111 42 54
111 30 21
110 14 07
109 54 50
109 40 43
109 28 57
109 50 29
110 20 34
110 20 41
110 20 35
no 41 47
111 01 43
111 06 .53
111 21 03
111 27 14
111 58 04
112 05 39
112 19 56
112 47 36
112 51 59
h. m.
10 54
10 43
h. m.
4 27
4 24
ft.
5.2
4.8
ft.
3.3
3.1
Piedras Blancas: Light-house
Point Conception : Light-house
Santa Barbara: N. tower, Mission Church
San Buenaventura: C. S. ast. station
Pt. Fermin, San Pedro Bay: Light-house.
Los Angeles: Court-house
9 37
9 53
9 36
3 15
3 21
3 13
4.8
4.9
5.5
2.2
2.2
2.5
Point Lonia: Light-house
9 29
9 32
3 07
3 20
5.2
5.1
2.3
2.3
San Diego: C. S. ast. station
Mexican Boundary : Obelisk
San Miguel Island": Seal Pt
9 23
3 02
4.9
2.2
Santa Rosa Island : P-. pt
Santa Cruz Island : NE. pt
9 29
3 06
4.9
2.2
Anacapa Island : E. pt
Santa Barl)ara Island : Summit
: :::::::: i
San Nicolas Island: Summit
9 20
9 28
9 28
3 04
3 08
3 06
4.9
5.1
6.0
2.2
2.3
2.2
Santa Catalina Island: Catalina Peak . . .
Ensenada Harbor: Head of bay, close to
beach
San Tomas: NW. shore of cove
Colnett Bay: Head of bav
9 27
3 05
5.8
2.6
San Martin Island: Hassler Cove
Port San Quentin: Sextant Pt
9 23
3 00
4.9
2.2
San Geronimo Island: Bight at E. end . .
Canoas Point: High bluff
Guadeloupe: North pt
La Playa Maria: Mound on W. side
Santa Rosalia Bay: Obs. spot, Cairn
Lagoon Head: Highest pt. of crater
Cerros Island : SE. extremity
9 15
2 53
7.6
3.4
9 05
2 42
7.8
3.5
San Benito Island: Summit of W. island.
San Bartolom6: N. side of entrance
Asuncion Island: Summit of island
San Ignacio Point: J* xtreme
9 00
2 37
8.2
2.8
Abreojos Point: Extreme of rocky ledge.
Sau Domingo Point: Edge of clifi
San Juanico f*oint: Knoll
Alijos Rocks : South Rock
9 00
2 48
6.7
2.3
8 29
2 17
5.7
1.6
Cape San Lazaro: Extreme
Magdalena Bay: Obs. spot (post) N^ of
Port Magdalena
8 25
2 12
5.5
1.5
Cape Tosco: Extreme
El Conejo Point: Extreme
Todos Santos: Foot of hill, Lobos Pt
San Lucas: Steep sand beach, NW. pt.
of bay
San Jose del Cabo: NE. side of entrance.
Arena Point : Extreme l...
Arena de la Ventana: Extreme
8 36
2 20
4.5
1.2
Pichilinque Bay: SE. pt. of San Juan,
Nepomezeino I
!
La Paz: Obs. spot, El Mogote
Lupona Point: P^xtreme
9 40
3 34
5.4
1.3
San f^varisto: 3 m. S. of S. Evaristo Hd.
San Marcial Point : E.xtreme
Salinas Bay: Beach, NE. pt. of bay.
Loreto: Cathedral
Pulpito Point: Summit
Muleje: Equipalito Pt
San Marcos Is'and: S. sand spit
Santa Maria Cove: Beach on NW. shore.
San Carlos Point: Extreme
Santa Teresa Bay: Beach on N. side
11 50
5 47
11.2
2.6
Page 202] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
"WEST COAST or NORTH AMERICA— Continued.
Place.
Las Animas: Lo^ pt
Raza Island: Landing place, S. side.
Angeles Bay: Bight on NW. shore..
Remedios Bay: Beach on W. shore .
Mejia Island: S. side
San Luis Island: SE. side
San Firinin: Beach, N. of bight
San Felipe Point: Peak, 1,000 feet
28 47 40
28 49 11
28 56 39
29 13 52
29 33 08
29 57 27
30 25 16
31 02 57
Philips Point: Beacon ! 31 46 10
Lat. N.
Long. W.
Georges Island : NE. shore
Cape Tepoca: Hill, 300 feet
Libertad Anchorage: Beach
Patos Island : SE. end
Tiburon Island: SE. end
Kino Point: 0.2 mile N. 88° W. of mound.
San Pedro: N. side of bay
Guaymas: Light-house
Claris Island : NW. part
Santa Barbara: N W. side of bay
Agiabampo: SE. side of entrance
Topolobampo : SE. end of Santa Maria I . .
Navachista: W. side of creek
Playa Colorado: N. side of entrance
Altata: N. side of entrance
Mazatlan : Light-house
Palenita Village: Boca Tecapan
San Bias: Custom-house
Maria Madre Island: SE. extreme
Mita Point: Extreme
Penas Anchorage: Mouth of Rio Real . . .
Cape Corrientes: Extreme
Perula Bay : Smooth Rock
San Benedicto Island: S. extreme
Socorro Island : SE. part
Roca Partida: Summit
Clarion Island : S. end
Clipperton Island: Summit
Navidad Bay: W. end of sandy beach...
ManzanillaBay: Flagstaff, U. S.consulate.
Sacatula River: Beach, W. side of bay. . .
Isla Grande: Tripod on NW. summit ...
Sihuatanejo Point: Tree on beach
Morro Petatlan: Junction of stony and
sandy beaches
Tequepa Harbor: Limekiln
Acapulco: Light-house
Maldonado: El Recordo Pt
Port Angeles: Light-house
Sacrificios Point: Highest pt. of cape
Port Guatulco: Cross
Morro Ayuca: SummitofN. edge of cape.
Salina Cruz: Light-house
Champerico: Inshore end of iron wharf. .
San Jos6 de Guatemala: Light-house
Acajutla: Light-house
Libertad: Light-house
La Union : Light-house
Chicarene Point: Extreme
Corinto: Light-house
San Juan del Sur: Signal station
Salinas Bay : Salinas Islet
Port Culebra: Extremity of Mala Pt
Ballena Bay: N. Estero Toussa .'
Parida Anchorage: S. pt. of Deer Id
Port Nuevo: Entrada Pt
Bahia Honda: W. end of Centinela I
Coiba (Quibo) Island: Observation pt. . ,
31 00 54
30 16 05
29 54 12
29 16 12
28 45 55
28 45 28
28 03 22
27 50 28
26 58 59
26 41 09
26 16 35
25 33 56
25 23 06
25 11 42
24 38 52
23 10 40
22 30 26
21 32 30
21 30 45
20 45 50
20 36 26
20 25 00
19 34 48
19 17 15
18 42 57
18 59 41
18 20 55
10 17 00
19 13 25
19 03 15
17 58- 21
17 40 15
17 37 50
17 31 28
17 16 13
16 49 10
16 19 37
15 39 09
15 40 41
15 44 58
15 52 17
16 09 49
14 17 44
13 55 15
13 34 20
13 28 49
13 20 00
13 17 09
12 27 54
11 14 45
11 03 10
10 36 46
9 43 45
8 10 13
8 04 30
7 43 32
7 24 20
113 12 48
113 00 05
113 34 35
113 40 00
113 35 19
114 25 49
114 39 47
114 52 10
114 43 31
113 16 30
112 53 26
112 45 04
112 28 51
112 21 46
111 58 37
111 16 00
110 54 28
109 57 17
109 40 48
109 17 30
109 10 23
108 49 00
108 23 37
107 59 37
106 26 47
105 44 25
105 18 40
106 33 14
105 33 37
105 16 00
105 39 21
105 08 54
110 49 22
110 56 53
112 04 07
114 44 17
109 13 00
104 43 26
104 19 50
102 07 06
101 40 25
101 33 23
101 27 14
101 04 32
99 55 50
98 35 05
96 30 43
96 15 04
96 08 10
95 46 43
95 12 31
91 55 36
90 49 45
89 50 26
89 19 25
87 51 00
87 47 06
87 12 31
85 52 59
85 43 38
85 42 46
85 00 46
82 14 32
81 43 30
81 31 58
81 41 51
Lun. Int.
Range.
H.W.
h. m.
11 30
10 07
9 08
08
9 07
9 07
50
L.W.
h. m.
2 50
2 50
2 55
3 05
3 15
2 55
3 00
2 50
2 45
3 15
3 10
3 59
2 51
5.8
3.8
2 52 3. 2
2 53
2.5
2 54 I 1.9
'2'38T'2.'6*
9 02
9 02
9 08
9 18
9 28
9 08
9 12
9 02
8 58
9 28
9 22
8.5
9.0
9.5
10.0
10.5
10.5
10.0
9.5
9.0
Neap.
5 26 i 5.0 1.2
1.4
0.9
1.0
1.1
1.3
0.9
4.6
4.9
5.1
5.4
5.7
5.7
5.4
5.1
4.9
10. 5 5. 7
11.0 5.9
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF NORTH AMERICA— Continued.
[Page 203
o
Place.
Lat. N.
Long. W.
Lun
Int.
Range.
H. W.
L. W.
Spg.
Neap.
ii
s
Cocos Island : Head of Chatham Bay
Panama: NE. bastion, ast. station
Taboga Island : Church
O 1 II
5 32 57
8 57 12
8 47 45
7 27 40
4 03 00
O 1 II
86 59 17
79 32 05
79 33 16
79 59 25
81 36 00
h. m.
h. m.
ft.
ft.
3 00
3 00
3 10
9 14
9 13
9 22
16.0
15.4
13.0
8.7
8.3
7.0
Cape Mala : Extreme
Malpelo Island: Summit
i 1 1
WEST INDIA ISLANDS.
i
K
M
&
P
s
Memory Rock : Center
Bahama Island : W. pt
26 56 53
26 41 18
79 06 54
79 00 38
77 10 45
76 57 36
78 23 48
79 06 00
79 18 26
78 06 02
77 34 26
75 44 39
75 10 34
75 45 17
75 28 20
75 51 41
74 51 54
75 46 24
74 59 00
76 13 00
76 51 48
77 21 58
77 46 45
77 53 55
77 57 06
75 26 00
75 07 27
74 28 20
74 50 08
74 20 37
74 22 54
74 20 21
74 22 48
73 49 15
73 38 03
72 47 03
73 50 29
73 40 17
73 42 33
72 28 18
72 12 51
72 07 14
71 31 12
71 07 29
70 29 54
69 21 24
68 47 24
74 09 41
74 29 34
74 53 44
75 .33 18
75 36 59
75 47 18
75 47 40
75 52 18
76 07 48
7 40
1 28
3.2
L7
Abaco Island : Light-house
25 51 30
26 31 10
27 15 42
26 02 00
25 34 30
22 45 10
22 22 30
21 42 00
22 01 15
22 14 02
22 20 44
22 31 15
22 51 00
23 32 15
23 06 00
25 00 00
25 31 20
25 05 37
24 43 45
25 49 40
25 49 12
24 06 15
23 50 50
23 56 40
23 37 45
22 06 40
22 32 40
22 47 30
22 51 00
23 05 30
22 34 38
22 16 30
21 40 30
20 56 00
21 30 40
21 37 30
21 30 00
21 54 00
21 29 33
21 30 55
21 06 30
20 35 00
20 02 00
20 15 10
20 21 40
20 41 41
20 47 14
21 04 24
21 09 00
21 07 00
21 07 30
21 07 05
1
Little Guana Cav : Light-house
Walker Cay: Highest part
Great Isaac Cay: Light-house
Gun Cay : Light-house
8 20
2 08
......
3.0
1.5
Ginger Cay: Center
Cay Lobos: Light-house
St. Domingo Cav : Center
Cay Verde: Hill at S. end
Ragged Island : Gun Pt
Nairn Cay : E. pt
Nurse Channel Cay : Beacon
Long Island: S. pt
Great Emma Island : Beacon
1
Clarence Harbor: Light-house
8 20
7 00
2 08
0 48
4.1
4.0
2.1
2.1
Eleuthera Island : Light-house
Royal Island : Eastern Pass
Nassau: Light-house
7 20
7 40
1 08
1 28
4.0
3.0
2.1
L5
Andros Island : Light-house
Great Stirrup Cav : Light-house
Little Stirrup Cay : W. end
San Salvador ( Cat I. ) : Light-house
Concepcion Island : AY. bay
7 00
0 48
4.0
2.1
AVatlings IslarSd: Hunchinbroke Rock ..
Rum Cay : Harbor Pt
1
1
Castle Island : Light-house
Fortune Island : S. end
1
Crooked Island: Moss flagstaff "
Bird Island: Light-house
Samana Cay: W. pt
1
Plana Cay: NW. pt.
j
Mariguana Island : SE. pt
7 20
1 08
3.0
1.5
Hogsty Reef: NW. Cay
Inagua Island: Light-house
7 50
1 38
3.5
1.8
Little Inagua Island: N W. pt
W. CaicosCay: Hill, SE. end
French Cay: W^. pt
I
Fort George Cay: Old magazine
Caicos Island: Parsons Pt., S. islet
Turk Island : Light-house
7 30
1 18
3.0
1.5
Square Handkerchief Bank: NE. breaker
Silver Bank : E. extreme
f
Navidad Bank : Center of E. side
Cape Maysi : Light-house
5 40
11 53
2.8
1.6
Port Baracoa: Light-house
Port Cavo Moa: Carenero Pt
Port Nipe: Roma Pt
Lucrecia Point: Light-house
Port Sama: E. side of entrance
Peak of Sama: Summit, 885 feet
Port Naranjo: E. side of entrance
Jibara: Fort San Fernando
6 20
0 08
2.4
1.4
Port Padre: Guinchos Pt
21 18 30 76 35 34
21 37 30 77 04 ,34
Port Nuevitas: Light-house
7 00
0 48
2.2
1:2
1
Page 204]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS— Continued.
Place.
Maternillos Point: Light-house
Cay Verde: NW. «nd
Cay Contites: S. pt
Paredon Grande Cay : Light-house
Cay Sal : Light-house
Bahia de Cadiz Cay: Light-house
Piedras Cay : Light-house
Matanzas: Summit of peak
Habana: Morro Hght- house
Transit pier, arsenal yard
Cape San Antonio : Light-house
San Felipe Cays: SW. pt
Isle of Pines: Port Frances
Piedras Cay : Light-house
Cienfuegos: Colorados Pt. light
Cape Cruz: Light-house
Santiago de Cuba: Light-house
Port Guantanamo : Fisherman Pt
Cayman Brae: E. pt
Little Cayman : W. pt
Grand Cayman: Fort George, W. end
Morant Point : Light-house
Port Antdnio : Folly Pt. Light
Port Maria: NW. wharf
St. Ann Bay: Long wharf
Falmouth : Fort
Montego Bay : Fort
St. Lucia: Fort
Savanna-la-Mar : Fort
Kingston : Plum Pt. light
Port Royal: Fort Charles, flagstaff
Morant "Cays: NE. Cay
Pedro Bank: Portland Rock, E. end
Baxo Nuevo: Sandy Cay
Samana Town : Fort
Cape Cabron : Extreme
Port Plata: Light-house
Grange Point: W. end
Manzanilla Point: Presidente Pt
Cape Haitien : Town fountain
Port Paix: Wharf
Nicolas Mole: Fort George, flagstaff
Gonaives: Verreur Pt
Gonave Island : W. pt
Arcadius Islands: Light-house
Port au Prince: Fort Islet light
Petite Riviere Village: Sand beach in
front of huts
Jeremie: Fort
Navassa Island: N. extreme
Formigas Bank: Shoal spot
Vache Island: Sand beach, near NW. pt.
Jacmel : Wharf .•.
Beata Island : NW.pt
Frayle Rock: Center
Alta Vela: Summit
Avarena Point: Extreme
Salinas Point ( Caldera) : Extreme
St. Domingo City : Light-house
Point Espada: Extreme
Lat. N.
21 40 02
22 08 45
22 11 14
22 29 10
23 56 30
23 12 34
23 14 10
23 01 54
23 09 21
23 08 03
21 51 44
21 55 00
21 35 30
21 57 45
22 01 58
19 50 13
19 57 31
19 54 39
19 45 15
19 39 10
19 17 45
17 55 05
18 11 31
18 23 00
18 26 24
18 30 34
18 29 25
18 27 45
18 12 20
17 55 32
17 55 56
17 26 30
17 06 20
15 53 00
19 12 29
19 21 17
19 49 15
19 54 45
19 45 34
19 46 20
19 57 40
19 49 15
19 25 42
18 55 26
18 48 13
18 33 54
18 37 15
18 38 15
18 25 10
18 33 00
18 06 00
18 13 30
17 36 45
17 37 00
17 28 50
18 07 00
18 12 00
18 27 54
18 19 43
Long. W.
77 08
77 37
77 39
78 09
80 27
80 29
81 07
81 43
82 21
82 21
84 57
83 31
83 09
81 07
80 26
77 43
75 52
75 09
79 46 07
80 07 17
81 23 17
76 11 08
76 26 31
76 54 22
77 12 52
77 39 52
77 56 16
78 10 52
78 08 54
76 46 45
76 50 38
75 58 20
77 26 28
78 39 04
19 23
16 00
41 23
39 03
47 20
11 42
49 45
23 07
42 52
18 34
39 05
22 01
74 23 55
74 05 54
75 02 03
75 44 24
73 43 40
72 34 30
71 33 44
71 41 00
71 39 11
70 59 18
70 35 18
69 52 00
68 27 34
Lun. Int.
Range.
H. W,
h. TO.
7 20
30
18
30
4 47
8 20
7 50
9 00
6 50
L. W.
h. TO.
Spg. I Neap.
1 08
2 18
1 56
2 18
11 00
2 30
2 00
2 48
0 39
[1.3]!.
I
[1.1].
[1.2]
[LI]
3.0
5.5
[1.2]
[2.5]
[2.2]
ft. I ft.
2.8 t 1.6
2.2 1.2
1.3 I 0.7
1.5 I 0.
2.0 i 1.1
2.2 I 1.1
2.6 I 1.3
1.5
2.9
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS— Continued.
[Page 205
Place
Mona Island : Light-house
Mayaguez : Mouth of Mayaguez R
Aguadilla Bay : Village
San Juan de Porto Rico: Morro light-
house
Cape San Juan : Light-house
Guanica: Meseta Pt
Culebrita Island : Light-house
Vieques (Crab) Island: Port Ferro light.
St. Thomas: Fort Christian, SW. bastion.
St. John Island : Ram Head
Tortola: Fort Burt
Virgin Gorda: Vixen Pt
Anegada: W. pt
E. extreme of reefs
Christiansted, Santa Cruz: SW. bastion
of fort
Sombrero : Light-house
Dog Island : Center
Anguilla: Custom-house
St. Martin : Fort Marigot light
St. Bartholomew : Fort Oscar
Saba : Diamond Rock
St. Eustatius: Fort flagstaff
St. Christopher: Basseterre Church
Booby Island : Center
Nevis: Fort Charles
Barbuda: Flagstaff, Martello Tower
Antigua, English Harbor: Flagstaff,
dockyard
Sandy Island : Light-house . .
Redonda Islet: Center
Montserrat: Plymouth Wharf
Guadeloupe, Basseterre: Light on mast.
Port Louis: Light on mast
Gozier Islet: Light-house.
Manroux Id. : Light-house
Point h Pitre: Jarry Mill. .
Desirade: E. pt
Petite Terre : Light-house
Marie Galante: Light-house
Saintes Islands: Tower on Chameauhill
Dominica, Prince Ruperts Bay: Sand
beach W. of church
Roseau: Flagstaff, Fort Young
Aves Island : Center
Martinique, Fort de France: Fort St.
Louis light
St. Pierre: Ste. Marthe Bat-
tery
CaravellePen.: Light-house
Cabrit Islet: Summit
St. Lucia, Port Castries: Light-house...
Barbados, Bridgetown: Flagstaff, Rick-
ett's Battery
S. Point: Light-house
Ragged Point: Light-house .
St. Vincent, Kingstown: Light-house..
Bequia Island, Admiralty Bay: Church
Grenada: St. George light-house
Tobago, Rocky Bay: Light-house
Lat. N.
Long. W.
Lun.
Int.
Range.
H. W.
L. W.
Spg.
Neap.
0 ' n
18 02 43
o / r/
67 50 30
67 09 04
67 16 08
66 07 28
65 36 31
66 54 11
65 13 34
65 25 26
64 55 52
64 42 03
64 36 47
64 21 48
64 24 58
64 10 45
64 42 16
63 28 13
63 16 00
63 04 39
63 05 45
62 51 30
63 15 16
62 59 09
62 43 14
62 35 25
62 37 29
61 49 54
61 46 07
61 55 11
62 19 10
62 13 24
61 44 09
61 32 15
61 29 40
61 32 05
61 33 15
61 00 44
61 06 45
61 19 15
61 35 55
61 28 14
61 23 52
63 37 46
61 04 30
61 11 12
60 53 20
60 52 33
61 00 48
59 37 19
59 31 50
59 26 04
61 14 34
61 14 09
61 45 06
60 42 38
h. m.
h. TO.
ft.
ft-
18 11 56
18 25 09
7 04
2 00
2.0
1.0
18 28 56
18 23 05
8 21
2 20
1.3
0.9
17 57 10
[1.0]
1.0]
;i-i]
[1.2]
18 18 44
18 05 20
18 20 23
18 18 08
[7 31]
[7 35]
[7 11]
[1 30]
[1 40]
[0 58]
18 25 04
18 30 39
18 45 11
18 36 30
17 45 09
18 35 37
18 16 42
18 13 06
18 04 07
17 53 58
[1.5]
17 39 10
17 29 10
17 18 12
17 13 38
17 07 52
17 35 50
17 00 00
[2.0]
17 06 54
16 55 18
16 42 12
15 59 50
16 25 09
16 11 57
[1.3]
16 13 14
16 13 56
16 19 56
16 10 17
15 52 59
15 51 32
15 34 34
15 17 27
4 00
10 12
1.5
0.8
15 42 00
14 35 44
14 43 54
14 46 13
14 23 23
3 50
10 02
1.1
0.6
14 01 54
13 05 42
13 02 45
2 50
9 02
3.0
1.5
13 09 40
1
13 09 19
13 00 25
2 50
9 05
1.6
0.8
12 03 02
11 10 08
2 30
3 50
8 42
10 02
1.5
2.1
0.8
1.1
Page 206] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS— Continued.
Place.
Lat. N.
Long. w.
Lun. Int.
Range. 1
H. W. L. W.
Spg.
Neap.
Testigos Islets: Center of Testigo Grande.
Sola Island : Center
O t II
11 25 02
11 19 00
10 59 43
10 57 45
11 47 57
11 56 16
12 02 06
11 59 30
12 06 45
12 06 36
12 31 05
O 1 II
63 05 48
63 36 00
h. m.
h. m.
ft.
ft.
Pampatar, Margafttal. : San Carlos Castle .
•Tortugas Island: S. end of W. Tortugillo
Islet
63 48 00
65 26 38
66 12 31
66 39 10
68 14 10
68 39 19
68 56 44
68 56 36
70 02 34
Orchila Island : S. side
Roques Islands: Pirate Cay
.
Bonaive Island: Light-house
Little Curasao Island : Light-house
Curasao Island: Time-ball station
Light-house
Oruba Island: Light-house
'
NORTH AND EAST COASTS OF SOUTH AMERICA.
i
s
9
0
W
i
a
>
•9
«
1
Chagres: San Lorenzo Castle
9 19 27
9 22 39
9 22 09
9 32 30
8 54 52
8 47 00
8 37 30
9 24 00
9 24 00
10 25 50
11 00 15
10 07 00
11 15 28
11 33 30
12 12 34
12 23 09
12 04 00
10 57 30
11 48 56
12 11 00
12 29 15
11 27 56
10 47 00
11 10 00
10 29 53
10 36 57
10 35 00
10 34 06
10 49 30
10 13 30
10 27 20
10 40 00
10 42 00
10 40 00
10 40 15
10 42 00
10 43 27
10 45 00
10 44 19
10 43 48
10 38 15
8 39 25
10 38 37
10 40 03
10 50 02
10 03 29
10 16 59
80 00 22
79 57 16
79 54 45
79 39 40
77 42 25
77 38 00
76 52 55
76 10 45
75 48 00
75 32 50
74 57 55
74 49 51
74 14 33
72 54 50
72 09 42
71 45 42
71 07 55
71 37 00
70 17 21
70 04 55
70 57 00
69 34 20
68 19 55
68 22 54
68 00 55
66 56 06
66 06 15
66 04 13
66 09 25
64 44 00
64 11 33
64 17 55
63 50 25
63 31 55
63 18 00
63 14 00
63 09 43
62 41 55
62 44 29
61 50 50
61 51 18
60 10 15
61 30 38
61 45 54
60 54 10
61 55 41
61 28 12
Toro Point: Light-house
Colon: Light-house
0 06
6 18
1.1
0.6
Porto Bello : Ft. St. Geronimo
Caledonia Harbor: Scorpion Cay
Carreto Port: Peak
11 30
5 17
L5
0.8
Caribana Point: Extreme
Fuerte Island: N. extreme
Cispata Port: Zapote Pt
Cartagena: Light-house
Sa vanilla: Light-house
Magdalena River: NW. pt. of Gomez I..
Santa Marta: Light-house
Rio de la Hacha: Light on church
Cape La Vela: Sand beach inside cape . .
Baiia Honda: E. pt., S. side
Espada Point: Extreme
Maracaibo: Zapara I. light
5 05
11 17
2.5
1.5
Estangues Point: 500 ft. from extreme . .
Cape San Roman : Extreme .
Marjes Islets: N. islet
Vela de Coro: Light-house
Tucacas Island : Ore house
St. Juan Bay: Cay
Puerto Cabello: Light-house
La Guaira: Light-house
6 00
12 12
,2.8
L7
Cape Codera: Morro.
Corsarios Bay: W. pt
Centinela Islet: Center
Barcelona: Morro
Cumana: Light-house
Escarseo Point: Extreme
Chacopata: Morro
Esmeralda Islet: Center
Carupano : Light-house
Pt. Herman Vasquez
Puerto Santo Bay: Sand spit S. of Morro.
Tres Puntas Cape : Extreme
UnareBay: Obs. spot, 200yds. S. of Morro
Pena Point: Extreme
Pato Island: E. pt
........
Mocomoco Pt. : Extreme
Port of Spain: King's Wharf light
Chacachacare Island: Rocks off SW. pt. .
Galera Point: NE. extreme, light-house.
Icacos Point: Light-house
4 20
10 30
3.2
1.9
San Fernando : Pierhead
APPENDIX IV. [Page 207
MARITIME POSITIONS AND TIDAL DATA.
NORTH AND EAST COASTS OF SOUTH AMERICA— Continued.
1
Place.
Lat. N.
Long. W.
Lun.
Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
S
a
g
Demerara: Georgetown light-house
Nickerie River: Light-house
0 1 II
6 49 20
5 58 30
5 49 30
5 44 50
5 16 50
5 02 40
4 56 20
4 49 30
4 23 20
4 20 45
2 46 30
1 40 17
Lat. S.
0 17 00
1 26 59
0 35 03
2 10 11
2 31 48
2 16 22
2 41 55
2 53 20
3 42 05
4 25 35
5 03 15
5 29 15
5 45 05
5 46 41
6 56 30
7 06 35
8 00 50
8 03 22
8 20 45
8 43 40
9 39 35
10 30 30
10 58 20
11 09 45
11 27 40
12 12 05
12 33 40
13 00 37
12 52 48
13 22 37
13 56 42
14 17 40
14 47 40
14 56 40
15 13 27
15 21 00
16 17 20
16 25 38
17 21 40
17 31 45
17 43 30
17 57 31
18 06 15
20 19 23
20 38 25
20 49 00
20 57 35
21 38 40
22 02 00
22 23 45
O 1 II
58 11 30
57 00 30
55 08 48
54 00 30
52 34 53
52 21 11
52 20 26
51 55 36
51 50 36
51 27 46
50 54 46
49 56 46
48 23 30
48 30 01
47 20 54
44 25 56
44 18 45
43 37 30
42 18 02
41 40 35
38 28 25
37 44 55
36 02 52
35 15 52
35 11 55
35 12 43
34 49 30
34 53 04
34 50 36
34 51 57
34 56 05
35 05 06
35 44 54
36 21 51
37 04 00
37 12 36
37 24 00
37 45 46
38 02 16
38 32 06
38 41 28
38 54 38
39 07 05
39 00 45
39 03 25
39 01 45
39 01 15
39 16 45
39 02 05
39 04 15
39 13 15
39 12 00
39 14 36
38 41 46
39 31 16
40 16 36
40 23 46
40 40 45
40 46 35
41 02 21
40 59 00
41 47 35
h. m.
' 4 18
h. m.
9 50
St.
8.6
ft.
3.9
Parainaribo : Stone steps
5 50
12 00
9.5
4.3
Maroni River: W. light-house
Salut Islands: Light-house
Enfant Perdu Islet: Light-house.
Cayenne: Light-house
4 27
10 30
6.0
2.7
Connetable Islet: Center
Cariniare Mount: Summit
Orange Cape : Extreme
Maye Mountain : Summit
i
North Cape: Extreme
i
Cape Magoari : Extreme
Para: Custom-house
ii 50
5 37
11.0
5.2
Atalaia Point: Light-house
Itacolomi Point: Light-house
Maranhao Island: Landing place
Santa Anna Island : Light-house
Tutoya: Entrance
Paranahiba River: Amargao Village
Ceara: Light-house
6 50
5 35
5 05
0 38
11 47
11 17
16.5
13.1
11.7
7.9
6.2
5.6
5 25
5 50
11 37
12 00
8.2
8.0
3.9
3.8
Jaguaribe River: Pilot station
Cai^ara: Village
Cape St. Roque : Extreme
Rio Grande do Norte: Light-house
Natal : Cathedral
4 05
10 17
8.8
4.2
Parahiba River: Light-house at entrance.
Parahiba: Cathedral
Olinda: Light-house
Pernambuco: Picao light-house
4 33
10 50
7.0
3.3
Cape St. Augustine: Light-house
Tamandare: Village
Maceio: Light-house
4 20
4 17
10 32
10 29
8.5
7.8
4.1
3.7
San Francisco River: Light-house at en-
trance •
Cotinguiba River: Light-house at en-
trance
Vaza Barris River: Semaphore at en-
trance
Real River: Light-house
Conde: Village
Garcia d' Avila: Tower
'
Bahia: Santo Antonio light-house
Itaparica : Fort on N. pt
4 10
10 22
7.6
3.6
Morro de Sao Paulo: Light-house
Camamu : Village
3 50
3 50
10 00
10 00
6.0
6.3
2.9
3.0
Contas: Church
Ilheoa: Church
Oliven^a: Center of village
3 35
9 47
6.4
3.1
Una: Center of village
Comandatuba: Center of village
Santa Cruz: Church
3 25
9 37
6.0
2.9
Porto Seguro: INIatriz Church
Prado : River entrance
Alcobaga: Center of village
Caravellas: Center of village
j
3 10
3 15
9 23
9 27
6.4
7.5
3.1
3.6
Abrolhos Island: Light-house
Porto Alegre: Center of village
Espiritu Santo Bay : Light-house
Guarapiri Islets : E. islet
2 50
9 00
4.0
L9
Benevente: Village
2 40
8 52
5.0
2.4
Itapemirim: Moscas Islet
Sao Joao da Barra: Light-house
Cape St. Tl .ome : Extreme
Macahe : Fort at entrance
1
2 20
8 30
9.2
4.4
Page 208] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
NORTH AND EAST COASTS OF SOUTH AMERICA— Continued.
riace.
Santa Anna Island : Summit
Barra Sao Joao: Village
Busies: Church
Cape Frio: Light-house
Port Frio: Village
Maricas Islands: S. islet
Rio de Janeiro: Fort Villegagnon Light.
Imperial Observatory. . .
Raza Island : Light-house
Petropolis: Center of town
Cape Guaratiba: Summit
Marambaya Island: Summit of SW. end.
Mangaratiba: Village
Palmas Bay : Beach at head of bay
Angra dos Reis: Landing-place
Ilha Grande: Light-house
Parati : Fort
Ubatuba: Cathedral
Porcos Grande Islet: Summit
Busios Islets: Summit
St. Sebastian Island: Boi Pt. light
Villa Nova da Princessa: Center
Santos:^ Moela I. light-house
Quay
Alcatrasses Island: Summit, 880 ft
Conceigao: Church i
Quemada Grande Island: Summit, 628ft.
Iguape: Quay
Bom Abrigo Islet: Light-house
Ilha do Mel : Light-house :
Paranagua: Quay
Antonina: Quay
Coral Islet: Center
Itacolomi Islet: Center
Sao Francisco: Center of town
Itapacaroya: Church
Cambria: Church
Arvoredo Island : Light-house
Anhatomirim: Light-house
St. Catharine Island: Rapa Pt
Naufragados light
Nostra Senhora do Deserto : Quay
Coral Island: Summit, 230 feet
Cape St. Martha: Light-house
Torres Point: Extreme
Rio Grande do Sul: Light-house
Lat. s.
Castillos: Beuna Vista Hill, 184 feet.
Cape Santa Maria: Light-house
Lobos Island : Center
Maldonado : Light-house
Flores Island : Light-house
Montevideo: Cathedral, SE. tower..
Colonia: Light-house
Martin Garcia Island : Light-house
Buenos Ayres: Cupola of custom-house.
La Plata
Indio Point : Light-house
Piedras Point: Extreme
Cape San Antonio: Light-house
Madanas Point: Light-house
Cape Corrientes: E. summit
Port Belgraoo: Anchor.-Stock Hill
Argentina: Fort
22 26 00
22 37 00
22 46 00
23 00 42
22 53 15
23 01 43
22 54 46
22 54 15
23 03 40
22 32 00
23 03 40
23 04 20
22 57 20
23 09 20
23 00 30
23 09 50
23 12 20
23 25 55
23 32 57
23 45 15
23 58 30
23 47 20
24 03" 06
23 56 00
24 06 30
24 10 32
24 28 45
24 42 35
25 06 40
25 30 55
25 31 20
25 26 30
25 44 10
25 50 15
26 14 17
26 46 45
27 01 35
27 18 00
27 25 30
27 22 55
27 50 27
27 36 00
27 56 40
28 38 00
29 20 20
32 06 40
34 21 19
34 40 01
35 01 39
34 58 15
34 56 55
34 54 33
34 28 20
34 10 50
34 36 30
34 54 30
35 15 45
35 26 50
36 18 24
36 53 00
38 05 30
38 57 00
38 43 50
Long. W.
43 15
59 45
54 05
00 00
01 15
54 05
09 24
10 16
08 45
11 01
33 24
59 26
02 29
08 24
19 04
05 45
42 04
04 04
03 50
00 39
15 20
21 04
15 57
19 09
40 49
47 44
41 04
32 54
51 50
19 53
31 03
43 14
23 14
25 51
39 29
36 59
36 44
22 20
34 25
26 09
35 16
34 14
33 44
49 45
43 39
07 44
Lun. Int.
53 47 16
54 09 14
54 53 16
54 57 10
55 55 04
56 12 15
57 52 27
58 15 40
58 22 14
57 54 15
57 10 45
57 05 28
56 44 15
56 38 54
57 30 01
61 59 15
62 15 27
H. W.
h. m.
2 30
2 50
1 35
2 50
2 55
2 35
4 00
8 20
2 00
6 30
6 43
9 50
6 00
L. W.
h. m.
Range.
Spg. Neap.
ft.
8 42 4. 9
9 00 4. 2
7 47
9 05
8 47
10 12
2 08
8 12
0 00
12 15
3 35
'6'66'
2.0
3.5
4.0
5.3
15.8
2.3
2.0
5. 3 2. 5
9 00 5. 0 2.
6:4 3.1
5.9 I 2.
1.8 0.9
0.9
2.3
2.7
2.1 I 1.4
3.5
8.2
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
NORTH AND EAST COASTS OF SOUTH AMERICA— Continued
[Page 209
Place.
Labyrinth Head : Summit
Union Bay: Indian Head
San Bias Harbor: SW. end of Hog Islet.
San Bias Bay: Summit of Rubia Pt
Rio Negro: Main Pt
Bermeja Head : E. summit
Port San Antonio: Point Villarino
San Antonio Sierra: Summit
Port San Jos6: San Quiroga Pt
Delgado Point: SE. cliff
Cracker Bay: Anchorage
Port Madryn: Anchorage off cave bluff
Chupat River: Entrance
Port St. Elena: St. Elena pen
Leones Island: SE. summit
Melo Port: W. pt
Port Malaspina : S. pt
Cape Three Points: NE. pitch
Port Desire: Largest ruin
Sea Bear Bay : Wells Pt
Port San Julian: Sholl Pt
Port Santa Cruz : Mount at entrance
Coy Inlet: Height S. side of entrance. . .
Gallegos River: Observation mound
Cape Virgins: SE. extreme
Cape San Diego: Extreme
Staten Island, Cape St. John: Light-
house, W. pt
Port Cork: Observation
mark, summit
Cape St. Bartholomew:
Middle pt
Good Success Bay: S. end of beach
Lennox Cove: Bluff, N. end of beach . . .
Goree Road: Guanaco Pt
Wollaston Island : Middle Cove
Barneveldt Islands: Center
Cape Horn: South summit, 500 ft
Hermite Island: St. Martin Cove
Lat. S.
39 26 30
39 57 30
40 32 52
40 36 10
41 02 00
41 11 00
40 49 00
41 41 10
42 14 15
42 46 15
42 57 00
42 45 40
43 20 45
44 30 40
45 04 00
45 03 00
45 10 10
47 06 20
47 45 05
47 57 15
49 15 20
50 08 30
50 58 27
51 33 21
52 18 35
54 40 35
54 43 24
54 45 16
54 53 45
54 48 02
55 17 00
55 19 00
55 35 30
55 48 54
55 58 41
55 51 20
Long. W.
62 03 22
62 07 46
62 09 30
62 10 12
62 45 11
63 08 16
64 54 41
65 12 29
64 27 56
63 37 16
64 28 20
64 59 00
65 03 36
65 22 10
65 36 01
65 52 30
66 32 36
65 51 46
65 54 45
65 45 40
67 42 30
68 23 00
69 09 47
69 00 31
68 22 12
65 05 53
63 47 00
64 03 00
64 45 45
65 13 48
66 49 00
67 10 00
67 19 00
66 43 48
67 16 15
67 34 00
Lun. Int.
H.W. L.W.
h. m. h. m.
10 50
10 35
7 05
0 00
10 35
9 20
9 00
8 40
8 18
4 20
4 19
3 50
4 07
4 38
4 23
0 52
3 50 I 10 03
6 12
10 33
10 32
10 03
10 02
Range.
14.7
23.5
13.2
16.8
18.3
29.5
39.6
40.0
45.6
38.7
9.9
6.7
4.8
Neap.
St.
7.7
12.3
6.9
9.6
15.4
20.7
20.9
23.9
20.2
5.2
6.0
5.2
3.8
WEST COAST OF SOUTH AMERICA.
False Cape Horn: S. extreme 55 43 15
Ildefonso Island: Highest summit 55 52 30
Diego Ramirez Island : Highest summit . 56 28 50
York Minster Rock: Summit, 800 ft \ 55 24 50
Cape Desolation : S. summit 54 45 40
Mount Skyring: Summit, 3,000 ft 54 24 48
Noir Island: SE. extreme 54 30' 00
Landfall Island: Summit of Cape Inman J 53 18 30
Cape Deseado: Peaked summit 52 55 30
Apostle Rocks: W. rocks 52 46 15
Cape Pillar: N. cliff 52 42 50
Dungeness Point: Light-house 52 23 55
Cape Espiritu Santo: NE. cliff 52 39 00
Catharine Point: NE. extreme ! 52 32 00
Cape Possession : Light-house 52 17 54
Cape Orange: N. extreme 52 28 40
Delgada Point: Light-house 52 28 00
Cape Gregory : Light-house 52 38 18
Cape San Vicente: W. extreme 52 46 20
04 40
17 30
41 30
01 30
36 10
10 20
00 00
18 15
36 30
46 50
42 20
25 45
34 00
45 20
57 10
24 00
33 00
14 16
25 25
3 50
2 20
1 50
0 32
8 19
8 20
8 24
8 35
8 47
9 23
10 03
8 33
8 03
6 45
2 07
2 08
2 12
2 25
6.0
4.8
4.7
2 40
3 20
4.0
39.4
39.0
30.0
39.0
39.0
21.0
3.9
3.7
3.7
3.1
20.6
20.4
15.7
20.4
20.4
11.0
'22489—03-
-14
Page 210J APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMEBICA— Continued.
1
Place.
■
Lat. S.
Long. W.
Lun
Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
6
Elizal)eth Islanc^ NE. ])luff
O t II
52 49 18
53 10 10
53 33 30
53 38 12
53 47 00
53 53 43
53 51 45
53 41 45
53 43 57
53 42 00
53 37 10
53 34 20
53 31 45
53 32 10
53 30 50
53 30 05
53 25 00
53 18 45
53 15 30
53 13 40
53 06 30
53 11 40
53 06 35
52 55 46
53 01 00
52 55 00
52 42 00
52 44 58
51 18 29
49 25 19
49 12 40
49 07 30
48 54 20
52 37 18
52 24 00
52 16 10
51 51 50
50 42 00
50 17 20
50 02 00
50 00 18
49 48 00
48 06 15
48 02 20
47 39 30
46 49 31
46 58 57
46 49 10
46 35 00
46 04 00
45 53 20
44 55 50
44 09 00
43 48 30
43 41 50
43 19 35
43 17 10
43 11 20
42 48 00
42 27 45
O f II
70 37 51
70 54 24
70 34 27
70 58 31
70 55 03
71 17 15
71 55 30
71 59 41
72 04 45
72 10 42
72 19 30
72 27 10
72 34 15
72 32 25
72 38 00
72 47 30
72 47 55
73 00 30
73 12 05
73 21 30
73 15 30
73 17 45
73 16 15
73 44 28
73 59 33
74 17 45
74 13 30
74 38 14
74 04 00
74 17 39
74 23 27
74 25 10
74 20 55
74 23 10
75 06 00
74 55 00
75 13 20
75 27 45
74 51 30
75 22 00
75 13 20
75 31 00
75 40 30
75 28 20
75 10 00
75 18 20
75 25 30
75 37 55
75 31 30
75 12 00
?5 06 00
75 08 45
74 07 45
73 59 35
74 42 00
73 41 50
74 22 00
72 44 40
72 30 30
73 45 20
//. m.
10 24
11 03
h. in.
4 24
5 03
ft.
8.0
5.0
ft.
4.2
2.6
Sandy Point: Light-house
Cape St. Valentine: Sununit, at extreme.
Port Famine: Observatory
11 58
12 21
0 28
5 58
6 21
6 53
6.0
8.0
7.0
3.1
4.2
3.7
Cape San Isidro: Extreme
Cape Fro ward : Summit of bluff
Mount Pond: Summit
Port Gallant: Wigwam Pt
1 20
7 40
8.0
4.2
Charles Island: White rock near NW. end
Rupert Island : Summit
Mussel Bay : Entrance
Tillv Bav: Sarah I
Borja Bay : Bluff on W. shore
1 54
8 11
5.5
2.9
Cape Quad : P^xtreme
Barcelo Bay : J^ntrance
Swallow Bay : Shag I
Cape Notch : Extreme
Playa Parda Cove: Summit of Shelter I . .
Pollard Cove: Entrance
Port Angosto: Hay Pt
St. Anne Island : Central summit
Half Port Bay : Point ^
Upright Port: Entrance
Port Tamar : Mouat Islet
1 53
8 08
5.0
3.9
1 31
7 44
4.5
3.5
1 09
7 21
4.0
3.1
0 55
7 07
6.0
4.6
Port Churruca: Summit of Blanca Pen . .
Valentine Harbor: Observation mount . .
Cape Parker: W. summit
Mercy Harbor: Summit of Battle I
Mayne Harbor: Observation spot
Port Grappler: Observation spot
Port Riofrio: Vitalia I
Eden Harbor: Observation spot
Halt Bav : Observation islet
Westminster Hall Islet: E. summit
Evangelistas Island: Light-house
Cape Victory: Extreme
0 55
7 08
4.4
3.4
Cape Isabel: W. extreme
Cape Santiago: Summit.
Molyneux Sound : Romalo I
Cape Tres Puntas: Summit, 2,000 ft
Port Henry : Observation spot
0 30
6 45
4.5
3.5
Mount Corso: SW. summit
Rock of Dundee: Summit
Santa Barbara Port: N. extreme obs. pt.
Guaineco Islands: Speedwell Bay, hill,
np:. pt
0 15
6 30
5.3
4.1
Port Otwav : Observation spot
0 10
6 25
5.3
4.1
Cape Tres Montes: Extreme
Cape Raper: Rock close to cape
Christmas Cove: SK. extreme
Hellyer Rocks: Middle
Cape Taytao: W. extreme
Socorro Island: S. extreme
Mayne Mountain: Summit, 2,080 ft
Port Low : Observation islet
0 00
6 13
4.4.
3.4
12 20
12 10
6 10
6 00
6.2
6.1
4.8
3.1
Huafo Island : S. extreme
Port San Pedro: Cove on S. shore
Cape Quilan: SW. extreme
Corcovado Volcano: Summit, 7,510 ft...
Minchinmadiva Volcano: S. summit,
8,000 feet
Castro: E. end of town
0 01
6 21
18.0
9.1
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMERICA— Continued.
[Page 211
Place.
Dalcahue: Chapel
Oscuro head : Observation pt
Coman Inlet: Olvidada I
Port Calbuco: Lg, Picuta
San Carlos de ARcud: Light-house
Condor Cove: Landing
Eanu Cove: Anchorage
Muilcalpue Cove: Landing place
Milagro Cove: Landing place
Laruehuapi Cove: Landing place
Valdivia : Niebla Fort light
Queule Bay : Choros Pt
Mocha Island : Light-house
Lebu River: Tucapel Head
Yanez Port: Anchorage
Lota: Light-house
Santa Maria Island : Light-house
Talcahuano : Fort Galvez
Light on Quinquina I
Llico: Village
Port San Antonio: Village
Aconcagua Mountain: Summit
Santiago : Observatory
Valparaiso: Playa Ancha Pt. light
Site of Fort San Antonio
Quintero Point: Summit
Pichidanque: SP]. pt. of island
Tablas Point: SW. extreme
Chuapa River: S. entrance pt
Maitencillo Cove: N. head
Talinay Mount: Summit
Lengua de Vaca: Light-house
Port Tongoi: Obs. spot. W. of village
Coquimbo : Tortuga Pt. light
Smelting works, N. of town.
N. islet
Pajaros Islets : Light-house
Choros Islands: SW. pt. of largest id
Chaiiaral Island: Light-house
Huasco: Light on mole
Herradura de Carrizal: Landing place. . .
Port Carrizal": Middle Point
Matamoras Cove: Outer pt. S. side
Salado Bay: Summit of Cachos Pt
Copiapo: Landing place
Caldera: Light-house
Light on mole head
Cabeza de Vaca Point: Extreme
Flamenco: SE. corner of bay
Chanaral Bay : Observation pt
St. Felix I. : Peterborough Cathedral Rock
Pan de Azucar Island : Summit
Lavata: Cove near SW. pt
San Pedro Point: Summit
Port Taltal : Light-house
Grande Point: Outer summit
Paposo Road : Huanillo Pt
Reyes Head : Extreme pitch
Cobre Bay: Pt. W. of village
Jara Head : Summit
Antofagasta: Light-house
Chimba Bay: E. pt. of large island
Lat. S.
O / l>
42 23 00
42 04 00
42 03 00
41 46 08
41 46 40
40 46 19
40 43 18
40 35 52
40 21 04
40 11 47
39 51 37
39 23 00
38 21 22
37 35 20
37 22 30
37 05 20
36 59 07
36 42 00
36 36 45
34 46 02
33 34 13
33 38 30
33 26 42
33 01 08
33 01 52
32 46 00
32 07 55
31 51 45
31 39 30
31 17 05
30 50 45
30 14 00
30 15 14
29 56 15
29 56 24
29 55 10
29 34 40
29 15 45
29 00 50
28 27 20
28 05 45
28 04 30
27 54 10
27 39 20
27 20 00
27 03 15
27 03 15
26 51 05
26 34 30
26 20 00
26 16 12
26 09 15
25 39 30
25 31 00
25 25 20
25 07 00
25 05 25
24 34 30
24 15 00
23 53 00
23 38 50
23 33 05
Long. W.
36 00
25 00
45 00
07 15
52 54
51 00
49 50
45 00
45 20
41 50
26 25
14 00
58 06
39 55
40 00
11 13
32 30
07 27
02 49
06 12
38 00
56 30
41 32
38 52
38 42
32 56
33 22
34 51
35 20
39 21
39 00
39 00
31 09
21 00
21 53
22 21
33 20
34 38
36 40
15 45
12 48
11 32
09 38
03 26
58 45
52 54
53 45
51 55
44 25
37 25
11 43
43 57
44 03
41 18
34 10
30 16
29 50
36 29
33 00
32 28
25 18
26 55
Lun. Int.
H. W.
1 10
0 04
0 00
10 25
10 18
10 20
10 15
10 10
10 05
10 10
10 04
10 05
9 57
9 44
9 37
9 35
9 30
9 26
9 15
8 58
8 23
8 50
8 21
8 50
9 00
9 05
9 10
9 20
9 35
9 30
9 05
L. W.
Range.
7 35
6 20
14.8
5.9
6 13
3 25
3 20
3 16
3 05
2 48
2 10
2 38
2 08
2 37
2 47
2 52
2 57 5. 0
7.2
5.6
4.9
3.3
4.9
5.3
4,9
6.0
5.3
5.0
4.1
4.0
3 26 3.9
4.1
3.9
4.2
4.1
4.9
4.9
4.9
5.0
4.9
5.0
4.9
3 07 : 4. 9
3 22 I 5. 0
3 17 i 4.9
2 52 I 4. 7
Neap.
7.5
3.0
3.7
2.8
2.5
1.7
2.5
2.7
2.5
3.0
2.7
2.5
2.1
2.0
2.0
2.1
2.0
2.1
2.1
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.5
2.4
Page 212] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMERICA— Continued.
■g
Place.
Lat. s.
Long. W.
Lun
.Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
Moreno Mountain! Summit
o / ;/
23 28 30
23 26 42
23 06 30
22 34 00
22 06 00
21 55 50
21 28 00
21 05 30
20 n 40
20 51 05
20 12 30
19 05 01
19 36 30
19 19 00
18 45 40
18 28 43
17 58 35
17 42 00
17 37 00
17 01 00
17 00 00
16 42 20
16 23 50
16 13 30
15 48 00
15 33 15
15 20 56
14 57 00
14 41 00
14 09 50
13 50 00
13 48 00
13 45 00
13 38 20
13 01 00
12 48 00
12 31 00
12 11 30
12 04 03
12 08 15
11 47 10
11 27 10
10 49 45
10 06 15
9 38 35
9 15 30
9 04 40
8 46 30
8 34 50
8 05 40
7 42 40
7 23 40
6 55 50
6 46 00
6 46 45
6 26 45
5 55 30
5 12 00
5 05 00
4 40 50
4 1^ 40
3 30 42
O 1 II
70 34 56
70 37 11
70 31 39
70 17 42
70 13 40
70 11 17
70 02 45
70 12 12
70 10 26
70 14 40
70 11 20
70 10 30
70 15 21
70 17 50
70 21 50
70 20 00
70 52 31
71 22 31
71 20 01
72 02 53
72 07 16
72 27 16
73 16 41
73 41 31
74 27 16
74 51 01
75 09 36
75 30 46
75 49 56
76 16 36
76 27 31
76 18 31
76 10 00
76 24 15
76 31 06
76 38 11
76 48 56
77 02 31
77 15 44
77 14 45
77 16 11
77 50 04
77 43 42
78 10 02
78 21 33
78 30 03
78 35 57
78 45 16
78 56 53
79 06 46
79 26 00
79 33 15
79 51 30
79 57 55
80 42 54
80 51 56
81 09 19
81 05 36
81 07 03
81 17 01
81 12 01
80 28 12
h. TO.
h. m.
ft.
A
Constitution Cove: Shingle pt. of island.
Mexillones Mount: Summit
9 35
9 44
8 55
3 22
3 31
2 42
3.9
4.0
4.8
2.0
2.0
2.4
Port Cobija: Landing place
Tocopilla: Extremity Point
San Francisco Head : W. pitch
Loa River: Mouth
i
Lobos Point : Outward pitch
9 00
2 47
4.9
2.5
Pabellon de Pica: Summit
6
Patache Point: Extreme
,
Iquique: Light-house
8 35
2 22
5.0
2.5
Mexillon Bay : Landing place
Pisagua: Pichalo Pt., extreme
8 32
2 20
5.0
2.5
Gorda Point: W. low extreme
Lobos Point: Summit
Arica: Iron church
7 49
1 37
5.6
2.8
Schama Mount: Highest summit
Coles Point: Extreme
«
ft*
Ho: Mouth of rivulet
7 55
1 43
5.3
2.7
Port Mollendo : Light-house
Islay: Custom-house
7 39
1 27
6.2
3.1
Quilca: W. head of cove
Pescadores Point: SW. extreme
Atico: E. cove
Chala Point: Extreme
Lomas: Flagstaff on pt
San Juan Port: Needle Hummock
Nasca Point: Summit
6 47
0 35
3.9
2.0
Mesa de Dofia Maria: Central summit. . .
Carreta Mount: Summit
San Gullan Island: N. summit
Paraca Bay: N. extreme of W. pt
Pisco: Light-house
6 16
0 04
3.8
1.9
Chincha Islands: Boat slip, E. side N. id.
Frayles Point: Extreme
"
Asia Rock: Summit
Chilca Point: SW. pitch
Morro Solar: Summit
San Lorenzo Island: Light-house
Callao: Palominos Rock Light
5 47
12 00
3.5
1.8
Pescadores Islands: Summit of largest. . .
Pelado Island : Summit
Sup^ : W. end of village
Huarmey : W. end of sandy beach
Colina Redonda: Summit
5 08
11 21
2.1
1.1
Saraanco Bay : Cross Pt
Chimbote : Village, N. part
4 50
11 03
2.0
LO
Chao Islet: Center
Guanape Islands: Summit of highest
Huanchaco Point: SW. extreme
Malabrigo Bay : Rocks
4 19
10 32
2.1
1.1
Pacasmayo : Light-house
Eten Head : Light-house
4 04
10 17
2.5
1.3
Lambayeque: Beach opposite
Lobos de Afuera Island: Cove on E. side.
Lobos de Tierra Island: Central summit.
Aguja Point: W. cliff summit
Paita, Saddle: S. summit
Paita: Light-house
3 20
9 33
3.5
1.8
Parinas Point: Extreme
Cape Blanco: Under middle of high cliff.
Tumbez: Malpelo Pt
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMERICA— Continued.
[Page 213
Place.
Guayaquil River: Lighten Santa Clara I.
Guayaquil, Concejo: S. pt. of city
Puna: Mandinga Pt. light
Point Santa Elena: Veintemilla light
Plata Isle: E. pt
Cape San Lorenzo: Marlingspike Rock..
Manta Bay: Light-house
Caraques Bay: Punta Playa
Cape Pasado: Extreme
Point Galera: N. extreme
Cape San Francisco: S\V. extreme
Lat. S.
10 40
12 24
44 30
12 00
16 55
03 30
0 56 50
0 35 25
0 21 30
Lat. N.
0 50 10
0 40 00
Esmeralda River : Light-house
Mangles Point: S. pt. of creek entrance.
Tumaco: S. pt. of El Morro I
Guascama Point: Extreme
Gorgona Island: Watering Bay
Buenaventura: Basan Pt
Chirambiri Point: N. extreme
Cape Corrientes: SW. extreme
Cupica Bay: Entrance to Cupica River.
Cape Marzo: SE. extreme
Isla del Rey: Extreme of Cocos Pt
Darien Harbor: Graham Pt
Flamenco Island : N. Pt
Chepillo Island: Center
Point Cham^: Extreme
03 30
36 00
49 36
37 10
58 10
49 27
17 06
28 46
41 19
6 49 45
8 12 30
8 28 50
8 54 30
8 56 32
8 39 00
Long. W.
80 25 29
79 52 19
79 53 45
80 59 00
81 03 55
80 55 55
80 42 50
80 25 24
80 30 37
80 05 40
80 07 55
79 42 00
79 03 30
78 45 29
78 24 24
78 11 16
77 11 45
77 29 44
77 33 28
77 30 31
77 40 55
78 54 40
78 05 35
79 31 15
79 07 55
79 41 45
Lun. Int.
Range.
H. W.
h. m
4 00
7 00
3 00
3 10
3 15
3 35
6 00
3 40
3 30
3 00
3 05
3 30
L. W.
10 13
1 00
Spg.
ft.
10.0
11.0
9 13
9 23
7.5
9 28
9 48
13.2
12 13
13.2
9 53
9 43
13.1
13.3
9 13
15.7
9 18
9 42
16.0
15.0
Neap.
ft.
5.1
5.6
4.0
3.8
5.0
7.1
7.1
7.0
7.2
8.5
8.7
8.1
ISLAITDS nr THE ATLANTIC OCEAN.
Faeroe Islands, Strom Islet: Thorshaven
Fort flagstaff
Halderoig Islet: Halde-
roig Church
Numken Rock
Rockall Islet: Summit, 70 feet
Corvo Island: S. pt
Flores Island : Santa Cruz Fort
Fayal Channel : N. Magdalen Rock
Fayal Island, Horta: Castle of Santa Cruz
Caldera: summit 3,351 ft .
Pico Island : Summit
St. George Island : Light-house
Graciosa Island: Santo Fort light
Terceira Island: Monte del Brazil, near
Angra
St. Michael Island : Custom-house, Ponta
Delgada
Pt. Arnel light
Santa Maria Island: Villa do Porto light
Formigas Islands : Highest rock
Porto Santo Island : Light-house
Desertas: Chao I., Sail Rock
Madeira Island : Funchal light
Fora I. light-house
Pico Ruivo, summit
6,056 ft
Pargo (W.) Pt
62 02 26
62 18 20
61 23 00
57 35 52
39 40 07
39 27 00
38 32 09
38 31 45
38 34 30
38 25 00
38 40 30
38 05 24
38 38 20
37 44 16
37 49 20
36 56 00
37 16 44
33 03 15
32 35 45
32 37 42
32 43 14
32 45 00
32 48 07
6 43 08
7 GO 36
6 45 30
13 42 21
31 08 00
31 08 49
28 34 00
28 37 39
28 44 00
28 28 12
28 13 00
28 00 45
27 13 45
25 40 40
25 08 21
25 10 00
24 47 06
16 16 20
16 33 30
16 55 16
16 39 31
16 57 30
17 16 05
11 30
0 20
0 15
0 40
0 35
5 18
3.9
6 32
4.4
6 27
5.7
6 52
6 47
6.6
1.8
2.0
2.6
3.0
"3."6
Page 214] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS IN THE ATLANTIC OCEAN— Continued.
1
Place.
Lat. N.
Long. W.
Lun.
Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
i
s
m
g
7
M -
9
t
s
N
u
|2
Salvage Islands: Cight-house, Gran Sal-
vage I -\.
O 1 II
30 08 00
29 23 50
28 57 24
28 50 56
28 45 25
28 03 00
28 10 42
28 07 06
28 35 25
28 28 12
28 16 35
28 08 00
27 46 30
28 50 06
17 06 50
17 04 00
16 54 36
16 49 00
16 38 00
16 34 00
16 50 50
16 34 00
16 13 20
16 11 00
16 09 10
15 07 30
15 18 06
14 53 40
14 53 00
14 50 30
32 19 22
32 19 37
32 15 05
32 21 40
0 55 30
Lat. S.
3 51 30
3 50 30
7 55 20
15 55 00
20 27 42
20 30 32
37 19 00
37 02 48
40 19 11
51 21 26
51 04 11
51 32 20
51 41 10
51 40 40
54 04 45
53 48 00
59 34 00
55 57 00
O / II
15 54 00
13 29 31
13 33 07
13 52 05
13 49 13
14 31 35
15 25 11
15 24 56
16 08 11
16 15 09
16 38 02
17 05 55
17 54 22
17 47 01
24 59 15
25 17 00
25 01 12
24 47 08
24 38 08
24 16 00
22 54 55
22 55 42
22 55 44
22 42 00
22 57 20
23 12 42
23 47 06
23 31 45
24 30 38
24 40 00
64 49 35
64 49 15
64 49 40
64 38 40
29 22 28
33 49 29
32 25 29
14 24 35
5 43 03
28 46 57
29 14 56
12 23 00
11 18 39
9 56 11
60 04 52
58 30 56
58 08 04
57 51 30
57 41 48
38 15 00
43 25 00
27 45 00
26 33 00
h. m.
h. m.
ft.
ft.
Alegranza Island: Delgada Pt. light
Lanzarote Island: Port Naos light
Pechinguera Pt. light.
Lobos Island : Martino Pt. light
Fuerta Ventura Island: Jandia Pt. light.
Gran Canada: Isleta Pt. light
Palmas light
0 50
7 00
8.5
3.9
0 40
6 50
9.3
4.3
Teneriffe Island: Anga Pt. light
Santa Cruz, Br. con-
sulate
1 15
7 27
7.8
3.6
Summitof peak, 12,180
ft
Gomera Island : Port Gomera
Ferro Island : Port Hierro
Palma Island : Light, NE. pt
0 20
6 30
8.6
4.0
San Antonio Island: Bull Pt. light
Summit, 7,400ft...
St. Vincent Island: Porto Grande light .
St. Lucia Island: N. pt
5 50
12 00
3.3
1.5
Raza Island : E. pt
St. Nicholas Island : Light-house
Sal Island: N. pt. light
s. pt:....
Boavista Island : N W. pt
NE. pt
Light-house
Mayo Island : English Jload
7 30
1 20
4.4
2.0
St. Jago Island: Reta Pt. light
Porto Praya, S. light
Fogo Island : N. S. da Luz,'village
Brava Island: Light-house
5 50
12 00
4.8
2.2
Ireland Island: Dock yard clock tower. .
Bastion C
7 04
0 52
4.0
2.6
Hamilton Island: Gibbs Hill light
St. Davids Island : Light-house
St. Paul Rocks: Summit, 64 ft
Rocas Reef: NW. sandy islet
5 05
5 00
5 20
3 00
3 35
3 40
11 18
11 13
11 30
9 10
9 48
9 53
10.0
6.0
2.0
2.8
3.5
4.0
4.6
2.7
0.9
1.3
1.6
1.8
Fernando Noronha: The Pyramid
Ascension Island : Fort Thornton
St. Helena Island: Obs. Ladder Hill . . . .
Martin Vaz Rocks: Largest islet
Trinidad Island: SE. pt
Inaccessible Island: Center
Tristan d' Acunha Islands: NW. pt
Gough Island : Penguin Islet
12 50
5 40
5. .2
2.4
Port Egmont: Observation spot
7 20
1 08
10.7
5.6
Mare Harbor: Observation spot
Port Louis: Flagstaff, govt, house
Port Stanley: Governor's house
Cape Pembroke: Light-house
5 31
11 27
4.3
2.2
South Georgia Island: N. cape
Shag Rocks: Center
Sandwich Islands: S. Thul6
Traverse I. volcano . .
i
1
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS IN THE ATLANTIC OCEAN— Continued.
[Page 216
Place.
New S. Orkney Is. : E. pt. Laurie I
E. summit Corona-
tion I., 5,397 ft...
New S. Shetland Islands, Deception
Island: Port Foster
Bouvets Island (Circumcision): Center..
Lat. s.
60 54 00
60 46 00
62 55 36
54 16 00
Long W.
44 25 00
45 53 00
60 35 00
Long. E.
6 14 00
Lun. Int.
H. W.
h. m.
L. W.
h. TO.
Range.
Spg.
ft.
Neap.
ft.
ATLANTIC COAST OF EUROPE.
Greenwich : Observatory
Oxford : University Observatory ...
Cambridge : Observatory
North Foreland: Light-house
South Foreland: Light-house
Dungeness: Light-house
Beachy Head : Light-house
Southsea Castle : Light-house
Portsmouth : Observatory
Southampton : Royal Pier light
Hurst Castle: W. light
Needles Rocks: Old light-house
St. Catharine: New light-house
Portland : Notch Bill light
Start Point: Light-house
Plymouth: Breakwater light
Eddystone: Light-house
Falmouth: St. Anthony Pt. light
Lizard Point: W. light-house
Porthcurnow: SE. cor. telegraph co.'ssta
Lands End: Longships lignt-house
Scilly Hands: St. Agnes light-house
Trevose Head : Light-house
Bideford : High light-house
Lundy Island : Light-house, N. pt
Bristol: Cathedral
Cardiff: Light-house, W. pier
Swansea: Light-house, W. pier
Caldy Island : Light-house
St. Anns: Upper light-house
Smalls Rocks: Light-house
Aberystwith : Light-house
Bardsey Island : Light-house
South Stack: Light-house on rocks
Holyhead: Light-house on old pier
Skerries Rocks : Light-house, highest I .
Bidstone: Light-house on hill
Liverpool : Rock light
Observatory
Morecambe Bay: Fleetwood highlight.
Calf of Man: Upper light-house
Isle of Man : Ayre Pt. light-house
St. Bees: Light-house
White Haven: W. pier-head light
Mull of Galloway: Light-house
Ayr, Firth of Clyde: Light-house, N. side
harbor
Troon: Light-house, inner pier
Lat. N.
51
28 38
51
45 34
52 12 52
51
22 28
51
08 23
50 54 47 1
50
44 15
50 46 35
50 48 03
50
53 45
50 42 07
50 39 42
50 34 30
50 31 10
50
13 18
50 20 02 1
50
10 49
50 08 30
49 57 40
50 02 44
50 04 10
49 53 33
50
33 00
51
04 00
51
12 05
51
27 24
51
27 48
51
36 50
51
37 52
51
41 00
51
43 15
52
24 20
52 45 00 1
53
18 30
53
18 54
53 25 15
53 24 02
53
26 38
53 24 04 1
53
55 03
54 03 14 I
54
24 56
54 30 50
54 33 00
54 38 10
55 28 10
55
32 55
Long. W.
0 00 00
1 15 04
0 05 40
Long. E.
1 26 48
1 22 22
0 58 18
0 13 00
Long. W.
05 15
05 58
24 00
33 04
35 25
17 47
27 30
38 28
09 27
15 53
01 00
12 06
39 18
44 45
6 20 38
5 01 55
12 30
40 35
35 55
09 42
56 00
40 59
5 10 30
5 40 15
05 40
47 50
42 00
37 01
36 20
10 42
02 27
04 16
00 20
49 37
22 01
37 50
36 00
51 20
4 38 10
4 41 00
1 10
11 24
11 09
10 35
11 10
11 31
0 35
11 05
6 29
5 25
5 20
4 45
4 15
5 45
5 00
7 00
6 45
5 45
5 40
5 41
5 40
7 25
7 24
10 00
11 08
11 00
10 55
11 00
11 05
11 40
7 46
18.8
5 53
5 43
4 23
4 58
16.8
19.8
21.5
19.8
4 19
6 48
4 53
1.3.2
12.8
12.2
0 09
11 38
11 33
6.7
14.9
15.3
10 58
14.2
10 28
15.9
11 58
11 13
0 48
0 33
11 58
11 53
11 54
11 53
1 13
1 12
22.7
26.9
31.3
36.2
27.1
25.3
24.0
20.9
14.2
14.9
3 48 i 15. 8
5 27
4 48
27.6
27.4
4 43
19.7
4 48
4 53
5 28
25.9
14.8
12.6
8.4
10.0
11.0
10.1
6.7
6.5
6.2
1.0
6.8
7.0
6.5
7.3
11.4
13.5
15.7
18.1
13.6
12.7
12.0
10.5
7.1
7.5
7.9
14.0
13.9
10.0
13.1
8.9
5.2
Page 216]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
Place.
Ardrossan : S. breakwater light
Pladda Island : *Light-hou8e
Glasgow: Observatory
Cantyre: Light-house
Rhynns of Islay : Light-house
Oban: Light-house on N. pier
Skerry vore Rocks: Light-house
Barra Head: Light-house
Glas Island: Light-house, Scalpay I
Stornoway : Arnish Pt. light
Butt of Lewis: Light-house
Cape Wrath : Light-house
Dunnet Head : Light-house
Kirkwall (Orkneys): New pier-head
light
Startpoint (Orkneys): Light-house
North Ronaldeay: Light-house
Fair Isle Skroo: Light-house
Sumburgh Head: Light-house
Blackness (Shetland Is.): Light-house
pier
Lerwick (Shetland Is. ) : Fort
Hillswickness (Shetland Is. ) : S. extreme.
Balta I. (Shetland Is.): Cairn on E. side.
Pentland Skerries: Upper light-house...
Tarbertness: Light-house
Buchanness: Light-house
Aberdeen (Girdleness) : Light-house
Buddonness: Upper light-house
Bell Rock: Light-house
May Island: Light-house
Inch Keith Rock: Light-house
Edinburgh : Observatory
Berwick: Light-house
Farn Island: NW. light-house
Coquet Island: Light-house
Tynemouth: Souter Point light-house. . .
North Shields: Light-house
Sunderland: N. pier light
Hartlepool : Light-house
Flam borough : New light-house
Humber River: Kilhngholme middle
light
Lat. X.
Spurn Head: Upper light-house
Lowestoft: Light-house
Orfordness: N. light-house
Harwich: Landguard Pt. light..
Cape Clear: Old light -house
Fastnet Rock : Light-house
Mount Gabriel : Ordnance survey station .
Castlehaven : Light-house
Mizen Hill: Ordnance survey station
Ban try Bay : Roancarrig light
Bull Rock : Light-house
Skelligs Rocks: Light-house
Valentia: Light-house
Port Magee
Dingle Bay: Light at entrance
Blasket Islands: Westernmost rock
Smerwick : Signal tower
Tralee Bay: Light-house
Beeves Rocks : Light-house
Limerick : Cathedral
Shannon River: Loop Head light
55 38 27
55 26 00
55 52 43
55 18 39
55 40 20
56 24 50
56 19 22
56 47 08
57 51 25
58 11 28
58 30 40
58 37 30
58 40 16
58 59 15
59 16 45
59 23 24
59 33 00
59 51 15
60 08 02
60 09 22
60 27 20
60 44 25
58 41 22
57 51 54
57 28 15
57 08 33
56 28 07
56 26 03
56 11 00
56 02 09
55 57 23
55 46 00
55 37 00
55 20 06
54 58 10
55 00 30
54 55 07
54 41 51
54 07 00
53 39 00
53 34 45
52 29 14
52 05 00
51 56 05
51 26 02
51 23 18
51 33 24
51 31 00
51 27 41
51 39 10
51 35 30
51 46 14
51 56 00
51 53 08
52 07 15
52 04 30
52 13 46
52 16 14
52 39 00
52 40 04
52 33 38
Long. W.
4 49 28
5 07 09
4 17 39
5 48 00
6 30 46
5 28 20
7 06 32
7 39 09
6 38 28
6 22 10
6 16 01
4 59 41
3 22 25
2 57 33
2 22 25
2 22 45
1 36 30
1 16 20
1 16 02
1 08 41
1 29 50
0 47 30
2 55 25
46 30
46 22
04 06
44 53
23 06
33 22
08 05
10 54
59 00
39 00
32 00
21 30
26 00
21 30
10 19
3
1
2
2
2
2
3
3
1
1
1
1
1
1
1
0 05 00
0 12 00
Long. E.
0 07 10
1 45 24
1 34 30
1 19 10
Long. W
9 29 03
9 36 25
9 32 44
9 10 20
9 48 19
9 44 49
10 18 03
10 32 45
10 19 16
10 23 17
10 15 30
10 40 00
10 21 40
9 52 53
9 01 18
8 37 23
9 55 54
Lun. Int.
H. W.
h. m.
11 35
0 55
10 20
5 10
"5*35'
9 57
10 50
9 35
10 20
9 30
10 00
0 24
0 50
1 56
1 58
2 08
3 11
3 12
3 21
4 20
5 16
9 47
11 05
11 56
3 50
4 10
3 30
3 40
3 40
3 50
6 00
L. W.
h. VI.
5 23
7 08
4 08
11 22
"ii'47"
"6'22'
3 44
4 37
3 22
4 17
3 17
3 47
6 36
7 02
8 08
8 11
8 28
9 31
9 32
9 43
10 36
11 29
3 35
4 53
5 44
10 03
10 23
Range.
Spg.
ft.
8.8
11.2
4.0
12.8
ii.'i'
13.' 4"
5.0
5.2
6.0
'6.4"
11.2
11.7
15.5
16.5
15.0
14.8
14.5
14.2
15.8
18.5
6.2
7.8
11.2
10.6
9 43
10.8
9 53
10.7
9 53
10 03
10.7
12.3
0 13
18.7
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
[Page 217
Place.
Eeragh Island : Light-house
Arran Island: Light-house
Gal way : Mutton I. light
Golam Head: Tower
Slyne Head : N. light-house
Clifden Bay: Gortrumnagh Hill
TuUy Mountain: Ordnance survey station
Inishboffin : Lyon Head light
Inishturk Island : Tower
Clew Bay: Inishgort light
Newport: Church
Clare Island: Light-house
Blacksod Point: Light-house
Eagle Island: W. light-house
Broadhaven : Guba Cashel light
Dounpatrick Head: Ordnance survey
station
Anghris Head: Ordnance survey station.
Knocknarea: Tumulus
Sligo Bay: Black Rock light
Knocklane: Ordnance survey station
Killvbegs (Donegal Bay): St. Johns Pt.
light.- .....:
Rathlin O'Birne Islet: Li^ht-house
Aran Island : Rinrawros light
Bloody Foreland: Ordnance survey sta-
tion
Tory Island: Light-house
Horn Head: Ordnance survey station . . .
Melmore Head : Tower
Fanad Point: Light-house
Glashedy Island: Ordnance survey station
Malin Head : Tower
Inishtrahull : Light-house
Inishowen Head : E. light-house
Moville: New Pier
Londonderry: Cathedral
Scalp Mountain : Ordnance survey station
Benbane Head : Summit
Rathlin Island: Altacarry light-house...
Maiden Rocks: W. light-house
Lough Larne: Farres Pt. light-house
Belfast Bay : Light, east side
Mew Islands: Light-house
Donaghadee: Light-house
South Rock : Light vessel
Dundrum Bay: St. John Pt. light
Carlingford Lough: Haulbowline Rk. It. .
Drofiheda: Light-house
Rockabill : Light-house
Howth Peninsula: Bailey light
Dublin : Observatory
N. wall light.,
Poolbeg: Light-house
Kingstown : IC. pier light
Killiney Hill: Mapas obelisk
Bray Head: Ordnance survey station ...
Wicklow : Upper light
Tara Hill: Summit
Black Stairs Mountain : Ordnance survey
station
Tory Hill: Ordnance survey station
Wexford : College
Forth Mount: Ordnance survey station. .
Tuskar Rock : Light-house
Great Saltee: S. end
Waterford : Hoop Pt. light
53 08 55
53 07 38
53 15 13
53 13 46
53 23 58
53 29 47
53 35 00
53 36 40
53 42 27
53 49 34
53 53 06
53 49 30
54 05 45
54 17 00
54 16 00
54 19 36
54 16 33
54 15 30
54 18 00
54 20 50
54 34 08
54 39 47
55 00 52
55 08 13
55 16 26
55 12 31
55 15 14
55 16 33
55 19 07
55 22 50
55 25 55
55 13 38
55 10 20
54 59 40
55 05 23
55 15 03
55 18 05
54 55 47
54 51 07
54 40 20
54 41 50
54 38 45
54 24 04
54 13 30
54 01 10
53 43 00
53 35 47
53 21 40
53 23 13
53 20 47
53 20 30
53 18 10
53 15 52
53 10 39
52 57 54
52 41 55
52 32 55
52 20 53
52 20 04
52 18 57
52 12 09
52 06 41
52 07 25
Long. W.
9 51 30
9 42 06
9 03 10
9 46 03
10 14 01
10 03 54
10 00 15
10 09 40
10 06 41
9 40 12
9 32 56
9 59 00
10 03 34
10 05 31
9 53 00
9 20 41
8 46 02
8 34 25
8 37 00
8 40 14
8 27 33
8 49 52
8 33 48
8 15 38
8 15 00
7 57 15
47 12
37 53
23 51
22 22
13 37
55 38
7 02 20
7 19 25
7 21 51
6 28 45
6 10 45
44 18
47 21
49 30
31 30
32 01
22 20
39 30
6 04 45
6 15 00
6 00 20
6 03 06
6 20 30
6 13 33
6 09 00
6 07 30
6 06 37
6 04 55
6 00 08
6 13 01
6 48 17
7 07 31
6 28 15
6 33 41
6 12 35
6 37 15
6 55 53
Lun. Int.
Range.
H. W.
h. m.
4 15
4 19
4 16
4 20
4 50
5 03
5 28
6 65
7 48
10 30
10 42
"ii"66'
10 45
10 45
10 55
11 00
10 52
10 30
10 10
7 05
5 30
Spg.
h. m.
10 28
10 19
13.4
15.1
10 29
13.2
10 33
12.1
11 03
10.4
5 10 ! 11 23
11.4
11 16
11.2
11 41
11.6
0 43
1 35
7.5
8.0
4 18
4 06
"4'48'
9.3
ii.'i'
4 33
4 33
15.8
11.6
4 43
12.7
4 48
4 27
13.0
10.9
4 18
3 58
11.8
8.7
0 53
4.9
11 43
'ii'is'
12.3
Neap.
ft.
5.7
6.4
5.2
4.5
5.3
4.8
5.3
3.4
3.6
4.5
"6."3
"7.'4
9.2
6.8
"7.' 5
7.6
6.4
6.9
5.1
2.9
5.1
6.' 2
Page 218] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
Place.
Waterford: Cath^ral
Great Newton Head: Metal Man Tower.
Dungarvan: Ballinacourty light
Knockmealdown Mount: Ordnance sur-
vey station
Helvick Head: Ordnance survey station.
Mine Head : Light-house
Youghal: Light-liouse
Capel Island : Tower
Ballycottin : Light-house
Cork Harbor: Haulbowline Coal Wharf.
Queenstown : Roches Pt. light
Kinsale: Light-house, S. pt
Seven Heads: Tower
Galley Head : Light on summit
Stag Rocks : Largest
Alderney Harbor: Old pier light
St. Heliers: Light on Victoria Pier
Lat. N.
52 15 33
52 08 13
52 04 27
52 13 39
52 03 00
51 59 33
51 56 34
51 52 54
51 49 30
51 50 33
51 47 33
51 36 11
51 34 14
51 31 50
51 28 05
49 43 00
49 10 29
Vardo: Fortress 70
Vadso : Light-house 70
North Cape : Extreme ; 71
Fruholm : Light-house 71
Hammerfest : Light-house 70
Tromso: Observatory ] 69
Hekkingen: Light-house 69
Andenes: Light-house 69
Lodingen (Hjertholm): Light-house 68
Lofoten Island: Skraaven I. light 68
Glopen light 67
Grvto : Light-house 67
Stot: Light-house 66
Tra?nen: Soe Islet light 66
Bronnosnnd: Light-house 65
Villa: Light-house 64
Halten Island : Light-house 64
Koppem '63
Agdenes: Light-house 63
Trondheini: Mumkholmen flagstaff ■. 63
Grip: Church :.' 63
Christiansund : Storvaden 63
Freikallen • 63
Hestskjaer: Light-house 63
Steinshesten 62
62
62
62
^ratenen : Light-house
Svinoen Islet
Hjcerringa Mountain : Summit
Hornelen Mountain: Summit 61
Batalden Island : Store 61
Kinnsund : Light-house 61
Alden 61
Helliso: Light-house 60
Bergen : Cathedral 60
Lorstakken Mountain : Summit 60
Marstenen Islet: Light-house 60
Furen Islet 59
Ulsire: Light-house 59
Hvidingso : Light-house I 59
Port Stavanger : Light-house ' 58
Obristadbrci'kke: Light-house .58
Synesvarde Mountain : Summit j 58
Kompas Mountain: Summit.
Lister: Light-house
Lindesnes : Light-house
Ryvingen Island: Light-house..
Christianssand: Odderoen light.
22 00
04 00
11 00
06 00
40 15
39 12
36 05
19 30
24 40
09 20
53 15
23 15
56 35
25 50
28 40
32 55
10 25
48 25
38 45
27 04
13 11
07 01
03 04
05 00
58 49
48 20
19 38
11 12
51 21
38 40
33 35
19 16
45 05
23 37
21 39
07 50
57 44
18 20
03 10
58 30
39 25
36 56
25 51
06 25
58 55
58 00
07 50
Long. W.
7 06 24
7 10 15
7 33 05
7 54 54
7 32 39
7 35 08
7 50 34
7 51 10
7 59 00
8 18 20
8 15 14
8 31 58
8 42 51
8 57 10
9 13 27
2 12 00
2 06 44
Long.
31 07
29 45
25 40
23 59
23 40
18 57
17 50
16 08
16 02
14 40
13 04
13 52
13 28
11 59
12 13
10 42
9 24
9 44
9 45
10 23
7 36
7 43
7 46
7 29
7 12
6 36
5 16
5 07
5 20
5 19
5 01
5 03
4 52
5 24
5 45
5 33
5 49
5 58
6 34
7 03
7 29
8 00
Lun. Int.
Range.
H.W.
h. m.
5 00
5 02
4 40
4 33
4 30
4 20
6 21
6 09
5 40
2 20
1 35
0 42
11 35
11 18
11 00
lO 15
9 43
4 16
L.W.
Spg. Keap.
h. m.
11 13
12.4
11 15
12.6
10 53
11.8
10 59
10 43
10 33
11.6
11.4
10.7
0 16
0 00
11 57
17.2
3L2
9.0
8 40
7 48
8.3
7.8
6 55
7.0
5 23
6.9
5 04
8.4
4 48
5.0
3 55
4.1
3 40
6.2
6.3
5.9
5.8
5.7
5.3
7.6
13.6
5.1
4.7
4.4
4.0
3.3
4.1
2.9
2.1
0.8
10 15
1.1
0.5
APPENDIX IV. [Page 219
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF ETJK.OPE— Continued.
o
Place.
Lat. N.
Long. E.
Lun. Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
i
9
1
Okso: Light-house
O 1 II
58 04 15
58 15 02
58 24 40
58 51 50
58 59 25
59 00 01
58 59 34
58 58 05
59 01 35
59 10 30
59 23 10
59 25 34
59 29 23
59 39 52
59 40 21
59 54 44
59 09 00
59 07 08
58 59 45
58 54 05
58 56 24
58 54 12
58 32 45
58 20 12
57 53 49
57 40 58
57 18 15
57 06 26
56 54 08
56 40 21
56 14 40
56 18 06
56 02 37
55 52 00
55 36 47
55 23 00
55 22 00
55 25 42
55 22 58
56 00 54
56 10 04
56 09 45
56 11 50
56 55 18
57 26 29
57 57 24
57 45 38
58 08 52
58 17 55
58 44 26
59 20 35
59 51 31
59 45 24
59 45 15
60 10 35-
60 15 19
60 20 26
60 22 15
60 22 26
60 31 41
60 40 29
60 43 48
60 55 57
61 18 22
61 32 54
o / //
8 03 30
8 31 36
8 47 55
9 36 15
9 45 50
9 45 14
10 03 28
10 09 26
10 31 55
10 36 25
10 32 45
10 29 52
10 19 15
10 38 08
10 36 55
10 43 35
10 50 15
11 24 09
10 47 20
11 00 45
11 10 28
11 00 36
11 02 16
11 13 24
11 28 04
11 53 54
11 54 16
12 14 32
12 29 48
12 51 38
12 51 47
12 27 11
12 41«30
12 49 48
12 59 49
12 49 02
h. in.
h. m.
/'.
St.
Hamberg: Mill
Arendal Inlet: Inner Torungerne light..
Jomf ruland : Light-house
Langotangen : Light-house
4 17
10 10
LO
0.7
Langesund: Church
Frederiksvsern : Lookout tower
4,34
10 00
1.3
1.0
Svenor: Light-house
Foerder Islet: Light-house.
Fulehuk : Light-house
Basto : Light-house
'
Horten : Church
Holmestrand : Church
Drobak : Church
Oscarsberg: Fort flagstaff . .
Christiania: Observatory
5 22
10 37
1.2
0.9
Strom tangen (Torgauten): Light-house.
Fredriksten : Fort clock tower
Torbjornskjter: Light-house
Koster; Light-house
Stromstad : Steeple
Nord Koster Islands : Light-house
Wadero Island: Light-house .
Hollo Island: Light-house
Paternoster Rocks: Light-house
Gottenburg: Signal station
Nidingen Islet: Light-house
Warberg: Castle tower
Falkenberg: Church
Halmstad : Palace
Engelholm : Church
Kullen Point; Light-house
Helsingborg: Light-house
Landskrona : Light-house
Malmo: Light-house
Falsterbo: Light-house
Trelleborg: Light-house
13 09 20
13 49 38
14 n 10
14 50 57
14 52 02
15 36 05
16 24 04
Ystad : Light-house
Sandhammaren : Light-house ^..
Hano Island : Light-house ;..
Karlshamn : Light-house
Karlskrona: Stum holm Tower
Oland Island : Light on S. pt
Gottland Island: Hoburg light, S. pt
Ostergarns light
Faro Island: Holmadden light
Sparo Vestervik : Granso light
18 11 06
18 59 27
19 22 36
16 40 36
16 59 22
16 11 28
17 52 09
18 03 30
17 37 39
18 41 34
19 24 34
18 49 49
18 22 36
18 26 33
18 24 21
18 09 49
18 22 38
17 08 29
17 33 50
17 02 57
17 04 18
17 01 51
Haradsskar Islet: Light-house
Norrkopings Inlopp : Light-house
Landsort: Light-house
Stockholm : Observatory
Upsala: Observatory
Norrtelge: Inn
Soderarm : Light-house
Svartklubben : Light-house
Osthammar : Church
Oregrund : Clock tower
Djursten : Light-house
Forsmark: Church
Orskar Rock : Light-house
Gefle: Church
Eggegrund Islet: Light-house
Hamrange: Church
Soderhamm : Court-house
Enanger: Church
::::::;::::: i
1
Page 220]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF ETTROPE— Continued.
Place.
Hudiksvalls : Coyrt-house
Gnarp: Church
Sundsvall: Church
Lungo: Light-house
Skags Head : Light-house
Holmogadd : Light-house
Umea: Bredekar Light
Bjuroklubb: Light-house
Pitea
Rodkallen : Light-house
Maloren : Light-house
Tomea: Light-house
Uleaborg: Karlo I. light
Ulko Kalla Rock: Light-house
Norrsher Islet: Kvarken light
Kaske: Shelgrund I. light
Bierheborg: Sebsher light
Nuistad: Ensher light
Abo: Observatory
Aland Island; Shelsher light
Ekkere light
Logsher light
Bogsher: Beacon
Ute Islet: Light-house
Gauge: Gange I. light
Rensher: Light-house
Helsingfors: Observatory
8oder Skars: Light-house
Kalboden Island: Light vessel
Rodsher Island: Light-house
Hogland Island: Lower light
Upper light
Sommer Island : Light-house ,.
Vieborg Bay: Nelva I. light
Stirsudden : Light-house
Kronstadt: Light on Frederikstadt t
tion
Cathedral
St. Petersburg: Observatory
Pulkowa : Observatory
Peterhof : Pier-head light
Oranienbaum: Light-house
Seskar Islet: Light-house
Narva: Light S. pt. of entrance
Stensher Rock: Light-house
Ekholm Islet: Light-house
Koksher: Light-house
Revel: Light N. end of W. mole . . .
Cathedral
Nargen Island : Light-house
Surop: W. light
Baltic Port: Light-house
Odenskholm Island: Light-house
Takhkona Point: Light-house
Dago Island : Dagerort light
Filzand Island: Light-house
Svalferort Tzerel : Light-house
Kuino: Light-house
Pernau: Light at S. entrance
Riga: Light on Fort Kametskoi dike
Cathedral
Runo Island: Light-house
Domesnes : Light-house
Windau : Light on S. jetty
Libau: Light at entrance of port
Lat. N.
61 43 57
62 02 51
62 23 30
62 38 35
63 11 55
63 35 34
63 39 33
64 28 50
65 19 10
65 18 53
65 31 30
65
65
64
63
62
61
60
60
60
60
59
59
59
59
59
60
60
59
59
60
60
60
60
60
59
59
59
59
59
59
60
59
59
59
59
59
59
59
59
59
59
59
58
58
57
58
58
57
56
57
57
57
56
48 30
02 20
20 05
14 08
20 06
28 29
43 10
26 57
24 45
13 20
50 50
31 11
46 30
46 00
56 10
09 43
06 40
58 45
58 08
00 40
06 22
12 31
14 43
11 05
58 14
59 44
56 30
46 19
53 26
55 40
02 08
28 04
49 10
41 06
42 00
27 05
26 28
36 22
27 55
21 30
18 06
05 25
55 02
23 02
54 37
05 50
23 10
03 28
56 36
48 02
48 10
24 00
31 01
Long. E.
17 07 37
17 16 22
17 19 05
18 05 05
19 02 50
20 45 35
20 18 35
21 34 45
21 30 00
22 21 55
23 34 00
24 12 00
24 34 00
23 27 00
20 37 40
21 11 24
21 22 34
21 01 00
22 17 03
19 34 00
19 31 20
19 54 05
20 25 50
21 22 00
22 58 08
24 24 43
24 57 17
25 25 51
25 37 30
26 41 05
27 01 40
26 58 44
27 33 46
27 58 36
29 03 01
29 47 12
29 46 07
30 19 22
30 19 40
29 54 54
29 46 38
28 23 01
28 03 31
26 23 00
25 48 58
25 02 37
24 46 10
24 44 45
24 31 57
24 24 05
24 04 30
23 23 15
22 36 15
22 11 36
21 49 56
22 04 15
23 59 34
24 49 25
24 00 59
24 08 25
23 15 00
22 39 15
21 34 00
20 59 40
Lun. Int.
Range.
L. W.
h. m.
Spg. Neap.
ft.
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATIiANTIC COAST OF EUROPE— Continued.
[Page 221
Memel: Light-house
Heiligen Creutz: Church tower
Brusterort : Light-house
Pillau : Light-house
Fischausen: City-hall tower
Konigsberg: Observatory
Tolkemit: Church tower
Elbing: Church tower
Tiegenort : Church tower
Danzig: Observatory
Neufahrwasser light
Weichselmunde: Fortress tower
Putziger Heisternest: Church tower
Oxhoft: Light-house
Hela: Light-house
Rixhoft: Light-house
Leba: Church tower
Stopelmunde: Church
Jershoft: Light-house
Rugenwalde: St. Mary's Church
Coslin: St. Mary's Church
Funkenhagen : Light-house
Colberg: St. Marv's Church
Gross-Horst : Light-house
Cammin: Cathedral tower
Wollin: Church tower
Stettin; N. Castle tower
Swinemunde : Light-house
Streckelsberg: Survey station near beacon
Usedom: Church tower
Lassau: Church tower
Wolgast: Church tower
Grieiswald: St. Nicholas Church
Griefswalder Oie : Light-house
Granitz: Castle tower
Bergen : Church tower
Arkona: Light-house
Stralsund: St. Mary's Church
Darsserort: Light-house
Wustrow : Church
Ribnitz: Church tower
Wamemunde: Church
Rostock : St. Jacob' s Church
Diedrichshagen : Survey station
Basdorf : Survey station
Wismar: St. Nicholas Church
Hohenschonberg: Survey station
Travemunde: Light-house
Burg: Church tower
Manenleuchte: Light-house
Petersdorf : Church tower
Hessenstein : Flagstaff of lookout tower .
Schonberg: Church
Bulk : Light-house
Kiel : Observatory
Eckemforde : Church
Schleswig: Cathedral
Kappeln: Church
Flensberg: Church
Duppel: Survey station
Schleimunde: Light-house
Augustenburg: Church
Hugeberg : Survey station
Apenrade: Church
Skoorgaarde : Survey station
Ballum : Church
List: E. light-house
Lat. N.
55 43 45
54 53 47
54 57 40
54 38 25
54 43 49
54 42 51
54 19 19
54 09 44
54 16 30
54 21 18
54 24 28
54 23 51
54 12 16
54 33 09
54 36 06
54 49 55
54 45 29
54 35 16
54 32 29
54 25 27
54 11 28
54 14 40
51 10 40
54 05 47
53 58 29
53 50 41
53 25 41
53 55 03
54 03 08
53 52 17
53 56 59
54 03 18
54 05 49
54 15 02
54 22 56
54 25 08
54 40 53
54 18 42
54 28 28
54 20 47
54 14 42
54 10 42
54 05 27
54 06 32
54 08 00
53 53 50
53 58 54
53 57 44
54 26 16
54 29 43
54 28 54
54 19 47
54 23 52
54 27 25
54 20 30
54 28 25
54 80 55
54 39 48
54 47 05
54 54 28
54 40 23
54 56 48
54 58 05
55 02 46
55 03 52
55 05 31
55 03 04
Long. E.
Lun. Int.
Range.
H. W.
21 06
20 01
19 59
19 53
20 00
20 29
19 31
19 23
19 08
18 39
18 39
18 41
18 40
18 33
18 49
18 20
17 33
16 51
16 32
16 24
16 11
15 52
15 34
15 04
14 46
14 37
14 33
14 17
14 01
13 55
13 51
13 46
13 22
13 55
13 37
13 26
13 26
13 05
12 30
12 24
12 26
12 05
12 08
11 46
11 41
11 28
11 05
10 52
11 11
11 14
11 04
10 32
10 22
10 12
10 08
9 50
9 34
9 56
9 26
9 45
10 02
9 52
9 58
9 25
9 23
8 39
8 26
h. m.
0 20
L. W.
Spg.
h. m.
6 33
5.2
Page 222]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
Place.
Keitum: Church
Fohr: St. Nicholaf Church
Ualgenberg: Survey station
Husum : Church '...
Tonning: Church
Busuin: Church
Helgoland : Ijight-house
Scharhorn : Beacon
Neuwerk : Li^ht-house
Cux haven : Light-house
Stade: Church steeple
Steinkirchen : Church
Altona : Observatory
Hamburg: Observatory
Berlin: Observatory
Harburg: Light-house
Hohe Weg: Light-house
Langwarden : Church
Bremerhaven: New harbor light.
Minsener Sand: Light vessel
Schillighorn: Light-house
Wilhelmshaven: Observatory
Wangeroog: Light-house
Spikeroog: Church
Langeoog: Belvedere
Balstrum : Church
Norderney: Light-house
Juist: Church
Emden: City Hall tower
Lat. N.
Falster: Gjedser light
Moen Island : Stege Church spire
Moen light, SE.pt
Prceste : Church spire
Kjorge: Church tower
Amager Island: Holloenderby Ch. spire. .
Nordse Rase light
Copenhagen: New observatory
Bornholm: Ronne light
Christianso Island: Great tower
Kronberg: High spire
Nakkehooed : Upper light
Hesselo Island : Light-house
Anholt Island : Light-house
Spodsbjerg: Light-house
Roeskilde: Cathedral
Nykjobing: Church tower
Oddensby : Church tower
Sejro Island : Sejro Point light
Kallundborg: Church
Omo Island: Church
Vordingborg: Waldeniar's tower
Veiro Island: Light-house
Langeland Island: Fakkebjerg light
JEto Island : Church spire
Lyo Island: Church tower
Assens: Church tower
Baago Island : Light-house
Kolding: Castle tower
Bogense: Church spire
Nyborg: Church spire
Turo Island : Church spire
Svendborg: Frue Church
Endelave Island: Church tower
Samso Island : Koldby Church tower
Horsens : Frelser Church spire
54 54 13
54 41 51
54 41 21
54 28 43
54 19 08
54 07 52
54 10 57
53 57 15
53 55 01
53 52 25
53 36 12
53 33 43
53 32 45
53 33 07
52 30 17
53 28 30
53 42 50
53 36 20
53 32 52
53 46 57
53 42 21
53 31 52
53 47 25
53 46 19
53 45 06
53 43 46
53 42 39
53 40 45
53 22 06
54 33 50
54 59 03
54 56 46
55 07 24
55 29 44
55 35 45
55 38 10
55 41 14
55 05 40
55 19 19
56 02 20
56 07 10
56 11 50
56 44 16
55 58 36
55 38 34
55 55 30
55 57 52
55 55 09
55 40 50
55 09 48
55 00 26
55 02 19
54 44 23
54 51 14
55 02 34
55 16 09
55 17 44
55 29 31
55 34 03
55 18 41
55 03 00
55 03 37
55 45 32
55 48 02
55 51 44
Long. E.
8 22 03
8 33 13
8 33 58
9 03 21
8 56 38
8 51 53
7 53 11
8 24 35
8 29 58
8 42 43
9 28 48
9 36 40
9 56 35
9 58 25
13 23 44
9 59 37
8 14 48
8 18 30
8 34 25
8 04 47
8 01 43
•8 08 48
54 09
41 45
35 41
22 03
13 58
6 59 53
7 12 25
n 58 03
12 17 16
12 32 40
12 03 07
12 07 36
12 38 24
12 41 26
12 34 47
14 42 00
15 11 39
12 32 02
12 20 50
11 42 50
11 39 15
11 51 36
12 05 02
11 40 29
11 24 06
11 05 07
11 05 04
11 09 32
11 54 59
11 22 23
10 42 13
10 24 11
10 09 16
9 53 50
9 48 09
9 28 40
10 05 29
10 47 47
10 40 02
10 36 48
10 16 20
10 33 37
9 51 19
Lun. Int.
Range.
H. W.
h. m.
1 35
2 10
1 45
1 11
11 29
0 39
4 00
'5"66'
L. W.
Spg.
h. m.
7 47
8 23
7 57
7 24
5 17
10.8
11.0
11.7
8.1
6 51
10.1
10 13
"ii'i2'
8.5
'e.'i'
0 25
6 38
10.1
0 54 i 7 07
0 10 ! 6 23
10.4
9.5
0 04
11 27
11 05
"'6"24"
6 17
5 15
13.2
8.0
4 53
7.3
6 36
9 33
3 21
0.6
Neap.
ft.
4.5
6.2
6.4
6.8
4.7
5.8
4.9
3.5
5.7
5.8
5.3
7.4
4.5
4.1
5.0
0.3
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF ETJROPE— Continued.
[Page 223
Lat. N.
Tuno Island : Light-house
Samsoe Island: Nordby Church tower .
Aarhns: Cathedral spire
Hjelm Islet: Light-house
Fornpes : Light-Jiouse
Hals: Church tower
Aalborg: St. Rudolph's Church
Cape Skaw, or Skagen: Old light-house
Hirtshals: Light-house .'
Haustholm : Light-house
Boobjerg : Light-house
Ringkjobing: Church spire
Loune: Church tower
Blaabjerg: Summit, 100 ft
Guldager: Church
Fano Island : Nordby Church
Mano Island: Church spire
Niewe Diep: Time-ball station
Amsterdam : W. church tower
Utrecht: Observatory
Leyden : Observatory
The Hague: Church tower
Scheveningen : Light-house
Brielle: Light-house
Rotterdam : Time-ball station
Hellevoetsluis: Time- ball station ,
Willemstadt: Light-house
Goedereede: Light on church tower
Flushing: Time-ball station
Light, Westhaven bastion . '.
Brussels: Observatory ,
Antwerp: Observatory
Notre Dame Cathedral .
Blankenberghe: Fort light-house .
Ostend : Light- house
Church tower
Nieuport: Templars tower
Paris: Observatory
Dunkerque : Tower
Gravelines: Light on N. breakwater . . .
Calais: Light on old fort
Cape Gris Nez : Light-house
Boulogne, C. Alprech: Light-house
Abbeville: Tower
Cay eux : Light-house
Dieppe: W. jetty light
Ailly Point: Light-house
St. Valery en Caux : Light on W. break-
water
Fecamp: N. jetty light
Cape La Heve: S. light
Havre: S. jetty light
Honfleur: Hospital jetty light
Caen : Church tower
Port Corseulles: W. jetty light
Point De Ver: Light-house
Cape La Hougue: Light-house
Cape Bartieur: Light-house
Cherbourg: Light, W. head of break-
water
Naval Observatory
Cape La Hague: Light-house
Casquets Rocks: Light on NW. rock . . .
55 56 58
55 57 06
56 09 26
56 08 00
56 26 36
56 59 54
57 02 54
57 43 46
57 35 06
57 06 50
56 30 48
56 05 27
55 47 17
55 44 50
55 31 52
55 26 26
55 16 11
52 57 50
52 22 30
52 05 10
52 09 20
52 04 40
52 06 16
51 54 29
51 54 30
51 49 19
51 41 48
51 49 08
51 26 33
51 26 24
50 51 11
51 12 28
51 13 17
51 18 47
51 14 13
51 13 50
51 07 53
48 50 11
51 02 09
51 00 18
50 57 45
50 52 10
50 41 57
50 07 05
50 11 42
49 56 06
49 55 04
49 52 28
49 46 05
49 30 04
49 29 01
49 25 32
49 11 14
49 20 18
49 20 28
49 34 19
49 41 50
49 40 29
49 38 54
49 43 22
49 43 17
Long. E.
10 26 51
10 33 00
10 12 50
10 48 32
10 57 40
10 18 53
9 55 22
10 36 38
9 56 44
8 36 10
8 07 23
8 14 52
8 14 36
8 14 43
8 24 12
8 24 03
8 32 38
46 36
53 04
07 50
29 03
18 30
15 10
10 45
28 50
07 40
26 26
58 35
35 48
34 32
4 22 18
4 24 44
4 24 12
3 06 54
2 55 51
2 55 22
2 45 34
2 20 14
2 22 31
2 06 34
1 51 07
1 35 02
1 33 47
49 56
30 46
05 01
0 57 35
0 42 34
0 22 12
0 04 08
0 06 22
0 13 43
Long. W.
0 21 10
0 27 24
0 31 08
1 16 21
1 15 56
1 43 44
1 38 08
1 57 15
2 22 41
Lun. Int.
Range.
H. W.
5 46
4 18
2 35
2 35
2 34
7 17
2 50
3 35
2 20
3 20
0 44
4 15
0 05
0 02
0 10
11 58
11 59
11 39
11 17
11 18
10 54
10 29
10 06
9 03
8 13
8 14
7 30
6 20
Spg. I Neap.
h. m.
ft-
11 58
10 30
1.0
1.2
8 47 2. 1
47 ! 4.5
46 i 4.7
1 05 I 3. 9
9 02
9 47
8 32
9 32
6 56
10 27
6 17
6 32
6 22
5 58
6 16
6 13
5 51
5 52
5 48
5 33
5 02
4 14
2 45
2 37
1 44
0 15
4.8
6.7
5.2
14.7
14.8
12.5
16.1
15.7
16.8
19.0
21.0
21.5
25.2
27.3
26.8
23.3
22.5
18.5
17.0
17.6
15.5
ft.
0.5
0.7
1.2
2.6
2.7
2.0
2.5
3.5
2.8
5.2
5.7
i.i
8.4
8.5
9.6
10.7
11.0
12.8
13.3
13.1
11.4
11.0
8.2
7.5
6.9
Page 224J
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
Place.
Port St. Peter, Guernsey: Light on Cas-
tle Coonet Breakwater
Douvres Rocks: Light-house
Cape Carteret: Light-house
Coutances: Cathedral tower
Granville : Light-house
Chausey Is. : Light on SE. end of large id
St. Malo: Roehebourne light
Cape Frehel: Light-house
Heau de Brehat: Light-house
Morlaix, He Noire: Light-house
De Bas Islet: Light-house
Abervrach : Light on Vrach Islet
Usiiant: Stiff Point light
Brest: Observatory
Brest (approach ) : Quelern light
De Sein Islet: Light-house
Bee du Raz: Light-house
Audierne: Pier-head light
Penmarch Rocks: Light-house
Glenan Islands: Light, Penfret I
De Groix Island: Light-house
Lorient: Church-tower light
Belle Isle: Light-house
Port Haliguen : Light on N. jetty
Haedic Island : Light-house
Port Navalo: Light-house
Vannes: St. Pierre Church
Le Four Rock : Light-house
Croisic: End of breakwater
Guerande: Steeple
Port St. Nazaire: Light-house
Paimbffiuf : Steeple
Nantes : Cathedral
Noir Moutier Island: Light-house
Le Pilier Island : Light-house
D'Yeu Island: Light-house
La Chaume: Light-house
Point de Grouin du Cou: Light-house..
R6 Island: Light, NW.pt
Rochelle: E. Quay light
Aix Island : Light-house
Rochefort: Hospital
Oleron Island: Light NW. pt
Point de la Coubre: Light-house
Point Cordouan: Light-house
Point de Grave: Light-house
Bordeaux: St. Andr6
Bayonne: Cathedral
Biarritz : Light-house
St. Jean de Luz; St. Barbe Point light .
Fuenterrabia: Light on Cape Higuera..
Port Pasages : Light at entrance
San Sebastian: Monte Igueldo light
Bilbao: Light on Galea Castle
Castro Urdiales: Santa Ana Castle light
Santofia: Pescador Point light
Santander: Cape Mayor light
San Martin de la Arena: Light-house. . .
San Vincent de la Barquera: End of new
mole
Rivadesella: Mount Somos light
Gijon: Santa Catalina light
Aviles: Light-house
Rivadeo: Light-house
Estaca Point: Light-house
Lat. N.
49 27 13
49 06 28
49 22 27
49 02 54
48 50 07
48 52 13
48 40 18
48 41 05
48 54 33
48 40 23
48 44 45
48 36 57
48 28 31
48 23 32
48 19 10
48 02 40
48 02 28
48 00 47
47 47 52
47 43 17
47 38 51
47 44 53
47 18 42
47 29 10
47 19 18
47 32 53
47 39 30
47 17 53
47 18 30
47 19 44
47 16 18
47 17 17
47 13 08
47 00 41
47 02 35
46 43 04
46 29 38
46 20 41
46 14 40
46 09 25
46 00 36
45 56 37
46 02 49
45 41 39
45 35 14
45 34 10
44 50 19
43 29 29
43 29 38
43 23 58
43 23 30
43 20 05
43 19 22
43 22 36
43 24 20
43 28 36
43 29 30
43 26 50
43 23 35
43 31 00
43 32 48
43 38 05
43 34 40
43 47 20
Long. W.
2 31 31
2 48 49
1 48 25
1 26 39
1 36 46
1 49 20
58 41
19 08
05 11
52 33
01 38
34 34
03 26
29 36
34 28
52 03
45 25
32 50
22 30
57 15
30 35
21 31
13 38
06 09
50 07
55 08
45 28
38 05
31 25
25 48
11 50
02 09
32 59
13 16
21 37
22 56
47 45
27 49
33 40
1 08 57
1 10 40
0 57 50
1 24 37
1 15 16
1 10 24
1 04 27
0 34 42
1 28 43
1 33 16
1 39 53
Lun. Int.
Range.
47 30
56 05
01 40
04 06
16 10
28 06
47 40
01 00
24 55
07 10
40 11
56 00
03 00
42 00
H. w.
h. m.
6 12
6 07
5 50
5 55
5 43
5 35
5 00
4 35
4 00
3 35
3 23
3 25
3 04
3 05
3 00
3 09
3 25
3 35
3 20
3 45
5 47
3 25
3 35
4 18
5 50
■3 05
3 18
3 20
3 27
3 27
3 45
3 35
6 30
3 07
3 00
2 50
2 45
2 45
L. W.
h. TO.
0 07
ft.
26.0
0 15
30.8
0 09
0 04
0 04
36.7
34.7
36.0
12 00
11 25
11 00
10 25
10 00
9 45
30.4
23.1
22.0
20.6
18.9
19.5
9 53
17.2
9 31
9 34
9 27
11.1
13.3
13.0
9 36
9 50
9 58
9 46
10 08
12 11
13.8
16.6
16.9
16.7
16.6
15.8
9 47
16.7
9 56
10 39
12 28
9 26
16.6
17.0
16.5
16.7
9 40
9 44
14.7
12.7
9 22
9 22
9 55
16.6
16.6
16.7
9 53
16.8
0 12
15.3
9 14
12.3
9 05
9 03
9 03
9 07
9 18
9 14
9 14
11.7
12.7
11.8
12.3
14.8
1L7
10.4
9 03
8 58
8 58
13.5
12.0
14.4
Neap.
ft.
11.5
13.5
16.0
15.2
15.7
13.3
10.6
10.1
9.5
8.7
9.0
5.1
6.1
6.0
6.3
7.7
7.9
7.7
7.7
7.4
7.7
7.7
7.9
7.7
7.7
6.8
5.9
7.7
7.7
7.7
7.8
7.1
5.8
5.5
5.9
5.5
5.7
6.9
5.5
4.9
6.3
4.9
3.9
APPENDIX IV. [Page 225
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUKOPE— Continued.
1
Place.
Lun. Int.
Range. 1
H. W. 1 L. W.
spg.
Neap.
1
©
s
<s
B
a.
Port Cedeira: Light-house
O / 1/
43 39 00
43 29 30
43 27 30
43 23 10
o / ri
8 05 30
8 13 29
8 20 20
8 24 26
h. VI.
2 43
2 44
h. m.
8 56
8 57
ft.
14.8
14.9
fl.
6.1
6.1
Ferrol: Old naval observatory
Priorino Chico light
Corufia: Hercules Tower light
2 43
2 42
8 56
8 55
14.8
10.0
6.1
4.6
Cape Finisterre: Light-house
42 52 45 9 15 28 1
Vigo" Cres I. light
42 12 30
41 09 10
40 10 47
39 24 49
39 21 00
38 46 49
38 42 31
38 29 15
37 01 20
37 07 48
36 58 23
37 11 00
37 15 08
36 43 58
36 27 40
36 31 30
36 10 50
35 59 53
36 07 19
36 07 10
36 06 25
8 54 00
8 40 35
8 54 15
9 30 29
9 22 30
9 29 46
9 11 10
8 56 00
8 58 00
8 39 53
7 51 48
7 24 00
6 57 12
6 26 30
6 12 20
6 19 00
6 02 08
5 36 31
5 26 12
5 21 17
Oporto : Light, N. S. de Luz
2 25
2 20
8 38
8 35
10.0
7.0
4.3
3.0
Cape Mondego : Light-house
Berlanga Island' Light-house
Peniche: Light-house
2 05
8 15
7.8
3.4
Cape Roca : Light-house
Lisbon : Royal Observatorv
2 20
2 10
8 05
8 20
11.1
11.6
4.8
5.0
Setubal: Light-house
Cape St Vincent: Light-house
Lagos : Church
1 55
8 08
13.0
5.6
Cape Sta. Maria: Light-house
Ayanionte ■ Lio'ht-house .... ...
Huelva* Plaza at head of mole
San Lucar: Chipiona light
1 15
7 28
12.3
5.6
Cadiz: Observatory^ of San Fernando
San Sebastian light
1 45
7 58
11.8
5.4
Cape Trafalgar: Light-house
Tarifa: Light-house.
1 32
7 52
5.6
2.6
Algeciras: Verde I. light
Gibraltar: Dockyard flagstaff
Europa Pt. light
5 20 42
1 35
7 55
3.7
1.7
COASTS OF THE MEDITEBBANEAN, ADBIATIC, AND BLACK SEAS.
B
SB
fa
Malaga: Light-house
36 42 39
36 50 12
36 42 57
37 33 28
37 35 50
37 33 22
37 34 38
38 12 30
4 24 38
2 27 50
2 11 12
1 15 12
0 59 09
0 57 58
0 50 20
0 .30 12
2 15
8 35
2.9
1.5
Almeria: Light-house
Cape de Gata: Light-house
Mazarron : Light-house
Cartagena : Arsenal gate
Esconibrera light
Porman : Light-house
Santa Pola Bay: Jjight-house
Alicante : N. mole light
38 20 12 ! 0 28 48
38 30 00 : 0 11 42
38 30 57 ; 0 10 06
38 33 30 1 0 04 02
Villajoyose: Light-house
Benidonne: Tower
Altea: Light-house
Calpe : Church tower
38 38 36
Long. E.
0 02 52
0 09 17
0 12 02
0 07 30
Long. W.
0 13 37
0 19 48
0 18 50
Long. E.
0 41 19
0 08 56
0 28 48
0 39 45
0 53 55
1 14 42
2 10 52
3 08 28
3 17 10
3 18 55
3 07 30
3 06 50
Morayva: Tower 38 40 51
Jarea: Cape San Antonio light 38 48 06
Denia: Mole-head light 38 51 00
Cape Cullera: Light-house
39 12 15
39 28 05
39 27 50
39 53 57
Valencia : Light-house
Mole-end light
5 00
11 30
1.5
0.8
Columbretes Islands: Light-house
Oropesa Cape: Light-house
40 04 53
40 27 48
40 33 30
40 43 10
Vinaroz : Mole-head light
Port Alfaques: Baila light
Cape Tortosa: Light-house
Tarragona: E. mole light
41 06 00
41 22 10
41 50 04
42 16 15
42 19 10
42 30 59
42 31 18
Barcelona: E. mole-head light
Palamos Bay: Molino Pt. light
Cadaques : Clock tower
Cape Creux : Light-house
Cape Bear: Light-house
Port Vendres: Fort Fanal light
22489—03-
-15
Page 226] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
Place.
Port Nouvelle: S. jetty light
Cette: Light, St. liiouis mole
Aigues Mortes: Espignette Pt. light.
Planier Rock : Light-house
Marseille: Janet Cliff light
New observatory
Ciotat: Berouard mole light
Toulon: St. Mandrien li^ht
Grand Riband Island : Light-house..
Cannes: Light-house
Antibes : Garoupe light
Nice: Light-house
Ville Franche: Mole-head light
Cape Ferret light . . .
Port Ibiza: Light-house
Cabrera Island : Light-house
Pi (Majorca) : Light-house
Port Mahon (Minorca): Light-house
Cape Spartivento: Light-house
Cape Sandalo: Light on San Pietro I
Porte Conte: Cape Caccia light ,
Port Torres: Light-house
Cape Testa: Light-house
Razzoli Island : Light-house
Caprera Island : Galera Pt ,
Cape Figari : Signal station
Cape Tavolara: Light-house
Cape Bellavista: Light-house
Cape Carbonera: Cavoli I. light
Cagliari; Light on mole
Bonifacio: Mount Pertusato light.
Ajaccio: Light-house
Corti: Church tower
Calvi: Light-house
Cape Corso: Giraglia I. light
Bastia: Light-house
Porto Vecchio: Chiape Pt. light ..
Cape Melle: Light-house
Genoa: San Benigno light
Spezzia: Fort Santa Maria light
Florence: Observatory
Leghorn (Livorno): Light on S. end of
curved breakwater
Capraia Island: Cape Ferrajone light
Elba Island, Porto Longone: Fort For-
cado light
Pianosa Island: Light on battery, W.
side of fort ,
Africa Rock : Light-house
Monte Christo Islet: Summit
Giglio Island, Cape Rosso: Light-house
Civita Vecchia: Light N. end of break-
water
Rome: Observatory
Gaeta: Orlando tower
Ponza Islet: Punto della Guardia light .
Naples: Observatory
Light on elbow of mole
Capri Island: Carena Pt. light
Lipari Island : Casa Bianca light
Ustica Island : NE. point light
Faro of Messina: Capo di Faro light
Milazzo: Light-house
Palermo: Observatory
Light on mole head
Trapani: Pal umbo Rock light
Lat. N.
43 00 47
43 23 50
43 29 17
43 11 57
43 20 43
43 18 22
43 10 21
43 05 10
43 01 01
43 32 51
43 33 61
43 41 32
43 41 58
43 40 30
38 54 10
39 06 34
39 33 00
39 51 53
38 52 34
39 08 44
40 33 50
40 50 25
41 14 36
41 18 24
41 14 15
40 59 52
40 54 55
39 55 45
39 05 15
39 12 35
41 22 10
41 52 50
42 18 14
42 35 10
43 01 45
42 41 47
41 35 45
43 57 17
44 24 15
44 04 00
43 46 04
43 32 33
43 02 57
42 45 14
42 35 06
42 21 28
42 20 15
42 19 13
42 05 38
41 53 54
41 12 27
40 52 38
40 51 46
40 60 15
40 32 07
38 28 43
38 42 40
38 16 02
38 16 10
38 06 44
38 07 56
38 00 39
LongE.
04 08
42 08
08 32
13 51
20 46
23 43
36 42
56 06
6 08 39
00 54
08 02
17 13
18 42
19 41
1 27 25
2 57 20
2 37 00
4 18 20
8 51 08
8 13 29
8 10 00
8 23 56
9 08 35
9 20 21
9 29 40
9 39 07
9 44 22
9 43 25
9 32 35
9 07 20
9 11 15
8 35 45
9 09 04
8 43 25
9 24 10
9 27 00
9 22 05
8 10 22
8 54 19
9 50 48
11 15 22
10 17 25
9 51 07
10 24 38
10 05 50
10 03 54
10 18 39
10 65 24
11 46 50
12 28 40
13 35 16
12 57 17
14 14 44
14 15 38
14 11 40
14 51 40
13 12 00
15 39 11
15 13 42
13 21 16
13 22 04
12 29 50
Liin. Int.
H. W.
7 31
8 22
4 00
L. W.
h. m.
2 00
2 24
Range.
Spg. Neap.
ft.
0.6
0.6
10 13
0.7
ft.
0.3
0.2
0.2
APPENDIX IV. [Page 227
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
Place.
Maritimo Island: Light on SW. pt
Marsala: W. mole light
Girgenti : Port Empedoche light
Gozo Island : Light on NW. pt
Malta Island, Valetta Harbor: Light-
house
Linosa Island : Landing Cove
Lampedusa Island: Carallo Bianco light
Cape Passaro : Light-house
Syracuse: Maniace Castle light
Augusta Port: Torre d' Avola light
Catania: Sciari Biscari light
Cape Taormina: Semaphore
Messina: San Ranieri light
Cape Peloro : Light-house
Cape Spartivento : Light-house
Cape Colonna: Light-house
Cotrone: Mole-head light
Taranto: Cape St. Vito light
Gallipoli : St. Andrea light
Cape Sta. Maria di Leuca: Light-house.
Cape Otranto : Light-house
Port Otranto: Castle
Brindisi: Light-house
Bari: St. Catalolo light
Viesti: Light on St. Croce Rock
Manfredonia: Light-house
Tremiti Islands: Caprara I. light
Ancona: Monte Cappucini light
Malamocco: Rocchetta Mole light
Venice: Site of tower of St. Mark
Grado: Church tower
Monfalcone: Church tower
Trieste: Observatory Nautical Academy
Theresa Mole light
Capo d'Istria: Light-house
Isola: Light-house
Pirano : Light-house
Salvo re Point: Light-house
Citta Nuova: Light-house
Parenzo: Cathedral tower
Rovigno: St. Eufemia light
Pola: N. cupola of observatory
Promontore Point: Porer Rock light
Nera Point: Light-house
Fiume: Cathedral tower
Porto Re : Light-house
Veglia: Mole head
Prestenizza Point: Light-house
Cherso: Kimen Point light
Galiola Rock: Light-house
Unie Island: Netak Point light
Lussin Piccolo: Sta. Maria Church
St. PietrodiNenibo Island: Health office
Gruizza Rock : Light-house
Zengg: Mole-head light
Terstenik Rock : Light-house
Carlobago : Light-house
Zara: Church tower
Bianche Point: Light-house
Zara Vecchia: Church tower
Port Tajer: Lestrice I. light
Lucrietta Island : Light-house
Sebenico: Mount Tartaro
Rogosnizza Port: Mulo Rock light
Zirona Grande Island: St. George
Church tower
Trani: Cathedral tower
Lat. N.
37 57 13
37 47 10
37 16 55
36 04 10
35 54 00
35 51 50
35 29 37
36 41 03
37 03 04
37 12 39
37 29 35
37 50 25
38 11 33
38 16 02
37 55 29
39 01 29
39 04 38
40 24 41
40 02 48
39 47 43
40 06 23
40 09 06
40 39 36
41 08 19
41 53 17
41 37 39
42 08 14
43 37 14
45 20 30
45 25 58
45 41 06
45 48 33
45 38 51
45 38 54
45 33 00
45 32 34
45 31 54
45 29 24
45 19 16
45 13 45
45 05 00
44 51 49
44 45 30
44 57 24
45 19 36
46 16 18
45 01 30
45 07 12
44 57 36
44 43 36
44 37 20
44 31 49
44 27 42
44 24 42
44 59 24
44 40 06
44 31 30
44 07 05
44 09 06
43 56 16
43 51 15
43 37 36
43 45 08
43 31 00
43 27 00
43 31 02
Long. E.
12 02 55
12 25 59
13 32 27
14 12 55
14 31 30
12 52 09
12 36 12
15 07 45
15 17 37
15 13 20
15 05 19
15 18 30
15 34 36
15 39 11
16 03 31
17 12 09
17 08 07
17 12 23
17 56 55
18 22 17
18 31 25
18 28 45
17 59 37
16 50 52
16 11 13
15 55 34
15 31 36
13 31 18
12 19 09
12 20 29
13 22
13 32
13 46
13 45
13 43
13 39
13 33
13 29
13 33
13 35
13 38
13 50
13 53
14 08
14 26
14 33
14 34
14 16
14 23
14 10
14 14
14 28
14 33
14 34
14 53
14 34
15 04
15 14
14 49
15 26
15 12
15 34
15 58
15 55
16 08 51
16 15 09
Lun. Int.
H.W.
h. m.
L. W.
h. m.
3 12
9 25
3 00
9 13
3 30
10 15
9 20
9 00
8 15
8 10
6 10
Range.
Spg. Neap.
0.9
9 43
4 45
3 50
3 25
2 35
2 25
1.8
3.3
2.0
3.4
1.2
0.2
0.3
0.5
0.9
0.6
0.9
0.3
1.1 ! 0.3
0 20 1.0
0.3
Page 228] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
Place.
Lat. N.
Port Spalato: Cathedral tower
Soltal., PortOliveTto: St. Nicholas tower.
Spalato Passage: Speo Pt. light
Makarska: Church tower
Porno Rock: Center
St. Andrea Rock: Summit
Lissa Island : Hoste Rock light
Pakonjidol Rock: Light-house
Lesina Island: Port Gelsa light
St. Giorgio Pt. light
Sabioncello Peninsula: Cape Gomena
light
Sorelle Rocks: Light-house
Curzola Island: Porto Bema mole head. .
Porto Valle Grande,
church tower
Lagostini Island: Glavat Rock light
Lagosta Island : St. George Chapel
Cazza Island : Light-house
Pelagosa Rock : Light-house
Meleda Island: Port Palazzo Ruin
Olipa Rock : Light-house
Pettini di Ragusa Rocks: Light-house...
Bobara Rock : Summit
Molonta Peninsula: Summit
Ostro Point: Light-house
Cattaro: Health office
Budua: Mole-head light
Katie Rock : St. Domenica Chapel
Antivari: Pt. Valovica light
Dulcigno: W. windmill
Cape Rodoni: Guard-house...
Cape Pali: Guard-house
Durazzo: Light-house
Cape Laghi : Ruin
Skumbi River: Pyramid at mouth.
Semeny River: Samana Pt. light . .
Vojazza River: Pyramid at mouth
Saseno Island: Light-house
Avlona: Light-house
Cape Linguelta: Extreme
Mount Cica: Pyramid
Port Palermo: Pyramid
Cape Kiefali : Pyramid
Fano Island: Pt. Kastri light
Port Pagonia: Ruin
Port Gomenitza: "Well Dogana
Port Parga: Madonna I
Port St. Spiridione: Convent
Corfu : Light-house
Paxo Island: Madonna I. light
Prevesa; Fort Nuovo minaret
Port Drepano: Observation island
Port Vliko: Custom-house
Port Vathi : Lazaretto light
Port Argostoli : St. Theodoro light
Patras: Light-house
Katakolo: Light-house
Zante: Mole light
Strovathi, or Strivali Island: Stamphani
Llight
Proti Passage: Marathon Pt
Navarin : Light-house
Mothoni: Round tower
Koroni Anchorage: Mole light
Petalidi Bay: Petalidi Pt
Candia Island, Port Suda: Light-house..
Megalo Kastron: Mole
light
43 30 07
43 23 50
43 19 12
43 17 46
43 05 28
43 01 43
43 04 30
43 09 24
43 09 50
43 07 30
43 02 50
42 57 42
42 54 19
42 57 37
42 45 54
42 45 05
43 45 05
42 23 30
42 47 06
42 45 30
42 39 00
42 35 08
42 27 04
42 23 36
42 25 30
42 16 42
42 11 43
42 05 15
41 55 47
41 35 10
41 23 31
41 18 40
41 08 44
41 02 12
40 47 00
40 36 14
40 30 12
40 25 30
40 25 17
40 12 00
40 02 57
39 54 29
39 51 53
39 39 27
39 29 50
39 16 32
39 39 54
39 37 05
39 11 30
38 56 30
38 47 25
38 40 40
38 22 04
38 11 36
38 15 00
37 38 20
37 47 10
37 15 12
37 03 38
36 54 10
36 48 40
36 47 50
36 57 20
35 28 55
35 20 30
Long. E.
16 26 06
16 11 10
16 24 30
17 01 36
15 27 30
15 45 29
16 12 28
16 27 14
16 41 55
17 12 00
17 00 19
17 12 44
16 51 32
16 43 07
17 08 54
16 51 45
16 29 29
16 15 12
17 22 51
17 46 48
18 03 08
18 10 49
18 25 36
18 32 00
18 46 12
18 50 36
18 56 25
19 04 19
19 12 29
19 27 15
19 24 54
19 27 14
19 26 47
19 26 30
19 20 14
19 19 14
19 16 15
19 27 55
19 17 45
19 38 33
19 47 53
19 54 55
19 26 06
20 07 12
20 17 09
20 24 55
19 43 09
19 56 30
20 12 34
20 45 40
20 44 16
20 42 44
20 43 37
20 29 30
21 43 50
21 18 55
20 55 26
21 01 14
21 34 35
21 40 29
21 42 40
21 58 00
21 56 42
24 09 39
25 09 44
Lun. Int.
H. W.
h. m.
4 00
3 40
L. W.
h. m.
Range.
Spg. Neap.
ft-
10 30
9 53
2.4
1.0
ft.
0.7
0.3
APPENDIX IV. [Page 229
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
1
o
Place.
Lat. N.
Long. E.
Lun. Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
«
V
V
s>
u
d
i
s
Kandeliupa Island : Light-house
StampaU Island, Maltezana Port: Agios
loanes
o / //
36 29 40
36 34 25
36 15 20
36 40 27
36 59 12
37 06 32
37 00 01
37 08 38
37 26 12
37 07 36
37 25 55
37 38 00
37 39 28
37 44 00
37 57 30
36 47 05
37 18 42
37 31 45
37 44 30
37 56 14
37 58 20
37 38 45
37 52 48
38 01 28
38 28 15
o r II
26 59 25
26 24 28
25 13 00
24 23 15
24 40 30
25 23 00
25 14 21
25 14 08
24 56 14
h. m.
h. m.
fl.
ft.
Christiana Islands: N. pt .. ..
Milo Island: Summit, Mt. St. Elias
Siphano Island : Light-house
Naxos Island, Naxia: Gate on Bacchus I.
Paros Island, Port Trio: Trio Pt
Port Naussa: St. Yanni
Church
!
Syra: Mole light
Sermo Island : Aniyno Pt
24 32 23
24 23 35
24 44 32
24 19 44
24 04 12
24 42 30
23 05 40
23 08 53
23 25 45
23 25 30
23 38 10
23 43 55
24 02 15
24 03 00
24 16 42
Therm ia Island: Ruins of Cythnus
Jura Island: North pt .. ... ..
1
1
Port St. Nikolo: Light-house
•-(■--■■■
St. Nikalao Island: Port Mandri
Andros Island, Cape Fasse: Light-house,
leraka : Acropolis
i
i
Port K heli : Light-house
Poros Island: Light-house
1
1
JEgina: Light-house
Pirajus: Light-house
\
Athens: Observatory
<
Cape Colonna: Extreme
1
Port Raphti: Statue I
Petali Island : Trago I. peak
Euripo Strait: Light-house
1
23 36 45
Skiathos Island: Mount Stavros
Salonika: S. bastion
Port Baklar: Cape Xeros
39 10 48 23 27 07
40 37 28
40 32 40
39 52 10
39 50 52
39 31 58
39 12 35
39 06 10
39 03 20
38 32 00
38 19 55
37 41 24
37 16 33
22 58 00
26 45 00
25 03 20
25 14 14
24 59 13
25 50 00
26 34 54
26 31 39
25 35 00
26 17 45
26 58 42
27 36 55
Lemnos Island : Kastro Castle
Port Moudros: Sangrada Pt
Strati Island : St. Strati Church
1
Mityleni Island, PortSigri: Light-house.
Mitvleni: LightonMity-
leni Pt
!
Port lero: Sidero Islet .
Psara Island: Fort
Tchesm6: C. K^zil light
Samos Island : Fonia Pt. light
Port Isene: Tower
Kos: Light-house
36 55 00 ! 27 18 25
36 48 00 ; 28 18 00
36 39 33 ' 29 06 13
36 26 00 28 16 24
Marmorice Harbor: Adassi Pt. light
Makrv Harbor: Kasil I
Rhodies Port: Arab's Tower light
Port Lindo: Tower
36 05 53
40 02 30
40 24 27
41 01 20
41 01 02
41 00 35
41 00 16
41 21 15
41 52 04
28 08 10
26 10 54
26 41 24
29 01 00
29 00 29
29 01 14
28 58 59
28 42 14
27 58 45
Dardanelles: Hellas Pt. light
(jallipoli : Light-house
:::::::;::: i
Bosphorus: Tofana Pt. light
Scutari: Leander Tower light
Constantinople: Seraglio Pt. light
St. Sophia Mosque
Cape Kara Burnu: Light-house
Yuiada Road : Fort Tersana
Burghaz : Light-house
42 27 52 27 35 54
43 10 00 27 58 35
44 10 20 28 39 14
45 09 47 29 41 14
Varna Bav : Light-house
Kusterjeh: Cape Kusterjeh light
Danube River: Salina light
Fidonisi Island: Light-house
Odessa : Observatory
45 16 00
46 28 36
46 34 27
44 36 55
44 29 50
45 21 03
46 45 00
42 58 00
41 39 30
30 14 14
30 45 34
31 33 36
33 36 26
33 36 25
36 28 30
36 46 40
40 55 10
41 38 15
Dnieper Bay: Fort Nikolaeo light
Sebastopol: E. light-house
Balaklava Bav : Hospital
Kertch: Light-house
Berdiansk: Breakwater light
Saukhoum : Light-house
Batoum: Light-house
Page 230] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERBAXEAN, ADRIATIC, AND BLACK SEAS— Continued.
Plac'o.
Trebizond : Light>4iouse
Sinope : Light-house
Bender ErekH : Light-house
Marmora Island : Light off E. pt
Artaki Bay: Zeitijn Adasi Islet
Tenedos Island: Ponente Pt. light
Port Ajano: Nikolo Rock
Port Ali-Agha: W. pt. of entrance
Smyrna: English consulate flag-staff . . .
Vourlah : Custom-house
Sighajik Harbor: Beacon on islet
Budrum : Light-house
Adalia: Light-house
Alexandretta: Light-house
Latakiyah: Light-house
Tripoli Roadstead: Bluff Islet light
Ruad Island : Light-house
Beirut: Light-house
Saida ( ancient Sidon ) : Light-house
SAr (ancient Tyre) : Light-house
Acre: Li^ht-house
Haifa: Light-house
Famagusta: Light-house
C. Gata: Light
Lamaka: Light-house
Port Said : High light-house
River Nile: Damietta Mouth
Rosetta Mouth light
Aboukir Bay: Nelson I. peak
Alexandria: Eunostos Pt. light
Ben Ghazi : Castle
Tripoli Harbor: Light-house
Sfax: Ras Tina light
Mehediah : Sidi Jubber
Monastir: Burj el Kelb battery
Hammamet Bay: Castle flag-staff
Kalibia Road : Light-house
Cape Bon : Light-house
Tunis: Goletta light
Cape Farina: Extreme
Benzert: N. Jetty light
Galita Island: Monte Guardia
Bona: Fort Genois light
Stora: Singe I. light
Cape Bougaroni : Light-house
Cape Carbon : Light-house
Algier : Light-house near Admiralty
Cape Tenez : Light-house
Oran: Mers el Kebir light
Habibas Island : Light-house
Zafarin Islands: Light Isabel Segunda I
Alboran Island : Light-house
Ceuta: Light-house
Tangier: Casbah tower
Cape Spartel : Light-house
41 01 00
42 01 20
41 18 03
40 38 10
40 23 30
39 50 00
39 01 21
38 50 10
38 25 40
38 21 48
38 12 21
37 02 00
36 52 00
36 35 30
35 30 30
34 29 25
34 52 00
33 54 10
33 34 20
33 16 30
32 54 35
32 47 40
35 07 10
34 33 45
34 54 00
31 15 41
31 31 40
31 29 30
31 21 23
31 11 43
32 06 51
32 54 03
34 39 01
35 30 24
35 45 24
36 23 20
36 50 12
37 04 45
36 48 19
37 10 42
37 16 38
37 31 16
36 57 15
36 54 29
37 05 17
36 46 41
36 47 16
36 33 07
35 44 21
35 43 22
35 11 05
35 58 00
35 53 44
35 47 00
35 47 14
Long. E.
39 46 25
35 13 20
31 25 49
27 46 09
27 47 30
25 58 34
26 47 57
26 57 20
27 09 10
26 47 00
26 47 32
27 27 05
30 45 34
36 10 20
35 46 30
35 44 24
35 51 00
35 28 25
35 21 30
35 14 40
35 08 00
35 05 00
33 57 22
33 01 30
33 38 59
32 18 45
31 51 00
30 19 10
30 06.00
29 51 40
20 02 40
13 10 50
10 41 17
11 05 15
10 50 42
10 37 10
11 07 00
11 03 15
10 18 31
10 17 30
9 53 21
8 56 12
7 46 40
6 53 11
6 28 37
5 06 22
3 04 13
1 20 36
Long. W.
0 41 38
1 07 57
2 25 45
3 03 29
5 16 46
5 48 31
5 55 41
Lun. Int.
H. W. i L. W.
h. m. h. m.
9 15
9 45
9 40
9 40
9 45
9 55
10 00
3 35
3 33
2 46
1 55
1 30
Range.
3 15 i 2.5
3 35
3 30
3 30
3 15
3 45
3 50
9 57
9 55
8 58
8 07
7 40
1.2
1.4
LO
1.1
1.2
1.9
4.2
3.0
2.6
3.3
8.0
Neap.
0.7
0.3
0.4
0.3
0.3
0.3
0.5
1.1
0.8
L3
1.5
3.7
WEST COAST OF AFRICA.
El Araish: S. pt. of entrance ...
Sali: Fort
Cape Dar el Beida: Light-house
35 12 50
34 04 10
33 36 00
6 09 13
6 48 00
7 33 00
1 35
7 45
10.4
4.8
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF AFRICA— Continued.
[Page 231
Place.
Cape Blanco, North : Extreme
Mogador Harbor: English consulate
Cape Ghir: Extreme
Cape Noun : Extreme
Cape Juby : Extreme
Cape Bojador: Extreme
Penha Grande
Ouro River entrance: Dumford Pt
Pedra de Galha
Cape Blanco, South : Extreme
Portendik: Village
St. Louis: Light-house
Almadie Point: Light-house
Cape Verde: Light-house
Port Dakar: Light-house
Cape Manoel : Light-house
Goree Island: Fort
Bird Island : Flagstaff
Bathurst: Flagstaff
Carabane: Light-house
Nunez River: Sand I
Ponga River entrance: Observation pt . .
Isles de Los: Light-house
Matacong Island: House
Scarcies River: W. end of Yellaboi I
Sierra Leone: Light on cape
N. battery
Sherbro Island: N. island
Sherbro River: Manna Pt
Gallinas River: AV. elbow of Kamaaounl.
Cape Mount: W. peak
Cape Mesurado : Light-house
Monrovia: Light-house
Marshall: Agent's house
Grand Bassa: Agent's house
Cestos: Factory
Sangwin River: Sangwin Pt
Sinon : Bloobarra Pt
Cape Palnias: Light-house
Tabou River: Tabou Pt
Axim Bay: Ft. St. Anthony
Cape Three Points: Light-house
Dix Cove: Fort
Tacorady Bay: Tacorady Pt
Chama Bay: Dutch Fort
El Mina Bay: Ft. St. George
Cape Coast Castle: Light-house
Accra: Light-house
Lat. N.
Volta River entrance: Dolbens Pt
Lagos River: Light-house
Benin River entrance: N. pt
Brass River: Entrance (approx. )
Calebar River (New) : Rough Corner . . .
Opobo River: W. pt. beacon (approx. ) . .
Quaebo River: Bluff Pt
Calebar River (Old) : Townsend flagstaff
( Dunketown)
Fernando Po Island: Light-house
San Bento River: Joho Pt. (approx.) ...
Princes Island: Diamond Rocks, center
of largest
St. Thomas Island: Ft. San Sebastian
light
Anno Bon Island: Turtle Islet.
Cape Lopez: Light-house
Mayumba Bay: Light- house . . .
33 08 00
31 30 30
30 38 00
28 45 00
27 56 00
26 07 57
25 07 06
23 36 03
22 12 37
20 46 27
18 18 45
16 01 31
14 44 45
14 43 20
14 40 30
14 38 55
14 39 55
13 39 45
13 28 00
12 35 00
10 36 37
10 03 15
9 30 30
9 16 10
8 57 05
8 30 00
8 29 57
7 40 36
7 22 45
7 00 08
6 44 30
6 19 10
6 19 00
6 08 06
5 54 08
5 26 25
5 12 42
59 15
22 10
24 47
52 18
45 00
47 45
53 00
5 01 00
5 04 48
5 06 20
5 31 50
5 46 00
6 25 15
5 46 01
4 16 40
4 23 07
4 27 00
4 30 40
4 56 24
3 46 10
1 35 00
1 40 42
0 20 30
Lat. S.
1 24 18
0 36 25
3 23 00
Long. W.
8 35 05
9 43 30
9 50 00
11 02 00
12 56 00
14 29 00
14 50 44
15 58 00
16 48 11
17 05 40
16 02 00
16 30 22
17 32 25
17 30 55
17 25 28
17 26 47
17 24 30
16 40 30
16 35 00
16 44 00
14 42 00
14 04 30
13 44 00
13 26 20
13 18 25
13 18 30
13 14 30
13 04 30
12 31 55
11 38 45
11 22 51
10 49 25
10 50 00
10 22 45
10 04 05
9 34 45
9 20 16
9 02 05
7 44 15
7 21 30
2 14 45
2 05 45
1 56 40
45 00
38 00
21 05
13 50
0 11 30
Long. E.
0 41 00
3 25 15
5 03 05
6 15 00
7 07 00
7 40 00
7 59 00
8 20 46
8 47 05
9 39 00
7 27 56
6 42 45
5 38 12
8 43 10
10 38 00
Lun. Int.
Range.
H.W. L.W. Spg. Neap
1 05
11 55
11 50
11 35
h. m.
"r'ii
5 43
5 38
ft.
'i6."9'
8.5
7.3
5 23
9 00
7 30
7 40
5 50
5 40
4 50
4 30
4 00
2 50
1 20
1 30
12 00
11 54
11 05
10 43
10 13
4 20 10 32
4 20 10 33
4 50 11 05.
4 25
10 38
5.5
5.9
11.4
11.6
10.4
6.0
4.8
4.3
4.7
6.0
4.2
3.3
7.0
ft.
5.0
3.9
3.4
2.5
2.7
5.2
5.3
4.8
2.5
2.0
1.8
1.9
2.5
1.8
1.3
2.9
1 Page 232] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF ATRICA— Continued.
1
Place.
Lat. S.
Long. £.
Lun. Int. Range. 1
H. W.
L. W.
Spg. 1 Neap. 1
Loango Bav : Indian Pt. light
o / //
4 40 00
4 49 00
5 18 30
5 32 30
6 04 36
6 31 50
8 48 24
12 20 00
12 34 43
13 12 30
13 26 05
15 09 00
15 47 30
16 30 00
18 23 00
22 57 00
26 17 00
26 37 52
26 58 30
29 15 12
30 18 33
30 33 07
33 07 51
33 48 52
33 56 04
34 21 12
O 1 If
11 46 30
11 45 00
12 08 00
12 11 00
12 15 00
12 25 25
13 13 20
13 32 00
13 23 45
12 48 55
12 36 00
12 12 00
11 52 40
11 42 00
11 57 12
14 30 00
14 57 20
15 07 02
15 12 22
16 52 02
17 16 20
17 27 30
18 01 21
18 22 33
18 28 40
18 29 26
*. 7?!.
4 13
/(. m.
10 26
ft.
6.5
St.
2.7
Black Point Bay : Sandy Pt
Malemba Bay : Landing Cove
Kabenda Bay: Kabenda Pt. light
Congo River entrance: Shark Pt
Margate Head: Summit
4 10
10 25
6.0
2.5
St. Paul de Loando: Flag staff, Ft. San
Miguel
3 40
9 53
4.8
2.0
Lobito Point : Extreme
Benguela: Telegraph office
3 30
9 43
5.5
2.3
Elephant Bay : Friar Rocks
St. Marv Bay: Bav I
Little Fish Bay : Light-house
Port Alexander: Bateman Pt
Great Fish Bay: Tiger Pt
3 00
9 12
5.7
2.4
Cape Frio: Extreme
Walfisch Bay : Light-house
Ichabo Island
Angra Pequena: Diaz Pt
Elizabeth Bay: S. pt. of Possession I
Port Nolloth: Magistrate's house
Hondeklip Bay
2 35
2 25
8 47
8 38
5.5
5.3
2.3
2.2
Roodewal Bay
Saldanha Bav : Constable Hill
2 20
8 33
5.1
2.1
Table Bay: Robben I. light
Cape Town : Observatory
1 36
7 47
4.6
2.0
Cape of Good Hope: Light-house
EAST COAST OF AFRICA AND THE RED SEA.
34 10 45
34 23 48
34 46 45
34 49 45
34 23 47
34 11 10
34 04 35
34 06 15
34 12 30
34 01 41
33 57 43
33 50 27
33 36 09
33 28 00
33 23 10
33 05 10
18 27 30
18 50 20
19 38 17
20 00 37
20 48 40
22 09 31
23 03 38
23 24 23
24 50 20
25 42 12
25 37 21
26 17 13
26 54 10
27 03 00
27 20 48
27 49 12
27 55 02
28 22 36
29 06 40
29 21 15
29 33 16
29 48 40
31 03 50
31 51 39
32 27 39
32 38 10
32 35 52
35 29 45
35 31 41
35 29 00
35 29 30
34 53 30
34 46 00
36 11 47
36 58 30
37 01 09
2 35
8 48
5.2
2.2
Cape Hangklip: Extreme
Quoin Point: Extreme
Cape Agulhas : Light-house
2 40
8 53
5.2
2.2
Port Beaufort: Flag-staff
St. Blaize: Light-house
3 18
9 31
5.6
2.0
Knysna Harbor: Fountain beacon
Plettenberg Bay: Summit of Seal Pt
St. Francis: Light-house
Cape Recife: Light-house .
Port Elizabeth : Light-house
3 21
9 33
5.4
1.9
Bird Islands: Light-house
Port Alfred: Signal staff
■
Waterloo Bay: Maitland Signal Hill
Madagascar Reef' Center
Cove Rock: Center
East London: Light-house
33 01 45
32 42 00
32 02 30
^^ 4« 1."^
3 37
9 50
5.0
1.8
Cape Morgan: Extreme
Hole-in-the-Wall
Rame Head* Extreme
Cape Hermes: Extreme 31 38 06
Waterfall Bluff ! 31 26 15
Port Natal (Durban): Light-house I 29 52 40
Dumford Point: Extreme | 29 00 12
Cape St. Lucia: Extreme ' 28 32 30
CapeVidal- Extreme ^s f^f ^(^
3 58
10 11
5.6
1.6
Delagoa Bay: Reut^en Pt. light
Cape Corrientes: Small rock
25 58 49
24 05 30
5 10
11 22
n.9
3.4
Innamban Bay: Barrow Hill light
Cape St. Sebastian: Extreme
23 45 30
22 05 00
21 31 00
20 38 10
20 10 42
18 52 50
18 01 24
17 51 50
4 30
10 42
n.o
3.2
Bazaruto Island: N pt light
Chuluwan Island* Light-house
Sofala: Fort on N. side of entrance
Zambesi River: Kangoni Mouth
Quillimane River: Light-house
4 15
10 27
13.5
3.9
Quillimane: Town
Mazemba River: Entrance
17 15 00 M8 04 00
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF AFRICA AND THE RED SEA— Continued
[Page 233
1
Place.
Lat. S.
Long. E.
Lun
Int.
Range.
H. W.
L. W.
Spg.
Neap.
Premeira Islands: Center of Casuarina I.
Angoxa Islands: Center of Hurd I
Mafamale Island : Center
O / II
17 06 30
16 33 24
16 20 30
15 08 00
15 02 12
15 00 45
14 58 20
14 53 00
13 23 40
12 55 45
12 19 30
11 09 18
10 41 20
10 19 22
10 16 31
10 06 43
9 59 30
9 44 22
9 25 36
8 57 15
7 38 10
6 49 41
6 26 10
6 09 43
5 00 35
4 04 30
3 12 48
2 15 42
2 13 35
1 13 00
0 22 35
Lat. N.
1 06 48
1 42 06
2 01 48
2 30 00
10 26 30
11 50 30
12 26 00
12 11 15
12 39 00
11 27 30
11 13 00
10 25 00
11 22 00
12 39 00
14 44 00
15 28 10
15 37 12
18 15 12
19 07 00
20 44 00
23 36 20
24 56 30
26 06 24
O 1 II
39 06 27
39 49 57
40 03 57
40 36 12
40 48 45
40 45 06
40 45 10
40 40 00
40 46 00
40 31 15
40 40 09
40 43 21
40 38 35
40 26 34
40 10 33
40 02 14
39 46 41
39 47 07
39 39 31
39 30 42
39 54 42
39 17 05
38 54 27
39 11 08
39 10 20
39 41 13
40 11 21
40 56 21
40 59 40
41 54 15
42 33 57
44 03 27
44 53 49
45 24 39
46 07 00
51 22 55
51 16 45
52 09 35
52 25 35
53 59 31
49 35 40
47 17 00
44 59 35
43 29 35
43 25 35
40 52 00
39 45 30
39 27 23
38 19 30
37 19 09
37 15 30
36 10 15
35 51 00
.34 17 03
h. m.
h. m.
Jt.
ft.
::::::::::::::: i
Port Mokamba: Mokambo Pt
i
Port Mozambique: St. George I. light...
San Sebastian light. .
Cape Cabeceira: Light-house
1
4 00
10 12
11.8
3.4
Port Conducia: Bar Pt
i
Lurio Bay : Pando Pt
1
Peniba Bav : N. pt. light
::::::::::::::::: i
Querimba Islands: Ibo I. light
Numba Island : K. pt
\
Cape Delgado : Light-house
3 59
10 11
11.3
3.3
Msimbati : Ran Matunda
Mikindini Harbor: Kinizi
Mgan Mwania: Madjori Rock
Lindi River: Fort flagstaff
3 55
10 08
10.9
4.5
Mchinga Bay : Observation spot
Kiswere Harbor: Rustmigi
Kilwa Kisiwani: Fort
Mafia Island: Moresby Pt
Dar-Es-Salaam : Flagstaff
1
Bagauioyo; French Mission
Zanzibar: English consulate
4 05
10 17
14.5
6.0
Tanga Bay: Light-house
Mombasa: Light-house
:::::;:::: i
Port Melinda: Vasco de Gama's Pillar . .
Lamo Bay : Lamo Castle
4 00
10 13
12.1
5.0
Manda Roads: E. side of Manda Toto I .
Port Durnford: Foot Pt
4 30
10 42
n.7
4.9
Kisimayu Bay: S. pt. of Kisimayu I
Brava: Well
4 15
10 27
7.5
3.1
Meurka Anchorage: S. pt. of town
Magadoxa: Tower
Murat Hill: Peak
Ras Hafun: E. extreme of Africa
Cape Guardafui : E. pt
6 00
12 12
6.1
2.5
Kal Farun Islet: Center
Abd-al-Kuri Island : NE. pt
1
Socotra Island: Tamarida, mosque
Ras Antareh: Extreme of rocky pt
Miiit Island : Center
7 05
1 17
7.5
3.1
1
Port Berbera: Light-house
1
Zeyla: Mosque
7 30
7 50
1 18
1 38
8.5
7.2
3.5
3.0
Perim Island: Light- house
Hanfelah Bay: Hanfelah Pt
Disei Island : Village Baj'
Massaua Harbor: N. pt. of entrance
Khor Nowarat: Shatireh Islet
0 45
6 57
4.0
1.7
Suakin : Light-house
2 10
8 22
L7
0.7
Makaua Island : S. pt
St. Johns Island : Peak
Daedalus Shoal : Light-house
[
Kosair Anchorage: SW. angle of fort
Brothers Island : Light- house
.1 _ ._ ..1
26 18 50 1 34 50 45
26 45 48 ' 33 59 43
6 40
0 28
2.0
0.8
Safajah Island: N. summit
Ashrafi Island: Light-house
27 47 21
28 20 52
29 06 29
29 53 05
28 13 47
27 35 45
27 33 00
26 13 00
24 38 35
24 05 15
33 42 28
33 06 31
32 39 43
32 32 50
33 36 56
35 30 30
35 32 30
36 27 00
37 17 45
38 02 45
1
Ras Gharib: Light-house
10 35
10 40
10 45
4 23
4 28
4 32
1.5
5.5
6.8
0.6
2.3
2.8
Zafarana: Light-house
Suez : Newport Rock
Tor: Ruined fort
Sherm Yahar: Entrance
i
Sherm Joobbah : Entrance
t
Sherm Wej : Light-house
Sherm Hassejy : Anchorage
1
Yembo: Anchorage
:::::: i
«
Page 234] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
PIAST COAST OF AFRICA AND THE RED SEA— Continued.
o
Place.
Lat. N.
Long. E.
Lun.
Int.
Range. 1
H.W.
L.W.
Spg.
Neap. 1
i
Sherm Rabigh : ^ichorage
Jiddah: Jezirah el Mifsaka I
0 / //
22 43 50
O 1 II
39 00 30
39 10 38
40 12 00
40 30 00
41 03 20
41 27 30
41 58 15
42 29 00
42 38 45
42 34 00
42 56 00
42 45 28
43 13 36
h. m.
h. VI.
ft. ft.
21 28 00
20 09 00
3 30
9 42
2. 0 0. 8
Lith: Agha Islet
Jelalil: Anchorage 19 55 30
Kunfidah: Islet ' 19 07 40
j
Khor Nohud: Entrance
18 15 50
Farisan I. Anchorage: Jebel Mandhakh .
Gizau : Fort ..
16 50 15
16 53 00
15 42 00
15 20 30
14 47 00
14 03 53
13 19 43
Loheiya: Hill Fort
1 15
7 27
2.9
1.2
Kauiardn Bay : Harbor. ....
Hodeida Road
Jebel Zukur Island: N. pt
Mokha: N. Fort
11 45
5 33
4.5
L9
ISLANDS OF THE INDIAN OCEAN.
i
d
>
•
fl
e
g
ss
Chitlac Islet: S. end
11 40 45
11 35 00
11 27 30
11 13 00
11 06 00
10 47 00
10 32 00
10 06 00
10 03 00
8 16 00
6 55 00
6 59 00
6 25 00
5 26 30
5 01 30
4 25 45
4 44 00
4 10 15
3 41 00
2 57 00
3 16 00
2 10 30
2 07 00
0 14 30
Lat. S.
0 41 30
5 40 56
4 52 26
5 53 00
4 37 15
3 43 06
5 15 00
7 13 37
16 25 12
19 40 22
19 52 36
19 59 45
20 08 46
20 24 20
72 42 54
72 09 54
72 59 00
72 44 00
72 41 00
73 40 00
72 37 40
72 15 10
73 35 54
73 01 15
72 55 54
73 12 54
72 41 54
73 20 00
72 53 00
72 57 24
73 28 00
73 30 24
73 24 54
73 34 24
72 48 00
73 03 00
73 35 54
73 13 00
73 06 54
53 41 03
53 23 38
55 27 10
55 27 23
55 12 19
71 43 47
72 23 50
59 46 40
63 25 38
57 39 14
57 32 35
57 29 26
57 47 14
Betrapar Islet: N. Island
Kittau Islet : S. end
10 20
4 00
6.3
3.0
Cardamum Islet: Center
Ameni Islet: N. end
Underut Islet: Center
Cabrut Islet: E. end
Seuheli Par: N. islet
Kalpeni Islet: S. end
Minikoi Island : Light-house
11 27
5 15
2.5
1.2
Heawandu Island : S. end
Kee-lah Island : N. end .
Mah Kundu Island: NE, extreme
Nar Foree Island
Hee-tah-doo Island
To-du Island : Center ..
Gafor Island : Center
Male, or Kings Island: Flagstaff
Pha-li-du Island : Northern end
0 20
6 25
2.9
1.4
Moluk Island: Center
Himniittee Island
Kimbeedso Island : S. end
Esdu Island : NE. pt
Wahdu Island : E. end
Addu Atoll: Gung I
Amirante Islands: Iledes Roches, N. beach
African Islands
Seychelle Is., Platte I. : S. end
Port Victoria: End of Ho-
doul Jettv
4 22
10 35
4.3
1.2
Bird Island: Tree
Chagos Archipelago, Peros Banhos: Dia-
mond Islet
Diego Garcia : N. end
of Middle I
Cargados Carajos: Establishment I., flag-
staff
1 30
1 50
0 20
7 43
8 03
6 32
5.8
4.0
5.5
L7
1.2
1.6
Rodriguez Island: Mathurina Bay, Point
Venus
Flat Island : Light-house
Cannonier Point: Light-house
Port Louis: Martello tower. Ft. George..
Grand Port: Fouquet I. light
0 48
7 00
1.6
0.3
APPENDIX IV. [Page 235
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE INDIAN OCEAN— Continued.
1
Place.
Lat. s.
Long. E.
Lun. Int.
Range. 1
H.W.
L. W.
Spg.
Neap.
it
-0
Reunion Island: St. Denis light
Bel- Air light
O 1 II
20 51 38
20 53 11
20 59 45
21 19 47
15 51 .37
10 21 30
10 06 45
7 00 30
7 06 00
25 39 10
25 12 30
25 03 00
23 38 25
22 05 18
21 54 24
20 18 18
19 49 30
17 53 00
17 29 00
16 12 10
16 07 00
15 46 30
15 43 45
15 11 42
14 40 18
13 59 00
13 55 40
13 27 15
13 23 38
12 49 30
12 27 20
12 03 18
11 57 30
12 23 20
12 44 02
12 49 00
12 56 48
13 21 15
15 15 48
15 54 50
15 27 55
16 14 00
17 00 05
16 42 30
17 23 16
18 09 47
19 55 00
21 58 10
24 46 25
24 59 42
24 58 50
25 01 30
22 22 30
21 29 00
12 26 30
12 47 02
12 16 20
L2 25 00
LI 34 48
LI 40 44
9 46 20
9 22 35
9 41 20
O / II
55 26 59
55 36 18
55 16 18
55 28 58
54 28 46
56 32 00
51 10 21
52 44 57
56 22 00
45 06 50
44 17 57
44 07 20
43 38 20
43 15 20
43 20 21
44 19 21
44 31 30
44 02 20
43 45 18
44 29 05
45 17 09
45 43 09
46 18 45
46 57 29
47 24 36
47 58 21
47 48 05
47 59 30
48 17 34
48 38 57
48 45 45
49 11 21
49 17 25
49 35 56
49 45 06
49 54 00
49 56 25
50 01 59
50 31 21
50 16 05
49 49 11
49 50 59
49 50 59
49 56 15
49 32 04
49 25 31
48 52 10
48 14 50
47 10 34
47 07 20
47 04 24
46 59 11
40 24 10
39 40 39
46 32 35
45 16 27
44 24 54
43 47 00
47 24 09
43 19 15
46 31 07
46 14 52
47 32 25
h. m.
h. m.
ft-
ft.
St. Paul light
St. Pierre light
Tromelin Island : N. end
Agalegas Island: NW. pt
11 50
5 38
3.5
0.6
FarQuhar Islands" Hall's house
Alphonse Island: SE. part (Trees)
Coetivv Island : N. en(
Cape St. Mary : S. extreme
Lev en Island : Center
Port Machikora : Barracouta I .
St. Augustine Bay : Nosi Vei I
5 40
11 52
9.8
2.9
Murderers Bay: Center of Murder I
Cape St. Vincent' Extreme ....
Mourondava : Village
Tsniano: Village
Kovra Rythi Point: Extreme
Coffin Island : Nosi Vao
Cape St. Andrew : Extreme
Boyanna Bay : Barabata Pt ........
Cape Tauzon : Extreme
Majunga (Mojanga): Light-house
Majamba Bay : W. pt
4 15
11 28
10.9
3.2
Narendri Bay : Modrmora Pt
Port Radama: Pt. Blair ...
Radama Islands: N. pt. Nossuvee I
Baratoube Bay : Ambubuka Pt.
Nosi Be : Hellville jetty
Minow Islands: N. pt. Great I
Cape San Sebastian : Extreme
Port Liverpool: N. pt. of entrance
Cape Amber: NE. extreme
Port Lady Frances: Sunson Pt
Port Looke: Pt. Bathurst
PortLeven: S. pt. Nosi Haul .
Andrava Bav : Berry Head
Vohemar : Flagstaff
Cape East: Ugoncy I
Venangue Be Bay : Entrance
Port Choiseul: Maran Seelzy Village
Cape Bellone : Extreme
3 45
9 57
5.1
1.5
St. Marys Island: Light on Madame I ..
Port Tantang: Flagstaff
::::::::.::: i
1
Fenerive Point: Flagstaff
Tamatave: Pt. Hastie
Mahanuru : Town
4 00
10 12
7.3
2.1
Matatane: Village
Santa Lucia: N. end of town, Obs. Rock.
Point Ytapere : Extreme
Ytapere Ba v : N. pt
!
Fort Dauphin : Flagstaff
4 15
10 27
4.7 1.3
Europa Island : Center
Bassas da India: E. pt
j
Geyser Reef: SE. extreme
Mayotta Island : Zaoudzi
4 00
10 13
1L9
2.0
Johanna Island: Landing place, Pomoni
Harbor
Mohilla Island: Numa Choa Harbor
Glorioso Islands: W. islet
Comoro Island: Islet in Mauroni Bay...
Assumption Island : Hummock
4 45
10 58
10.0
L7
Aldabra Island: Westl., E. sideentrance.
Cosmoledo Islands: Observation islet
1
Page 236J APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE INDIAN OCEAN— Continued.
1
Place.
Lat. S.
Long. E.
Lun.
iHt.
Range. 1
H. W.
L. W.
Spg.
Neap.
M
N
2
•s
M
e
«
s
«
Prince Edwards Islands: Marion I., Obs.
spot, NE. side.?
o / //
46 49 30
46 36 00
46 22 00
46 01 00
46 28 18
46 10 40
46 26 00
48 40 00
48 26 45
49 42 00
49 21 22
o r II
37 49 15
50 41 30
51 30 15
50 40 00
51 50 00
50 35 00
52 13 00
69 04 00
68 48 20
68 54 00
70 04 31
70 15 00
70 29 50
73 15 30
73 52 00
72 31 45
77 31 53
77 29 15
96 53 02
105 45 57
A. TO.
h. m.
ft.
ft.
Penguin Islands: Center of SW. islet ...
Possession Island : N W. pt
Twelve Islands: Summit NE. I
Navire Bav
Hog Island: Summit
East Island: Center
Christmas Harbor
Blighs Cape
Cape Bourbon
:::::: i
Mollov, Port Roval Sound: U. S. Tr. of
Venus Obs., 18*74
0 14
6 36
4.6
L3
Cape Challenger
49 41 00
Balfour Rock
49 29 00
53 02 45
53 13 00
53 02 50
38 42 51
37 50 00
12 06 22
10 25 19
::::::::::: i
Heard Island: Cape Laurens, NW. end..
Sealing station .
McDonald Island, Summit
St. Pauls Island : Ninepin Rock
10 40
10 50
5 20
7 10
4 28
4 38
11 32
1 00
3.0
3.3
5.1
4.5
0.9
1.0
1.5
L3
Amsterdam Island: Summit, 2,750 feet..
Keeling or Cocos Islands: Direction I
Christmas Island: Flying Fish Cove
SOUTH COAST OF
ASIA.
1
i
£
Aden : Telegraph station
Lat. N.
12 47 16
13 22 00
13 24 50
13 28 45
14 20 10
14 31 15
14 43 50
14 49 00
14 54 40
15 12 00
15 38 00
16 30 00
16 59 00
17 32 45
17 53 15
19 00 25
20 10 00
20 31 30
22 32 40
23 38 00
23 52 00
23 51 30
24 21 50
25 21 00
26 24 13
26 30 00
25 21 34
24 29 02
25 17 24
26 10 55
26 13 56
30 32 00
29 22 56
29 15 25
28 59 07
26 47 40
26 33 37
Long. E.
44 59 07
45 40 50
46 26 35
46 39 00
48 56 45
49 07 35
49 35 05
49 57 05
50 16 35
51 10 30
52 14 20
52 48 00
54 43 29
56 03 05
56 20 35
57 51 35
58 38 35
58 58 35
59 48 35
58 30 50
58 08 00
57 26 00
56 46 12
56 22 56
56 32 22
56 31 29
55 24 12
54 22 14
51 33 32
51 13 46
50 32 17
47 51 23
48 00 55
50 21 11
50 50 35
53 23 36
54 02 21
7 49
1 41
4.9
2.0
Sughra: Sheik's house
Mokatein : Black ruin
Howaivuh: Sheik's house
Banderburum : SE. house of town
Makalleh Bay: Flagstaff
8 20
2 07
6.8
2.8
Shahah Roads: Custom-house
Sharmoh : Single house
Kosair: High house
Sihut : Center of town .
Ras Fartak: Extreme pt
Damghot: Town
Merbat: Town
8 50
2 38
7.0
2.9
Kuria Maria Is., Hullaniyeh I. : NE. bluff
Ras Sherbedat : Point
Cape Isolette: Islet
Masirah Island : Point Abu-Rasas
Point Ras Ye
9 45
9 15
9 30
3 32
3 03
3 20
9.6
8.9
6.0
4.4
4.1
2.8
Ras-al-Hed : Extreme pt
Maskat ( Muscat ) : Maskat Pt
Deimaniveh Islands: E. islet
Sueik : Fort
Sohar' SE tower of town hall
Khaur Fakan Bay: W. end of village...
Ras INIusendom : N. end of island
Great Quoin Islet: Center
Sharjah: High tower with flagstaff
Abu-Thabi: Fort flagstaff
Al Beda'a Harbor: Nes8ahPt.,N. extreme
Ras Rakkin: NW. pt
Bahrain Harbor: Portuguese fort
Basrah: Custom-house flagstaff
6 15
11 30
6.4
3.7
Kuweit Harbor: N. end of town
Khdrig Islet: Fort fla^taff
0 06
6 17
8.3
4.8
Abu Shahr: Residencv flagstaff
7 12
1 13
2.6
1.5
Shaikh Shu'aib Islet: E. end.
Kais Islet: NE. pt
0 30
6 40
6.6
3.8
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
SOUTH COAST OF ASIA— Continued.
[Page 237
Place.
Lat. N.
Basidiih: Chapel 26 39 12
Haujam Islet: Ruined mosque ' 26 40 49
Kasm: Fort ' 26 57 27
Jashak Bay: Telegraph office 25 38 19
KubKalat: High peak, 1,680 feet 25 29 45
ChahbarBay: Telegraph office 25 16 43
GwatarBay: Islet 25 03 17
!
Gwadar Bay : Telegraph office | 25 07 19
Pasni: Telegraph office 25 15 52
Onnarah: Telegraph office
Sunmiyani: Jam's house..
Cape Monze: Peak
Karachi : Manora light
Observatory
Mandavi : Light-house
Bey t ( Bet ) : Light-house
Dwarka: Light-house
Temple spire
Porebander: Light-house
Mangarol: Light-house
Diu Head : Light-house
Kutpur: Light-house
Bhaunagar: Light-house
Perim Island : Light-house
Cambay : Flagstaff
Surat River: Tapti light
Surat: Minaret Adrusah
Bassein : Center of town
Bombay : Observatory
Kenery Island light
Bankot: Fort Victoria
Ratnagherry : Fort
Viziadrug: Fort flagstaff
Cape Ramas: W. bastion of fort ...
Goa: St. Denis Church
Agaada light
Vingorla: Signal-station light
Vingorla Rocks: Light-house
Sedashigar Bay: Oyster Rock light.
Kumpta: Light-house
Hindwar: Monument
Kundapur: Light-house
Mangalore: Light-house
Kannanur: Light-house
Tellicherri : Flagstaff
Mahe : Light-house
Calicut: Light-house
Cochin : Light-house
Alipee : Light-house
Quilon: Tongacherri Point light
Trevandrum : Observatory
Cape Comorin : Light-house
Trichendore : Pagoda on pt
Tuticorin : Light-house
Paumben Pass : Light-house
Manaar: Center of town
Colombo : Light-house ,
Dondra Head : Light-house ,
Point de Galle: Light-house
Great Bassas Rocks: Light-house
Little Bassas Rocks: Light-house ,
Batticaloa: Light-house
Trincomali : Dock-yard flagstaff. .
Calimere Point: Light-house
Negapatam : Light-house
Pondicherri: Light-house ...
25 11 55
25 25 19
24 50 03
47 37
49 50
50 00
29 20
14 00
14 00
38 00
06 00
41 20
02 21
47 00
35 54
17 00
05 20
12 19
20 10
53 45
42 08
58 00
59 30
33 26
05 12
21 24
29 25
51 10
53 20
49 00
25 00
17 28
38 15
52 17
5i 10
45 00
42 00
15 10
58 00
30 00
53 20
30 47
04 00
29 55
47 10
17 20
8 59 00
6 55 40
5 55 30
6 01 25
6 10 10
6 25 00
7 45 00
8 33 30
10 18 00
10 45 28
11 55 40
Long. E.
55 16 47
55 54 25
56 17 37
57 46 14
59 40 32
60 37 40
61 26 24
62 19 42
63 28 37
64 37 02
66 35 39
66 39 58
60 58 06
67 01 33
69 20 15
69 04 40
68 57 06
68 58 54
69 36 00
70 06 32
70 50 45
71 49 35
72 14 00
72 21 08
72 35 10
72 38 40
72 49 27
72 48 44
72 48 56
72 48 49
73 02 40
73 15 56
73 19 39
73 54 50
73 54 00
73 46 10
73 37 00
73 27 15
74 03 40
74 22 30
74 26 40
74 39 50
74 50 40
75 21 51
75 29 40
75 31 10
75 46 40
76 14 40
76 20 40
76 34 00
76 56 45
77 32 35
78 07 47
78 11 26
79 12 50
79 53 52
79 50 40
80 34 12
80 13 04
81 28 15
81 44 00
81 41 00
81 13 42
79 51 30
79 50 47
79 50 10
Lun. Int.
h. m.
10 50
9 20
9 20
8 50
10 15
"i2'65'
4 27
11 26
'Ai
10 34
10 50
11 21
11 33
0 18
1 55
2 02
8 10
8 37
L. W.
h. m.
4 35
3 05
3 05
2 35
4 00
'5*39'
11 18
5 08
4 10
4 11
4 28
4 59
5 06
6 16
1 52 7 51
1 37 7 36
7 49
8 07
1 44
2 37
Range.
Spg.
11.6
7.8
^.1
7.3
10.8
12.0
5.2
5.0
6.5
2.7
2.1
2.5
3.0
2.0
2.0
2.0
2.1
Neap.
5.3
3.6
3.7
3.8
3.4
5.2
29. 8 15. 1
4.9
2.5
2.4
3.4
1.4
1.0
1.3
0.8
0.5
0.4
0.4
0.5
0.9
Page 238]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
SOUTH COAST OP ASIA— Continued.
Place.
Madras: Observatory
Light-house
Pulicat: Light-house
Armeghon : Light-house
Kistna: Light-house
Masulipatam : Flagstaff
Coconada: Light-house
Vizagapatam: Fort flagstaff
Kalingapatam : Light-house
Gopalpur: Light-house
Gaujam: Fort
Juggernath : Great temple
False Point : Light-house
Balasor River: Chandipur light ..
Saugor Island: Light-house
Diamond Harbor: Flagstaff
Calcutta: Ft. William semaphore.
Chittagong River: Light-house
Akyab: Oyster Reef light
Old temple
Ramree Island: S. pt
Chedubah Island: N W. peak
Cape Negrais: Extreme
Bassein River: Alguada Reef light
Bassein: Port Dalhousie
Andaman Is.: Table Id., Light-house .
Port Cornwallis, Rock in
entrance
Port Blair, Light- house.
Little Andaman Island,
SE.pt
Krishna Shoal: Light vessel
Rangoon River: Grove Pt. light
Rangoon : Great Dagon pagoda
Moulmein : Docks
Moulmein River: Amherst Pt. light. . .
Double Island : Light-house
Tavoy River: Light-house
Mergui: Court-house
Tenasserim
St. Matthew Island: Hastings Harbor..
Pak Chan River: Light-house
Tongka Harbor, Junkseylon Island:
Light-house
Pulo Penang: Fort Cornwallis
Dinding Channel : Hospital Rock
One Fathom Bank : Light-house
Cape Rachado : Light-house
Malacca; Stat. St. Pauls Hill
Singapore Strait: Coney Island light...
Singapore: Fullerton Battery
Singapore Strait: Pedra Branca light . . .
Summit Bintang great
hill, 1,253 feet
Rhio Straits, Pulo Sauh: Light-house ..
Terkolei : Light-house
Little Garras: Light-house
Rhio, Bintang Island: Residency flag-
staff
Pitong Island : Peak
Abang Besar Island : N. pt
Linga Island : Flagstaff
Singkep Island: Mountain summit.
Menali Island: N. pt
Nicobar Islands, Car Nicobar: N. pt . . .
l^t. N.
13 04 06
13 05 15
13 25 15
13 53 08
15 47 00
16 09 45
16 56 21
17 41 34
18 19 00
19 13 00
19 22 30
19 48 17
20 20 20
21 27 15
21 38 40
22 11 10
22 33 25
22 11 00
20 05 00
20 08 53
18 51 00
18 50 30
16 01 30
15 42 14
16 01 30
14 12 30
13 18 40
11 40 40
10 27 00
15 37 26
16 30 01
16 46 00
16 26 00
16 04 45
15 52 00
13 36 40
12 26 15
12 06 00
10 05 05
9 58 00
50 00
24 45
13 05
52 10
24 08
11 30
1 09 57
1 17 11
1 19 57
1 04 20
1 03 13
0 57 10
0 44 30
0 55 50
0 36 52
0 36 30
Lat. S.
0 12 34
0 26 13
0 57 51
Lat. N.
9 15 40
Lun. Int.
Long. E.
H.W.
80 14 51
80 17 00
80 19 12
80 12 30
80 59 00
81 11 00
82 15 05
83 17 42
84 07 30
84 52 06
85 03 29
85 49 09
86 44 00
87 02 20
88 02 00
88 11 07
88 20 12
91 49 00
92 39 00
92 52 40
93 56 30
93 31 00
94 13 16
94 12 00
94 23 00
93 22 30
92 57 10
92 45 15
92 31 10
95 37 32
96 23 00
96 07 30
97 38 00
97 33 05
97 35 00
98 13 00
98 35 59
99 03 00
98 10 15
97 35 00
98 25 30
100 21 44
100 34 15
100 59 12
101 51 02
102 15 00
103 44 47
103 51 15
104 24 08
104 27 21
104 10 30
104 19 52
104 21 19
104 25 43
104 04 42
104 11 31
104 36 14
104 30 15
105 38 20
92 48 00
h. m.
8 41
8 42
8 48
9 21
1 25
1 02
9 40
3 05
9 50
9 40
4 26
3 07
2 12
10 50
10 40
11 50
5 50
7 20
10 18
9 40
L. W.
h, tn.
Range.
Spg. Neap.
ft.
2 26 3. 1
2 36
2 34
4.5
4.4
3 00 I 6. 8
9 06 11.2
7 56
3 28
9 55
3 37
3 27
11 15
10 49
8 49
4 20
4 10
5 40
12 00
"I'os
"'4'62
3 14
6 00 1 12 13
13.1
18.7
6.3
16.9
11.7
19.2
15.6
18.0
14.4
10.5
"7.*6"
7.1
11.6
ft.
'{'.2
1.9
1.8
2.6
4.4
5.6
"3.'6'
2.9
2.1
7.0
5.0
7.4
3.8
6.2
"4.' 5
"3.'2
3.1
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
SOUTH COAST OF ASIA— Continued.
[Page 239
Place.
Nicobar Islands, Nancowrv Harbor:
Naval Pt
Great Nicobar: AV.
pt. Galathea Bay . .
Acheen (Acheh) Head: Pulo Bras light
N. extreme
Diamond Point: Light-house
Point Baru or Datu: Extreme
Point Bon or Djabon : Extreme
Moeara-Kompehi : Fort
Djambi: Flagstaff of fort
Palembang: Residency flagstaff
Lam pong Bay: Telok Betong light
Blimbing Bay
Kroe: V'^illage
Engano Island: Barioe anchorage
Bintoean: River mouth
Mega Island : N. pt
Benkulen : Light-house
Bantal : Village
Indrapura Point: Extreme
Pisang: Light-house
Padang: Light-house
Siberaet Island : Sigeb Pt
Katiagam : Village
Batoe Islands: N. point of Simoe Islet.
Summit of Tello
Lat. N.
8 02 10
6 46 20
5 45 00
5 34 40
5 15 58
Lat. S.
0 00 32
Ayer Bangis: Fort flagstaff
Natal: Fort flagstaff.
Nias Island : Lagoendi Bay
Sitoli
Lapan
Siboga: Flagstaff
Singkel : Post-office
Bangkaru Islands: Bay
Simaloe Island: NW. pt
Tampat Toewon; Flagstaff
Analaboe
Batve Toetong: Landing place.
00 55
23 13
35 33
59 26
27 00
55 02
11 24
18 50
48 35
59 25
47 22
44 54
10 35
0 59 56
0 57 53
0 53 58
0 07 41
0 03 13
0 02 56
Lat. N.
0 11 41
0 33 11
0 34 47
17 36
24 16
44 24
16 47
02 32
51 30
14 59
08 14
38 21
Long. E.
93 29 42
93 49 20
95 04 33
95 19 00
97 30 11
103 47 58
104 21 30
103 59 14
103 36 41
104 45 34
105 15 58
104 32 36
103 55 42
102 07 28
103 20 18
101 00 58
102 14 50
101 17 25
100 50 06
100 19 28
100 20 19
98 53 58
99 45 20
98 05 55
98 16 43
99 22 09
99 06 33
97 43 43
97 36 46
97 12 28
98 46 08
97 45 06
97 06 53
95 56 02
97 10 13
96 07 23
95 34 29
Lun. Int.
Range.
H. W.
h. m.
9 05
10 00
11 50
5 50
5 35
5 29
L. W.
Spg.
Neap.
h. TO.
2 52
ft-
8.3
ft.
2.8
3 44
5 34
5.2
8.7
2.3
3.7
5 40 11 52
2.6
0.7
12 03
4.0
1.1
11 48
5.5
1.4
11 42 2.8
0.7
EAST COAST OF ASIA.
Java Head : First Pt. light
Sunda Strait: Krakatoa I. peak
North Watcher Island: Light-house. . .
Lucipara I. : Beacon
Banka Island: Tobol Ali Fort . . . .
Berikat, summit
Nanka I. : Light-house
Banka Island: Mintok light
Blinyu
Crassok Pt
Shoal water Island : Light-house
Pulo Lepar: Light-house
Pulo Jelaka: Light-house
Billiton Island: Tandjong Pandanflag
staff
Langkuas I. light
' Caspar Island: Peak
Lat. S.
6 44 30
6 08 46
5 12 17
3 13 05
3 00 48
2 34 18
•2 23 20
2 04 03
1 38 26
1 29 00
3 19 10
2 56 52
2 52 05
2 44 40
2 32 12
2 24 30
105 11 48
105 26 58
106 27 33
106 13 02
106 27 22
106 50 36
105 44 30
105 09 45
105 46 28
106 57 30
107 12 42
106 54 38
107 00 43
107 38 46
107 37 15
107 03 33
5 30
6 50
[9 05]
[6 50]
[2 08]
[3 17]
11 42
0 37
2.5
3.8
[2 52] [10. 1]
[0 38]
[9.3]
[8 21] [5. 6]
[9 29] [6. 6]
0.7
1.1
Page 240]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
Place.
Carimata Island : Sharp peak
Pulo Eu: Center?
Pulo Aor: S. peak, 1,805 feet
St. Barbe Island: Center of W. side
Direction Island: S. pt
Dato Island: Summit
St. Julian Island: Summit
Tambelan Island: S. pt
Tamban I. obs. station
Victory Island : S. pt
Anamba Islands: White rock
Pulo Repon
Pulo Domar
St. Pierre Rock: S. pt.
Natuna Islands: Pyramidal rocks
Semione I
Pulo Varella: Center
Pulo Brala: Center
Tringano River: N. pt
Great Redang Harbor: Bukit Maria I . .
Kalantan: Entrance small river
Cape Patani: NE. pt
Singora: SW. pt. of Ticos I
Koh Krah Islet: SE.pt
Bangkok: Old British factory
Cape Liant: NW. rock of Koh Mesan . .
Chentabun River: Entrance, Bar I
Koh Chang: Small island on W. side ..
Koh Kong: S. pt. of river entrance
Kusrovie Rock: Center
Koh Tang Rocks: SW. rock of group . .
Panjang Island : NW. corner of SW. bay.
Obi Islands: Light-house
Saigon : Observatory
Mitho: S. gate of citadel
Cape St. James : Light-house
Cape Padaran: Extreme
Cape Varella: Extreme
Quin Hon : Battery flagstaff
Condore Islands: Light-house
Safatu Island : Summit
Ceicer de Mer Island : SW. hill
Natuna Islands: Murundum I., SE. pt. .
Low I
Canton Pulo: Light-house
Cham-Callao Islet: Watering place
Tourane Bay: Light-house
Hon-Me: Sunmiit
Nam-Dinh : Citadel tower
Hon Dau Island: Light-house
Hai-Fong: Observation pagoda
Hai-Duong: Citadel tower
Ha-Noi: Citadel tower
Pak-Hoi : Custom-house flagstaff
Hainan Island : Cape Bastion, extreme .
Gaalong Bay, E. Brother
Lat. S.
1 33 24
2 07 00
2 26 30
Lat. N.
0 07 26
0 14 19
0 06 37
0 55 00
0 56 52
00 27
34 41
18 10
25 00
44 31
51 42
03 00
31 00
3 17 00
4 53 00
5 21 40
5 44 21
6 11 53
6 58 01
7 13 54
8 24 47
13 44 20
12 35 08
12 27 43
12 01 20
11 33 00
11 06 25
10 21 20
9 18 14
8 25 20
10 46 47
10 21 16
10 19 51
11 21 00
12 53 40
13 45 23
8 40 06
9 58 23
10 32 36
2 02 55
3 00 00
15 23 34
15 57 10
16 07 00
19 22 14
20 25 30
20 40 03
20 51 44
20 56 29
21 01 57
21 29 00
18 09 00
18 11 30
Long. K.
Lun.
Int.
Range.
H. W.
L. W.
Spg.
Neap.
0 1 II
108 55 13
h. m.
h. m.
ft.
ft.
104 17 00
104 34 06
1
107 13 00
108 01 47
108 37 05
106 45 00
107 32 57
106 24 10
106 18 27
105 35 58
105 52 00
105 22 57
108 38 55
107 21 40
107 42 30
103 40 00
103 38 00
103 08 00
103 01 37
8 00
1 48
5.8
2.5
102 20 47
101 18 39
100 36 12
100 45 27
8 20
2 08
2.8
L2
100 28 42
100 56 47
8 00
2 00
7.3
3.1
102 04 19
102 15 47
10 00
3 50
4.5
2.1
102 57 14
102 47 49
102 56 34
103 29 14
104 48 30
106 42 10
106 20 38
5 00
11 20
9.8
4.2
107 04 55
108 58 00
109 23 42
109 14 52
106 41 42
109 06 00
108 56 27
109 06 10
107 48 00
109 05 35
108 32 47
108 11 30
105 55 22
106 08 41
106 47 10
106 41 08
9 00
2 48
4.3
2.1
106 17 56
105 48 40
109 06 00
109 35 00
5 00
11 12
14.0
6.6
109 41 30
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued,
[Page 241
Place.
Hainan Island : Light-house
Paracel Islands : Triton I
Observation bank . . .
Lincoln I
Woody I
Pratas Island : NE. part
Ty-f ung-kyoh Island : Center
Tien-pak Harbor: Pauk Pyah Islet ...
Song-yui Point: Extreme
Hui-lang-san Harbor: Mamechow Islet
Mandarins Cap: Summit, 200 ft
Macao ; Fort Guia light
Fort San Francisco
Canton : Dutch Folly light
Raleigh Rock : Center
Gap Rock: Light-house
Hongkong: Cathedral
Wellington Battery
Lema Island : Lema Head
Nine-pin Rock : Center
Tuni-ang Island : Summit
Single Island : E. summit
Mendoza Island : Summit
Pank Piah Rock: Summit
Pedra Blanca Rock: Summit, 130 ft...
Chino Bav: Obs. spot
Cupchi Point: Hill
Breaker Point: Light-house
Cape of Good Hope: Light-house
Swatau : British consulate
Lamock Island : Light-house
Brothers Islets: SE. Islet
Tong-sang Harbor: Fall Peak
Chapel Island : Light-house
Amov : Taitan I. light
Dodd Island : Light-house
Chinchin Harbor: Pisai Islet
Pyramid Point: Extreme
Ockseu Island : Light-house
Sorrel Rock: Summit
Lamyit Island : High Cone Peak
Hungwha Channel : Sentry I
Turnabout Island : Light-house
East Dog Island : Light-house
Min River: Pagoda, Losing I
TemplePt
Alligator Island : Summit
Tung-yung Islands: Peak, N. end
Coney Island: Summit
Double Peak Island : Highest peak . . .
Pih-seang Island : Town I
Dangerous Rock: Summit
Tae Islands: Summit
Nam-<juan Harbor: Bate I
Ping-fong Island : Summit
Pih-quan Peak: Summit
Port Namki : E. horn
Pih-ki-shan Island: Summit
Pe-shan Islands: Summit, SW. end...
Tung-chuh Island: Summit
Kweshan Islands; Patahecock
Nimrod Sound : IVIiddle islet
Tong-ting Islet: Summit
Chin-hai: Citadel
Ning-po: Square I. light
Chusan Islands: Ting-hai Harbor
Lat. N.
20 01 15
15 46 30
16 36 00
16 40 07
16 49 55
20 42 03
21 22 30
21 24 15
21 31 00
21 34 00
21 28 00
22 11 40
22 11 24
23 06 35
22 02 00
21 48 50
22 16 52
22 16 23
22 03 40
22 15 45
22 27 06
22 24 06
22 30 42
22 32 54
22 18 30
22 48 14
22 48 07
22 56 24
23 14 00
23 20 43
23 15 43
23 32 30
23 47 15
24 09 49
24 23 16
24 25 44
24 49 13
24 52 12
24 59 36
25 02 18
25 12 00
25 16 30
25 26 10
25 58 10
25 59 00
26 08 26
26 09 29
26 22 37
26 30 00
26 36 06
26 42 30
26 51 25
26 58 52
27 09 20
27 09 42
27 19 18
27 26 18
27 37 36
28 05 07
28 43 45
29 22 45
29 34 20
29 51 53
29 57 08
29 59 21
30 04 30
Long. E.
110 16
111 14
111 40
112 43
112 20
116 43
111 10
111 15
111 38
111 46
112 21
113 34
113 33
113 16
113 47
113 56
114 09
114 10
114 19
114 22
114 36
114 39
114 50
115 01
115 06
115 47
116 04
116 29
116 47
116 40
117 17
117 42
117 36
118 13
118 10
118 30.
118 41
118 58
119 27
119 10
119 35
119 45
119 56
119 59
119 27
119 37
120 24
120 29
120 10
120 11
120 22
120 32
120 42
120 25
120 32
120 27
121 06
121 12
121 30
121 55
122 13
121 43
122 35
121 43
121 45
122 03
Lun. Int.
H. W.
L. W.
h. in.
h. m.
11 50 5 37
9 50 3 38
'2'66T"8'66'
Range.
Spg.
8.2
6.3
"5."i"
Neap.
9 20 2 52 4. 4 2. 0
0 30 7 00
9 45 , 3 33
ft.
3.8
3.0
2.' 4
1
1 1
1
2 50
9 00
7.5
3.5
11 20
5 08
12.0
7.6
0 05
6 13
15.6
9.9
\
19. 3 12. 2
19. 0 12. 0
50 I 3 38 ! 17. 2 i 10. 9
1 00
7 12 8.
4.6
22489—03-
-16
Page 242]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
Place.
Video Island: Summit
West Volcano Island: Light-house
Chapu: Battery
Gutzlaff Island: Light-house
Saddle Islands: N. Saddle light...
West Barren Island: Summit
Shanghai: Kng. consulate flagstaff
Wusung: Light-house
Shaweishan Island: Light-house..
Lat. N.
30 08 04
30 20 50
30 36 00
30 48 37
30 51 41
30 44 07
31 14 42
31 23 18
31 25 27
Pescadores Islands:
Fisher I. light 23 32 53
Second pt. on N. side I
Makung Harbor.. 23 32 54
South Cape : Light-house
Takau: Saracen Head
Port Heongsan
Tam-sui Harbor: White Fort
Kelung Harbor: Light-house
Soo (Sauo) Bay: Beach near village..
Botel Tobago Sima: S. extreme
Tanjong Datu
Sardwak River: Po Pt. light
Sardwak: Fort
Cape Sirik : Light-house
Tanjong Barram
Bruni River: Light-house
Labuan I. , Victoria Hbr. : Light-house.
Sandakhan Harbor: Light-house
Unsang: Anchorage
Cape Kaniongan: E. pt. of Borneo
Pamaroongl. : E. pt. delta River Koetei.
Pulo Laut: S. pt. Koengit Islet
Selatan Point: Extreme of Sita Pt
Bandjermasin: Residency flagstaff
Sampit Bay : Bandaran Pt
Kottaringin Bay : Samadra I
Succadana: Town
Padang Tikar: Point
Port Laykan: SW. pt. of Celebes
Macassar: Fort light
Palos Bay: Village at head
Cape Rivers: NE. Cape, Slime Islet...
Gorontalo: Light-house
Manado Bay : Light-house
Bajuren Island : Summit
Tagulanda Island : Peak
Seao Island : Conical peak
Sauguir Island : S. pt. Cape Palumbatu.
Taluat Island: Kabruang I., SE. pt...
Cape Flesko: Extreme
21 55 00
22 36 14
24 46 00
25 10 24
25 09 12
24 35 28
22 01 40
05 15
43 50
33 55
45 20
36 15
02 00
15 25
50 10
16 30
04 00
Lat. S.
0 45 00
05 42
10 40
18 55
16 00
54 00
14 00
0 40 00
5 36 00
5 08 09
0 57 00
Lat. N.
1 20 00
0 29 41
Cape Talabo: E. end..
Wowoni Island: N. pt
Bouton Island: N. pt .
E. pt .
Fort..
Cape Lassa: Extreme .
Salayar Island : N. pt .
S. pt .
31 00
07 00
22 00
44 00
21 00
3 49 00
0 27 00
Lat. S.
0 46 00
3 58 00
4 23 30
5 15 00
5 29 15
5 35 00
5 47 00
6 26 00
Long. E.
Lun. Int.
Range.
H. W.
122 45 48
121 51 25
121 03 00
122 10 12
122 40 17
123 08 27
121 28 55
121 29 36
122 14 12
119 28 05
119 30 12
120 51 00
120 15 54
120 55 00
121 25 00
121 44 28
121 49 20
121 39 45
109 39 07
110 30 30
109 20 40
111 21 20
113 58 57
115 03 00
115 16 05
118 07 20
119 16 00
118 56 00
117 37 00
116 01 40
114 42 18
114 34 56
113 08 00
111 24 00
109 58 00
109 16 00
119 26 00
119 23 55
119 47 30
120 43 30
123 03 08
124 50 00
125 22 00
125 24 30
125 26 00
125 39 00
127 02 30
124 26 00
123 27 00
123 00 00
123 04 00
123 16 00
122 36 41
120 29 00
120 30 00
120 28 30
h. TO.
L. W.
Spg. Neap.
0 12
9 45
10 00
10 15
6 00
4 00
5 20
9 35
12 00
[7 45]
7 00
4 40
6 00
h. m.
St.
06
).l
3 32
4.0
3 47
4 03
12 13
8.0
3.0
5.8
10 12
11 35
9.0
14.1
3 23
5 50
5.5
5.2
[1 33] [7.0]
0 47
7.2
10 55
3.9
12 15
4.3
4.8
1.7
3.4
1.3
2.5
3.9
6.1
2.4
2.2
3.1
2.9
3.1
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
[Page 243
Place.
light
Anjer: Fourth pt. light
Bantam : Flagstaff
Batavia: Observatory
Buitenzorg: Palace tower ..
Boompjeo Island: Racket I.
Cheribon : Light-house
Tegal: Flagstaff
Pekalongan: Light W. of entrance.
Samarang: Light-house
Rembang: Residency flagstaff
Surabaya: Time-ball station .'.
Paauruan : Light-house
Madura Island: Light-house
Soemenep flagstaff
Besuki : Light-house
Cape Sedano: NE. pt. of Java
Banju wangi : Fort
Bantenan: S. pt. of Java
Barung Island: S. pt
Kambangan Island: Light-house ..
Cape Anjoe: Extreme
Lat. s.
Karimon Djawa Island: Flagstaff
Rawean Island : Sangkapura flagstaff
Great Solombo Island: N W. pt
Arentes Island : S. pt
Bali Island: Bliling light-house
Peak, 11,326 ft
Badong Bav, Kotta village.
Lombok Island: Peak 12,379 ft
Ampenam light
Sumbawa I. : Sumbawa village
Tambora Volcano, sum-
mit E. side of crater
Bima, flagstaff
Postilion Islands: N. island
Maria Reigersbergen I
Ardassier Islands: S. id
Brill Reef: Light-house
Hegadis Island
Token Bessi I. : Wangi-Wingi, NW. pt.
Binongko, S. pt
Gunong Api : Volcano
Lucipari Islands: N. islet
Flores Island : Reo village
Ende village
Flores Head, extreme
Komba Island: Peak, S. part
Adenara Island: Summit, Mount Woka.
Lombata Island: Mount Lamararap
Pantar Island : S. peak of saddle on S. pt
Ornbay Island : Dololo anchorage
Timor Island: Deli, custom-house
Atapopa
Koupang, Fort Concor-
dia
Rotti Island: W. pt
Saru Island: Seba Bay, on NW. side
Sandalwood Island : Nangamessie
Wetta Island : Ilwaki road
Roma Island: W. pt
6 04 15
6 01 20
6 07 40
6 35 45
5 56 15
6 43 00
6 51 09
6 51 29
6 57 09
6 42 18
7 12 10
7 37 30
7 02 00
7 02 30
7 43 25
7 49 00
8 12 30
8 47 00
8 32 00
7 46 30
7 25 00
5 52 57
5 51 18
5 32 28
5 05 46
8 05 30
8 21 00
8 42 30
8 23 00
8 34 15
8 32 00
8 12 30
8 27 00
6 31 00
7 30 00
7 35 00
6 05 50
6 07 00
5 15 00
6 17 00
6 43 00
5 28 30
8 16 15
8 50 55
8 04 45
7 48 00
8 20 30
8 33 00
8 34 00
8 12 00
8 34 00
9 00 00
10 09 54
10 46 00
10 29 00
9 35 03
7 53 00
7 38 00
Long. E.
105 53
106 08
106 48
106 49
108 22
108 34
109 08
109 41
110 25
111 20
112 43
112 55
112 41
113 53
113 41
114 26
114 22
114 25
113 15
109 02
106 24
Lun. Int.
Range.
H. W.
110 25 29
112 39 10
114 23 42
114 35 00
115 03 48
115 28 00
115 08 47
116 27 30
116 04 09
117 20 33
117 57 00
118 43 55
118 43 00
117 56 00
117 22 00
118 56 50
122 40 00
123 32 00
123 59 00
126 43 30
127 30 00
120 29 55
121 38 40
122 52 00
123 31 00
123 15 00
123 22 00
124 06 00
124 23 00
125 33 57
124 52 00
123 33 57
122 52 00
121 46 00
120 14 30
126 22 00
127 19 00
7 11
[11 58]
[6 00]
12 07
11 44
10 00
8 33
10 50
7 50
0 00
L. W.
Spg.
Neap.
h. m.
0 58
ft-
2.4
ft.
0.7
[5 46]
[3.0]
[12 13] [4.0]
5 54
5 31
3 45
2 21
4 38
1 37
6 12
0 45
10 50
6 58
4 37
11 20
4.9
6.2
7.8
i.7
5.8
5.7
5.7
8.5
1.7
2.3
2.6
5.2 I 1.8
3.0
2.0
2.0
2.0
2.9
5 07
16.5
5.6
Page 244]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
Lun. Int.
Place.
Moa Island: Bu^alo Peak, 4,100 ft
Sermalta Island : NE. pt
Damma Island : Kulewatta Harbor, N.pt.
Nila Island : Center.
Mano or Bird Island: NW. extremity..
Timor Laut Island: Olilet, on E. coast..
Vordate Island : S. pt
Mulu Island : N. pt
Arm Islands: S. island
N.pt
Great Ki Island : S. pt
Tello Islands: S. island, summit
Tehor Island: NE. pt
Matabella Islands: Kukur
Goram Islands: Goram Mosque
Banda Island: Mole
Bouro Island, Kajeli : Fort Defense
Ceram Island : Kawa
Amboina Island: Light-house
Xulla Islands, Taliabo Island: NW. pt. .
Mangola Island: E. pt ..
Besi Island: E. pt
Oby Major Island : W. pt
Popa Island: Outer Extremity Bay
Mysole Island : Ef be Harbor
Gebey Islands: NW. pt
Gillolo Island: Cape Tabo: E. extreme .
Cape Salawag: NE. pt . .
Derrick Point: N. ex-
treme
Molucca Is. , Makkian I. : Fort Reeburgh .
Ternate Island: Residency
flagstaff
Batian Island : Church
Meiaco-Sima Is., Kumi I: N. Beach ...
Broughton Bay: Land-
ing place
Port Haddington:
Hamilton pt
Tai-pin-san: Hirara,
Karimata Anch
Raleigh Rock: Summit, 270 ft.
Ti-ao-usu Island: Summit, 600 ft
Hoa-pin-su Island : N. face
Loo Choo Islands, Great Loo Choo:
Nafa-Kiang
Yori-sima, 413 ft. .
Yerabu-sima peak,
687 ft
Kakirouma: Sum-
mit, 2,207 ft
Iwo-sima: Volca-
no, 541 ft
Oho-sima: N. ex-
treme
Kikai-jima: Sum-
mit, 867 ft
Lat. S.
Range.
8 12
8 14
7 03
6 44
5 32
7 55
7 04
6 35
10
20
56
20
44
33
03
31
3 22
2 55
41
44
48
28
30
11
04
Lat. N.
0 02 02
0 11 00
1 26 00
2 12 00
0 24 00
0 47 13
Lat. S.
0 38 03
Lat. X.
24 26 00
24 21 30
24 25 00
24 48 18
25 55 00
25 58 30
25 47 07
26 12 25
27 02 00
27 21 00
27 44 00
27 53 00
28 31 40
28 18 00
Long. K.
128
129
128
00 I 129
50 1.30
131
131
131
134
134
132
131
131
131
131
129
127
128
128
122
126
126
127
129
130
01 00
00 00
28 00
29 00
17 44
23 30
55 00
40 00
24 00
40 00
54 00
58 00
47 00
50 00
25 23
53 18
06 18
07 04
10 00
20 00
21 19
01 00
18 00
55 48
12 00
122 56 00
124 17 40
124 06 40
125 17 57
124 .35 00
123 40 00
123 30 31
127 40 10
128 25 24
128 33 10
128 59 00
128 14 30
129 42 30
129 59 00
H. W.
L. W.
Spg.
ft.
Neap.
7 57
7 32
9.0
4.2
6.6
3.1
2 20
8 32
7.5
5.5
129 17 30
128 52 00
128 37 00
128 03 30
127 21 00
127 22 39 j 5 00
127 28 21
11 10
3.9
7 27
1 14
4.9
2.1
6 30
0 15
5.8
2.5
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
LPage 245
1
Place.
Lat. N.
Long. E.
Lun
Int.
Range.
H.W.
L.W.
Spg. Neap.
1
•
M
e
a
a
3
■a
S
Baliibac Island, Cape Melville: Light-
house -
O / If
7 49 25
8 20 25
9 22 30
9 43 43
10 50 00
10 29 19
11 26 25
10 51 26
11 09 09
11 25 47
11 53 53
12 02 09
12 39 46
11 54 28
12 06 45
12 20 03
12 50 15
13 28 40
13 31 35
13 06 05
12 17 15
13 49 30
13 45 22
13 56 17
14 12 20
14 21 48
14 22 27
14 29 50
14 35 49
14 35 31
14 52 36
14 55 33
15 19 30
15 34 48
15 45 43
16 04 06
16 27 15
16 37 15
17 11 43
17 16 55
17 33 56
17 47 17
18 01 09
18 31 08
18 39 02
18 21 43
18 28 32
18 32 02
18 50 26
18 52 54
19 03 03
19 22 00
19 80 00
O / II
117 00 00
117 09 35
118 17 30
118 43 03
119 31 10
119 05 36
119 29 55
121 00 25
120 56 26
120 45 38
120 00 48
120 12 56
120 27 18
121 30 24
121 20 10
121 03 33
120 44 42
120 22 33
120 59 17
121 29 20
121 01 53
120 09 58
121 02 56
120 43 37
120 38 10
120 36 40
120 33 48
120 54 40
120 57 19
120 58 06
120 13 52
120 00 15
119 57 11
119 54 16
119 54 00
120 06 01
119 56 10
120 18 25
120 26 14
120 25 07
120 22 51
120 25 04
120 28 44
120 35 35
120 50 53
121 37 27
122 04 14
122 05 49
121 48 26
121 15 42
121 11 28
121 32 00
121 52 00
h. m.
h. m.
Si.
ft.
Paldwan Island, Cape Bovliluyan: S.
extreme
Victoria Peak, 5,680 ft.
Port Royalist: Tide
Pole Pt. Light
Taytay Fort
Port Barton : Bubon Pt.
Kabuli I. : Summit, N.
extreme
[11 30]
[5 20]
[6.5]
Cuyo Island : Obs. spot
Agutaya Islet: Summit of Mt. Aguade. .
Quiniluban Islet: Summit
•
Culion Island: Fort l
Busuanga Island: Mt. Tundalara
Apo Islet: Summit
Caluya Island : Summit
Semerara Island : N. extremity
tremity
Sablayan Pt.,Vantay.
Monte Calavite
Escarceo Pt
j
Pt. Dumaly
Ylin Island
Lubang Island, Port
Tulig
Luzon Island, Batangas: Ast. station...
Balayan: Plaza Rizal
Loro Peak : Summit, 3, 985
feet
[11 07]
[4 50]
[4.9]
Caballo I.: Light-house .
Corregidor Island: Light-
house
[10 22]
[3 56]
[4.4]
Cavite: SangleyPt. light.
Manila: Pasig light-house
Manila: Cathedral
Subig: Town
10 44
[4 10]
[4.6]
[9 42]
[4 33]
[3.8]
CaponesIslet:Light-house
Iba: Ast. station
Port Masinloc: Bani Pt..
Santa Cruz: Plaza
Sual: Army Hospital
Silaqui Islet: Summit . . .
Port San Fernando:
Main street
[10 20]
;iO 21]
[9 40]
[3 33]
[3 44]
[3 29]
[2.4]
[2. 3]
[2.6]
Candon: Ast. station
Port Santiago: Remark-
able tree S. of port
Vigan : Race track
Salomague Island: Port
Salomague flagstaff
Currimao: Town >..
Capa Bojeador: Light-
house
Mairaira Pt. : Semaphore
Aparri : Plaza
5 43
-0 02
3.2
1.9
, Port San Vicente: San
Vicente Islet
CapeEngano: Rona Islet
Camiguin I. : Summit
Fuga Island: W. summit.
Dalupiri Island : Peak . . .
Calayan Island : NE. pt
6 00
-0 12
5.0
2.7
Babayan Claro Island : W. pt
Page 246]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
Place.
Lat. N.
Balingtang Islands
Batan Island : Morfnt Irada
Ibayat Island : Mount Santa Rosa
Yami Island: Islet off SW. part
Luzon Island, Port Dimasalasan: En-
f 1*3.11 OP
Polillo I.V PoVt'PoliYlo' '.
Tabaco: Church belfry .
Cautanduanco Islands:
N. islet
Cautanduanco Islands:
S. extreme
Point Calaan : S. extreme'
Port Sorsogon, Tinacos
Islet
Masbate Island, Palanog: Pier
Bugui Pt. light-house..
Camasusu I.: Summit .
Tintolo Point: Extreme
Burias Island : Busainga
Marinduque I. : Summitof MountCatala.
Maestro de Campo Island, Port Con-
cepcion: Point Fernandez
Ban ton Island : Ban ton Mountain
Tablas Island : Tablas Head
Sanguilan Pt
Carabao Island: W. pt
Romblon Island: Sabang Pt. light
Summit over port
Sibuyan Island : Summit
Samar Island, Guiuan : Pier
Catbalogan : Fort
Maripipi Island: Summit ^ . .
Leyte, Tacloban
Ormoc: Ast. station
Palompon : Church
Maasin
Bohol I., Lapiniu I. : Mount Basiao
Cebu Island, Cebu : Plaza
Siquiquor Island, Port Canoan: S. pt. of
entrance
Negros Island, Port Bunbonon: E. pt.
of entrance
Dumaguete : Town
Volcano of Malaspina,
8,192 ft
Bacalod: Town
Guimaras I., Inampulugan I., SW. pt ..
Panay Island, Iloilo: Fort
San Jos^
Pan de Azucar
Batbatan Island: Summit
Pucio Point: Extreme...
Port Batan: Village
Capiz: Town
Siargao Island, Port Sapao: Semaphore.
Gibdo Island : Semaphore
Bucas Island: E. pt. of Port Sibanga . . .
Mindanao Island: Surigao
Cape St. Augustin . . .
Mindanao Island, Davao: Mole
Saranguni Islets: W.
islet
Basianang Bay: N.
pt. of Donauang I.
Polloc: Small hill
back of town
19 58 30
20 28 30
20 48 00
21 04 56
17 20 17
14 51 00
13 21 33
14 09 00
13 28 30
12 31 20
12 52 20
12 22 10
12 36 00
12 10 03
11 56 09
13 07 40
13 18 10
12 54 03
12 56 56
12 38 42
12 33 44
12 03 15
12 36 00
12 35 33
12 24 55
11 01 30
11 46 44
11 47 30
11 15 08
11 00 17
11 02 37
10 07 39
10 03 22
10 17 30
9 15 17
9 03 37
9 18 25
10 24 35
10 40 21
10 26 38
10 41 27
10 44 08
11 16 47
11 28 20
11 45 30
11 35 40
11 35 06
10 11 26
9 53 00
9 41 34
9 47 53
6 14 30
7 01 22
5 22 30
6 28 50
7 21 15
Long. £.
122 14 00
122 01 20
121 52 30
121 58 24
122 19 20
121 54 48
123 43 53
124 06 48
124 04 48
124 04 18
123 49 22
123 35 58
123 14 36
123 12 47
123 07 34
123 02 45
121 54 33
121 43 08
122 04 48
122 08 38
121 58 32
121 53 53
122 17 08
122 16 26
122 33 23
126 43 14
124 51 37
124 18 15
124 59 56
124 36 20
124 22 07
124 50 15
124 32 35
123 54 18
123 34 26
123 06 09
123 18 43
123 07 05
122 55 42
122 40 20
122 34 26
121 54 27
122 09 09
121 52 36
121 58 59
122 28 50
122 45 03
126 02 53
125 31 17
125 58 22
125 28 30
125 47 48
125 34 35
125 13 48
123 57 37
124 11 42
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
h. m.
h. TO.
ft-
ft-
6 08
0 00
5.2
2.8
[4 30]
[10 20]
[5.5]
6 53 1 25
1.5
1.1
11 47
4 50
2.8
2.0
11 06
5 22
4.2
1.9
[11 40]
[6 15]
[6.5]
6 00
-0 13
6.9
5.1
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF A RIA— Continued.
[Page 247
o
i
g
•
»
e
a.
a.
a
i
2
i
£
e
Place.
Lat. N.
Long. E.
Lun.
Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
Mindanao Island, Santa Cruz Islands:
SE islet
o / //
6 52 15
6 54 03
7 18 05
7 45 41
8 40 15
8 08 29
9 10 19
10 43 00
10 27 00
9 35 30
7 43 00
7 00 38
4 54 10
4 49 30
4 55 30
5 50 00
5 00 30
5 13 00
5 25 15
5 27 10
5 32 40
5 41 30
5 44 30
5 54 45
6 02 30
6 03 40
5 52 30
6 15 15
6 42 43
35 39 00
36 02 50
36 45 29
37 24 00
37 27 41
37 34 10
37 36 00
38 23 37
38 58 16
39 09 00
38 56 00
40 35 00
39 30 46
39 16 00
38 43 17
38 47 50
38 52 38
38 40 00
39 04 00
38 27 00
37 58 00
37 27 40
36 26 45
36 24 30
36 07 00
O 1 II
122 04 00
122 04 52
122 03 18
122 04 58
123 23 13
123 50 44
124 42 50
121 33 00
121 03 00
121 23 30
118 27 00
118 26 06
119 22 45
119 48 00
119 46 45
118 11 00
119 44 15
120 40 45
120 35 00
120 11 30
120 48 25
120 49 45
120 55 00
121 00 40
121 18 20
120 58 40
119 55 55
120 29 30
121 56 50
119 51 30
120 17 30
122 16 48
122 42 00
122 15 05
121 31 09
121 26 21
120 55 00
117 42 48
117 11 44
118 31 00
122 00 00
121 18 03
121 35 59
121 08 26
121 15 54
121 51 59
122 11 30
123 10 34
124 34 40
124 34 30
126 36 27
126 28 00
126 24 00
126 01 09
h. m.
h. TO.
ft.
/t.
Zamboanga: Fort...
Sibuco Bay: Hill S.
of beach
6 50
0 42
3.8
2.8
Port Sta. Maria:
Fort
Dapitan: Village
Misamis: Fort
Camiguin Island: Mount Camiguin
Sombrero Rock : Center
1
[10 48]
[4 50]! [5.1]
1
Piedra Blanca : Center ....
Cagayanes Islands: Rocky islet be-
tween two larger islands . .
San Miguel Isles: E. pt. of Manuk Ma-
nukan
Cagayan Jolo Island: Middle of W.
coast ....
Omapui Island: NW. extreme
Sibutu Island: Hill on E. coast
Simonor Island: NW. pt
1
Bahaltolis Island: Sandakan Harbor...
Bongao Island : S. pt
1
Keenapoussan Island : Center .
Bubuan Island : Lagoon entrance
Cuad Basang Island: SW. pt
1
i
Siassi: Town
5 54
-0 18
8.6
6.4
Bulipongpong Island : Center hill
Tapul Island: Center hill, 1,676 ft
Jolo Islands: Maimbun Anchorage, dry
bank
i
Dalrymple Harbor, Tul-
yan Islet
Jolo light-house
[9 38]
[3 10]
[5.0]
Doc Can Islet: W. extreme . .
Pangituran Island: SW. pt. .. ....
j _
Basilan Island : La Isabela
W^ang-kia-tia Bay: Langwang temple ..
Kyauchau Bay : Yunuisan light
Staunton Island: Landing place, N. side.
Shantung Promontory: Light-house
Weihaiwei: Light, S. side harbor
Chifu: Light-house
4 50
11 03
11.4
6.0
4 00
9 20
10 25
10 12
3 08
4 13
6.8
9.0
8.1
5.0
6.6
6.0
Fort
Miautao Island: Peak of N. Island
Pei-ho: S. Taku Fort, S. Cavalier
Tientsin: Shore opp. NE. angle of wall. .
Shaluitien Island: Light-house
Niuchwang: Lightship
6 50
1 00
4.5
3.3
4 30
10 50
11.7
8.7
Hulu-shan Bav: N. side
1
Liao-ti-shan Promontory: SW. pt. light
Port Arthur: Obs. spot
1
10 05
3 53
7.5
5.5
Ta-lien-wan Bay: Isthmus on S. San-
shan I
Round Island : Summit
Thornton Haven, Hai-yun-tan Island:
Beach opposite Temple Point
Choda Island: S. pt
Sir James Hall Islands: N. island
Chemulpo : So W^olmi
4 19
10 31
28.8
11.6
Marjoribanks Harbor: Manzoc Islet
Tas de foin Islet: Center
Guerin Island: Summit, 969 ft.. ..
1
Page 248]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
Place.
Lat. N.
Kokoun-tan Islands: Camp Islet
Barren Island : Center, 600 ft
Sea Rock: Center, 160 ft
Modeste Island: N. peak, 1,228 ft
Ross Island: Peak, 1,920 ft
Kuper Harbor: NE. extreme of Josling I .
Port Hamilton: W. pt. of Obs. Island..
Bate Islands: Summit Thornton Islet
Montravel Island: Center, 1,041 feet
Quelpart Island: Beaufort I., middle
of W. side
Observation Island: Point of W. arm...
Sentinel Island: Summit, 400 feet
Broughton Head : Extreme
Tsau-liang-hai Harbor: Light-house
Tsu Sima : Observation rock
Iki Sima: Summit, S. end of island
Oro No Sima: Summit, 277 ft
Kosime No Osima: Summit Wilson I. . .
Yeboshi Sima: Light-house
Yobuko Harbor: Bluff opposite Nicoya.
Hirado No Seto: Taske light
Goto Island : Ose Saki light
Pallas Rocks: S. rock
Meiaco Sima: Ears Peak
Nagasaki : Transit Venus Station
Kuchinotsu : Light-house
Kagoshima: Breakwater light
.Tsukarase Rocks: Summit, 96 ft
Uji Shima: High peak, 1,097 ft
Yamagawa Harbor: Spit N. of town
Satano Misaki : Light-house
Kusakaki Jima: Ingersoll Rocks, 530 ft.
Kuro Sima: 2, 160 ft
Iwo Shima: Peak, 2,469 ft
Yakuno Shima: Mount Matomi,6,252 ft.
Firase Rocks: Highest, 92 ft
Kuchino Shima: Summit, 2,230 ft
Guaja Shima: Summit, 1,687 ft
Naka no Shima: Peak, 3,400 ft
Suwanose Jima: Volcano, 2,706 ft
Tokara Jima: Summit, 860 ft
Yoko Shima: Summit, 1,700 ft
Shimonoseki Strait: Meji Zaki, extreme.
Rokuren Island : Light-house
Shirasu Reef: Light-house
Susaki: SW. battery
Tomo Roads: Tamatsu Sima
Port Okayama: Take Sima temple
Wusimado Pt. : Wusimado Peak, 548 ft.
Akashi-no-seto: Maico Fort
Hiogo: Wada Misaki light
Kobe: Light-house
Osaka: Fort Temposan light
Sakai: Pier-head light
Osaki Bay : Tree Islet, S. pt
Yura No Uchi: Pier
Tanabe Bay:- Fossil pt
Oo-sima Hbr. : Kashinosaki light, E. pt.
Uragami Harbor: Village pt
0\va.shi Bay: Hikimoto
Mura Harbor: Osima Islet
35 48 08
35 21 00
34 42 00
34 42 30
34 06 00
34 17 20
34 01 23
33 57 00
33 59 00
33 29 40
34 39 00
34 33 00
34 48 00
35 07 15
34 18 55
33 44 30
33 52 10
33 53 50
33 41 30
33 32 30
33 23 31
32 36 45
32 13 12
32 03 00
32 43 21
32 36 05
31 35 39
31 20 00
31 12 00
31 12 43
30 59 30
30 51 00
30 50 00
30 47 00
30 17 00
30 05 00
29 59 00
29 54 00
29 52 00
29 38 00
29 08 00
28 47 30
33 57 46
33 58 53
33 59 11
33 23 19
34 22 37
34 35 58
34 37 27
34 38 05
.34 39 20
34 41 18
34 39 45
34 35 12
34 07 42
33 57 34
33 41 14
33 28 15
33 33 37
34 06 10
34 13 ^
Lun. Int.
Long. E.
Range.
H.W.
126 31 00
125 58 00
126 19 45
125 16 00
125 07 00
126 35 28
127 18 34
126 18 00
126 55 00
126 58 25
128 14 00
128 40 00
128 44 00
129 02 10
129 13 06
129 42 30
130 02 00
130 25 20
129 58 50
129 52 43
129 33 21
128 36 10
128 04 39
128 25 00
129 52 25
130 13 40
130 33 49
129 46 20
129 29 00
130 37 00
130 39 30
129 28 00
129 55 30
130 18 00
130 32 00
130 03 00
129 56 00
129 33 00
129 52 30
129 42 00
129 13 30
129 01 30
130 57 50
130 52 07
130 47 36
133 17 00
133 23 23
133 59 24
134 09 21
135 01 51
135 10 56
135 11 34
135 26 00
135 27 44
135 08 19
135 07 21
135 23 04
135 51 59
135 54 25
136 14 35
136 48 61
9 06
7 36
8 56
L. W.
9 23
7 54
6 40
7 20
30
5 55
11 16
h. 111.
2 52
10.5
1 23
2 44
7.0
3 10
6.4
1 41
1 00
8.4
ib'.h'
1 08
9.5
2 20
6.7
12 08
5 04
6.0
10.2
7 30
6 23
1 26
4.7
0 10
4.7
Neap.
ft.
4.2
3.0
2.4
2.5
3.5
*4."4
3.9
2.4
2.0
4.5
2.0
2.0
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
[Page 249
Place.
Matoya Harbor: Anori-saki light
Oinoi Saki: Light-house
Shimizu Bay : Mound on pt
Mikomoto Island : Light-house
Simoda Harbor: Center I
Yokosuka Harbor: Eyi Yama pt
Yokohama: P^nglish Hatoba light
Tokio: Naval Observatory
No Sima Saki: Light- house
Vries Island (O Sima) Volcano: Sum-
mit, 2,512 ft
Kozu Shima V^olcano: Summit, 2,000 ft.
Mikake Jima: Summit, 2,690 ft
Redfield Rocks: S. rock
Mikura Jima: Summit
Broughton Rock: Summit, 60 ft
Fatsizio Island : Observation spot
Aoga Shima: Center
Bayonnaise Island: Summit, 26 ft
Smith Island : Summit, 250 ft
Ponafidin Island: Summit, 1,328 ft
Lots Wife Rock: Summit, 300 ft
Inaboye Saki : Light-house
Kinkwosan Island: Light-house
Kamaishi Harbor: SE. end of village . .
Yamada Harbor: Ko Sima, 90 ft
Siriya Saki: Light-house
Toriwi Saki: Center of Low Islet off . . .
Awomori: Light-house
Tatsupi Saki: N. side
Bittern Rocks: SW. rock
Tobi Shima: Takamori Yama
Awa Sima: NE. extreme
Sado Island: Ya Saki
Fushiki Harbor: Light-house
Cape Roigen : Extreme
Niigata: Buddhist temple
Mana Sima: Summit, 200 ft
Manao Harbor: Sorenjo Pt
Tsuruga: Town
Oki Islands: N. pt
Taka Yama (Cape Louisa) : Extreme. . .
Ai Sima: Summit, 300 ft
Mino Sima: Summit, 492 ft
Kado Sima: Tsuno Shima light
Hakodate: Light-ship
Endermo Harbor: Bluff on E. side
Okishi Bay: Light-house
Noshiaf Saki : Light-house
Nemuro: Benten Sima light
Notsuke Anchorage: Village
Noshiaf Misaki : Light-house
Risiri Islet: Peak, 5,713 ft
Lat. N.
Kunashir Island: St. Anthonys Peak .
Iturup Island : NE. pt
Urup Island: Cape Vanderlind
Broughton Island : Summit. . . y.
Simusir Island: Prevost Peak
Ketoy Island: S. pt
Matana Island: Peak
Shiash-Kotan Island : Center
Kharim-Kotan Island : Peak
Oune-Kotan Island : SW. pt
Moukon rushi Island : Center
Poro musir Island: Fool's Peak
Soumshu Island : Center
Lun. Int.
34 21 57
34 35 52
35 00 51
34 34 25
34 39 49
35 17 30
35 26 52
35 39 18
34 54 17
34 43 30
34 13 15
34 05 00
33 56 50
33 52 00
33 39 00
33 04 24
32 29 00
32 00 40
31 27 00
30 28 26
29 46 28
35 42 13 I
38 16 57 1
39 16 30 I
39 27 17
41 25 58
41 33 34
40 50 00
41 16 17
40 31 00
39 12 02 I
38 29 23 '
38 19 55 I
36 47 47 I
37 28 00
37 55 14
37 35 00
37 02 37
35 40 24
36 30 00
34 40 00
34 32 00
34 48 00
34 21 12
41 47 36
42 19 54
42 56 52
43 22 56
43 20 22
43 33 11
45 26 30
45 11 00
44 20 00
45 38 30
45 37 00
46 42 30
47 02 50
47 17 30
48 06 00
48 52 00
49 08 00
49 19 00
49 51 00
50 15 36
50 46 00
Long. E.
Range.
H. W.
136 54 09
138 13 49
138 31 19
138 56 30
138 57 30
139 39 43
139 38 41
139 44 30
139 53 24
139 23
139 08
139 31
138 48
139 34
139 17
139 50
139 43
140 00
140 02
140 14
140 19
140 52
141 35
141 52
141 59
141 27
140 56
140 44
140 22
139 31
139 32
139 15
138 27
137 03
137 22
139 03
136 54
136 58
136 01
133 23
131 36
131 18
131 09
130 50
140 41
140 59
144 52
145 49
145 34
145 18
141 38
141 19
146 15 00
149 14 00
149 34 00
150 28 30
151 52 50
152 24 00
153 12 30
154 08 00
154 39 00
154 44 00
154 32 00
156 15 20
156 26 00
5 52
5 52
5 25
5 04
L. w.
Spg.
Neap.
4 30
2 30
11 41
3 40
3 32
3 41
3 48
3 33
4 50
12 04
12 04
11 30
11 17
10 45
8 42
5 28
10 00
9 45
9 53
10 00
9 46
11 05
4.3
3.9
4.9
3.7
3.4
0.6
1.1
3.0
3.5
3.0
3.1
2.1
3.7
ft.
1.7
1.6
1.9
1.4
1.3
0.4
0.5
1.8
^'' Or- the'
l^NIVERSITY
^^'
Page 250] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
*s
Place.
Lat. N. Long. E.
Lun. Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
t
0
i
t
9
P
Cape Clonard : E^reme
O > t> O 1 II
36 05 45 ! 129 33 30
36 36 00 1 129 20 00
37 09 30 1 131 55 00
37 30 00 ' 130 53 00
39 19 12 127 32 48
42 14 30 ! 137 17 00
42 38 05 1 130 48 45
42 33 40 1 131 10 00
43 05 13 131 53 56
42 41 00 133 02 00
43 22 00 135 15 00
43 53 40 j 135 27 19
44 30 00 136 02 00
44 43 45 136 22 30
44 46 15 ! 136 27 15
45 05 00 136 44 00
h. m.
h. m.
ft.
ft.
Ping-hai Harbor
Liancourt Rocks: Summit, 410 ft
Matu Sima: Peak, 4,000 ft
i
■ 1
1
Port Lazaref: S. IJ miles from the S.
end of Bontenef I
i
Wawoda Rock : Summit, 12 ft
Expedition Bay : Light-house
Port Novogorod : Light-house
Vladivostok : Cape Galdobin light
Caj>e Povorotnyi : Light-house
2 45
9 00
1.9
0.8
Port Olga: Light-house
St. Vladimir Bay: Orekhera Pt
Shelter Bay
Sybillo Bay
Pique Bay
Bullock Bav
Luk^ Point: Extreme
45 19 30
45 41 30
47 20 00
48 59 30
51 28 00
45 53 10
46 01 20
i4 24 30
53 08 05
55 11 00
56 25 28
56 22 30
59 19 45
51 02 00
52 52 37
53 04 30
54 56 00
54 32 24
56 10 00
58 26 00
59 55 00
62 14 30
60 18 00
63 12 00
64 16 00
64 25 55
64 24 30
64 46 00
137 10 15
137 38 15
138 58 00
140 23 40
140 48 00
142 04 51
143 26 30
142 46 30
140 42 58
137 40 00
138 25 50
143 15 45
143 07 14
156 46 00
158 46 42
160 04 00
166 43 00
168 09 00
163 24 00
163 34 00
170 22 00
179 04 30
Long. W.
172 04 00
159 50 00
173 10 00
173 07 15
172 12 30
172 07 00
Cape Disappointment: Extreme
Cape Suff ren : Extreme
Cape St. Nikolaia: Light-house
De Kastri : Light-house *
9 50
10 45
3 40
4 40
2.7
6.3
1.1
2.6
Sakhalin I., Cape Notoro: Light-house.
Cape Siretoku: Extreme ..
Cape Elizabeth: N. pt
Nikolaevsk: Cathedral
11 20
5 08
4.2
1.7
Great Shantar Island :N. pt
Port Aian: Cape Vneshni
0 10
7 30
8.4
3.4
St. Jona Island: Summit, 1,200 ft
Okhotsk: Battery
::: i :
Cape Lopatka: Extreme
3 55
3 30
10 08 ! 4. 6
1.9
2.1
Petropavlovsk : Rakof light
9 45
5.1
Cape Shipunski : Extreme
Bering Island: Cape Khitroff
Mednoi, or Copper Island : SE. extreme.
Cape Kamchatka: Extreme
Karajinski Island : S. pt
Cape Oliutorski: Extreme, 2,480 ft
Cape Navarin: Extreme, 2,512 ft
St. Matthew Island: Cape Upright, SE. pt
St Lawrence Island: N pt
6 00
12 15
4.5
1.8
1
Cape Tchoukotskoi' Extreme
Port Providence: Emma Harbor
Cape Indian : Extreme
Arakam Island : Cape Kiguinin
Anadir River* Mouth
1
Long. E.
64 50 00 178 40 00
Long. W.
65 00 30 [ 175 54 00
66 02 00 169 32 30
1
Cape Bering' Extreme '
East Cape : Extreme ... .... ...
1
1
ISLANDS OF THE PACIFIC.
m
0
Si
i
Malpelo Island: Summit, 1,200 ft
Cocos Island: Head of Chatham Bay...
Redondo Rock* Summit 85 ft
4 03 00
5 32 57
0 13 30
0 20 00
0 18 50
0 34 25
81 36 00
86 69 17
9l' 03 00
89 58 43
90 30 08
90 44 9.^
Towel's Island: W. cliff
Bindloe Island: S. summit
Abingdon Island : Summit, 1,950 ft
AVenman Island: Summit, 550 ft
d
1 22 55 91 49 4.3
:::;:::::::: i
tf
1
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
[Page 261
Place.
Albemarle Island : Iguana Cove
Marlborough Island: Cape Hammond..
James Island: Sugarloaf, 1,200 ft
Jervis Island : Summit
Duncan Island : Center hill
Indefatigable Island : N\V. bay
Barrington Island: W. summit, 900 ft..
Charles Island: Summit, 1 ,780 ft
Fatu Huku or Hood Island : E. summit,
640 ft
Chatham Island: Mount Pitt, 800 ft
Christmas Island: N. pt. of Cook Islet..
Fanning Island: Flagstaff, entrance to
English Hbr
Washington Island
Palmyra Island
Baker Islet: Center
Howland Islands: Center island
Arorai or Hurds Island: S. pt
Tamana Island : Center
Onoatoa Island : Center
Taputeuea or Drummond Island: SE. pt.
Nukunau or Byron Island: SH pt
Peru or Francis Island: NW. pt
Nonuti or Sydenham Island
Aranuka or Henderville Island: W. pt.
of W. island
Apamama or Hoppers Island: Entrance
islet
Maiana Island: S. pt
Tarawa Island : NE. pt
Apaiang Island: S. pt
Maraki Island: N. pt
Taritari Island: S. pt
Ebon Atoll: Rul:)e Pt
Jaluit or Bonham Islands: Jarbor Pier.
Burrh Island: Port Rhin, N. pt. of en-
trance
Majuro or Arrowsmith Islands: An-
chorage Djarrit I
Arno Atoll: NE. pt
Odia Islands: S. islet
Namu Island : S. pt
Jabwat Island : Center
Aurh or Ibbetson Island: NE. end, an-
chorage
Maloclab Islands: NW. end Karen Islet.
Wotje or Romanzov Islands: Christmas
Harbor
Litkieh Island: NW. pt
Ailuk Islands: Capenmr Islet
Bigar Islet : Center
Kongelab or Pescadores Islands: Center
of group
Rongerik or Radakala Islands: Obser-
vation spot
Ailinginae Island: Easternmost Islet...
Bikini or Eschholtz Islands: W. ex-
treme
Wottho or Schanz Island : Center
Eniwetok Islands: North or Engibil..
Ujelang or Providence Island: Center
of atoll
Lat. S.
Long. W.
Lun.
Int.
Range.
H. W.
L. W.
Spg.
Neap.
O / tl
0 59 00
0 31 00
0 15 20
0 25 00
0 36 30
0 33 25
0 50 30
1 19 00
1 25 00
0 44 15
Lat. N.
1 57 17
3 51 26
4 41 10
91 29 12
91 36 00
90 52 53
90 43 30
90 41 00
90 33 58
90 06 13
90 28 13
89 40 08
89 16 58
157 27 45
159 21 50
160 24 30
162 05 00
176 32 39
176 43 09
LonR. E.
177 01 13
176 07 00
175 39 00
175 12 20
176 31 33
175 57 09
174 24 00
173 32 40
173 51 14
173 03 30
173 03 00
173 07 00
173 25 30
172 45 40
168 41 31
169 39 31
171 46 00
171 24 30
171 55 51
168 46 00
168 03 00
168 26 00
171 09 00
170 49 00
170 16 05
169 01 57
169 59 20
170 07 00
167 24 57
167 35 00
166 35 00
166 24 25
166 04 00
162 15 00
161 08 30
h. m.
2 00
h. m.
8 13
ft.
6.2
ft.
3.1
2 45
8 58
5.2
2.6
::::::::::::::::
2 00
8 13
6.2
3.1
2 10
8 23
6.0
3.0
2 20
4 25
6 00
8 33
10 38
12 15
6.5
2.4
2.4
3.3
1.4
1.4
5 52 15
0 13 30
5 25
11 40
1.5
0.9
0 49 00
Lat. S.
2 40 54
7 10
1 00
6.2
3.6
2 35 00
1 50 00
1 29 14
1 23 42
1 17 14
0 36 00
Lat. N.
0 11 10
0 20 54
0 51 30
1 38 45
'
1
i
1
'
4 30
10 45
4.7
2.7
1 44 15
2 03 00
4 45
11 00
4.7
2.7
3 01 30
4 35 25
5 55 07
6 14 00
7 05 30
7 09 17
7 15 00
8 14 00'
8 27 00
8 19 00
8 54 21
9 28 09
10 03 40
10 17 25
11 48 00
11 19 21
4 45
11 00
4.7
2.7
5 00
11 15
5.0
2.8
4 50
11 00
6.2
3.6
1
11 24 00
[
11 07 00
11 40 00
10 05 00
11 40 00
9 39 00
i j
i
Page252J APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
*j
Place.
Lat. X.
Long. E.
Liin. Int. 1 Range. 1
H.W.I
L. W.
Spg.
Neap.
•
a
*
m
m
«
d
2
3
i
•9
n
«
*
«
■
«
M
1
h
0_
4>
fl
2
■d
«
Greenwich Island: Northern islet
•
Matelotas group: Easternmost of the
S. islands
0 / If
1 04 00
8 18 30
9 29 00
9 52 30
0 / n
154 47 55
137 33 30
138 04 00
139 42 00
h. m.
h. m.
ft.
ft.
Yap Island: Light in Tomil Bay
Eau Island : Center
7 15
1 00
3.4
1.9
Uluthi or Mackenzie Islands: Mogmog
Islet ;
10 06 00 139 46 00
Feys or Tromelin Island: E. extreme ..
9 46 00
140 35 00
140 52 00
143 11 00
143 57 30
144 31 00
144 36 00
146 50 00
145 55 45
Sorol or Philip Island : Center 1 8 06 00
Eauripik or Kama Islands: E. islet ' 6 40 00
Oleai group: Raur Islet, N. pt
Ifalik or Wilson Islets: N. end
Faraulep Island : S. end
7 21 45
7 15 00
8 35 00
8 03 00
7 43 30
W. Faiu Islet: Center
Oliniarao Islet: Center
Toass Island: Center
7 29 30 146 24 30
7 22 00 147 06 48
8 09 00 147 42 00
Satawal Island : Center
Coquille or Pikelot Island: Center
Suk or Polusuk Island : S. end
6 40 00
7 38 00
8 59 45
8 25 30
7 18 30
5 55 00
5 29 18
3 51 00
7 39 00
5 48 00
7 00 35
6 41 45
6 14 00
5 20 06
6 53 55
7 02 00
7 08 00
7 19 00
7 40 30
8 08 00
4 20 00
3 02 00
5 20 00
13 25 48
14 07 30
14 59 22
15 08 30
15 17 10
16 20 00
16 41 00
17 17 00
17 36 00
18 04 00
18 46 20
19 45 00
20 00 00
20 32 54
149 21 00
Los Martires: Ollap Islet, N. pt
Namonuito Islands: Magur Islet
Hall Island: Namuine Islet
149 27 30
150 14 30
151 49 15
151 56 30
153 13 30
153 58 00
155 00 54
155 05 00
157 31 30
158 12 21
159 50 00
160 38 43
163 00 45
134 05 24
Hogolu (Hogulu) Group: N. end of
Tsis Islet. .'.
Namoluk Islands: NW. islet
Mortlock Islands: Lukanor, Port Cha-
misso
Nukuor or Monteverde Islands: E. pt. .
Oraluk or Bordelaise Island: Center . . .
Ngatik or Valientes Islands: E. extreme.
MokilorDuperrey Islands: Aoura, NE.pt
Pingelasp or MacAskill Islands: E. end
of island
4 00
10 15
4.3
2.4
Ualan or Strong Island: Chabrol Harbor.
Angaur Island: SW. pt
6 00
12 15
3.5
2.0
Pililu Island: S. pt
133 18 03
134 27 00
134 32 30
134 39 30
134 17 00
132 21 00
131 11 00
132 16 00
144 39 30
145 13 04
Earakong or Akamokan Island: Center.
Korror Islands: Korror Harbor, Mal-
akal pier .
Baubeltaub Island : Cape Artingal
Kyangle Islets: Center of largest
Warren Hastings Island: Center
Nevil or Lord North Island: Center
Sonserol Island : Approx
Guam Island: Fort Sta. Cruz, San Luis
d' Apra.
7 20
1 20
2.6
1.5
Rota Island' Summit
Tinian Island : Sunharon village
Saipan Island: Magicienne Bay, land-
ine
145 36 20
145 43 55
145 42 50
145 39 00
Tanapag Hbr. , Garapag .
Anataxan Island: Center
7 00
0 50
2.0
1.1
Sariguan Island: Center
145 47 00
145 57 00
145 55 00
145 52 00
145 41 45
145 30 00
145 21 00
144 54 00
Guguan Island: Center
Alamaguan Island ■ Center
. . .
Pagan Island: SW. pt
Agrigan Island : SE. pt
Asuncion Island : Crater, 2,600 ft
Urracas Islands ■ Lai^est islet
Farralon de Pajaro.«: S. end
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
[Page 253
Place.
Lat. N.
Lun. Int.
Long. E.
H. W.
L. W.
Range.
Spg. Neap.
Wake Island: Center ; 19 10 54
Gaspar Rico Reef: N. clump of rocks. .. 14 41 00
Johnston or Comwallis Islands:
staff on W. island
Clipperton Island : Center
Flag-
Hawaii Island: Hilo, Kanaha Pt. light.
Kawaihae light
Kealakeakua Bay light.
Kailua, stone church...
Kahoolawe Island: Summit
Maui Island: Kanahena Pt. light
Lahaina light
Molokai Island: Light-house
Oahu Island: E. pt. Makapuu station ..
Diamond Head
Honolulu, Tr. of V. Obs .
Honolulu, Reef light
Kauai Island: Hanalei, Black Head
Waimea, stone church . . I
Bird Island: Center
Necker Island : Center
French Frigate Shoal: Islet (120 ft.) ...
Gardiner Island : Center
Maro Reef: NW. pt
Laysan Island : Light-house
Lisiansky Island: Light- house
Pearl and Hermes Reef: NE. extreme.. i
Midway Islands: N. end Sand Islet
Ocean Island: Sand Islet '
Marcus Island: Center
Bonin Is. , Parrys Group: N. rock
Kater Island: N, rock
Peel Island: Port Lloyd, ob-
servatory
Volcano Is., San Alessandro or North
Island: Center
Sulphur Island
San Augustine Island:
Center ,
Rosario Island : Center, 148 ft
Douglass Rocks: Center
Borodino Islands: Center of N. island..
Center of S. island . .
Rasa Island : Center
Fatu Hiva Island : S. pt
Motane Island: SSE. pt
Tahuata Island: Port Resolution, wa-
tering place
Hiva-Oa Island : C. Balguerie
Fatu Huku Island: Center
Roa Poua Island : Obelisk Islet
Nuka-Hiva Island : Port Tai-o-hae light.
Hiaou Island: S. pt
Motu-ili Island : Summit, 130 ft
Ua-Huka or Ua-L^na Island: N. pt
Fetouhouhou Island : NE. pt
Caroline Islands: Solar Eclipse Transit
Pier
Vostok Island : Center
Flint Island : S. extremity
16 44 48
10 17 00
19 46 14
20 03 00
19 28 00
19 38 26
20 33 39
20 36 00
20 52 00
21 06 17
21 18 16
21 15 08
21 17 57
21 17 55
22 12 51
21 57 17
23 05 50
23 35 18
23 46 00
25 00 40
25 31 00
25 48 00
26 00 00
27 56 30
28 13 15
28 24 45
24 14 00
27 45 00
27 31 00
27 05 37
25 14 00
24 48 00
24 14 00
27 15 32
20 30 00
25 59 38
25 52 45
24 27 00
Lat. S.
10 32 00
10 01 40
9 56 00
9 45 00
9 27 30
9 29 30
8 55 13
8 03 30
8 44 00
8 54 00
7 55 00
10 00 01
10 06 00
11 25 23
166 31 30
168 54 28
Long. W.
169 32 24
109 13 00
155 05 31
155 48 00
155 55 00
156 00 15
156 35 04
156 26 00
156 35 00
157 18 32
157 39 07
157 48 44
157 51 34
157 51 54
159 30 47
159 40 08
161 58 17
164 40 47
166 17 57
168 00 52
170 39 20
171 44 00
173 57 00
175 46 00
177 21 30
178 27 45
Long. E.
153 58 00
142 06 53
142 11 53
142 11 23
141 11 00
141 13 00
141 20 00
140 50 28
136 10 00
131 19 30
131 12 17
131 01 50
Long. W.
138 39 20
138 48 30
139 09 00
138 47 40
138 55 10
140 04 45
140 04 00
140 44 00
140 38 30
139 33 30
140 34 40
150 14 30
152 23 00
151 48 34
h. m.
h. m.
ft-
3 09
9 06
2.3
1.3
2 20
8 10
0,9
3 32
2 38
9 58
8 56
2.2
2.1
1.2
1.1
3 46 j 9 59
'4"66' "i6"26
1.5
0.8
2.0
1.1
3 30
6 10
9 45
1.1
0.6
0 00
2.4
1.4
2 30
8 45
3.1
1.9
3 50 10 05
4 00
3.5
2.1
10 14 I 1. 1
0.7
Page 254]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
Place.
Maiden Island: Flagstaff, W. side
Starbuck Island: l^lagstaff, W. side
Penrhyn or Tongarewa Island : NNW. pt.
Jarvis Island: Center
Reirson Island : Church
Humphrey Island: N. pt
Union or Tokelau Islands: Spot N. of
Fakaofu or Bowditch Islet ,
Union or Tokelau Islands: Nuku-nono,
or SE. island, Duke of Clarence I
Union or Tokelau Islands: Clump on
S. island, Oatafu or Duke of York I. . .
Canton or Mary Island: N. pt
Enderbury Island: W. pt ,
Pho'nix Island, N. pt
Birneys Island : S. pt
Gardners Island : Center
McKean Island: Center
Hulls Island: W. pt
Mukulaelae or Mitchells Island: S. pt. . ,
Funafuti or EUice Island : E. pt
Nukufetau or De Peysters Island: S. pt
Vaitupu Island : S. end
Nui or Netherland Island: S. pt
Nauomaga Island : Center
Niutao Island : Church
Nanomea Island: Center
Ocean or Paanopa Island : Center (appx )
Pleasant Island : Center
Indispensable Reefs: S. pt. of S. reef..
Rennel Island: SE. extreme
AV.end
San Christoval Island: Point Wanga-
laha
Guadalcanar Island: Wanderer Bay,
mouth of Boyd Creek
Florida Island: Mboli Harbor, Tree Islet
Malaita Island: Village, Mary I., Port
Adam
Stewart Islands: Largest islet
Isabel Island: N. side of Cockatoo Islet
Gizo or Shark Island: N. point village.
Choiseul Island: Choiseul Bay en-
trance
Traisury Islands: Observation Islet
Bougainville Island: Hiisker Pt., Ga-
zelle Harbor
Buka Island : Cape North
Lord Howe Group: Center, small SW.
islet
Center, small NE.
islet
NW. pt. of Ham-
mond I
New Britain, Blanche Bay: Matupi I.
N. pt
Duke of York Island: Makada Har-
bor, Spit Pt
Lat. S.
4 03 00
5 37 00
8 55 15
0 22 33
10 02 00
10 20 30
9 23 02
9 13 06
8 39 40
2 44 25
3 08 30
3 42 28
3 34 15
, 4 37 42
3 35 10
4 30 95
9 18 00
8 25 19
8 04 02
7 32 00
7 15 45
6 12 00
6 06 00
5 39 00
0 52 00
0 25 00
12 50 15
11 52 15
11 33 45
10 17 32
9 41 47
9 01 30
9 30 00
8 23 00
8 30 50
8 05 40
6 42 40
7 24 30
6 35 00
5 00 00
5 38 00
5 18 00
5 18 00
4 14 12
4 06 25
Long. W.
155 01 00
155 56 00
158 07 00
159 54 11
161 05 30
161 01 12
171 14 46
171 44 40
172 28 10
171 45 29
171 10 00
170 42 37
171 32 07
174 40 18
174 17 26
172 13 28
Long. E.
179 50 00
179 07 25
178 28 51
178 41 01
177 16 50
176 16 30
177 20 01
176 06 15
169 35 00
167 05 00
160 26 00
160 40 15
159 55 00
161 33 30
159 39 30
160 27 20
161 27 40
162 58 15
159 38 20
156 50 15
156 23 16
155 34 00
155 05 00
154 35 00
159 21 00
159 34 00
159 17 00
152 11 35
152 06 15
Lun. Int.
Range.
H, W.
L. W.
Spg. Neap.
ft. m.
ft.
ft.
6 00
12 15
1.5
0.9
6 00 12 13
2.4
1.4
5 00
11 15 4.6
2.7
6 45
0 33
3.3 2.0
5 00
11 15
3. 5 2. 1
12 00
5 47 I 2. 7
1.6
9 00
2 45 i 2. 1
1.3
APPENDIX IV. [Page 265
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
u
Place.
Lat. S.
Long. E.
Lun. Int.
Range. 1
H. W.
L.W.
Spg.
Neap.
i
g
s
■0
m
«
S
e
a
a
M
©
i
«
2
a
»
m
N
B
b
»
New Ireland: Carteret Harbor, Cocoa-
nut I
0 / //
4 41 26
3 11 00
2 47 30
2 33 43
2 26 30
1 35 00
1 55 10
2 25 40
2 22 00
0 45 00
0 53 15
1 28 00
2 51 00
1 25 40
2 44 00
3 47 00
8 22 00
8 41 00
9 25 30
10 14 30
10 43 35
10 37 00
6 43 00
8 24 00
9 03 30
9 38 00
9 41 00
9 43 53
10 42 00
10 52 40
11 23 25
11 29 10
16 50 00
16 55 50
17 43 00
17 07 20
17 24 39
19 08 00
19 14 00
22 10 30
23 15 02
9 48 00
10 21 00
10 23 30
10 40 00
11 17 30
11 40 24
o / //
152 42 25
151 35 30
150 57 35
150 04 33
149 55 36
149 37 00
146 40 56
147 28 .35
147 55 00
145 17 00
145 33 04
145 08 00
146 15 00
135 28 12
132 04 00
134 06 00
137 40 00
143 36 04
147 07 04
148 30 30
150 14 20
150 40 34
147 53 20
151 01 24
152 47 00
150 30 00
150 58 00
150 44 43
152 42 04
152 47 12
154 08 00
154 25 14
149 58 00
149 11 54
150 42 04
152 06 20
155 52 24
158 40 00
159 00 00
155 28 24
155 33 04
166 53 15
166 17 15
165 47 30
166 00 30
166 32 14
166 57 45
h. m.
ft. m.
ft.
ft.
Katharine Haven
Holz Haven, E. side
New Hanover Island: Water Haven,
creek mouth.
North Haven
anchorage
St. Matthias Island: SW. extreme
Admiralty Island: Nares Harbor, obs.
islet
2 50
9 03
2.4
1.4
2 30
8 43
2.4
1.4
St. Andrew Island: Violet Islet, 60 ft ..
Jesus Maria Island : SE. pt
Commerson Island: Center of largest
islet
Anchorite Island : N. pt
Hermit or Loaf Island: Pem6 Islet
Purdy Island: Mole Islet
Point d' Urville : extreme
Drei Cap Peninsula: Wass Islet
Triton Bay: Fort Dubus, Dubus Haven.
Cape Walsche: Extreme
6 55
7 08
7.3
4.3
Fly River: Free Islet, S. pt
Port Moresby: N. end of Jane I
Cape Rodney : Extreme
8 50
2 38
8.0
4.8
South Cape: S. pt. Su Au I
9 15
8 25
3 00
2 12
8.1
5.8
4.8
3.4
Hayter Island : VV^. end
Cape Cretin : Cretin Islets
Trobriand Islands: NE. pt. Cape Denis.
Woodlark Islands: N. pt
4 45
7 05
10 58
0 53
....
3.0
4.2
1.8
2.5
D'Entrecasteaux Is. : Ferguson I., SW.
extreme
Well Island, E. pt.
Normanbyl., obs.
islet
St. Aignan Island : Summit
1
Rossel Island : E. pt
Adele Island : S. extreme
Coringa Islands: Chilcott Islet
Herald Cays: NE. Cay
j
Tregosse Islands; S. islet
i
Lhou Reef: Observation Cay
1
.
Bampton Island
1
Renard Island : Center
1
Wreck Reef: Bird Islet
1
Cato Island : Center
1
Duff or Wilson Group: N. island
Matema or Swallow Group: Nimanu
Islet
Tinakula Island: Summit, 2,200 ft
Nitendi Island: NE. pt.. Cape Byron ..
Tapua Island: Basilisk Harbor, S. pt. of
entrance
Vanikoro: Ocili village
4 50
11 05
3.8
2.3
Page 256] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
i
•9
5
a
M
a
V
t
9
8
«
•9
S
«
Place.
Lat. 8.
Long. E.
Lun.
Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
Torres or Ababa Island: Hayter Bay,
Middle I.....
O ' II
13 15 00
13 48 00
14 11 00
14 58 00
16 26 00
17 44 58
18 47 30
0 / II
166 33 00
.167 30 31
167 30 00
168 02 00
167 47 15
168 18 50
168 58 00
169 27 30
170 11 15
169 44 45
171 20 30
172 05 15
168 56 45
170 10 00
177 07 15
178 32 15
177 57 09
178 10 24
177 38 00
178 49 00
177 09 00
178 24 40
178 06 53
179 44 27
179 56 25
179 14 08
178 59 29
178 57 46
179 20 44
178 54 15
178 48 32
179 16 08
Long. W.
179 58 46
179 51 00
179 54 26
179 17 00
179 32 17
179 10 00
179 05 45
179 10 33
179 19 49
178 50 27
179 04 00
178 52 00
178 27 04
178 30 54
178 44 00
h. m.
h. m.
ft.
ft.
Vanua Lava Island: Port Patterson,
Nusa Pt
6 40
0 30
3.8
2.3
Santa Maria Island: Lasolara Anchor-
ase
Aurora Island : Laka-rere
MallicoUo Island: Port Sandwich, pt.
on E. side
4 38
5 15
10 50
11 27
3.8
3.0
1.9
1.8
Vate or Sandwich Island: Havannah
Harbor, Matapou Bay flagstaff
Erromango Island: Dillon Bay, Pt.
Williams
Tanna Island: Port Resolution, Mission.
19 31 17
Erronan or Futuna Island: NW. pt 19 31 20
Aneitvum Island: Port Anatom, Sand
Islet
•
20 15 17
5 10
11 23
3.1
1.9
Matthew Island: Peak, 465 feet
Hunter Island: Peak, 974 feet
22 20 12
22 24 02
22 38 07
Walpole Island: S. pt
Mitre Island: Center 11 55 00
Rotumah Island: Epipigi Peak 12 30 10
Kandavu Island: N. rock Astrolabe Reef i
light ! 18 38 15
Mt. Washington, N.
peak 19 07 09
.
6 15
0 00
4.2
2.5
N'galoa Harbor, outer
beacon
19 05 30
6 40
0 25
4.0
2.4
Vatu Lele Island : S. pt
18 36 00
17 40 45
Ovalau Island : Levuka light-house
Yiti Levu Island; Summit of Malolo
Islet 17 44 45
Suva Harbor, low
light
18 06 50
6 30
0 15
3. 6 2. 2 1
Mbega or Mbengha Island: Swan Har-
bor, Leaven Pt
18 22 00
19 09 38
18 32 49
17 59 32
17 37 11
17 27 14
17 15 21
16 42 01
16 57 53
16 49 19
16 08 00
16 46 00
Matuku Island: N. side of Matuku en-
trance
Moala Island: Rocks off N. pt
Ngau Island: Herald Bay, E. side
Wakaya Island : Rocky Peak
Makongai Island: Dilliendreti Peak
Goro Island: NW. pt
V^anua Levu Island : Mount Dana
Nandi, observation
islet
:::::;::::: i
Savu Savu Pt. ; ex-
treme
6 00
12 13
4.3
2.6
NE. Pt
Taoiuni Island: Somu-Somu town
Thikombia Island: E. hummock \ 15 44 45
Naitamba Island : Center 17 03 00
Vatu Vara Island: N. end, summit i 17 25 33
Kanathea Island: S. pt | 17 17 20
Vanua Mbalavu Island: NW. pt 17 10 00
Mango Island: Pier end 1 17 25 26
Thithia Island: Highest peak 17 44 12
Tuvutha Island: Peak 17 39 33
Naian Island: Summit, 580 ft i 17 59 00
Lakemba Island: Kendi Pt i 18 14 10
6 10
0 00
3.1
1.9
Oneata Island : Summit of Loa I
Mothe Island: Summit
18 25 46
18 38 56
18 46 00
Mamuka Island : Center, 260 feet
1
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
[Page 257
Place.
Kambara Island : Highest peak
Totoya Island : Black Rock Bay, W. side
Fulanga Island: W. bluff
Ongea Leva Island : Center
Vatoa or Turtle Island: Hummock
Ono Islands: Peak
Michaeloff Island : Center
Simonoff Island : Center
Fatuna or Home Island: Mt. Schouten.
Uea or Wallis Island: Fenua-fu Islet...
Niua-fu or Good Hope Island: NW.
extreme
Keppel Island : Center
Boscawen Island: Center
Savaii Island : Paluale village
Upulo Is. : Apia Harbor, obs. spot
Tutuila Island : Pago-Pago, obs. pt
Manua Island: Village, NW. side
Rose Island: Center
Iniue or Sarage Island : S. pt
Danger, or Bernardo, Is. : Middle rock .
Suwarrow or Souwaroff Island: Cocoa-
nut Islet
Palmerston Islands: W. islet
Scilly Islands: E. islet
Bellingshausen Island : Center
Mopelia (Lord Howe) Island: Center..
Maitea Island: Summit
Tahiti Island : Light-house
Tubuai-Manu or Maia-iti I. : NW. pass. .
Eimeo Island : Talu H br. , Vincennes Pt .
Huaheine Island : Light-house
Ulietea Island : Regent Pt
Tahoa Island: Center
Bola-Bola Island: Otea-Vanua village. .
Tubai or Motu-iti Island: N. pt. of reef. .
Marua or Maupili Island: Center
Ducie Island: NE. entrance
Pitcairn Island: Village
Henderson or Elizabeth Island: Center.
Oeno Island : N. pt
Mangareva or Gambler Island : Flagstaff
Maruteaor Lord Hood Island: Center..
Maria or Moerenhout Island: Center
Vahanga Island : W. pt
Morane or Cadmus Island : Center
Tureia or Carysf ort Island : E. pt
Mururoa or Osnabrug Island: Obs. spot.
Tematangi or Bligh Island: N. pt
Nukutipipi : SW.pt
Hereheretue or St. Paul Island: Center.
Vanavana or Barrow Island: Center
Nukutavake or Queen Charlotte I. : N. pt
Reao or Clermont Tonnere Island: NW.
point
Puka-ruha or Series Island: NW. pt
Vahitahi Island : W. pt
Ahunui or Byam Martin Island : NW. pt.
Pinaki or Whitsunday Island: E. pt
Tatakoto or Gierke Island: Flagstaff on
western coast
Lat. S.
18 56 15
18 58 57
19 03 00
19 04 00
19 49 11
20 39 10
21 00 09
21 01 39
14 14 20
13 23 35
15 34 00
15 52 00
15 58 00
13 45 00
13 48 56
14 18 06
14 19 00
14 32 00
19 10 00
10 52 47
13 14 30
18 05 50
16 28 00
15 48 00
16 52 00
17 53 00
17 29 10
17 36 39
17 29 23
16 42 30
16 50 00
16 35 00
16 31 35
16 11 00
16 26 00
24 40 20
25 03 50
24 21 20
24 01 20
23 07 36
21 31 30
22 01 00
21 20 00
23 07 50
20 46 20
21 50 00
21 38 00
20 43 00
19 53 17
20 46 07
19 16 30
18 29 00
18 16 00
18 43 30
19 37 00
19 25 00
17 19 30
Long. W.
178 59 05
179 52 58
178 47 25
178 33 25
178 13 38
178 43 27
178 44 03
178 49 47
178 06 45
176 11 47
175 40 40
173 52 00
173 52 00
172 17 00
171 44 56
170 42 14
169 32 00
168 09 00
169 50 00
165 51 30
163 04 10
163 10 00
154 30 00
154 31 00
154 00 00
148 05 00
149 29 00
150 36 56
149 50 30
151 01 28
151 27 21
151 35 00
151 46 00
151 48 00
152 12 00
124 48 00
130 08 30
128 19 00
130 41 00
134 57 54
135 33 05
136 10 15
136 38 53
137 06 15
138 27 45
138 56 30
140 38 45
143 03 15
144 57 00
139 08 45
138 48 30
136 26 30
137 03 30
138 53 15
140 15 45
138 40 45
138 26 26
Lun. Int.
Range.
H. W. L. W.
Spg. Neap.
h. m. 1 h. m.
ft. ft.
6 35 [ 0 20
"6"i6T"6"66'
3.5
2.1
3.1
1.9
6 40 0 28
4.4
2.7
25 0 13
7 00
6 00
0 45
12 13
3.1
2.7
4.6
1.9
1.6
2.7
3 10 i 9 23
2.4 1.4
12 00
5 48
LO
0.6
12 10 6 00
1.4
0.8
1 50
03
2.4 1.4
22489—03-
1 Page 268] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
1
Place.
Lat.S.
Long. W.
Lun. Int.
Range. 1
H.W.
L.W.
Spg.
Neap.
e
I
s
9
s
s
m
■0
1
«
M
e
a
a.
r
Hao or La Harpe Island: NW. pass
Paraoa or Gloceater Island: Center
Ravahere Island: S. pt
O f 11
18 05 20
19 08 45
18 18 30
17 49 35
17 35 28
17 20 30
14 49 00
14 12 00
15 50 00
15 44 20
16 39 10
16 44 29
17 20 20
16 47 49
17 28 41
16 26 09
16 31 00
15 43 15
15 30 00
15 50 00
14 43 00
14 29 10
15 14 30
15 50 30
14 53 00
33 37 36
33 46 00
26 18 07
26 16 00
26 27 41
27 10 00
27 35 46
27 55 30
23 55 00
23 21 45
22 29 00
22 45 00
21 47 00
21 49 00
21 11 35
20 17 00
20 01 00
20 04 00
19 18 00
18 54 00
18 39 02
19 41 35
19 45 00
21 08 00
23 37 06
28 55 00
29 15 30
30 15 00
30 35 00
21 44 45
O 1 II
140 59 30
141 41 10
142 11 31
143 05 23
142 35 16
141 29 43
138 46 45
141 15 37
140 53 35
142 08 40
144 14 45
142 53 34
145 30 54
144 17 18
143 31 17
143 57 59
145 22 45
144 38 34
145 24 45
146 02 45
145 11 00
146 20 00
147 11 00
148 15 00
148 39 45
78 50 02
80 46 00
79 54 56
80 06 56
105 28 00
109 26 00
144 17 20
143 28 21
147 48 00
149 35 35
151 23 41
152 55 00
154 51 00
157 56 00
159 47 00
157 23 00
157 34 00
158 08 00
158 54 00
159 32 00
174 01 00
174 59 50
175 03 00
175 12 00
178 55 45
179 07 45
177 55 40
178 31 45
178 37 00
Long. E.
174 37 45
h. m.
2 40
h. TO.
8 55
ft-
2.4
Jt-
1.4
Reitoru or Bird Island: N. beach
Hikueru or Melville Island, E. pt
Tauere Island: NW. pt
1
Puka-puka Island : E. pt
Napuka Island : W. pt
Angatau or Araktcheff Island: W. pt ..
Tukume or Wolkonsky Island: NW . pt.
Tuanske Island: N W. pt
i
1 ,
Nihiru Island (Tuanake): SAV. pt
Anaa Island: Islet in N. pass
Tepoto Island: N. pt
!
Haraiki or Crocker Island: SW. pt
Makemo or Phillips Island: AV. pass...
Fakarana or Wittgenstein Island: SE. .
pass
Taiaro or Kings I. : Middle of W. shore .
Aratika Island: E. pt
Toau or Elizabeth Island: Amyot Bay.
Takapoto Island: S. pt
Aheu Island : Lagoon Entrance
Rangiroa Island: E. pt
4 30
10 43
2.1
1.3
Makatea Island: W. pt
Matahiva Island: W. pt
Juan Fernandez Island: Fort S. Juan
Batista ,
Mas-afuera Island: Summit, 4,000 ft ...
St. Ambrose Island: N. part creek
St. Felix Island : Center
Sala y Gomez: NW. pt
4 00
0 40
0 10
10 15
6 53
6 25
3.3
2.8
2.4
2.0
1.7
1.4
Easter Island : Cooks Bay, mission
Rapa or Oparo Island: Tauna Islet
Bass Islets (Morotiri): SE. islet, 344 ft .
Tubuaior Austral Is., Vavitoa I. : Center.
Tubuai I.: Flag
staff, N. side
Rurutu I. : N. pt . .
Rimitara I. : Cen-
ter
Hull Island: NW. pt
3 00
9 13
2.4
1.4
Mangara Island: Center
Rarotonga Island : N W. pt
6 00
12 15
2.7
1.7
Mauki or Parry Island : Center
Mitiero Island: Center
!
Vatiu or Atiu Island : Center
Hervey Islets: Center
Aitutaki Island: Center
Vavau Island: Port Valdes, Sandy Pt..
Kao Island : Summit, 5,000 ft
6 20
0 10
3.8
2.3
Tofua Island : Summit, 2,800 ft
Tongatabu Island: Light-house
Minerva Reefs, N. Minerva: NE. side..
S. Minerva: S. side of
entrance
6 20
7 50
0 10
1 35
3.8
5.5
2.3
3.3
Kermadec Is. , Raoul or Sunday I. : Den-
ham B. flag staff
Macauley I. : Center
Curtis I. : Center
Conwav Reef: Center
6 00
12 13
3.3
2.7
APPENDIX IV. [Page 269
MAKITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THT3 PACIFIC— Continued.
1
o
o
Place.
Lat. S.
Long. E.
Lun. Int.
Range. 1
H. W. L. W.
Spg.
Neap.
Loyalty Is., Uvea or Halgan I.: Uvea
Church.
o / //
20 27 06
20 46 00
21 42 00
21 29 12
22 00 10
22 16 22
O / II
166 36 25
1
h. m. h. m.
!
ft.
fl.
LifuL: Wreck Bay, NW.
shore
167 02 30
168 00 00
165 58 50
166 05 00
6 30 ! 0 18
1
4.2
2.5
Mare or Britannia I. : S. pt.
Port Kanala: Observatory
1
Port St. Vincent: ^larceau I
5 40 11 52
3.3
3.1
2.0
1.9
Noumea : Light-house ..
166 25 52
8 25 2 13
Balari Pass' Amedee I Ught
22 28 44 166 28 51
22 42 30 167 27 55
Port Alcmene : Alcmene I
7 55
7 30
1 45
I 17
3.6
4.7
2.2
3.9
Norfolk Island: Inner end of jetty
Elizabeth Reef : Center
29 03 45
29 56 00
31 31 38
167 58 06
159 04 30
159 05 58
159 16 10
Lord Howe Island: S. end of middle
beach
8 20
2 08
5.4
.3.3
Balls Pyramid- Summit, 1,816 ft . ...
31 45 10
Macquarie Island : N. pt 54 19 00
158 56 00
166 13 20
169 08 41
178 43 05
179 00 27
Long. W.
176 32 15
1
Auckland Is. : Port Ross, Terror Cove. .
Campbell Island: S. harbor. Shoal Pt..
Antipodes Island: Summit, 600 ft
Bounty Islands : Anchorage N. I. , West
Group ..
50 32 15
52 33 26
49 42 00
47 43 00
43 57 24
43 49 03
11 50
11 45
3 20
5 38
5 33
9 30
3. 2 2. 6
3. 5 2. 9
5. 3 4. 3
Chatham Island, Whare-Kauri Island:
Port Waitangi, Pt. Hanson
,
Chatham Island, Whare-Kauri Island:
Port Hutt, Gordon Pt
176 42 00
5 22
0 23
2.5
2.1
AUSTRALIA.
i
1
s
e
i
£
«
B
s
■
Groate Eylandt: SE. pt
14 16 00
13 45 00
12 14 00
11 53 00
10 59 00
11 36 00
11 57 00
11 54 00
10 57 00
11 22 02
11 08 00
11 51 00
12 13 20
12 23 20
12 30 58
13 59 00
14 25 50
15 13 45
14 42 00
13 44 00
13 52 00
13 57 07
14 15 00
13 55 00
14 14 00
14 23 00
14 51 00
15 16 36
15 06 00
14 59 20
15 13 15
15 46 00
Long. E.
136 58 00
136 15 00
137 00 00
136 34 00
136 46 00
136 07 00
134 45 00
134 12 00
132 36 30
132 09 18
130 19 00
129 58 00
131 :6 30
130 37 00
130 27 00
129 37 00
129 20 42
129 48 14
128 10 00
126 57 00
126 12 00
125 38 45
125 39 00
124 55 00
125 12 00
125 00 00
124 42 00
125 07 00
125 01 00
124 32 11
124 14 00
124 04 00
Bickerton Island : Summit
Cape Arnheim : Extreme
Cape Wilberforce: E. extreme
8 00
1 48
9.8
5.8
Cape W^essel: Extreme
Dale Point: Extreme
Cape Stewart: Extreme
Liverpool River: W. pt. entrance
Cape Croker: Extreme
6 17
0 05'
12.0
7.1
Port Essington: Government house
Melville Island: Cape Van Diemen
Bathurst Island : Cape Fourcroy
Adelaide River: E. entrance pt'
Port Darwin : Charles Pt. light
5 15
4 57
3 50
5 45
6 45
11 27
11 18
10 00
11 58
0 27
16.8
17.0
16.7
21.9
23.0
9.9
10.0
9.9
12.9
13.6
Port Patterson : Quail Islet
Port Keats: Tree Pt
Pearce Point: Extreme
Victoria River: Water Vallev
Cape Dussejour : Rock off cape
Cape Londonderry : Extreme
Cape Bougainville: Extreme
Cassini Island : S. pt
Cape Voltaire: Flat Hill
Barker Islets: Center
Montalivet Islands: W. islet
Maret Islets: N. islet
Colbert Islet: Center
Prince Regent River: Mount Trafalgar .
Port Nelson: Careening beach
De Freycinet Islets: Beacon on summit.
Red Islet: Center.
Cockell Islet: W. pt
Page 260]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
AUSTRALIA— Continued.
Place.
MacLeay Islets: Rock off N. end
PortUsbome: S*pt
Fitz Roy River: Escape Pt
Cape L' Ev^que: Extreme
Lacepede Island : N W . islet
Cape Baskerville: Extreme
Cape Latouche Tr^ville : Extreme
Turtle Isles: Center of N. isle
Cape Lambert: Extreme
Legendre Island: NW. extreme
Rosemary Island : W. summit
Enderby Island: Rocky Head
Montebello Island: N. extreme of reef.
Barrow Island: N. pt
Northwest Cape: Extreme
Cape Cuvier: Extreme
Cape Inscription : Extreme
Houtman Rocks: N. islet
Port Gregory
Cape Leschenault: Extreme
Rottnest Island: Light-house
Perth (Fremantle) : Arthur Head light
Peel : Robert Pt
Cape Naturaliste: Extreme
Cape Leeuwin : Light-house
D' Entrecasteaux Point: Extreme
Nuyts Point: Extreme
West Cajie Howe: Extreme ,
Eclipse Islets: Summit of largest
King George Sound: Commissariat
house near Albany jetty
Bald Isle : Center
Hood Point : Doubtful Isles
Recherche Archipelago: Termination
Isle
Culver Point: Extreme
Dover Point: Extreme
Fowler Point : Extreme
Streaker Bay : Port Blanche
Coffin Bay : Mount Dutton
Cape Catastrophe: W. pt
Neptune Isles: SE. islet
Port Lincoln : English Church
Franklin Harbor: Observation spot
Port Augusta: Flagstaff
Port Victoria: Wardang Island hut
Cape Spencer: S. pt
Investigator Strait: Troubridge light. .
Port Wakefield: Light-house
Port Adelaide: Wonga Shoal light
Cape Jervis : Light-house
Cape Borda: Light-house
Cape Willoughby: Light-house
Port Victor: Flagstaff.
Cape Jaffa : Margaret Brock light-house
Cape Northumberland: Light-house ...
Cape Nelson : S. extreme
Portland Bay : Lawrence Rock
Port Fairy: Griffith Island summit
Cape Otway : Light-house
King Island: Cape Wickham light
Port Phillip: Point Lonsdale light
Geelong: Custom-house
Mell)ourne : Observatorv
Lat. S.
Long. E.
Lun
Int.
ki
inge.
H. W.
L. W.
Spg.
Neap.
O / It
15 52 00
O / n
123 45 00
123 36 27
123 39 47
122 55 45
122 05 30
122 15 00
121 54 00
118 48 00
117 11 00
116 45 00
116 30 00
116 23 00
115 22 00
115 27 45
114 10 08
113 21 00
112 57 09
113 35 33
114 14 30
115 30 00
115 30 12
115 44 23
115 44 00
115 00 15
115 08 00
116 01 00
116 38 00
117 40 00
117 53 45
117 54 04
118 27 00
119 34 00
121 58 00
124 39 00
125 30 00
132 33 00
134 13 40
135 24 56
135 56 09
136 06 24
135 51 03
136 57 22
137 45 24
137 22 21
136 53 30
137 49 39
138 09 00
138 26 58
138 05 29
136 34 39
138 07 45
138 37 09
139 39 39
140 39 40
141 32 39
141 40 02
142 14 37
143 30 39
h. in.
h. m.
ft.
ft.
15 39 25
17 24 25
16 23 00
16 50 00
17 09 00
18 29 00
19 54 00
20 36 00
20 19 00
11 30
5 10
17.6
10.4
20 27 00
20 35 00
20 16 45
20 40 40
21 46 41
24 00 00
25 29 19
28 18 05
28 12 00
31 18 00
32 00 20
32 03 12
32 27 00
[10 16]
[3 43]
[2.1]
33 31 45
34 21 55
34 52 00
35 05 00
35 09 00
35 11 54
35 02 20
34 55 00
[10 53]
[4 40]
[2.6]
34 24 00
34 30 00
32 57 00
32 34 00
32 01 30
32 48 00
11 50
9 35
5.1
0.3
34 29 29
35 00 15
0 35
6 55
5.5
0.3
35 20 15
34 43 22
33 44 08
32 29 42
34 28 25
8 20
2 15
11.4
0.7
35 18 21
35 07 31
34 12 00
34 50 25
35 36 45
4 31
4 04
10 45
10 22
10.2
6.3
0.6
0.9
35 45 30
35 51 00
35 34 06
4 00
10 15
5.8
0.3
36 57 00
38 04 18
38 26 00
11 52
5 40
4.2
0.2
38 24 39
38 23 47
0 20
6 35
2.7
2.1
38 51 45
39 35 38
143 57 03
144 37 00
144 21 47
144 58 35
38 18 00
38 08 52
37 49 53
10 43
2 02
2 19
4 30
8 20
8 41
2.5
3.0
1.9
1.9
2.3
1.5
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
AUSTRALIA— Continued.
[Page 261
Place.
Cape Schanck : Light-house
Port Western : Extreme of W. head
Wilson PromontoiV: Light, SE. pt
Kent Island: Deal Island light
Flinders Is. : Strzelecki Peaks, SE. peak
Goose Island: Light on S. end
Banks Strait: Swan Island light
Port Albert: Light-house
Gabo Island : Light-house
Cape Howe (east): Extreme
Cape Green : SE. pt
Twofold Bay: Lookout Pt. light
Dromedary Mountain: Summit
Montagu Island : Light-house
Bateman Bay : Observation head
Ulladulla: Inner end of pier
Jervis Bay : Light-house
Kiama Harbor : Outer extreme of S. head
WoUongong: Summit of head
Sydney : Observatory
Port Jackson: Outer S. head light ...
Broken Bay: Baranjo Head light
Newcastle: Nobby Head light
Port Stephens: Light-house
Sugar Loaf Point: Light-house
Port Macquarie : Entrance
Solitary Islands: S. Isle light
Clarence River: S. Headlight
Lat. S.
Richmond River: N. Head light
Brisbane : Signal station
Lookout Point: Extreme
Cape Moreton : Light-house
Double Island Point: Light-house
Indian Head : Extreme
Sandy Cape: Light-house
Burnett River: S. Head light
Lady Elliot Islet: Light-house
Bustard Head : Light-house
Rodd Bay : Spit end
Port Curtis: Gatcombe Head light
Cape Capricorn : Light-house
Port Bowen: Observation rock
Percy Isles: Pine I. light
Northumberland Isles : Summit of Prud-
hoe I
Cape Palmerston : N. extreme
Cape Conway: SE. pt
Port Molle: S. side of entrance
Cumberland Island: Whitsunday I.,
summit on W. side
Port Denison: Obs. pt., W. side of Stone
Isle
Gloucester Island: Summit near N. end.
Holborne Islet: Center
Cape Bowling Green: Light-house
Cape Cleveland : Light-house
Palm Islands: SE. point of SE. island..
Rockingham Bay: Peak of Goold Isle..
Barnard Island: Light-house
Frank land Island: High islet
Cape Tribulation : Extreme
Hope Island: S. islet
Cook Mountain: Summit
Cape Bedford : SE. extreme
38 29 42
38 29 15
39 08 00
39 29 45
40 11 45
40 18 40
40 43 40
38 45 06
37 34 15
37 30 10
37 15 40
37 04 18
36 18 30
36 14 30
35 43 58
35 21 41
35 09 15
34 40 25
34 25 30
33 51 41
33 51 30
33 35 00
32 55 15
32 45 10
32 26 20
31 25 30
30 12 00
29 25 30
28 51 30
27 27 32
27 26 20
27 02 10
25 56 00
25 00 15
24 43 20
24 45 00
24 07 00
24 01 20
24 01 20
23 53 00
23 29 30
22 31 40
21 39 00
21 19 16
21 32 00
20 32 20
20 18 50
20 15 30
20 00 50
19 57 30
19 41 50
19 19 20
19 11 25
18 45 .30
18 09 30
17 40 40
17 09 45
16 04 20
15 45 00
15 29 45
15 16 30
Long. E.
144 52 51
145 01 34
146 25 16
147 18 39
148 04 00
147 47 39
148 07 24
146 37 43
149 55 10
149 58 39
150 03 04
149 54 45
150 01 34
150 13 34
150 12 34
150 29 29
150 46 26
150 52 19
150 55 14
151 12 23
151 18 15
151 20 30
151 48 19
152 13 20
152 33 40
152 55 19
153 17 00
153 23 10
153 35 55
153 01 48
153 33 50
153 28 04
153 13 00
153 23 00
153 13 40
152 25 00
152 45 15
151 41 04
151 37 15
151 23 50
151 14 04
150 45 44
150 14 00.
149 43 .30
149 31 04
148 58 00
148 53 15
149 00 00
148 16 54
148 27 34
148 23 00
147 27 40
147 01 10
146 42 50
146 11 04
146 11 00 .
146 02 30
145 29 34
145 28 30
145 17 30
145 23 15
Lnn. Int.
H.W.
L.W.
Range.
Spg. Neap.
10 38
8 40
8 05
20
"26'
8 40
8 35
8 15
9 00
10 45
10 05
8 55
h. m. \ ft. i ft.
4 25
"2'27'
1 52
"2"67'
'2"67'
2 27
2 23
2 00
2 46
"2"66'
2 43
4.5
5.2
5.3
4.2
4.7
5.8
4.1
"4.'6'
4 30 6. 4
6.2
3.4
3.1
3.2
'3." 3
2.5
2.8
3.6
2.4
"2." 4
3.9
3 53 9. 0 5. 4
7.5 I 4.5
Page 262] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
AUSTRALIA— Continued.
Place.
Lat. s.
Long. E.
Lun. Int. 1 Range. 1
H.W.
L.W. Spg.
Neap.
e
i
c
(3
«
s
9
Murdock Point ^Extreme ,
O / II
14 37 15
14 10 00
O ' II
144 57 30
144 32 34
144 15 19
143 42 15
143 36 19
143 34 00
143 15 15
143 29 00
143 06 00
142 56 19
II. TO.
h. TO. ft.
ft.
Cape Melville: NE. extreme
1
Flinders Island: N. extreme of N. island.
14 07 45
Claremont Point: Extreme 14 00 30
Cape Sidmouth: Extreme 13 24 45
Cape Direction: NE. extreme i 12 51 00
Cape Grenville: Extreme 11 58 15
Sir Charles Hardv Island: N. extreme ,
of SE. isle ' ' 11 55 00
Bird Island: NW. isle 11 46 30
9 00
2 47 1 9. 6
5.8
Hannibal Isles: E. isle
11 36 30
10 41 30
10 37 45
10 22 00
10 46 00
10 36 05
17 36 40
17 35 10
17 06 50
Cape York : Sextant Rock
142 32 24
142 39 20
142 21 19
142 10 50
141 53 49
140 37 06
139 45 56
139 38 36
1 00
7 10 8.0
4.7
Mount Adolphus: Summit
Travers Isles : Center
Prince of Wales Island: Cape Cornwall,
extreme
Booby Island : Center
4 20
10 30
7.8
4.7
Flinders River: Entrance
Albert River: Kangaroo Pt
Sweers Island : Inscription Pt
TASMANIA.
Cape Portland: NW. pt
40 44 15
41 03 25
41 07 05
41 10 00
41 08 30
41 02 50
40 23 40
40 40 10
40 22 00
41 04 00
41 41 00
42 11 37
42 11 00
43 19 00
43 33 30
43 44 30
43 29 40
43 21 00
42 53 25
43 14 00
42 52 00
42 13 00
41 34 00
40 59 40
147 56 09
146 47 54
146 33 30
146 24 30
146 12 00
145 56 39
144 47 45
144 39 44
144 39 19
144 44 00
144 57 00
145 12 34
145 10 30
145 53 00
146 01 04
146 22 04
147 08 49
147 23 40
147 20 07
148 02 00
148 00 00
148 18 04
148 19 30
148 20 50
Port Dalrymple: Low Head light
Port Sorrell: NW. entrance head
Port Frederick : Entrance
Leven River: W. entrance head
Emu Bay : Blackman Pt .
11 10
5 00
9.0
6.9
Hunter Island : N. pt
Cape Grim: Outer Doughboy Islet
Albatross Islet: N. pt
Arthur River: Entrance
Pieman River: Rocks close to entrance.
Macquarie Harbor: Entrance Islet
Cape Sorrell : Light-house .
7 20
1 07
2.7
2.1
Port Davey : Pollard Head
Southwest Cape: Extreme pt.
Mewstone Rock: Center
Cape Bninj'^: Light-house .
Bruny Island : Penguin Islet
Hobart Town: Transit of Venus station.
Cape Pillar* Tasman Islet ...
8 05
1 52
4.2
3.2
Cape Frederik Hendrik: Extreme
Freycinet Peninsula: Summit .
St. Patrick Head: N. pt....
Eddystone Point : Extreme
NEW ZEAIiAND.
0
If.
Three Kings Islands: NE. extreme of
NE. island
34 m 20
34 25 07
34 31 00
35 00 20
35 01 44
35 17 00
172 08 49
173 03 34
173 00 54
173 32 39
173 45 48
174 06 06
North Cape : Cape Islet
Parenga-renga Harbor: Kohan Pt
Maunganui Harbor: White Pt
Wangaroa Harbor: Peach Islet
Bay of Islands: Motu Mea Islet
7 40
7 26
1 30
1 55
6.4
5.9
4.5
4.2
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
NEW ZEAIiAND— Continued.
[Page 263
Place.
Wangaruru Harbor: Grove Pt
Wangari Harbor: Loot Pt
Great Barrier Island: Needles Pt
Auckland Harbor: Light-house
Coromandel Harbor: Tuhnia I
Cape Colville: N. pt
Cuvier Island: Light-house
Tauranga Harbor: Mount Maunganui,
860 ft
AVhite Island: Summit, 863 ft
Cape Runaway : Extreme
East Cape: Islet, 420 ft
Tolaga Bay : Matu-heka Islet
Mahia Peninsula: S. extreme of Port-
land I
Ahuriri Harbor: Light-house
Kidnappers Cape: Extreme
Cape Palliser: Light-house
Port Nicholson: Pencarrow light
Wellington: Queen's Wharf light
Mana-watu River: Light-house
Wanganui River: N. head
Egmont Mountain: Summit, 8,270 ft...
New Plymouth: Flag-staff
Kawhia Harbor: S. head
Aotea Harbor: S. head
Whaingaroa Harbor: S. entrance pt
Manukau Harbor: Paratutai flag-staff..
Kaipara Harbor : Light-house
Hokianga River: Flag-staff at entrance.
Cape Campbell : Light-house
Port Cooper: Lyttleton custom-house ..
Akaroa Island: Light-house
Ashburton River: N. entrance pt
Waitangi River: N. entrance head
Otago Harbor: Taivoa Head light
Molyneux Bay : Landing place ,
Nugget Point: Light-house
Bluff Harbor: Light-house
Tewaewae Bay: Pahia Pt
Solander Islands: Summit, 1,100 ft
Preservation Inlet: Light-house
West Cape : Extreme
Queenstown: U. S, Tr. of Venus station
Milford Sound: Freshwater Basin
Cascade Point: N. extreme
Grey River: Entrance
Hokitika: Entrance light ,
Cape Foul wind : Light-house
Cape Farewell : Extreme
Nelson: Bowlder Bank light
D' Urville Island : Port Hardy
Port Gore: Head of Melville Cove
Port Underwood; Flag Pt
Port William: Howell's House
Paterson Inlet: Glory Cove
Port Adventure: White Beach, S. end..
Port Pegasus: Cove abreast Anchor-
age I
Codfish Island : N W. extreme
Snares Islands: SW. islet.
Lat. s.
35 23 48
35 51 09
36 01 15
36 50 06
36 48 35
36 28 20
36 26 20
37 36 25
37 30 00
37 30 45
37 40 00
38 20 50
39 18 00
39 28 30
39 38 00
41 36 45
41 21 40
41 17 17
40 27 10
39 57 00
39 18 00
39 03 35
38 04 50
37 59 35
37 46 22
37 03 00
36 23 00
35 32 05
41 44 00
43 46 40
43 54 00
44 04 50
44 54 50
45 46 55
46 24 05
46 27 10
46 37 00
46 20 40
46 36 00
46 10 00
45 54 50
45 02 07
44 40 20
44 00 30
42 26 20
42 42 20
41 45 40
40 29 50
41 16 05
40 46 35
41 01 55
41 20 28
46 50 30
46 58 30
47 03 52
47 11 40
46 45 45
48 06 43
Long. E.
174 21 24
174 31 14
175 25 34
174 51 00
175 24 34
175 21 04
175 49 00
176 10 14
177 10 49
177 59 34
178 35 09
178 20 14
177 53 15
176 54 14
177 06 44
175 18 45
174 51 04
174 47 25
175 14 40
174 59 44
174 03 59
174 04 35
174 48 04
174 50 04
174 52 19
174 31 14
174 08 00
173 21 59
174 17 14
172 44 17
173 00 20
171 48 34
171 11 14
170 44 02
169 47 53
169 50 04
168 23 00
167 42 19
166 54 04
166 38 15
166 25 49
168 40 06
167 54 45
168 21 34
171 11 54
170 59 30
171 27 44
172 41 04
173 17 30
173 54 04
174 11 22
174 08 24
168 05 34
168 09 54
168 10 57
167 40 51
167 36 49
Lun. Int.
H. W.
166
44
h. m.
7 15
7 05
7 20
7 05
L. W.
h. m.
1 05
0 55
1 10
0 55
7 05
0 55
8 10
8 00
2 00
1 50
05 ! 12 15
4 40
'4'52'
9 40
10 50
"i6'54
3 30
Range.
Spg. Neap.
ft.
6.5
6.7
10.8
10.7
6.6
6.8
3.5
5.7
3.6
6.3
9 15
9 10
3 05
3 00
11.6
11.9
9 08
9 05
9 00
8 40
4 45
3 45
2 55
2 .50
2 50
2 30
11 00
10 00
12.3
12.6
10.0
9.2
7.5
7.4
3 31
1 05
ii'io'
9 39
5.6
7 15
"s'oo'
7.8
'7."5'
10 10
10 20
4 00
4 10
9.8
9.5
9 55
9 45
6 00
1 00
11 45
3 45
3 35
12.0
11.6
12 15 I 7.6
9 15
7.8
5 40
7.9
4.6
4.8
7.7
7.6
4.4
4.7
5.8
3.0
4.9
3.1
5.4
8.2
8.5
8.7
9.0
7.1
6.5
6.5
5.8
4.4
"6.'2
"5.'9
7.7
7.5
9.4
9.2
6.6
6.2
Page 264]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
THE ARCTIC REGIONS.
Place.
Cape Waleingham^ Extreme
Mile Island: N. p*
Marble Island : E. end
Cape Kendall: Extreme
Iglooik Island: E. pt
Victoria Harbor: N. shore
Elizabeth Harbor: Entrance
Magnetic Pole, 1831
Port Neill: N. pt. of entrance
Port Bowen: N. cove
Batty Bay : S. pt. of entrance
Port Leopold: Whaler Pt
Careys Islands
Discovery Harbor
Alert' s Winter Quarters
Cape Joseph Henry : N. extreme
Cape Hecla: N. extreme
Cape Columbia: Extreme
Melville Island: Winter Harbor
North Cape
Liakhov Islands: E. pt. of New Siberia
Cape Tscheljuskin : E. pt
Nova Zembla: Vaigats I. , N. pt
Cape Costin (Kostina) .
NE. pt., Cape Desire...
Franz Josef Land : Wilczek I
Mezen: Epiphany Church
Morjovetz Island : Light-house
Archangel : Trinity Church
Jighinsk Island : Light-house
Onega: St. Michael's Church
Salovetski : Light-house
Cape Sviatoi Nos: Light-house
Bear Island
Spitzbergen Island : S. cape
Cloven Cliff
Danes I., Robbe
Bay
Thank God Harbor
Cape York : Extreme
Upernivik: Flagstaff
Proven: Village
Omenak Island: Village
Godhavn: Village
Jacobshavn : Village
Claushavn : Village
Christianshaab: Village
Egedesmunde : Village
Whalefish Island: Boat Inlet
Holsteinberg: Village
Kangamint
Ny Sukkertop: Village
Godthaab: Flagstaff
Sermelik Fjord : Kasuk Peak
Fiskernaes: Village
Jensen Nunatak: Peak
Ravn Storo: Peak
Frederikshaab: Church
Kangarssuk Havn : Village
Arsuk: Pingo Beacon
Kajartalik Island : Summit
Ivigtuk: House
Bangs Havn : Anchorage
Aurora Harbor
Lat.N.
00 00
04 00
33 00
42 00
21 00
09 17
38 14
05 00
09 13
13 39
13 00
50 05
49 00
04 40
27 00
40 00
54 00
07 00
47 10
55 00
75 10 00
77 41 00
70 25 00
70 55 00
76 58 00
79 55 00
65 50 18
66 45 50
64 32 06
65 12 17
63 53 36
65 07 00
68 08 51
74 30 00
76 35 00
79 50 00
79 42 00
38 00
55 00
47 48
20 42
40 00
14 04
13 12
07 30
49 06
42 30
58 30
55 54
48 42
24 30
10 36
29 12
05 12
50 00
42 36
59 36
28 20
10 24
09 42
12 12
47 30
48 36
Long. W.
28 00
50 00
06 00
15 00
31 00
30 33
10 56
47 00
00 54
54 48
08 00
12 00
10 00
45 00
18 00
38 00
45 00
20 00
48 15
57 00
91
87
81
91
92
96
89
88
91
90
73
64
61
63
64
70
110
179
Long. E.
150 30 00
104 01 00
59 10 00
53 01 50
65 40 00
58 45 00
44 17 00
42 30 00
40 33 30
36 51 30
38 08 30
35 37 00
39 48 54
20 00 00
17 23 00
11 40 30
11 07 00
Long. W.
61 44 00
65 30 00
55 53 42
55 20 00
51 59 00
53 24 07
50 56 30
50 55 30
51 00 00
52 46 00
53 27 00
63 40 18
53 23 00
52 54 00
51 45 48
51 10 48
50 43 36
48 57 00
50 20 48
49 44 00
48 51 00
48 26 00
48 30 42
48 10 30
47 52 00
47 46 48
Lun. Int.
Range.
H.W.
4 00
6 50
11 38
10 35
1 20
10 00
7 18
5 05
9 02
L.W.
h. m.
ft.
10 15
"'olo'
12.0
"8."6'
5 29
4 20
7 40
3.8
3 50
7.0
2 00
11'30
3 10
2.2
3.8
9.1
9 05 2 55
0 14
12 14
"i6"56'
8 05
6 20
13.9
6 25
5 58
5.3
5.4
4 38
8.0
1 52
0 07
7.5
10.0
6 40 0 27
12.5
6 12 j 0 00
'6"i5 6 03'
9.0
'i2.'6"
Neap.
ft.
5.1
"4." 2
5. 5 2. 9
2.6 I 1.0
4.0
1.3
2.1
5.2
3.0
2.0
3.0
3.6
4.8
6.0
3.6
"4." 8
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
THE ARCTIC REGIONS— Continued.
[Page 265
Julianshaab: Village
Neunortalik: Village
Frederiksthal : Village
Cape Farewell : Staten Huk
Aleuk Islands : Center
Cape Tortlenskjold: Extreme
Cape Bille: Extreme
Cape Juul: Extreme
Cape Lo wenorn : Extreme
Dannesbrog Island : Beacon
Ingolsfjeld
Rigny Mount : Summit
Pendulum Islands
Cape Philipp Broke
Cape Bismark: Extreme
Jan Maven Island: Mt. Beerenberg,
6,870ft
Youngs Fore-
land, or Cape
Northeast
Mary Muss Bay..
Langanaes Point.
Rissnaes Point
Grimsey Norddranger: Tr. Station
Skagataaa Point
North Cape: Kalfatindr
Straumness Point
Fugle or Staabierg Huk: Point
Snaefells Yokul : Tr. Station
Reykiavik : Observatory
Cape Skagi : Light-house
Reykianaes : Light-house
Ingolfshofde: Tr. Station
Papev Island: Tr. Station
Reytnur Fjeld: Tr. Station
Balatangi : Light-house
Dia Fjeld: Tr. Station
Lat. N.
60 43 07
60 08 12
60 00 00
59 49 00
60 09 00
61 25 00
62 01 00
63 14 00
64 30 00
65 18 00
66 19 02
69 00 12
74 40 00
74 55 00
76 47 00
71 04 00
71 08 00
71 00 00
22 45
32 40
33 42
07 30
27 29
26 30
30 15
48 04
08 40
04 09
48 06
48 19
35 42
55 27
16 14
45 00
Long. W.
46 01 00
45 16 00
44 40 00
44 01 42
42 55 00
42 15 00
42 00 00
40 50 00
39 30 00
38 30 00
35 11 00
26 10 24
18 17 00
17 33 00
18 40 00
7 36 00
7 26 00
8 28 00
14 30 46
16 10 24
17 57 36
20 05 26
22 23 04
23 08 00
24 31 26
23 45 08
21 55 00
22 39 04
22 39 00
16 36 13
14 08 31
13 41 10
13 32 22
14 23 35
Lun. Int.
Range.
H. W.
h. m.
4 56
5 33
2 55
4 00
11 05
11 10
L. W.
Spg.
Neap.
h. m.
11 09
11 46
9 10
10 13
4 53
4 58
11 21
5 06
ft.
7.0
8.6
9.4
7.5
ft.
2.8
3.4
3.8
3.0
6.7
3.7
3.9
2.1
3.8
2.2
5 10 11 25
14.5
Page 266J
INDEX TO APPENDIX IV.
Page.
Admiralty Islands 255
Adriatic Sea 226-228
Africa, east coast 232, 233
north coast 230
west coa.«t 230-232
Alabama 196
Alaska 198,199
Aleutian Islands 199
Algeria 230
Arabia 236
Arctic regions 264, 265
Argentina 208, 209
Asia, east coast 239-250
islands . 243, 244
south coast 236-239
Atlantic Ocean, islands. 213-215
Australia 259-262
Austria 227,228
Azores Islands 213
Bahama Islands 203
Balearic Islands 226
Baluchistan 237
Banka Strait 239
Belgium 223
Belize 197
Bermuda Islands 214
Black Sea 229,230
Borneo 242
Brazil 207,208
British Columbia 200
Burma 238
California 200, 201
Canary Islands . . 214
Cape Breton Island 192, 193
Verde Islands 214
Caroline Islands 252
Celebes Island 242
Central America, east
coast . . . 197, 198
west coast . . . 202, 203
Cevlon 237
Chile 209-212
China 240-242, 247
Sea 240
I^ntrance 240
Cochin China 240
Colombia, north coast . 198, 206
west coast 213
Connecticut 194
Cook Islands 258
Coral Sea Archipelago 255
Corsica 226
Costa Rica 198
Crozet Islands 236
Cuba 203,204
Cyprus 230
Delaware 195
Denmark 222,223
REGIONS AND COASTS.
Page.
Ecuador 213
Egypt 230
Ellice Islands 254
Europe, Atlantic coast. 215-225
Falkland Islands 214
Fiji Islands 256,257
Florida 195,196
Formosa Island 242
France, north and west
coasts 223,224
France, south coast 225, 226
Galapagos Islands 250, 251
Gaspar Strait 239
Georgia 195
Germany 221,222
Gilbert Islands 251
Great Britain 215-218
Greece 228,229
Greenland 264, 265
Guatemala 197
Guiana 207
Haiti 204
Hawaiian Islands 253
Holland 223
Honduras 197,198
Iceland 265
India 237,238
Indian Ocean, islands. . 234-236
Italy 226,227
Jamaica 204
Japan 248,249
Java 243
Kerguelen Islands 236
Korea..... 247,248,250
Kuril Islands 249
Labrador 191,192
Laccadive Islands 234
Ladrone Islands 252
Linschoten Islands 248
Louisiade Archipelago 255
Louisiana 196
Lower California 201, 202
Madagascar 235
Madeira Islands 213
Magdalen Islands 192
Mame 193
Malaysia 238,239
Maldive Islands 234
Mariana Islands 252
Marquesas Islands 253
Marshall Islands 251
Maryland 195
Page.
Massachusetts 194
Mauritius Island 234
Mediterranean Sea 225-230
Mexico, east coast 196, 197
west coast 202
Mississippi 196
Morocco 230
Mosquito Coast 198
New Brunswick 192, 193
Caledonia 259
Newfoundland 191,192
New Guinea Island 255
Hampshire 194
Hebrides Islands 256
Jersey 195
South Wales 261
York 194
Zealand 262,263
Nicaragua 198
North America, east
coast . . . 191-198
west coast . . . 198-203
Australia 259
Carolina 195
Island, New Zea-
land 262,263
Norway 218-219
Nova Scotia 193
Oregon 200
Pacific Ocean, islands -- 250-259
Pelew Islands 252
Persia 236, 237
Peru 212
Philippine Islands 245-247
Phoenix Islands 254
Porto Rico 205
Portugal 224,225
Prince Edward Island 192
Queen Charlotte Islands . . . 199
Queensland 261,262
Red Sea 233-234
Rhode Island 194
Russia, south coast 229
west coast 220
St. Lawrence, River and
Gulf 192
Samoan Islands 257
Santa Cruz Islands 255
Sardinia 226
Siam, Gulf 240
Siberia 250
Society Islands 257
Solomon Islands 254
South America, north and
east coasts 206-209
INDEX TO APPENDIX IV.
[Page 267
Page.
South America, W. coast 209-213
Australia 260
Carolina 195
Island, New Zealand.. 263
Spain, north and west
coasts 224,225
south and east coasts. . 225
Stewart Island 263
Sumatra 239
Sweden 219,220 Uruguay
REGIONS AND COASTS — Continued.
Page.
Tasmania 262
Texas 196
Tonga Islands 258
Trinidad 206
Tuamotu Archipelago. . 257, 258
Tunis 230
Turkey 228,229,230
208
Aalborg 223
Aarhus 223
Ababa Island 256
Abaco Island 203
Abang Besar Island 238
Abbeville 223
Abd-al-Kuri Island 233
Aberdeen 216
Abervrach 224
Aberystwith 215
Abingdon Island 250
Abo... 220
AboukirBay 230
Abreojos Point 201
Abrolhos Island 207
Ab.secon Inlet 195
Acajutla 202
Acapulco 202
Accra 231
Acheen Head 239
Aconcagua Mountain 21 1
Acre 230
Adakh Island 199
Adalla 230
Adams, Port 247
Addu Atoll 234
Adelaide, Port 260
River 259
Adele Island 255
Aden 236
Adenara Island 243
Admiralty Head 200
Islands 255
Adolphus Mountain 262
Adventure, Port 263
^gina 229
Aero Island 222
Ji^rstenen 218
Africa Rock 226
Agalegas Island 235
Agdenes .•. 218
Agiabampo 202
Agrigan Island 252
Aguadilla Bay 205
Aguja Point 212
Agulhas.Cape 232
Agutava Islet 245
Aheu Island 258
Ahunui Island 257
Ahuriri 263
AiSima 249
Aian 250
Aignan, St., Island 255
Aigues Mortes 226
Ailinginae Islands 251
Aillick Harbor 191
Ailly Point 223
Ailuk Islands 251
Aitutaki Island 258
Aix Island 224
Ajaccio 226
Ajano 230
Akamokan Island 252
Akaroa Island 263
Akashi-no-seto 248
Akpatok Island 191
Akyab 238
Alacran Reef 197
Alamaguan Island 252
Aland Island 220
AlargateReef 198
Albany 194
Albatross Islet 262
Albemarle Island 251
Albert, Port 261
River 262
Alboran Island 230
Albuquerque Bank 198
Alcatrasses Island 208
Alcmene 259
Alcoba^a 207
Aldabra Island 235
Aldeu 218
Alderney Harbor 218
Alegranza Island 214
Alegre, Porto 207
Alert's Winter Quarters ... 264
Alessandro, San, Island 253
Aleuk Islands 265
Alexander, Port 232
Vancouver 200
Alexandretta 230
Alexandria 230
Alfaciues, Port 225
Alfred, Port 232
Algeciraa 225
Algier 230
Ali-Agha, Port 230
Alicante 225
Alij OS Rocks 201
Alipee 237
Alligator Island 241
Reef 196
Alraadie Point 231
Almeria 225
Alphonse Island 235
Alta Vela 204
Altata 202
Altea 225
Altona 222
Alvarado 196
Amager Island 222
Amber, Cape 235
Amboina Island 244
Ambrose, St. , Island 258
Amchitka Island 199
Page.
Vancouver Island 199, 200
Venezuela 206
Victoria .». . 260, 261
Virginia 195
Washington 200
Western Australia 259, 260
West India Islands 203-206
Yucatan 197
Amelia Island 195
Ameni Islet 234
Amherst Harbor 192
Amirante Islands 234
Amour Point 192
Amoy 241
Amsterdam 223
Island 236
Ana, Sta., Lagoon 197
Anaa Island 258
Anacapa Island 201
Anadir River 250
Analaboe 239
Anamba Islands 240
Anataxan Island 252
Anchorite Island 255
Ancona 227
Andaman Islands 238
Andenes 218
Andrava Bay 235
Andrea, St. , Rock 228
Andrew, St 193
Cape 235
Island 255
Andrews, St. , Island 198
Andros Island, Bahamas... 203
Grecian Arch 229
Anegada 205
Aneityum Island 256
Angatau 258
Angaur Island 252
Angeles Bay 202
Los 201
Port, Mexico 202
, Washington 200
Anghris Head 217
Angosto, Port 210
Angoxa Island 233
AngradosReis 208
Pequena 232
Anguilla 205
Anhatomirim 208
Anholt Island 222
Animas, Las 202
Anjer 243
Anjoe, Cape 243
Ann, Cape 194
St., Bay 204
Anna, Sta., Island, N.Brazil. 207
S. Brazil .... 208
Annapolis, Maryland 195
Nova Scotia 193
Anne, St., Island 210
Annisquam 194
Anno Bon Island 231
Anns, St., C. Breton 1 192
England 215
Anowik Island 199
Page 268J
INDEX TO APPENDIX IV.
Page.
Antareh, Ras 233
Antibes 226
Anticosti fcland 192
Antigua 205
Antipodes Island 259
Antivari 228
Antofagasta .*... 211
Antonina 208
Antonio, Port 204
San, Cape, Argentina . 208
Cuba 204
Mt. and Island... 214
Port, Argentina. . 209
Chile 211
Sierra 209
Antwerp 223
AogaShinia 249
Aor, Pulo 240
Aotea 263
Apaiang Island 251
Apalaehicola 196
Apamama 251
Aparri 245
Apenrade 221
Apo Islet 245
Apostle Rocks 209
AragoCape 200
Araish, El 230
Arakam Island 250
Araktcheff Island 258
Aran Island 217
Aransas Pass 196
Aranuka Island 251
Aratika Island 258
Arcadius Islands 204
Areas Cays 197
Archangel 264
Ardassier Islands 243
Ardrossan 216
Arena de la Ventana 201
Point, California 200
L. C^alif ornia .... 201
Arenas Cay 197
Arendal Inlet 219
Arentes Island 243
Argentina 208
Argostoli, Port 228
Arica 212
Arichat Harbor 193
Arkona 221
Armeghon 238
Amheiin, Cape 259
Arno Atoll 251
Arorai Island 251
Arran Island 217
Arrowsmith Islands 251
Arru Islands 244
Arsuk 264
Artaki Bay 230
Arthur River 262
Port 247
Arvoredo Island 208
Ascension Bay 197
Island 214
Ashburton River 263
Ashrafi Island 233
Asia Rock 212
Assateague Island 195
Assens 222
Assumption Island 235
Astoria 200
PLACES — continued.
Page.
Asuncion Island, Ladrones. 252
L.Calif 201
Atalaia Point 207
Athene 229
Atico 212
Atiu Island 258
Atka Island 199
Atkinson Point 200
Attu Island 199
Auckland 263
Islands 259
Audierne 224
Augusta 193
Port, Australia 260
Sicily 227
Augustenberg 221
Augustin, St., Cape, Brazil. 207
Philippines. 246
Augustine, San, Island 253
St., Bay 235
Harbor 195
Aurh Island 251
Aurora Harbor 264
Island 256
Austral Islands 258
Avarena Point 204
Aves Island 205
Aviles 224
Avlona 228
Axim Bay 231
Awa Sima 249
Awomori 249
Ayamonte 225
Ayer Bangis 239
Ayr 215
Baago Island 222
Babayan Claro Island 245
Baccalieu Island 191
Baganiovo 233
Bahal tolls Island 247
Bahama Island 203
Bahia,Brazil 207
Colombia 206
de Cadiz Cay 204
Honda, C. America 202
Bahrain Harbor 236
Bajo Nuevo 197
Bajuren Island 242
Baker Islet 251
Bakers Island 193
Baklar 229
Balabac Island 245
Balaklava Bay 229
Balari Pass 259
Balasor River 238
Balatangi 265
Balayan 245
Bald Isle 260
Balfour Rock 236
Bali Island 243
Balingtang Islands 246
Ballena Bay 202
Balls Pyramid 259
Ballum 22i
Ballycottin 218
Balstrum 222
Balta Island 216
Baltic Port 220
Baltimore 195
Bampton Island 255
Page.
Banda Island 244
Banderburum 236
Band jerinasin 242
Bangkaru Islands 239
Bangkok 240
Bangor 193
Bangs Havn 264
Banjuwangi 243
Banka Island 239
Strait 239
Bankot 237
Banks Strait 261
Bantal 239
Bantam 243
Bantenan 243
Banton Island 246
Bantry Bay 216
Baracoa 203
Barataria Bay 196
Baratoube Bay 235
Barbados Island 205
Barbara, Santa, California . 201
Island 201
Mexico 202
Port 210
Barbe, St. , Island 240
Barbuda 205
Barcelo Bay 210
Barcelona, Spain . . 225
Venezuela 206
Bardsey Island 215
Barfleur, Cape 223
Bari 227
Barker Islets 259
Barnard Island 261
Barnegat Inlet 195
Barneveldt Islands 209
Barnstable 194
Barra Head 216
Sao Joao 208
da 207
Barren Island 248
West 242
Barrier, Great, Island 263
Barrington Island 251
Barrow Island, Australia . . 260
Tuamotu Arch . . . 257
Point 198
Bartholomew, St 205
Cape 209
Bartolom^, San 201
Barton, Port 245
Baru,.Point 239
Barung Island 243
Bas, De, Island 224
Basdorf 221
Basianang Bay 246
Bilsiduh 237
Basilan Island 247
Baskerville, Cape 260
Basrah 236
Bass Islets 258
Bassa, Grand 231
Bassas Rocks 237
da India 235
Bassein, Burma 238
India 237
River 238
Basseterre 205
Bastia 226
Bastion, Cape 240
INDEX TO APPENDIX IV.
[Page 269
Page.
Basto 219
Batalden Island 218
Batan Island 246
Port 246
Batangas 245
Batavia 243
Batbatan Island 246
Bate Islands 248
Bateman Bay 261
Bath 193
Bathurst 231
Island 259
Batian Island 244
Batoe Islands 239
Batoura 229
Batticaloa 237
Battle Islands 191
Batty Bay 264
Batve Toetong 239
Baubeltaub Island 252
Bauld Cape 191
Baxo Nuevo 204
Bay of Islands 262
Baynes Sound 200
Bayonnaise Island 249
Bayonne 224
Bazaruto Island 232
BeachyHead 215
BealeCape 199
Bear Island 264
Cape 225
Beata Island 204
Beaufort, N. Carolina. ..... 195
S.Carolina 195
Port 232
Beaver Harbor 200
Beaver-tail Light 194
Bee du Raz 224
Beda'a,Al 236
Bedford, Ca]ie 261
Bees, St 215
Beeves Eocks 216
Beirut 230
Bel Air 235
Belfast 193
Bay 217
Belgrano 208
Belize 197
Bell Island 191
Rock, Scotland 216
Bellavista Cape 226
Belle Isle, France 224
Labrador 191
Bellingshausen Island 257
Bellone, Cape 235
BenGhazi 230
Benbane Head 217
Bender Erekli 230
Benedicto, San, Island 202
Benevente 207
Benguela 232
Benicia 200
Benidonne 225
Benin River 231
Benito, San, Island 201
Benkulen 239
Bento, San, River 231
Benzert 230
Bequia Island 205
Berbera 233
Berdiansk 229
PLACES — continued.
Page.
Bergen, Germany 221
Norwav 218
Berikat '. 239
Bering, Cape 250
Island 250
Berlanga Island 225
Berlin 222
Benneja Head 209
Bermudas 214
Bernal Chico 196
Bernardo Islands 257
Berwick 216
Besuki 243
Betrapar Islet 234
Beverly 194
Beyt 237
Bhaunagar 237
Blanche Point 227
Biarritz 224
Bickerton I.«land 259
Bideford 215
Bidstone 215
Bierneborg 220
Bigar Islet.. 251
Bikini Islands 251
Bilbao 224
Bille, Cape 265
Billiton Island 239
Bindloe Island 250
Bintang Hill 238
Bintoean 239
Bird Island, Australia 262
Bahamas 203
BandaSea 244
N. Pacific 253
Seychelle Islands. 234
Tuamotu Arch. . . 258
W. Africa 231
Islands, Magdalen Is. . 232
Birneys Island 254
Bismark, Cape 265
Bittern Rocks 249
Bjuroklubb 220
Blaabjerg 223
Black Head 191
Point Bay 232
Stairs Mountain 217
Blackness 216
Blacksod Point 217
Blair, Port 238
Blaize, St 232
Blanco Cape, N., Africa 231
Oregon 200
Peru 212
S. , Africa 231
Peak 198
Blankenberghe 223
Bias, San, Argentina 209
Cape, Florida 196
Mexico 202
Blasket Islands 216
Bligh Island 257
Blighs Cape 236
Blimbing Bav 239
Blinyu ' 239
Block Island 194
Bloody Foreland 217
Blueflelds 198
BluffHarbor 263
Boar Islands 191
Boavista Island 214
Page.
BobaraRock 228
Bodie Island 195
Bogense 222
Bogsher 220
Bohol Island 246
Bojador, Cape 231
Bojeador, Cape 245
Bola-Bola Island 257
Bom Abrigo Islet 208
Bombay 237
Bon, Cape 230
Point 239
Bona 230
Bonacca Island 197
Bonaive Island 206
Bona venture Head 191
Island 192
Bonavista Cape 191
Bongao Island 247
Bonham Islands 251
Bonifacio 226
Bonin Islands i . 253
Boobjerg 223
Booby Island, Leeward Is. . 205
Queensland 262
Boompjeo Island 243
Boon Island 193
Borda, Cape 260
Bordeaux 224
Bordelaise Island 252
Borja Bay 210
Bornholm 222
Borodino Islands 253
Boscawen Island 257
Bosphorus 229
Boston 194
.Botel Tobago Sima 242
Bougainville, Cape 259
Island 254
Bougaroni, Cape 230
Boulogne 223
Bounty Islands 259
Bourbon, Cape 236
Bouro Island 244
Bouton Island 242
Bouvets Island 215
Bovlilu van, Cape 245
Bowditch Islet 254
Bowen, Port, Australia 261
BaffinsBay 264
Bowling Green, Cape 261
Boyanna Bay 235
Bradore Bay 192
Brala, Pulo 240
Brangmans Bluff 198
Bras, Pulo 239
Brass River 231
Brava Island, C.Verde Is.. 214
E. Africa 233
Brazos Santiago 196
Bray Head 217
Breaker Point 241
Bremerhaven 222
Bremerton 200
Brest 224
Brewers Lagoon 198
Bridgeport 194
Brielle 223
Brill Reef 243
Brindisi 227
Brisbane 261
Page 270j
INDEX TO APPENDIX IV.
Page.
Bristol, England 215
Rhode Island 194
Britannia Island 259
Broadhaven 217
Broken Bay 261
Bronnosnnd 218
Brothers Island, Red Sea . . 233
Islets, China 241
Broughton Bay 244
Head 248
Island 249
Rock 249
Brunet Island 191
Bruni River 242
Brunswick, Georgia 1 95
Maine 193
Bruny, Cape 262
Island 262
Brussels 223
Brusterort 221
Bryer Island 193
Bubn^n Island 247
Bucas Island 246
Buchanness 216
Buddonness 216
Budrum 230
Budua 228
Buenaventura 213
San 201
Buenos Avres 208
Bugui Point 246
Buitenzorg 243
Buka Island 254
Bulipongpong Island 247
Biilk 221
Bull Harbor 200
Rock 216
Bullock Bay 250
Burg 221
Burghaz 229
Burias Island 246
Burin Harbor 191
Burnett River 261
Burntcoat Head 193
Burrh Island 251
Busios 208
Islets 208
Bustard Head 261
Busuanga Island 245
Busum 222
Butt of Lewis 216
Button Islands 191
Byam Martin Island 257
Byron Island 251
Caballo Island 245
Cabeceira, Cape 233
Cabeza de Vaca 211
Cabrera Island 226
Cabron Cape 204
Cabrut Islet 234
Cadaques 225
Cadiz 225
C'admus Island 257
Caen "... 223
Cagayan Jolo Island 247
Cagayanes Islands 247
Cagliari 226
Caigara 207
Caicos Island 203
West, Cay 203
PLACES — continued.
Pivge.
Calaan, Point 246
Calais, France 223
Maine 193
Calavite, Monte 245
Calavan Island 245
Calbuco 211
Calcasieu Pass 196
Calcutta • 238
Caldera 211
Caldy Island 215
Calebar River, New 231
Old 231
Caledonia 206
Calf of Man 215
Calicut - 237
Calimere Point 237
Callao 212
Calpe 225
Caluya Island 245
Calvi 226
Caniamu 207
Camaron Cape 198
Camasusu Island 246
Cam bay 237
Cambria 208
Cambridge, England 215
United States 194
Camiguin Island, Luzon . . . 245
Mindanao 247
Cammin 221
Campbell, Cape 263
Island 259
Campeche 197
Campobello Island 193
Canaria, Gran, Island 214
Canaveral Cape 195
Cancun Island 197
Candia Island 228
Candon 245
Cannes 226
Cannonier Point 234
Canoas Point 201
Canso, Cape 193
North 193
Canton 241
Island 254
Pulo 240
Cantyre 216
Cape Town 232
Cape Verde Islands 214
Capel Island 218
Cape d'Istria 246
Capones Islet 245
Capraia Island 226
Caprera Island 226
Capri Island 226
Capricorn, Cape 261
CarNicobar 238
Carabane 231
Carabao Island 246
Caraques Bay 213
Carataska Lagoon 198
Caravellas., 207
Carbon, Cape 230
Carbonera Cape 226
Cardamum Islet 234
Cardiff 215
Careys Islands 264
Cargados Carajos 234'
Caribana Point 206
Carimare Mountain 207
Page.
Carimata Island 240
Carl ingford Lough 217
Carlobago 227
Carlos, San, deAncud 211
Point 201
Carmen Island 197
Caroline Islands, N. Pacific. 252
S.Pacific 253
Carousel Island 192
Carreta Mountain 212
Point 198
Carreto, Port 206
'^^arrizal. Port 211
Cartagena, Colombia 206
Spain 225
Cartago Mountain 198
Carteret Cape 224
Harbor 255
Cartwright Harbor 191
Carupano 206
Carysfort Island 257
Reef 195
Cascade Point 263
Casquets Rocks 223
Cassini Island 259
Castillos 208
Castle Island 203
Caatlehaven 216
Castro 210
Urdiales 224
Catlsland 196
Catalina Harbor 191
Sta., Island 201
Catania 227
Catastrophe, Cape 260
Catbalogan 246
Catharine Point 209
St 215
Island 208
Cato Island 255
Catoche Cape 197
Cattaro 228
Cautanduanco Islands 246
Cavite 245
Caxones 198
Cayenne 207
Cayeux 223
Caymans 204
Cazza Island 228
Ceara 207
Cebu Island 246
Cedar Keys 196
Cedeira 225
Ceicer de Mer Island 240
Celebes 242
Centinela Islet 206
Ceram Island 244
Cerros Island 201
Cestos 231
Cette 226
Ceuta 230
Ceylon 237
Chacachacare Island 206
Chacopata 206
Chagos Arch 234
Chagres 206
ChahbarBav 237
Chala Point.".... 212
ChaleurBay 192
Challenger, Cape 2.36
Chama Bav 231
INDEX TO APPENDIX IV.
[Page 271
Page.
Cham-Callao Island 240
Chame, Point 213
Chamisso Island 198
Champerico 202
Chanaral Bay 211
Island 211
Chandeleur Islands 196
Chao Islet 212
Chapel Island 241
Chapu 242
Charles Cape 195
Island, Chile 210
Galapagos Group. 251
Hudson Strait 191
Charleston 195
Charlottetown 192
ChateauBay 192
Chatham Harbor 194
Island, Galapagos
Group 251
S. Pacific 259
ChatteCape 192
Chaume,La 224
Chausey Islands 224
Chedubah Island 238
Chemulpo 247
Chentabun River 240
Chepillo Island 213
Cherbourg 223
Cheribon 243
Cherso 227
Chiachi Islands 199
Chicarene Point 202
Chidleigh Cape 191
Chifu 247
Chignecto Cape 193
ChignikBay 199
Chilca Point 212
ChimbaBay 211
Chimbote 212
Chincha Islands 212
Chinchin Harbor 241
Chinchorro Bank 197
Chin-hai 241
ChinoBay 241
Chirambiri Point 213
Chirikof Island 199
Chitlaclslet 234
Chittagong River 238
Choda Island 247
Choiseul Island 254
Port... 235
Choros Islands 211
Christiana Islands 229
Christiania 219
Christianshaab 264
Christianso Island 222
Christianssand 218
Christiansted 205
Christiansund 218
Christmas Cove 210
Harbor 236
I., Indian Ocean 236
N. Pacific 251
Christopher, St 205
Christoval, San, Island 254
Chuapa River 211
Chuluwan Island 232
Chupat River 209
Churriica, Port 210
Chusan Islands 241
PLACES — continued .
Page.
Claris Island 202
Cica. Mount 228
Cienfuegos 204
Ciotat 226
Cispata, Port 206
CittaNuova 227
Civitavecchia 226
Clara, Sta 200
Clare Island 217
Claremont Point 262
Clarence Harbor, Bahamas. 203
Port, Alaska 198
River 261
Clarion Island 202
Claushavn 264
Clear Cape 216
Clearwater Point 192
Gierke Island 257
Clermont Tonnere Island 257
Cleveland, Cape 261
Clew Bay 217
ClifdenBay 217
Clipperton Island, Mexico . 202
N.Pacific 253
Clonard, Cape 250
Coast Castle, Cape 231
Coatzacoalcos 197
Cobbler Rock 198
Cobija 212
CobreBay 211
Cochin 237
Cockell Islet 259
Cockscomb Mountain 197
Coconada 238
Cocos Island, C. America . . 203
N.Pacific 250
Cod, Cape 194
CoderaCape 206
Codfish Island 263
Codroy Island 192
Coetivy Island 235
Coffin Bay 260
Island, Madagascar 235
Nova Scotia 193
Cofre de Perote Mt 196
Coiba Island 202
Colberg 221
Colbert Islet 259
Coles Point 212
Colina Redonda 212
ColnettBay 201
Colombo 237
Colon 206
Colonia 208
Colonna, Cape, Greece 229
Italy 227
Columbia, Cape 264
Columbretes Islands 225
Columbus Island 198
Colville, Cape 263
Coman Inlet 211
Comandatuba 207
Commerson Island 255
Comorin, Cape 237
Comoro Island 235
Concei^ao 208
Conception Island 203
Point 201
Conde 207
CondorCove 211
Condore Islands 240
Page.
Conducia 233
Conejo, El, Point 201
Coney Island 241
ConfitesCay 204
Congo River 232
Congrehoy Peak 197
Conn^table Islet 207
Constantinople 229
Constitution Cove 212
Contas 207
Conte, Port 226
Contoy Island 197
Conway, Cape 261
Reef 258
Cook Cape 199
Mountain 261
CookraHill 198
Cooper, Port 263
Copenhagen 222
Copiapo 211
Copper Island 250
Coquet Island 216
Coquille Island 252
Coquimbo 211
Coral Island 208
Islet 208
Corcovado Volcano 210
Cordouan, Point 224
Corfu 228
Coringa Islands 255
Corinto 202
Cork, Ireland 218
Port, Staten Island ... 209
Cormorant Island 200
Corn Islands 198
Corn wal lis Islands 253
Port 238
Coro, Vela de 206
Coromandel Harbor 263
Coronation Island 215
Corregidor Island 245
Cotrientes, Cape, Argentina . 208
Colombia 213
Mexico 202
S. Africa 232
Corsarios Bay 206
Corseulles, Port 223
Corso, Cape 226
Mountain 210
Corti 226
Coruna 225
Corvolsland 213
Coslin 221
Cosmoledo Island 235
Cotinguiba 207
Cotrone 227
Coubre, Point de la 224
Courtown Cays 198
Coutances 224
Cove Rock 232
Cow Head 192
Coy Inlet 209
Cozumel Island 197
Cracker Bav 209
Crassok Point 239
Crescent City 200
Cretin, Cape 255
Creux, Cape 225
Crocker Island 258
Croisic 224
Croker, Cape 259
Page 272]
INDEX TO APPENDIX IV.
Page.
Crooked Island 203
Crozet Islands 236
Cruz Cape 204
Sta., Brazil 207
California 201
Island 201
Islands, Philijv
pines 247
S. Pacific ... 255
Leeward Islands . 205
Luzon 245
Port 209
Cuad Basang Island 247
Cuba 203,204
Culebra 202
Culebrita Island 205
Culion Island 245
Cullera, Cape 225
Culver Point 260
Cumana 206
Cumberland Island 261
Cumshewa Harbor 199
Cupchi Point 241
Cupica Bay 213
Cura^-ao Island 206
Little 206
Currimao 245
Currituck Beach 195
Curtis Island 258
Port 261
Curzola Island 228
Cuttyhunk Light 194
Cuvier, Cape 260
Island 263
Cuxhaven 222
Cuyo Island 245
Cyprus 230
Dfedalus Shoal 233
Dago Island 220
Dakar, Port 231
Dalcahue 211
Dale Point 259
Dalrymple Harbor 247
Port 262
Dalupiri Island 245
Damghot 236
Dam ma Island 244
Danger Islands 257
Dangerous Rock 241
Dannesbrog Island 265
Danube River 229
Danzig 221
Dapitan 247
Dardanelles 229
Dar el Beida, Cape 230
Dar-es-Salaam 233
Darien, Colombia 213
Georgia, U.S 195
Darsserort 221
Darwin, Port 259
Dato Island 240
Datu, Point 239
Dauphin, Fort 235
Davao 246
Davey, Port 262
Davids, 8t. , Island 214
De Kastri 250
De Pevsters Island 254
Deadman Rock 192
PLACHS — continued .
Page.
Deception Island 215
Deimaniveh 236
Delagoa Bay 232
Delgada Point 209
Delgado, Cape 233
Point 209
Demerara 207
Denia 225
Denis,St 235
Denison, Port 261
D'Entrecasteaux Islands 255
Point 260
Deseado Cape 209
Desert, Mt., Rock 193
Desertas 213
Desirade 205
Desire, Port 209
Desolation Cape 209
DiaFjeld 265
Diamond Harbor 238
Point 239
Diedrichshagen 221
Diego Garcia 234
• Ramirez Island 209
San 201
Cape 209
Dieppe 223
Digges Islands 191
Dimasalasan, Port 246
Dinding Channel 238
Dingle Bay 216
Diomede Island 198
Direction, Cape 262
Island 240
Disappointment, Cape, Sib. 250
Washington 200
Discovery Harbor 264
Disei Island 233
DiuHead 237
DixCove 231
Djabon, Point 239
Djambi 239
Djursten 219
Dnieper Bay 229
Doc Can Islet 247
Dodd Island 241
Dog Island 205
Domar, Pulo 240
Domesnes 220
Domingo, San, Point 201
St., Cay 203
City 204
Dominica ^ 205
Donaghadee 217
Dondra Head 237
Donegal Bay 217
Double Island 238
Point 261
Peak Island 241
Douglass Rocks 253
Dounpatrick Head 217
Douvres Rocks 224
Dover Point 260
Drei Cap Peninsula 255
Drepano, Port 228
Drobak 219
Drogheda 217
Dromedary Mountain 261
Dnimmond Island 251
Dublin 217
Ducie Island 257
Page.
Duff Islands 255
Duke of Clarence Island . . . 254
York I., N.Britain. 254
S. Pac... 254
Dulce Gulf 197
River 197
Dulcigno 228
Dumaguete 246
Dumaly Point 245
Dumf ord Point 232
Duncan Island 251
Dundee, Rock of 210
Dundrum Bay 217
Dungarvan 218
Dungeness 215
New 200
Point 209
Dunkerque 223
Dunnet Head 216
Duperrey Islands 252
Duppel .' 221
Durazzo 228
Durnford, Port 233
D' Urville Island 263
Point 255
Dussejour, Cape 259
Dwarka 237
Eagle Island 217
Earakong Island 252
East Cape, Madagascar 235
New Zealand 263
Siberia 250
Dog Island 241
Island, Crozet Is 236
Magdalen Is 192
Easter Island 258
Eastport 193
Eau Island 252
Eauripik Islands 252
Ebon Atoll 251
Eckemforde 221
Eclipse Harbor 191
Islands 260
Eddvstone 215
'Point 262
Eden Harbor 210
Edenshaw Cajje 199
Edenton 195
Edinburgh 216
Eeragh Island 217
Egedesmunde 264
Eggegrund Islet 219
Egmont Mountain 263
Port 214
Eimeo Island 257
Ekholm Islet 220
Elba Island 226
p]lbing 221
Elena, St., Port 209
Sta., Point 213
Elephant Bav- 232
Eleuthera Island 203
Elias, St. , Mount 199
Elizabeth Bav 232
Cape ..." 193
City 195
Harbor 264
Island, Chile 210
Tuamotu Arch 257, 258
Port 232
INDEX TO APPENDIX IV.
[Page 273
I "age.
Elizabeth Eeef 259
Ellice Islands 254
Emden 222
Emma, Great, Island 203
Emu Bay 262
Enanger 219
Endelave Island 222
Enderbury Island 254
Enderby Island 260
Endermo 249
Enfant Perdu Islan<l 207
Engano, Cape 245
Engano Island 239
Engelholm 219
English Cay 197
Eniwetok Islands 251
Enrag6Cape 193
Ensenada 201
Entry Island 192
Erroniango Island 256
Erronan Island 256
Escarceo Point 245
Escarseo Point 206
Eschholtz Islands 251
Escudo de Veragua 1 98
Escumenac Point 192
Esdu Island 234
Esmeralda Islet 206
River 213
Espada Point, Colombia . . . 206
Hayti 204
Espenberg, Cape 198
Esperanza Inlet 1 99
Espiritu Santo Bay 207
Cape 209
Esquimau 200
Essington, Port 259
Estaca Point 224
Estangues Point 206
Estevan Point 199
Etches, Port 199
Eten Head 212
Eu, Pulo 240
Eureka 200
Euripo Strait 229
Europa Island 235
Eustatius, St 205
Evangelistas Islantl 210
Evaristo, San 201
Expedition Bay 250
Faero Islands 213
Fair Isle Skroo 216
Fairy, Port 260
Faiu, W., Islet 252
Fakaofu Islet 254
Fakarana Island 258
Falkenberg 219
Falkland Islands 214
Falmouth, England 215
Jamaica 204
False Cape Horn 209
Point 238
Falster Island 222
Falsterbo 219
Famagusta 230
Famine, Port 210
Fanad Point 217
Fanning Island 251
Fano Island, Adriatic 228
Denmark 223
I'LACES — continued.
Page.
Farallon Islet 200
Faraulep Island 252
Farewell, Cape, Greenland. 265
New Zealand 263
Farina, Cape 230
Farisan Island 234
Farn Island 216
Faro Island, Sweden 219
of Messina 226
Farquhar Islands 235
Farrall Rock 198
Farralon de Pajaros 252
Fartak, Ras 236
Fastnet Rock 216
Father Point 192
Fatsizio Island 249
Fatu Hiva Island 253
Huku Island, Galapagos 251
Marquesas . . 253
Fatuna Island 257
Fayal Channel 213
Island 213
Fecamp 223
Fehpe, San, Cavs 204
Point' 202
Felix,*St., Island, Chile ... 211
S. Pacific ... 25S
Fenerive Point 235
Fermin Point 201
Fernandina 195
Fernando Noronha 214
Po Island 231
San, River 196
Port 245
Trinidad 206
Ferolle Point 192
Ferro Island 214
Ferrol 225
Fetouhouhou Island 253
Feys Island 252
Fidonisi Island 229
Figari Cape 226
Filzand Island 220
Finisterre, Cape 225
Firase Rocks 248
Fire Island 1 94
Firmin, San 202
Fischausen 221
Fish, Great, Bav 232
Little, Bay 232
Fiskernaes 26^
Fitz Roy River 260
Fiume 227
Five Fathom Bank 195
Flamborough 216
Flamenco 211
Island 213
Flat Island 234
Flattery, Cape 200
Flensberg 221
Flesko, Cape 242
Flinders Island 262
Islands 261
River 262
Flint Island 253
Florence 226
Flores Island, Azores 213
Indian Arch 243
Uruguay 208
Florida Island 254
Flower Cove 192
Page.
Flushing 223
Fly River 255
Foerder Islet 219
Fogo Island 214
Fohr 222
Foreland, North 215
South 215
Formigas Islands 213
Shoal 204
Formosa Island 242
Fornws 223
Forsmark 21.9
Forsyth Point 199
Forth Mountain 217
Fortune Island.. -1 203
Foulwind, Cape 263
Four, Le, Rock 224
Fowey Rocks 195
Fowler Point 260
Francis Island 251
St., Cape, C. Colon V. . . 232
N^wf'dl'd . . 191
Francisco, San 200
Cape 213
Head 212
River 207
Sao 208
Frankland Island : 261
Franklin Harbor 260
Franz Josef Land 264
Eraser River 200
FrayleRock 204
Fravles Point 212
Frederick, Port 262
Frederik Hendrik, Cape. . . 262
Frederikshaab 264
Frederiksthal 265
Frederiksvaern 219
Fredriksten 219
Freels Cape 191
Frehel, Cape 224
Freikallen 218
Fremantle 260
French Cav 203
Frigate Shoal 253
Freycinet, De, Islets 259
Peninsula 262
Frio, Cai)e, Brazil 208
W. Africa 232
Port 208
Froward Cape 210
Fruholm 218
Frying Pan Shoals 195
Fuenterrabia 224
Fuerta Ventura Island 214
Fuerte Island 206
Fuga Island 245
Fugle Huk 265
Fulanga Island 257
Fulehuk 219
Funafuti Island 254
Funk Island 191
Funkenhageh 221
Furen Islet 218
Fushiki 249
Futuna Island 256
GaalongBay 240
Gabo Island 261
Gabriel Mountain 216
Gaeta 226
22489—03-
-18
Page 274]
INDEX TO APPENDIX IV.
Page.
Gafor Island 234
Galapagos Islands 250, 251
Galera Point, Ecuador 213
Trinidad 206
Galgenl>erg 222
Galiola Rock 227
Galita Island .♦ 230
Gallant, Port 210
Galle, Point de 237
Gallegos River 209
Galley Head 218
Gallinas River 231
Gallipoli, Italy 227
Turkey , 229
Galloway, iVliill of 215
Galveston 196
Galway 217
Gambler Island 257
Gange 220
Gannet, Outer, Island 191
Rock 193
Gap Rock 241
Garcia d' Avila 207
Gardiner Island 253
Gardners I., I^ong Island . . 194
S. Pacific 254
Garra^, Little 238
Gaspar, Island and Strait . . 239
Rico Reef 253
Gasparilla Island 196
Gaspe Cape 192
Gata, Cape, Cyprus 230
de, Spain 225
Gaujam 238
Gay Head 194
Gebey Islands 244
Geelong 260
Gefle 219
Genoa 226
Geoi^e, Fort, Cay 203
St., Cape, Florida 196
Newfdl'd . . 192
Nova Scotia. 193
Island, Alaska . .-. 199
Azores 213
Georges Island 202
St., Cay 197
Georgetown 195
Georgia, South, Island 214
Geronimo, San, Island 201
Geyser Reef 235
Gharib, Has 233
Ghir,Cape 231
Gilxlo Island 246
Gibraltar 225
Giglio Island 226
Gijon 224
Gilbert Islands 251
Gillolo Island 244
Ginger Cay 203
Girgenti 227
Gizau 234
Gizo Island 254
Glas Island 216
Glasgow 216
Glashedy Island ^21 7
Glenan Islands 224
Glocester Island 258
Glorioso Islands 235
Gloucester Island, Aus 261
Massachusetts 194
PLACES — continued.
Page.
Glover Reef 197
Gnarp 220
Goa 237
Godhavn 264
Godthaab 264
Goedereede 223
Golam Head 217
Gomenitza 228
Gomera Island 214
Gonaives 204
Gonave Island 204
Good Hope, Cape, Africa.. 232
China 241
>• Island 257
Success Bay 209
Goose Island 261
Gopalpur 238
Goram Islands 244
GordaCay 198
Point 212
Gore, Port 263
Goree Island 231
Road 209
Gorgona Island 213
Goro Island 256
Goroiitalo 242
Goto Island 248
Gottenburg 219
Gottland Island 219
Gough Island 214
Gozier Islet 205
Gozo Island 227
Gracias a Dios Cape 198
Graciosa Island 213
Grado 227
Grand Manan Island 193
Port 234
Riband Island 226
Grande Point 211
Grange Point 204
Granitz 221
Granville 224
Grappler, Port 210
Grave, Point de 224
Gravelines 223
Gready Harbor 191
GreatBirdRock 192
Rock Head 198
Green, Cape 261
Island, Labrador 191
Newfoundland. . . 192
Nova Scotia 193
Greenly Island 192
Greenspond Island 191
Greenwich 215
Island 252
Gregory, Cape 209
Port 260
Grenada 205
Grenville, Cape 262
Grey River 263
Greytown 198
Griefswald 221
Grief swalder Die 221
Grim, Cape 262
Grimsey Nordd ranger 265
Grip 218
GrisNezCape 223
Groate Eylandt 259
Groix, Island de 224
Gross-Horst 221
Page.
Grouin du Cou, Point de 224
Gruizza Rock 227
Gryto 218
Guadalcanar Island , 254
Guadeloupe, L. California. . 201
West Indies 205
Guaineco Islands 210
Guaira, La 206
Guaja Shima 248
Guam Island 252
Guana, Little, Cay 203
Guanape Islands 212
Guanica 205
Guantanamo 204
Guarapiri Islets 207
Gnaratiba Cape 208
Guardafui, Cape 233
Guascama Point 213
Guatulco, Port 202
Guayaquil 213
Guaymas 202
Guerande 224
Guerin Island 247
Guguan Island 252
Guimaras Island 246
Guiuan 246
Guldager 223
Gull Island, Little 194
Gullan, San, Island 212
Gun Cay 203
Gunong Api Island 243
Gutzlaff Island 242
Gwadar Bay 237
Gwatar Bay 237
Habana 204
Habibas Island 230
Hacha, Rio de la 206
Haddington, Port 244
Haedic Island 224
Hafun, Ras 233
Hagenmeister Island 198
Hague, Cape la 223
The 223
Hai-Duong 240
Hai-Fong 240
Haifa 230
Hainan Island 240, 241
Haitien, Cape » 204
Hai-vun-tan Island 247
Hakodate 249
Half Port Bay 210
Half-Moon Cay, Belize 197
Nicaragua 198
Halgan Island 259
Halifax 193
Haliguen, Port 224
Hall Island 252
Islands, Sir James 247
Halmstad 219
Hals 223
Halt Bay 210
Halten Island 218
Hamberg 219
Hamilton Island 214
Mountain 200
Port 248
Hammamet Bay 230
Hammerfest 218
Hampton.. 194
Hamrange 219
INDEX TO APPENDIX IV.
[Page 275
Page.
Hanalei 253
Hanfelah Bay 233
Hangklip, Cape 232
Hannibal Isles 262
Hano Island 219
Ha-Noi 240
Hao Island 258
Haradsskar Islet 219
Haraiki Island 258
Harbor Grace 191
Harburg 222
Hardy, Sir C, Island 262
Harpe, La, Island 258
Harrison Cape 191
Hartlepool 216
Harvey, Port 200
Harwich 216
Hatteras Cape 195
Haujani Islet 237
Haustholni 223
Haute Island 193
Havre 223
Cape le 193
Hawaii 253
Hayter Island 255
Heard Island 236
Hearts Content 191
HeaudeBrehat 224
Heawandu Island 234
Hecate Bay 199
Cove 200
Hecla, Cape 264
Hed, Rasal 236
Hee-tah-doo Island 234
Hegadis Island 243
Heiligen Creutz 221
Hekkingen 218
Hela 221
Helena, St., Island 214
Helgoland 222
Heliers, St 218
Hellevoetsluis 223
Helliso 218
Hellyer Rocks -... 210
Helsinborg 219
Helsingfors 220
Helvick Head 218
Henderson Island 257
Henderville Island 251
Henlopen Cape 195
Henrv Cape 195
Port 210
Heongsan, Port 242
Herald Cays 255
Hereheretue Island 257
Hermes, Cape 232
Hermit Island 255
Hermite Island 209
Herradura de Carrizal 211
Hervey Islets 258
Hesquiat Harbor 199
Hesselu Island 222
Hessenstein 221
Hestskjaer 218
Heve, Cape la 223
Hiaou Island 253
Hikueru Island 258
Hillswickness 216
Hilo 253
Himmittee Island 234
Hiniiwar 237
PLACES — continued.
Page.
Hiogo 248
Hirado No Seto 248
Hirtshals 223
Hi va-Oa Island 253
Hjelm Islet 223
Hjertholm 218
Hjoerringa Mountain 218
Hoa-pin-su Island 244
Hobart Town 262
Hodeidah Road 234
Hog Island, Indian Ocean. . 235
Virginia.. 195
Islands 197
Hogland Island 220
Hogolu Islands 252
Hogsty Reef 203
Hogulu Islands 252
HoheWeg 222
Hohenschonberg 221
Hokianga River 263
Hokitika 263
Holborne Islet 261
Hole-in-the-Wall 232
Hollo Island 219
Holmestrand 219
Holmogadd 220
Holsteinberg 264
Holvhead 215
HoiiDau Island 240
Hondeklip Bav 232
Honfleur .....' 223
Hongkong 241
Hon-M6 240
Honolulu 253
Hood Island 251
Lord, Island 257
Point, Australia 260
Port, Cape Breton Id . . 193
Hope Island 261
Hopedale Harbor 191
Hopes Advance, Cape 191
Hoppers Island 251
Horn, Cape 209
Head 217
Island 196
Home Island 257
Hornelen Mountain 218
Horsens 222
Horten 219
Hospital Bight 197
Hougue, Cape La 223
Houtman Rocks 260
Howaivuh 236
Howe, Cape, East 261
West 260
Lord, Island 257, 259
Islands 254
Sound 200
Howland Islands 251
Howth Peninsula 217
Huafo Island 210
Huaheine Island 257
Huanchaco Point 212
Huarmey 212
Huasco 211
Hudiksvalls 220
Huelva 225
Hiigeberg 221
Hui-lang-san 241
Hull Island..... 258
Hulls Island 254
Page.
Hulu-shanBay.. 247
Humber River 216
Humboldt 200
Humphrey Island 254
Hungwha Channel 241
Hunter Island, N. Hebrides. 256
Tasmania 262
Hurds Island 251
Hurst Castle 215
Husum 222
Hvidingso 218
Iba 245
Ibayat Island 246
Ibbetson Island 251
Ibiza, Port 226
Icacos Point, Belize 197
Trinidad 206
Ichabo Island 232
Icy Cape 198
leraka 229
Ifalik Islands 252
Iglooik Island 264
Ignacio, San, Point 201
Iguape 208
IkiSima 248
Ildefonso Islands 209
Ilha Grande 208
Ilheos 207
Ho 212
Iloilo 246
Inaboye Saki 249
Inaccessible Island 214
Inagua Islands 203
Inch Keith Rocks 216
Indefatigable Island 251
Indian, Cape 250
Harbor : 191
Head 261
Tickle 191
Indianola 196
Indio Point 208
Indispensable Reefs 254
Indrapura Point 239
Ingolfshofde 265
Ingolsfjeld 265
Inishboffin 217
Inishowen Head 217
Inishrahull 217
Inishturk Island 217
Iniue Island 257
Innamban Bay 232
Inscription, Cape 260
Investigator Strait 260
Ipswich 194
Iquique 212
Ireland Island 214
Isaac, Great, Cay 203
Isabel Cape 210
Island 254
Point 196
Isene 229
Isidro, San, Cape 210
Isla Grande 202
Island Harbor 199
Islav 212
Isle'of Man 215
Isola 227
Isolette, Cape 236
Istria, Caped' 227
Page 276]
INDEX TO APPENDIX IV
Page.
Itacolomi Islet 208
Point 207
Itapacaroya Point 208
Itaparica 207
Itapemirim 207
Itnrup Island 249
Ivigtuk f 2()4
IwoShima 248
Iwo-sima 244
Jabwat Island 251
Jackson, Port 261
Jacksonville 1 95
Jacinel 204
Jacobshavn 264
Jaffa, Cape 260
Jago, St., Island 214
Jaguaribe River 207
Jaluit Island 251
Jamaica 204
James Island 251
St., Cape, C. China... 240
Vancouver 1 . 199
Jan May en Island 265
Jara Head 211
Jarea... 225
Jarvis Island 254
Jashak Bay 237
Java 243
Head 239
Jean, St. , de Luz 224
Jebel Zukur Island 234
Jelaka, Pulo 239
Jelalil 234
Jensen Nunatak 264
Jeremie 204
Jershoft 221
Jervis Bav 261
Cape 260
Island 251
J esus Maria Island 255
Jibara 203
Jiddah 234
Jighinsk Island 264
Joao, San, da Barra 207
Johanna Island 235
John, St., Cape, Newfdl'd. 191
Staten Island 209
Island ^205
Johns, St., Island, Red Sea. 233
N. Brunswick . . . 193
Newfoundland. . . 191
River 195
Johnston Islands 253
Jolo Islands 247
Jomf ruland 219
Jona, St. , Island 250
Jos6, San, California 200
de Guatemala 202
del Cabo 201
Port 209
Joseph Henry, Cape 264
Juan Fernandez Island 258
San 205
Cape 205
delSur 202
Point 197
Port, Peru 212
Vancouver 1 . 200
St., Bay...- 206
Juanico, San, Point 201
PLACES — continued .
Page.
Jubv, Cape 231
Judith Point 194
Juggernath 238
Juist 222
Julian, San, Port 209
St., Island 240
Julianshaab 265
Juneau 199
Jupiter Inlet 195
Jura Island 229
Juul, Cape 265
Kabenda Bay 232
Kabuli Island 245
Kado Sima 249
Kagoshima 248
Kahoolawe Island 253
Kaipara Harbor 263
Kais Islet 236
Kajartalik Island 264
Kakirouma 244
Kal Farun Islet 233
Kalama 200
Kalantan 240
Kalboden Island 220
Kalibia 230
Kalingapatam 238
Kallundborg 222
Kalpeni Islet 234
Kama Islands 252
Kamaishi 249
Kamardn Bay 234
Kambangan Island 243
Kambara Island 257
Kamchatka, Cape 250
Kanala, Port 259
Kanathea Island 256
Kandavu 256
Kandeliusa Island 229
Kangamint 264
Kangarssuk Havn 264
Kaniongan Point 242
Kannanur 237
Kao Island 258
Kappeln 221
Kara Burnu, Cape 229
Karachi 237
Karajinski Island 250
Karimon Djawa Island 243
Karlshamn 219
Karlskrona 219
Ka^ke 220
Kasm 237
KatakoloBay 228
Kater Island 253
Katiagam 239
Katie Rock 228
Kauai Island 253
Kawhia Harbor 263
Keats, Port 259
Kee-lah Island 234
Keeling Islands 236
Keenapoussan Island 247
Keitum 222
Kelung 242
Kendall, Cape 264
Kent Island 261
Keppel Island 257
Kermadec Islands 258
Kertch 229
Ketoy Island 249
Page.
Key West 196
Khurig Islet 236
Kharim-Kotan Island 249
Khaur Fakan Bav 236
Kheli '. 229
Khor Nohud 234
Xowarat 233
Ki Islands 244
Kiama Harbor 261
Kidnappers Cape 263
Kiefali, Cape 228
Kiel 221
Kikai-jima 244
Killiney Hill 217
Killybegs 217
Kilwa Kisiwani 233
Kimbeedso Island 234
King George Sound 260
Island, Alaska 198
Australia 260
Kings Island 258
Kingston 204
Kingstown 217
Kink wosan Island 249
Kinnsund 218
Kino Point 202
Kinsale 218
Kirkwall 216
Kisimayu Bay 233
Kiska Island '. 199
Kistna 238
Kiswere 233
Kittan Islet 234
Kjorge 222
Knocklane 217
Knockmealdown Mountain. 218
Knocknarea 217
Knox Bay 2OO
Cape 199
Knysna 232
Kobe 248
Kodiak Island 199
Koh Chang 240
Kong 240
Krah Islet 240
Tang Rocks 240
Kokoun-tan Islands . . . 248
Koksher : 220
Kolding 222
Komba Island 243
Kompas Mountain 218
Kongelab Islands 251
Konigsberg 221
Koniushi Island 199
Koppem 21 8
Koprino Harbor 200
Koroni Anchorage 228
Korror Islands 252
Kos 229
Kosair, Arabia 236
Red Sea 233
Kosime No Osima . . : 248
Koster 219
Kottaringin Bay 242
Kovra Rythi Point 235
Kozu Shima Mountain 249
Krakatoa Island 239
Krishna Shoal 238
Kroe 239
Kronberg 222
Kronstadt 220
INDEX TO APPENDIX IV.
[Page 277
Page.
Krusenstern Cape 198
Kub Kalat 237
Kuchino Shima 248
Kuchinotsu 248
Kuino 220
Kullen Point 219
Kumi Island 244
Kunipta 237
Kunashir Island 249
Kundapur 237
Kuntidah 234
Kuper Harbor 248
Port 199
Kiiria Maria Islands 236
KuroSima 248
Kusakaki Jima 248
Kusrovie Rock 240
Kusterjeh 229
Kutpur 237
Kuweit 236
Kweshan Islands 241
Kyangle Islets 252
Kyauchau Bay . . 247
Kyuquot Sound 1^'9
Labuan Island 242
Labyrinth Head 209
Laccadive Islands 234
Lacepede Island 260
Lady Elliot Island 261
Frances, Port 235
Lagartos 197
Laghi, Cape 228
Lagoon Head 201
Lagos 225
River 231
Lagosta Island 228
Lagostini Island 228
Lakemba Island 256
Laniaka 230
Lambayeque 212
Lambert, Cape 260
Lamo Bay 233
Lamock Island 241
Lampedusa Island 227
Lam pong Bay 239
Lamyit Island 241
Landfall Island 209
Lands End 215
Landskrona 219
Landsort 219
Langanaes Point 265
Langeland Island 222
Langeoog 222
Langesund 219
Langford, Port 199
Langkuas Island 239
Langotangen 219
Langwarden 222
Lanzarote Island 214
Laruehuapi Cove 211
Lassa, Cape 242
Lassau 221
Latakivah 230
Latouche Treville, Cape ... 260
Laun 191
Laurie Island 215
Laut, Pulo 242
Lavaca 196
Lavata 211
PLACES — continued.
Page.
Lawrence, St. , Island , Alaska 198
Siberia 250
Laykan, Port 242
Laysan Island 253
Lazaref , Port 250
Lazaro, San, Cape 201
Leander Shoal 192
Leba 221
Lebu River 211
Leeuwin, Cape 260
Legendre Island 260
Leghorn 226
Lema Island 241
Lemnos Island 229
Lengua de Vaca Point 211
Lennox Cove 209
Leones Island 209
Leopold, Port 264
Lepar, Pulo 239
I^epreau Cape 193
Lernia 197
Lerwick 216
Leschenault, Cape 260
Lesina Island 228
L' Etang Harbor 193
Leven Island 235
Port 235
River 262
L' Eveque, Cape 260
Lewis, St., Cape 191
Leyden 223
Levte Island 246
Lhou Reef 255
Liakhov Islands 264
Liancourt Rocks 250
Liant, Cape 240
Liao-ti-shan 247
Libau 220
Libertad, C. America 202
Mexico 202
Lifu Island 259
Lighthouse Rocks 199
Limerick 216
Limon, Port 198
Lincoln Island 241
-^— Port 260
Lindesnes 218
Lindi River 233
Lindo, Port 229
Linga Island 238
Linguelta, Cape 228
Linosa Island 227
Lipari Island 226
Lisbon 225
Lisburne Cape 198
Lisian.sk y Island 253
Lissa Island 228
List 221
Lister 218
Lith 234
Litkieh Island 251
Little Hope Island 193
Lituya Bay 199
Liverpool 215
Port 235
River. : 259
Livorno 226
Lizard Point 215
Llico 211
Loa River 212
Page.
Loango Bay 232
Lobito Point 232
Loboa Cay, Bahamas 203
Mexico 196
de Afuera Island 212
Tierra 212
Island, Canaries 214
T Jruguaj^ 208
Point, N. Chile 212
S. Chile 212
Lodingen 218
Lofoten Island 218
Loggerhead Key 196
Loheiyah 234
Loma Point 201
Lonias Point 212
Lombata Island 243
Lombok Island 243
London, East 232
Londonderry 21 7
Cape 259
Long Island, Bahamas 203
United States 194
Loo Choo Islands 244
Looke, Port 235
Lookout Cape, N. Carolina. 195
1 Point, Australia 261
Maryland 195
Lopatka, Cape 250
Lopez, Cape 231
Lorenzo, San, Cape 213
Island 212
Loreto 201
Lorient 224
Loro, Mount 245
Lorstakken Mountain 218
Los, Isles de 231
Lota 211
Lots Wife Rock 249
Lough Larne 217
Louis, Port, Falkland Is . . . 214
Guadeloupe 205
Mauritius Island. 234
St 231
Louisburg 193
Louisiade Archipelago 255
Loune 223
Low Island 240
Port 210
Lowenorn, Cape 265
Lowestoft 216
Loyalty Islands 259
Lubang Island 245
Lucar, San 225
Lucas, San 201
Lucia, Santa 235
St 204
Cape 232
Id., C. Verde Is. . 214
Windward Is 205
Lucipara Is\Jind 239
Lucipari Islantk 243
Lucrecia Point 203
Lucrietta Island 227
Liiis, San, Island 202
Luke Point 250
Lundy Island 215
Lunenburg 193
Lungo 220
Lupona Point 201
Page 278]
INDEX TO APPENDIX IV
Page.
LiirioBay 233
Lussin Piccolo 227
Luzon Island 245, 246
Lyo Island 222
Maasin a. 246
Macah6 207
IVlflORo 241
MacAskiil" Islands! ........ 252
Macassar 242
Macauley Island 258
Maceio 207
Machias 193
Island 193
Machikora 235
Mackenzie Islands 252
MacLeay Islets 260
Macquarie Harbor 262
Island 259
Port 261
Macquereau Point 192
Madagascar 235
Reef, Africa 232
Yucatan 197
Madame Island 193
Madanas Point 208
Madeira Island 213
Madras 238
Madryn, Port 209
Madura Island 243
Maestro de Campo Island. . 246
Mafamale Island 233
Mafia Island 233
Magadoxa 233
Magdalen Cape 192
Islands 192
Magdalena Bay 201
River 206
Magnetic Pole 264
Magoari Cape 207
Mah Kundu Island 234
Mahanuru 235
Mah6 237
Mahia Peninsula 263
Mahon, Port 226
Maiana Island 251
Maiden Rocks 217
Mairaira Point 245
Mill t Island 233
Maitea Island 257
Maitencillo Cove 211
Majamba Bay 235
Majorca 226
Majunga 235
Majuro Islands 261
Makalleh Bay 236
Makarska 228
Makatea Island 258
Makaua Island 233
Makemo Island 258
Makers Ledge, South 192
Makkian Island 244
Makongai Island 256
Makry 229
Mala Point 203
Malabrigo Bay 212
Malacca 238
Malaga 225
Malaita Island 254
Malamocco 227
Malaspina, Port 209
PLACBS — continued .
Page.
Maiden Island 254
Maldonado, Mexico 202
Uruguay 208
Male Island " 234
MalembaBay 232
Malin Head ". 217
Mallicollo Island 256
Malmi) 219
Malo, St 224
Maloclab Islands 251
Maloren 220
Malpelo Island, Galapagos. 250
Panama 203
Malta 227
Marauka Island 256
Manaar 237
Mana Sima 249
Manado Bay 242
Manao 249
Mana-watu River 263
Manda Roads 233
Mandarins Cap 241
Mandavi 237
Manfredonia 227
Mangalore , 237
Mangara Island 258
Mangaratiba 208
Mangareva Island 257
Mangarin Point 245
Mangarol 237
Mangles Point 213
Mango Island 256
Manila 245
Mano Island, Asia 244
Denmark 223
Manoel, Cape 231
Manta Bay 213
Manua Island 257
Manukau Harbor 263
Manvers, Port 191
Manzanilla Bav 202
Point ' 204
Maracaibo 206
Maraki Island 251
Marambaya Island 208
Maranhao Island 207
Marble Island 264
Marblehead 194
Marcial, San, Point 201
Marcos, San, Island 201
Marcus Island 253
Mare Harbor 214
Island, California. .... 200
S. Pacific 259
Maret Islets 259
Margaret Bay 193
Margate Head 232
Maria Island 257
INIadre Island 202
Port 204
Sta., Cape, Portugal. . . 225
Uruguay . . . 208
Cove 201
di Leuca, Cape 227
Island, Azores 213
Chile 211
S. Pacific . . . 256
Port 247
Mariana Islands 252
Maricas Islands 208
Marie Galante 205
Page.
Marienleuchte 221
Mariguana Island 203
Marinduque Island 246
Marion Island 236
Maripipi Island 246
Maritimo Island 227
Marjes Islets 206
Marjoribanks 247
Marks, St 196
Marlborough Island 251
Marmora Island 230
Marmorice 229
Maro Reef 253
, Maroni River 207
Marsala 227
Marseille 226
Marshall 231
Islands 251
Marstenen Islet 218
Marta, Sta 206
Martha, St. , Cape 208
Martin de la Arena, San 224
Garcia Island 208
San, Island, L. Calif . . 201
St. , I. , Leeward Is 205
Vaz Rocks 214
Martinique 205
Martires, Los 252
Marua Island 257
Marutea Island 257
Mary Island 254
St., Bay 232
Cape, Madagascar . 235
Newfound-
land 191
Nova Scotia. 193
Reefs 192
Marys, St. , Island 235
MarzoCape 213
Mas-af uera Island 258
Maabate Island 246
Masinloc 245
Masirah Island 236
Maskat 236
Massaua Harbor 233
Masset Harbor 199
Masulipatam 238
Matabella Islands 244
Matacong Island 231
Matagorda 196
Matahiva Island 258
Matamoras Cove 211
Matana Island 249
Matanzas Peak 204
Matatane 235
Matelotas Islands 252
Matema Islands 265
Maternillos Point 204
Matinicus Rock 1 93
Matoya 249
Matthew Island 256
St., Island, Alaska 198
Burma 238
— Siberia 250
Matthias, St. , Island 256
Matu Sima 250
Matuku Island 256
Mauger Cay 197
Maui Island 253
Mauki Island 258
Maunganui Harbor 262
INDEX TO APPENDIX IV
[Page 279
Maupili Island 257
Mauritius 234
May, Cape , 195
Island 216
Mayaguez 205
Maye Mountain 207
Mayne Harbor 210
Mountain 210
Mayo Island 214
Mayotta Island 235
Maysi Cape 203
Mayumba Bay 231
Mazarron 225
Mazatlan 202
Mazeraba River 232
Mbega Island 256
Mchinga Bay 233
McKean Island 254
Mecate Mountain 196
Mecatina Islands 192
Mednoi Island 250
Mega Island 239
Megalo Kastron 228
Mehediah 230
Meiaco Sima 248
Meiaco-sima Islands 244
Mejia Island 202
Mel, Ilhado 208
Melbourne 260
Meleda Island 228
Melinda 233
Melle, Cape 226
Mellish Reef 255
Melmore Head 217
Melo, Port 209
Melville, Cape, Baliibac I.. 245
Queensland 262
Island, Australia 259
Barrows Strait. . . 264
Tuamotu Arch 258
Memel 221
Memory Rock 203
Menali Island 238
Menchikof C'ape 199
Mendocino Cape 200
Mendoza Island 241
Merbat 236
Mercy Harbor 210
Mergui 238
Mesa de Dona Maria 212
Messina 227
Mesurado, Cape 231
Meurka 233
Mew Islands 217
Mewstone Rock 262
Mexican Boundary 201
Mexico, City of .'. 196
Mexillon Bay 212
Mexillones Mountain 212
Mezen 264
Mugan Mwania 233
Miautao Island 247
Michael, St. , Fort 198
Island 213
Michaeloff Island 257
Middleton Island 199
Midway Islands 253
Miguel, San, Island 201
Islands 247
Mikake Jima 249
Mikindini 233
PLACES — continued .
Page.
Mikomoto Island 249
Mikura Jima 249
Milagro Cove 211
Milazzo 226
Mile Island 264
Milford Sound 263
Milo Island 229
Min River 241
MinaBay, El 231
Minchinmadiva Mountain . 210
Mindanao Island 246, 247
Mindo»o Island 245
Mine Head 218
Minerva Reefs 258
Minikoi Island 234
MinoSima 249
Minorca 226
Minots Ledge 194
Minow 235
Minsener Sand 222
Mintok 239
MiramichiBay 192
Misamis 247
Miscou Island 192
Mississippi River, mouth . . 196
City 196
Misteriosa Bank 197
Mita Point 202
Mitchells Island 254
Mitho 240
Mitiero Island 258
Mitre Island 256
Mityleni Island 229
MizenHill 216
Moa Cayo, Port 203
Island 244
Moala Island 256
Mobile 196
Mocha Island 211
Mocomoco Point 206
Modeste Island 248
Moeara Kompehi 239
Moen Island 222
Moerenhout Island 257
Mogador 231
Mohilla Island 235
Mojanga 235
Mokamba, Port 233
Mokatein 236
Mokha 234
Mokil Islands 252
Molle, Port 261
Mollendo, Port 21 2
MollerPort 199
Molloy 236
Molokai Island 253
Molonta Peninsula 228
Molucca Islands 244
Moluk Island 234
Molyneux Bay 263
Sound 210
Mombasa 233
Mona Island 205
Monastir 230
Mondego, Cape 225
Monfalcone 227
Monhegan Island 193
Monomoy Point 194
Monrovia 231
Montagu Island 261
Montalivet Islands 259
Page.
Montauk Point 194
Monte Christo Islet 226
Montebel lo Island 260
Montego Bay 204
Montepio 196
Monterey 201
Monteverde Islands 252
Montevideo 208
Montravel Island 248
Montreal 192
Monts, Point de 192
Montserrat 205
Monze, Cape 237
Mopelia Island 257
Morane Island 257
MorantCays 204
Point 204
Moray va 225
Morecambe Bay 215
Moreno Mountain 212
Moresby, Port 255
Moreton, Cape 261
Morgan, Cape 232
Morjovetz Island 264
Morlaix 224
Morotiri Islands 258
Morro Avuca 202
de Sao Paulo 207
Petatlan 202
Solar 212
Mortlock Islands 252
Mosquito Cays 198
Motane Island 253
Mothe Island 256
Mothoni 228
Motu-ili Island 253
Motu-iti Island . . . ; 257
Moudros 229
Moukon rushi Island 249
Moulmein 238
River 238
Mount, Cape 231
Mourondava 235
Moville 217
Mozambi<iue . 233
Msimbati 233
Mugeres Island 197
Muilcalpue Cove 211
Mukulaelae Island 254
Muleje 201
Mulu Island 244
Mura Harbor 248
MuratHill 233
Murderers Bay 235
Murdock Point 262
Murundum Island 240
Mururoa Island 257
Muscat 236
Musendum, Ras 236
Mussel Bav 210
Mysole Island 244
Nachvack Bay 191
Nafa-Kiang 244
Nagai Island 199
Nagasaki 248
Naian Island 256
Nain 191
Nairn Cay 203
Naitamba Island 256
Naka no Shima 248
Page 280]
INDEX TO APPENDIX IV.
Page.
Nakkehooed 222
Nam-Dinh 240
Namki, Port 241
Namoluk Islands 252
Nainonuito Islands 252
Nam-quan A 241
Naniu Island 251
Nanaimo 200
Nancowry Harbor 239
Nanka Island 239
Nanomea Island 254
Nanoose Harbor 200
Nantes 224
Nantucket Island 194
S.Shoal 194
Naples 226
Napuka Island 258
Nar Foree Island 234
Naranjo, Port 203
Narendri Bay 235
Nargen Island 220
Narva ,---.220
Nasca Point 212
Nasparti Inlet 199
Nassau 203
Natal, Brazil 207
Port, Africa 232
Sumatra 239
Natashquan Point 192
Natuna Islands 240
Naturaliste, Cape 260
Nauoinaga Island 254
Navachista 202
Navalo, Port 224
Navarin 228
Cape 250
Navassa Island 204
Navesink Highlands 195
Navidad Bank 203
Bav 202
Navire Bay 236
Naxos Island 229
Nazaire, St., Port 224
Necker Island 253
Needles Rocks 215
Negapatam 237
Negrais, Cape 238
Negro, Rio 209
Negros Island . 246
Neill, Port 264
Nelson 263
Cape 260
Port 259
Nemuro 249
Neptune Isles 260
Nera Point 227
Netherland Island 254
Neunortalik 265
Neuwerk 222
Nevil Island 252
Neville, Port 200
Nevis 205
New Bank 197
Bedford 194
Britain 254
Caledonia 259
(iuinea 255
Hanover 255
Haven 194
Hebrides 256
Ireland 255
PLACES — continued.
Page.
New London 194
Orleans 196
Plymouth 263
South Orknevs 215
Shetland 215
Westminster 200
York 194
Newbem 195
Newburyport 194
Newcastle 261
Newfoundland 191,192
Newport, Ireland ».. 217
Rhode Island 194
Newton Head, Great 218
Ngatik Islands 252
Ngau Island 256
Nias Island 239
Nice 226
Nicholas, St. , Island 214
Nicholson, Port 263
Nickerie River 207
Nicobar, Great, Island 239
Islands 238, 239
Nicolas Mole 204
San, Island 201
Nidingen Islet 219
Nieuport 223
NieweDiep 223
Nihiru Island 258
Niigata 249
Nikalao, St., Island 229
Nikolaevsk 250
Nikolaia, St., Cape 250
Nikolo, St., Port 229
Nila Island 244
Nile River 230
Nimrod Sound 241
Nine-pin Rock 241
Ning-po 241
Nipe, Port 203
Nitendi Island 255
Niua-fu 257
Niuchwang 247
Niutao Island 254
NoSmaSaki 249
Noir Island 209
Noir Moutier Island 224
Nolloth, Port 232
Nome Cape 198
Nonuti Island 251
Nootka Sound 199
Nord Koster Islands 219
Norderney 222
Norfolk 195
Island 259
Norman Cape 192
Norrkopings Inlopp 219
Norrsher Islet 220
Norrtelge 219
North Cape, Arctic Amer. . 264
Brazil 207
C. Breton 1 192
Iceland 265
New Zealand 262
Norwav.. 218
Harbor . . . .' 199
Island, Vancouver 199
Volcano Islands. . 253
Lord, Island 252
Standing Creek 197
Northumberland Cape 260
Page.
Northumberland Isles 261
Northwest Cape 260
Norwalk Island 194
Noshiaf Misaki 249
Saki 249
Nosi Be 235
Nostra Senhora do Deserto. 208
Notch Cape 210
Notsuke 249
Nottingham Island 191
Noumea 259
Noun, Cape 231
Nouvelle, Port 226
Nova Zembla 264
Novogorodj Port 250
Nuevitas, Port 203
Nuevo, Port 202
Nugget Point 263
Nui Island 254
Nuistad 220
Nuka-Hivi 253
Nukufetau Island 254
Nukunau Island 251
Nuku-nono 254
Nukuor Islands 252
Nukutavake Island 257
Nukutipipi Island 257
Numba Island 233
Nunez River 231
Nunivak Island 198
Nurse Channel Cay 203
Nuyts Point 260
Ny Sukkertop 264
Nyborg 222
Nyk jobing 222
Oahu 253
Oatafu Island 254
Oban 216
Obi Islands 240
Obispo Shoal 197
Obristadbroekke 218
Observation Island 248
Oby Major Island 244
Occasional Harbor 191
Ocean Island, N. Pacific . . . 253
S. Pacific 254
Ockseu Island 241
Ocracoke 195
Oddensby 222
Odenskholm 220
Odessa 229
Odia Islands 251
Oeno Island 257
Offer Wadham 191
Oho-sima 244
Okayama, Port 248
Okhotsk 250
Oki Islands 249
Okishi Bay 249
Okso 219
Oland Island 219
Old Fort Island 192
Point Comfort 195
Providence 198
Oleai Islands 252
Oleron Island 224
Olga, Port 250
Olimarao Islet 252
Olinda 207
OlipaRock.- 228
INDEX TO APPENDIX IV.
[Page 281
Page.
Oliutorski, Cape 250
Olivenga 207
Omapui Island 247
Omena': Island 264
Omo Island 222
Omoa 197
Oinoi Saki 249
One Fathom Bank 238
Oneata Island 256
Onef^a 264
Ongea Levu Island 257
Ono Islands 257
Onoatoa Islands 251
Oo-Sima Harbor 248
Oparo Island 258
Opobo River 231
Oporto 225
Oraluk Island 252
Oran 230
Orange Cape, Brazil 207
Magellan Strait.. 209
Oranienbauni 220
Orchila Island 206
Oregrund 219
Orfordness 216
Orizaba JNIoiintain 196
Orkney Islands 216
Ormarah 237
Ormoc 246
Ornbay Island 243
Oro No Sima 248
Oropesa Cape 225
Orskar Rock 219
Oruba Island 206
Osaka 248
Osaki Bay 248
Oscarsberg 219
OscuroHead 211
Osnabrug 257
Ostend 223
Osthammar 219
Ostro Point 228
Otago Harbor 263
Otranto, Cape and Port 227
Otwav, Cape 260
Port 210
Oune-Kotan Island 249
Ouro River 231
O valau Island 256
Owashi Bay 248
Oxford 215
Oxhoft 221
Paanopa Island 254
Pabellon de Pica 212
Pacasmayo 212
Padang 239
Tikar 242
Padaran, Cape 240
Padre, Port 203
Pagan Island 252
Pagonia, Port 228
Painiboeuf 224
Paita 212
Paix, Port 204
Pajaros Islets 21 1
Pak Chan River 238
Pak-Hoi 240
Pakonjidol Rock 228
Palamos Bay 225
Palanc )<; 24()
PLACES — continued.
Page.
Palawan Island 245
Palenibang 239
Palenita 202
Palermo 226
Port 228
Pali, Cape.... 228
Pallas Rocks 248
Palliser, Cape 263
Palm Islands 261
Palma Island 214
Palmas Bav 208
Capo ■- 231
Point 197
Palmerston, Cape 261
Islands 257
Palmyra Island 251
Palompon 246
Palos Bay 242
Pamaroong Island 242
Pampatar Island 206
Pan de Azucar Island 211
Panama 203
Panay Island •. 246
Pangituran 247
Panjang Island 240
Pank Piah Rock 241
Pantar Island 243
Papey Island 265
Paposo Road 211
Para 207
Paraca Bay 212
Paracel Islands 241
Parahiba River and Port.. 207
Paramaribo 207
Paranagua 208
Paranahiba River 207
Paraca Island 258
Parati 208
Paredon Grande Cay 204
Parenga-renga 262
Parenzo 227
Parga 228
Parida 202
Parinas Point 212
Paris 223
Parker Cape 210
Paros Island 229
Parry Island 258
Parrys Group 253
Pasado Cape 213
Pa-sages, Port 224
Pascagoula, East 196
Pasni 237
Passaro, Cape 227
Pasuruan 243
Patache Point 212
Patani, Cape, 240
Paternoster Rocks 219
Paterson Inlet 263
Pato Island 206
Patook River 197
Patos Island 202
Patras .• 228
Patrick, St. , Head 262
Patterson, Port 259
Paul, St. , de Loando 232
Island, N. Amer. 192
'- Tuamotu ... 257
Reunion Island . . 235
Rocks 214
Pauls, St. , Island 236
Pago.
Paumben Pass 237
Paxo Island 228
Paypoton Mountain 197
Pa?., La 201
Pearce Point 259
Pearl and Hermes Reef 253
Cays 198
Pedra Blanca Rock 241
Branca 238
de Galha 231
Pedro Bank 204
San 202
Point 211
Port 210
Peel : 260
Island 253
Pegasus, Port 263
Pei-ho 247
Pekalongan 243
Pelado Island 212
Pelagosa Rock 228
Peloro, Cape 227
Pemba Bay 233
Pembroke Cape 214
Pena Point 206
Penang, Pulo 238
Penas Anchorage 202
Pendulum Islands 265
Penguin Islands 236
Penha Grande 231
Peniche 225
Penmarch Rocks 224
Penrhyn Island 254
Pensacola 196
Pentland Skerries 216
Percy Isles 261
Perim Island, Africa 233
India 237
Pernambuco 207
Pernau 220
Peros Banhos Islands 234
Perth 260
Peru Island 251
Perula Bay 202
Pescadores Islands, Asia, E.
coast 242
N. Pacific 251
Peru 212
Point 212
Pe-shan Islands 241
Petali Island 229
Petalidi Bay •. 228
Peter, St., Port 224
Peterhof 220
Petersburg, St 220
Petersdorf 221
Petit Manan Island 193
Petite Ri viCre 204
Terre 205
Petropavlovsk 250
Petropolis 208
Pha-li-du Island 234
Philadelphia 195
Philip Island 252
Philipp Broke, Cape 265
Philips Point 202
Phillip, Port 260
PhiUips Island 258
Phoenix Island 254
Pi 226
Pianosa Island 226
Page 282]
INDEX TO APPENDIX IV.
Page.
Piohidanque 211
Pichilinque Bay 201
Pico Island 213
Pictou Harbor 193
Piedra Blanca 247
Piedras Blancas ^ 201
Cay, Cuba, N. coast. . . 204
S. coast 204
Point. 208
Pieman River 262
Pierre, St., Newf'dl'd 191
Reunion 1 235
Rock 240
Pietro di Nembo, St. , Island . 227
Pigeon Point 200
Pih-ki-shan Island 241
Pih-quan I^eak 241
Pih-seang Island 241
Pikelet Island 252
Pilier, Le, Island 224
Pililu Island 252
Pillau 221
Pillar, Cape, Chile 209
Tasmania 262
Pinaki Island 257
Pine, Cape 191
Pines, Isle of 204
Pingelasp Islands 252
Ping-fong Island 241
Ping-hai Harbor 250
Pinnacle Islet 198
Pinos Point 201
Pique Bay 250
Piraeus - 229
Pirano 227
Pisagua 212
Pisang 2.39
Pisco 212
Pitcairn Island 257
Pitea 220
Pitong Island 238
Placentia Harbor 191
Point 197
Pladda Island 216
Plana Cay ..., 203
PlanierRock... 226
Plata, Isle 213
La 208
Port 204
Platte Island 2,34
Playa Colorado 202
Maria, La 201
Parda Cove 210
Pleasant Island 254
Plettenburg Bay 232
Plum Island 194
Plymouth, P^ngland 215
U. S 194
PoileBay 192
Pola 227
Sta., Bay 225
Polillo Island 246
Pollard Cove 210
Polloc 246
Polusuk Island 252
Porno Rock 228
Ponafidin Island 249
Ponapi Island 252
Pond Mountain 210
Pondicherri 237
Ponga River 23 1
PLACES — conti nued .
Page.
Ponza Islet 226
Poolbeg 217
Popa Island 244
Popof Island 199
Porcos Grande Islet 208
Porebander 237
Porinan 225
Poro musir Island 249
Poros Island 229
Port au Prince 204
of Spain 206
Royal, Jamaica 204
S. Carolina 195
Said.. 230
Portendik 231
Porthcurnow 215
Portland, Bay 260
Cape 262
England 215
Maine 193
Porto Bello 206
Re 227
Rico... 205
Santo 213
Seguro 207
Yecchio 226
Portsmouth, England 215
U. S 194
Possession, Cape 209
Island 236
Postilion Islands 243
Povorotnyi, Cape 250
Prado 207
Pratas Island 241
Premeira I.^lands 233
Preservation Inlet 263
Prestenizza Point 227
Prevesa 228
Pribilof Island 199
Prince Edward Island 192
Edwards Islands 236
Prince of Wales Cape 198
Island 262
Sound 191
Regent River 259
Princes Island 231
Proeste 222
Progreso 197
Promontore Point 227
Proti Passage 228
Proven 264
Providence 1 94
Island 251
Port 250
Psara Island 229
Pucio Point 246
Puerto Cabello 206
Santo Bay 206
Puka-puka Island 258
Puka-ruha Island 257
Pulicat 238
Pulkowa 220
Pulpito Point 201
Puna 213
Purdy Island 255
Putziger Heisternest 221
Pyramid Point 241
Pyramidal Rocks 240
Quaco, Cape 193
Quad, Cape 210
Page.
Quaebo River 231
Quebec 192
Queen Charlotte Island 257
Queenstown, Ireland 218
N.Zealand 263
Quelpart Island 248
Quemada Grande Island. . . 208
Quentin, San, Port 201
Querimba Islands 233
Queule Bay 211
Quilan, Cape 210
Quilca 212
Quillimane 232
River 232
Quilon 237
Quin Hon 240
Quiniluban Islet 245
Quintero Point 211
Quita Sueno Bank 198
Quoddy Head 193
Quoin Great, Island 236
Point 232
Race, Cape 191
Island 200
Rachado, Cape 238
Radakala Islands 251
Radama Islands 235
Port 235
Ragged Island 203
Ragusa Rocks, Pettini di . . 228
Rakkin, Ras 236
Raleigh Rock, China 241
Formosa 244
Ramas, Cape 237
Rame Head 232
Ramree Island 238
Rangiroa Island 258
Rangoon 238
River 238
Ranu Cove 211
Raoul Island 258
Rapa Island 258
Raper Cape 210
Raphti, Port 229
Rarotonga Island 258
Rasa Island 253
Rathlin Island 217
O'Birne Island 217
Ratnagherry 237
Ravahere Island 258
Ravn Storo 264
Rawean Island 243
Ray Cape 192
Raza Island, Brazil 208
C.Verde Is 214
L.California 202
Razzoli Island 226
Re Island 224
Real River 207
Reao Island 257
Recherche Archipelago 260
Recife Cape 2.32
Red Islet 259
Redang, Great, Harbor 240
Redfield Rocks 249
Redonda Islet 205
Redondo Rock 250
Refuge Cove 199
Reirson Island 254
Reitoru 258
INDEX TO APPENDIX IV.
[Page 283
Rembang 243
Kemedios Bay 202
Kenard Island 255
Islands 255
Reiinel Island 254
Kensher 220
Repon, Pulo 240
Re-olution Island 191
Reunion Island 235
Revel 220
Rev, Isladel 213
Reyes Head 211
Point 200
Reykianaes _ 265
Reykiavik 265
Revthur Fjeld 265
Rhio 238
Rhodes, Port 229
Rhvnns of Islay 216
Ribnitz '.. 221
Rich Point 192
Richmond 195
Harbor 192
River 261
Riga 220
Rigny Mount 265
Riniitara Island 258
Ringkjobin 223
Rio Grande del Norte 196
do Norte 207
Sul 208
Janeiro 208
Riofrio, Port 210
Risiri Islet 249
Rissnaes Point 265
Rivadeo 224
Rivad«sella 224
Rivers, Cape 242
Rixhoft 221
Roa Poua Island 253
Roatan 197
Roberts Point 200
Roca, Cape 225
Partida, Mexico, E.
coast 1 96
AV. coast 202
Rocas Reef 214
Rochefort 224
Rochelle 224
Rockabill 217
Rockall Islet 213
Rockingham Bay 261
Rockland 193
Rodd Bay 261
Rodkallen 220
Rodney, Cape 255
Rodoni, Cape 228
Rodriguez Island 234
Rodsher Island 220
Roeskilde 222
Rogosnizza 227
Roigen, Cape 249
Rokuren Island 248
Roma Island 243
Romain Cape 195
Roman, San, Cape 206
Romanzof Cape 198
Romanzov Islands 251
Romblon Island 246
Rome 226
Ronaldsav, North 216
PLACES — continued.
Page.
Roncador Cay 198
Rongerik Islands 251
Roodewal Bav 232
Roque, St. , Cape 207
Roques Islands 206
Rosa, Sta. , Island 201
Rosalia, Sta. , Bay 201
Ro.salind Bank 198
Rosario Island 253
Rose Island 257
Spit Point 199
Rosemary Island 2H0
Rosier Cape 1 92
Ross Island 248
Ros-sel Island 255
Rostock 221
Rota Island 252
Rotterdam 223
Rotti Island 243
Rottnest Island 260
Rotumah Island 256
Round Island 247
Roundhill Island 191
Rovigno 227
RoxoCape 196
Royal Island 203
Royalist, Port 245
Ruad Island 230
Riigenwalde 221
Rum Cay 203
Runaway, Cape 263
Runo Island 220
Ruixirt Island 210
Rurutu Island 258
Ryvingea Island 218
Saba 205
Sabine Pass 196
Sabioncello Peninsula 228
Sablayan Point 245
Sable Cape 193
Island 193
Sacatula River 202
Sacrificios Island 196
Point 202
Saddle Group 242
Island 191
Sado Island.. 249
Safajah Island 233
Safatu Island 240
Saida 230
Saigon 240
Saintes Islands 205
Saipan Island 252
Sakai 248
Sakhalin Island 250
Sakonnet Point 194
SalCav 204
Island 214
Sala y Gomez 258
Salado Bay 211
Salavar Island 242
Saldanha Bay 232
Salem 194
Sali 230
Salina Cruz 202
Salinas Bay, C. America 202
L. California 201
Point 204
Sali.tfbury Island 191
Salomague Island 245
Page.
Salonika 229
Salovetski 264
Saltee, Great 217
Salut Islands 207
Salvador, San 203
Salvage Islands 214
Salvore Point 227
Sama, Port and Peak 203
Samana 204
Cay 203
Samanco Bay 212
Samar Island 246
Samarang 243
Sambro Islands 193
Samoan Islands 257
Samos Island 229
Sampit Bay 242
Samso Island 222
Samsoe Island 223
Sand Island 196
Key 196
Sandakhan Bay 242
Sandalo, Cape 226
Sandalwood Island 243
Sandfly Cay 197
Sandhammaren 219
Sandwich Island 256
Islands 214
Sandv Cape 261
Hook 195
Point 210
Sanguin River 231
Sanihel Island 196
Sankaty Head 194
Sannakh Island 199
Santander 224
River 196
Santiago Cape 210
de Chile 211
-Cuba 204
Port 245
Santona 224
Santos 208
Sapelo Island 195
Sarage Island 257
Saranguni Islands 246
Saniwak 242
River 242
Sariguan Island 252
Sarstoon River 197
Saru Island 243
Saseno Island 228
Satano Misaki 248
Satawal Island 252
Saugor Island 238
Sauguir Island 242
Sauh, Pulo 238
Saukhoum 229
Saunders, Port 192
Sauo Bay 242
Savaii Island 257
Savanilla 206
Savannah 195
Savanna-la-Mar 204
Savbrook 194
Scalp Mountain 217
Scarcies River 231
Scatary Island 193
Schama Mountain 212
Schank, Cape 261
Schanz Island 251
Page 284J
INDEX TO APPENDIX IV.
Page.
Scharhorn 222
Scheveningen 223
Schillighorn 222
Schleimunde 221
Schleswig 221
Schonberg „ 221
Scilly Islands, Englana 215
■ S. Pacific 257
Scott Cape 200
Scutari 229
Sea Bear Bay 209
Rock 248
Seal Cays 197
Island 193
Seao Island 242
Seattle 200
Sebastian, San, Cape,M'g'sc'r 235
Spain 224
St., Cape, S. Africa... 232
Island 208
Sebaatopol 229
Sebenico 227
Sedano, Cape 243
SedashigarBay 237
Seguin Island 193
Sein, I. de 224
Sejro Island 222
Selatan Point 242
Seldom-come-by Harbor 191
Semeny River 228
Semerara Island 245
Semiamoo Bay 200
Semione Island 240
Sentinel Island 248
Series Island 257
Sermalta Island 244
Sermelik Fjord 264
Sermo Island 229
Serrana Bank 198
Serranilla Bank 198
Seskar Islet 220
Setubal 225
Seuheli Par 234
Seven Heads 218
Seychelle Islands 234
Sfax 230
Shag Rocks 214
Shahah 236
Shahr, Abu 236
Shaikh Shu'aib Islet 236
Shaluitien Island 247
Shanghai ._ 242
Shannon River ." 216
Shantar Islands 250
Shantung 247
Sharjah 236
Shark Island 254
Sharmoh 236
Shavveishan Island 242
Shelburne HarV>or 193
Shelter Bay 250
Shepherd Island 198
Sherbedat, Ras 236
Sherbro Island 231
River 231
Sherm Hassejy 233
Joobbah 233
Rabigh 234
Wej 233
Yahar . 233
Shetland Islands' '. 216
PLACES — continued.
Page.
Shiash-Kotan Island 249
Shields, North 216
Shimizu Ba.v 249
Shimonoseki Strait 248
Shinnecock Buy 194
Ship Island 196
Shoal 196
Shipunski, Cape 250
Shirasu Reef 248
Shoals, Isles of 194
Shoal water Cape 200
Island 239
Siargao Island 246
Siassi 247
Siberaet Island 239
Siboga 239
Sibuco Bay 247
Sibutu Island 247
Sibuyan Island 246
Sidtnouth, Cape 262
Sierra Leone 231
Sighajik 230
Sigri, Port 229
Sihuatanejo Point 202
Sihut 236
Silan 197
Silaqui Islet 245
Silver Bank 203
Simaloe Island 239
Simeonof Island 199
Simoda 249
Simon, St. , Island 195
Simonoff Island 257
Simonor Island 247
Simons Bay 232
Simusir Island 249
Singapore 238
Singkel Island 239
Singkep Island 238
Single Island 241
Singora 240
Sinon 231
Sinope 230
Siphano Island 229
Siquiquor Island 246
Sirik, Cape 242
SiriyaSaki 249
Sisal 197
Sitka 199
Sittee Point 197
Skagataas Point 265
Skagi, Cape 265
SkagsHead 220
Skaw, Cape 223
Skelligs Rocks 216
Skerries Rocks 215
Skerry vo re Rocks 216
Skiathos Island 229
Skidegate Bay 199
Skoorgaarde 221
Skumbi River 228
Skyring Mountain 209
SligoBay 217
Slyne Head 217
Smalls Rocks 215
Smerwick 216
Smith Island, Japan 249
Washington 200
Sni vrna 230
Snaefells Yokul 265
Snares Islands 2()3
Page.
Socorro Island, Chile 210
Mexico 202
Socotra Island 233
SoderSkars 220
Soderarm 219
Soderhamm 219
Sofala 232
Sohar 236
Sola Island 206
Solander Islands 263
Solitary Islands 261
Solombo, Great, Island 243
Solomon Islands 254
Solta Island 228
Sombrero 205
Key 196
Rock 247
Sommer Island 220
Song-yui Point 241
Sonserol Island 252
SooBay 242
Sooke Inlet 200
Sorelle Rocks 228
Sorol Island 252
Sorrel Rock 241
Sorrell, Cape 262
Port 262
Sorsogon, Port 246
Soumshu Island 249
South Cape, Formosa 242
N. Guinea 255
Rock 217
Water Cay 197
Southampton 215
Southsea Castle 215
Southwest Cape 262
Reef 196
Spalato Passage 228
Port 228
Sparo Vestervik 219
Spartel, Cape 230
Spartivento Cape, Italy 227
Sardinia 226
Spencer, Cape 260
Spezzia 226
Spikeroog 222
Spiridione, St. , Port 228
Spitz bergen 264
Spodsbjerg 222
Spurn Head 216
Square Handkerchief Bank . 203
Staabierg Huk 265
Stack, South 215
Stade 222
Stag Rocks 218
Stamp Harbor 199
Stampali Island 229
Stanley, Port 214
Starbuck Island 254
Start Point 215
Startpoint 216
Staten Island 209
Staunton Island 247
Stavanger 218
Steilacoom 200
Steinkirchen 222
Stemshesten 218
Stensher Rock 220
Stephens, Port 261
Stettin 221
Stewart, Cape 259
INDEX TO APPENDIX IV.
[Page 285
Stewart Islands 254
Stirrup Cavs 203
Stirsudden 220
Stockholm 219
Stonington 19-1
Stopelmiinde 221
Stora 230
Storiiowav 216
Stot '. 218
Stralsimd 1:21
Strati If^land : 229
StraumneHS Point 265
Streaker Bav 260
Streckelsberg 221
Stro>ionof Cape 199
Stroinytad 219
Stromtaiigen 219
Strong Island 252
Strovathi Island 228
Stuart Island 198
Suakin 233
Sual 245
Subig 245
Sucoadana 242
Suda,Port 228
Sueik 236
Suez 233
Suff ren, Cape 250
Sugar Loaf Point 261
Sughrah 236
Suk Island 252
Suli)hur Island 253
Sunibawa Island 243
Sum burgh Head 216
Sunda Strait 239
Sunday Island 258
Sunderland 216
Sundsvall 220
Sunraivani 237
Sup6/- 212
Sur 230
Surabava 243
Surat.: 237
River 237
Surigao 246
Surop 220
Susaki 248
Suvvanose Jima 248
Suwarrow Island 257
Svalferort Tzerel 220
Svartklubben 219
Svendborg 222
Svenor 219
Sviatoi Nos 264
Svinoen 218
Swallow Bay 210
Islands 255
Swan Islands 197
Swansea : 215
Swatau 241
Sweers Island 262
Swinemunde 221
SybilloBay 250
Sydenham Island 251
Sydney, Australia 261
Harbor, C. Breton I . . 192
Synesvarde Mountain 218
Syra 229
Syracuse 227
Tabaco 246
Taljasco River 197
PLACES — continued.
Page.
Tablas Island 246
Point 211
Table Bav 232
Head 191
Island 238
Taboga Island 203
Tabou River 231
Tacloban 246
Tacoma 200
TacoradyBay 231
Tae Islands 241
Tagulanda Island 242
Tahiti 257
Tahoa Islanc I 257
Tahuata Island 253
Taiaro Island 258
Tai-pin-san 244
Tajer, Port 227
Taka Yama 249
Takapoto Island '. . 258
Takau 242
Takhkona Point 220
Talabo, Cape 242
Talcahuano 211
Ta-lien-wan Bay 247
Talinay Mountain 211
Taltal, Port 211
Taluat Island 242
Tamana Island 251
Tamandar^ 207
TamarPort 210
Tamatave 235
Tambelan Island 240
Tampa Bay 196
Tampat Toe won Point 239
Tampico 196
Tam-sui Harbor 242
Tanabe Bay 248
Tancook Island 193
Tandjong Pandan 239
Tanga Bay 233
Tangier 230
Tanjong Barram 242
Datu 242
Tanna Island 256
Tantang, Port 235
Taoiunu 256
Taormi na Cape 227
Tapua Island 255
Tapul Island 247
Taputeuea 251
TaraHill 217
Taranto 227
Tarawa Island 251
Tarbertness 216
Tarifa 225
Taritari Island 251
Tarpaulin Cove 194
Tarragona 225
Taa de Foin Islet 247
Tatakoto 257
Tatsupi Saki 249
Tauere Island 258
Tauranga Harbor 263
Tauzon, Cape 235
Tavolara Cape 226
Tavov River 238
Taytao Cape 210
Taytay Fort 245
Tchesme 229
Tchoukotskoi, Cape 250
Tegal 243
Page.
Tehor Island 244
Tellicherri 237
Tel lo Islands 244
Tematangi Island 257
Tenasserim 238
Tenedos Island 230
Teneriffe Island 214
Tenez, Cape 230
Tepoca Cape 202
Tepoto Island 258
Tequepa 202
Terceira Island 213
Teresa, Sta. , Bav 201
Terkolei ' ■ 238
Terminos Lagoon 197
Ternate Island 244
Terstenik Rock 227
Testa, Cape 226
Testigos Islets.. _ 206
Tewaewae Bav 263
Thabi, Abu. .'. 236
Thank God Harbor 264
Thermia Island 229
Thikombia Island 256
Thithia Island 256
Thomas, St.,Id.,B.ofBiafra 231
West Indies. 205
Thome, St. , Cape 207
Three Kings Islands 262
Points Cape, Africa . . . 231
Argentina . . 209
Honduras .. 197
Ti-ao-usu Island 244
Tiburon Island 202
Tiegenort 221
Tien-pak 241
Tientsin 247
Tilly Bay 210
Timbalier Island 196
Timor Island 243
Laut Island 244
Tinakula Island 255
Tinian Island 252
Tintolo Point 246
Tirby Point 198
Toass Island 252
Toau 258
Tobago 205
Tobi Shima 249
Tobol Ali 239
Tocopilla 212
Todos Santos 201
To-du Island 234
Tofua Island 258
Tokara Jima 248
Tokelau Islands 254
Token Bessi Island 243
Tokio 249
Tolaga Bav 263
Tolkemit.' 221
Tomas, San 201
Tomo Roads 248
Tongarewa Island 254
Tongatabu Island 258
Tongka Harbor 238
Tongoi 211
Tong-sang Harbor 241
Tong-ting Islet 241
Tonning 222
Topolobampo 202
Tor 233
Torbjornskjaer 219
Page 286j
INDEX TO APPENDIX IV.
Page.
Tordenskjokl, Cape 265
Torgauten 219
ToriwiSaki 249
Tornea 220
Toro Point 206
Torres Island 256
Point * 208
Port 226
Tortola 205
Tortosa, Cape 225
Tortugas Island 206
Tory Hill 217
Island 217
Tosco Cape 201
Totoya Island 257
Toulinguet Islands 191
Toulon 226
Tourane Bay 240
Towers Island 250
Townsend, Port 200
Trsenen 218
Trafalgar, Cape 225
Tralee Bay 216
Trani 227
Trapani 226
Travemunde 221
Travers Islands 262
Treasury Islands 254
Trebizond 230
Tregosse Islands 254
Trelleborg 219
Tremiti Islands 227
Trepassey Harbor 191
Tres Montes Cape 210
Puntas Cape, Chile ... 210
Venezuela . . 206
Trevandrum 237
Trevose Head 215
Triangle Island 200
Triangles 197
Tribulation, Cape 261
Trichendore 237
Trieste 227
Trincomali 237
Tringano River 240
Trinidad Head 200
Island 214
Tripoli, Africa 230
Turkey 230
Tristan d' Acunha 214
Triton Bay 255
Island 241
TriunfoCape 197
Trobriand Islands 255
Tromelin Island, Carolinels. 252
Indian Ocean 235
Troniso 218
Trondheim 218
Troon 215
Truxillo 197
Tsau-liang-hai 248
Tscheljuskin, Cape 264
Tsmano 235
TsuSima 248
Tsukarase Rocks 248
Tsuruga 249
Tuanske Island 258
Tubal Island 257
Tubuai Islands 258
Tubuai-Manu Island 257
Tucacas Island 206
Tuckers Beach 195
PLACES — continued.
Page.
Tukume Island 258
Tully Mountain 21 7
Tumaco 213
Tuinbez 212
Tung-chuh Island 241
Tung-yung Islands 241
Tuni-ang Island 241
Tunis 230
Tuni) Island 223
Tupilco River 197
Tureia Island 257
Turk Island 203
Turnabout Island 241
Turo Island 222
Turtle Island 257
Isles 260
TuskarRock 217
Tuspan Reefs 196
Tuticorin 237
Tutova 207
Tutuila Island 257
Tuvutha Island 256
Tuxtla Volcano 196
Twelve Islands 236
Twofold Bay 261
Tybee Island 195
Ty-fung-kyoh Island 241
Tynemouth 216
Ua-Huka Island 253
Ualan Island 252
Ubatuba 208
Uea Island 257
Ujelang Island 251
Uji Shima 248
Uleaborg 220
Ulietea Island 257
Ulko Kalla Rock 220
Ulladulla 261
Ulsire 218
Uluthi Islands 252
Umea 220
Una 207
Unalaska Island 199
UnareBav 206
Underut Islet 234
Underwood, Port 263
Unga Island 199
Unie Island 227
Union Bay 209
Islands 254
Port de la 202
Unsang 242
Upernivik 264
Upright Port 210
Upsala 219
Upulo Islands 257
Uragami 248
Urracas Islands 252
Urup Island 249
Usborne, Port 260
Usedom 221
Ushant 224
Ustica Island 226
Ute Islet 220
Utilla Island 197
Utrecht 223
Uvea Island 259
Vache Island 204
Vadso 218
Vahanga Island 257
Page.
Vahitahi Island 257
Vaitupu Island 254
Valdes Island 200
Valdivia 211
Valencia 225
Valentia 216
Valentine Harbor 210
St., Cape 210
Valery en Caux, St 223
Valiente Peak 198
Valientes Islands 252
Valparaiso 211
Vanavana Island 257
Vancouver 200
Vanikoro 255
Vannes 224
Vanua Lava Island 256
Levu Island 256
Mbalavu Island 256
Vardo 218
Varella Cape 240
Pulo -. 240
Varna Bay 229
Vate Island 256
Vathi, Port 228
Vatiu Island 258
Vatoa Island 257
Vatu Lele Island 256
- — Vara Island 256
Vavau Island 258
Vavitoa Island 258
Vaza Barris River 207
VegUa 227
Veiro Island 222
Vela,La,Cape 206
Venangue Be Bay 235
Vendres, Port 225
Venice 227
Ver, Point de 223
Vera Cruz 196
Verde Cape 231
Cay, Bahamas 203
Cuba 204
Vicente, San, Cape 209
Port 245
Victor, Port 260
Victoria 200
Harbor 264
Port, Australia 260
Seychelle Islands. 234
River 259
Victory Cape 210
Lsland 240
Vidal, Cape .• 232
Video Island 242
VieborgBay 220
Vieques Island 205
Vieste 227
Vigan 245
Vigo 225
Villa 218
Nova da Princessa 208
Villajoyose 225
Ville Tranche 226
Vinaroz 225
Vincent, San, de la Barquera 224
St., Cape, Madagascar. 235
Portugal 225
Id., C. Verde Is.. 214
Windward Is. 205
Port, S. Pacific... 259
^"ineyard Haven 194
INDEX TO APPENDIX IV.
[Page 287
Page.
Vingorla 23"
Rocks 237
Virgin Gorda 205
Virgins, Cape 209
Viti Levu 256
Vizagapatam 238
Viziadrug 23"
Vladimir, St., Bav 250
Vladivostok 250
Vliko, Port 228
Vohemar 235
Vojazza River 228
Volcano Island, West 242
Islands 253
Volta River 231
Voltaire, Cape 259
Vordate Island 244
Vordingborg 222
Vostok Island 253
Vourlah 230
Vriea Island 249
Wadero Island 219
Wadsworth, Fort 194
Wahdu Island 234
Waimea 253
Waitangi River 263
Wakaya Island 256
Wake Island 253
Wakefield, Port 260
Walfisch Bay 232
Walker Cav 203
Wallis Island 257
Walpole Island 256
Walsche, Cape 255
Walsingham, Cape 264
Wanganui River 263
Wangari Harbor 263
Wangaroa Harbor 262
Wangaruru , 263
Wangeroog 222
Wang-kia-tia Bay 217
Warberg 219
Warnemunde 221
Warren Hastings Island . . . 252
Washington 195
Island 251
Watch Hill Point 194
Watcher, North, Island 239
Waterfall Bluff 232
Waterford 217, 218
PLACES — continued.
Page.
Waterloo Bav 232
Watlings Island 203
WawodaRock 250
Wedge Island 193
Weggs Cape 191
Weichselmunde 221
Weihai wei 247
Wellington 263
Wenman Island 250
Wessel, Cape 259
AVest Cape 263
Western, Port 261
Westminster Hall Islet 210
Wetta Island 243
Wexford 217
Whaingaroa Harbor 263
Whale Back 194
Whalefish Island 264
AVhite Haven 215
Head Island 193
Island 263
Rock 240
Whitsunday Island 257
Whittle Cape 192
Wicklow 217
Wilberforce, Cape 259
Wilhelmshaven 222
Willemstadt 223
William, Port 263
Willoughby, Cape 260
Wilmington 195
Wilson Islands 255
Islets 252
Promontory 261
Windau 220
Winter Harbor 264
Wismar 221
Wittgenstein Island 258
Wolgast 221
Wolkonsky Island 258
Wollaston Island , . 209
Wollin 221
Wollongong 261
Wood Island, Labrador 192
Maine 193
Woodlark Islands 255
Woody Island 241
Wostenholme Cape 191
Wotje Islands 251
Wottho Island 251
Wowoni Island 242
Page.
Wrangell 199
Wrath, Cape 216
Wreck Reef 255
AVusimado Point 248
Wustrow 221
Wusung 242
Xulla Islands 244
Yakuno Shima 248
YakutatBav 199
Yamada . . /. 249
Yamagawa 248
Yami Island 246
Yanez 211
Yap Island 252
Yaquina Head 200
Yarmouth 193
Yeboshi Sima 248
Yembo 233
Yerabu-sima.. 244
Yen, Island de 224
Ylin Island 245
Yobuko 248
Yoke Shima 248
Yokohama 249
Yoko-shima 244
Yokosuka 249
York, Cape, Greenland 264
Queensland 262
Minster Rock 209
Youghal 218
Ystad 219
YtapereBav 235
Point .". 235
YuiadaRoad 229
YuraNoUchi 248
Zafarana 233
Zafarin Islands 230
Zambesi River 232
Zamboanga 247
Zante 228
Zanzibar 233
Zapotitlan Point 197
Zara 227
Vecchia 227
Zempoala Point 196
Zengg 227
Zeyla 233
Zirona Grande Island 227
288 LUNAB DISTANCES.
APPENDIX V.
LUNAE DISTANCES.
By reason of the comparative rapidity of motion of the moon relatively to the earth, it occurs that
the angular distance, measured from the earth, between the moon and a body that occupies a fixed, or
nearly fixed, position in the celestial sphere, is constantly changing. If, therefore, an observer accu-
rately measures with a sextant the angle between the moon and one of the various celestial bodies for
which the lunar distance is tabulated in the Nautical Almanac, this observed distance, reduced to true
distance, affords a means for determining the absolute instant of time at which the observation was
taken; and from this may be deduced the longitude and the chronometer error.
If it were practicable to obtain results with a close degree of accuracy l)y this method, it would be an
invaluable aid to the navigator, eliminating all anxiety as to change of rate of the chronometer, and
even rendering it possible to navigate a vessel without such an instrument. It is unfortunately the case,
however, that the method does not afford results that may be regarded as reliable within small limits,
since a very small error in the observed angle, which it may not be possible to avoid even though every
care be taken, causes a large error in the deduced time. Navigators of the present day do not, there-
fore, employ the method of lunar distances except under extraordinary circumstances, such as when an
accident to the chronometer occurs, or, on a very long voyage, when there is reason to suspect the cor-
rectness of the chronometer error as brought forward by the rate.
In order to facilitate the method of determining the longitude from lunar distances, there is pub-
lished in the Nautical Almanac, for every third hour of Greenwich mean time, the angular distances of
the center of .the moon from the center of the sun, from the brightest planets and from certain blight
fitted stars selected in tlie path of the moon. All the distances that can be observed on the same day
are grouped together under that date, and the columns are read from left to right across both pages of
the same opening. The letter W. or E. is affixed to the name of the sun, jilanet, or star to indicate
that it is on the west or east side of the moon. An observer on the surface of the earth having meas-
ured a lunar distance, corrected it for instrumental errors and for the semidiameters of the objects, and
cleared it from the effects of refraction and parallax, finds the true or geocentric distance. With this
distance and the distances in the Nautical Almanac of the same bodies on the same day, the Greenwich
mean time of the observation can be found, as will hereafter be described.
The unavoidable errors to which the observation of lunar distance is subject are diminished by
making a number of measurements. Errors of the instrument may be diminished by measuring
distances on opposite sides of the moon, when possible, ana combining the results.
Before taking the observation, the Nautical Almanac must be examined to see from what objects the
•distances are computed. If the star or planet selected for observation is not recognized from its position
relatively to other bodies in the heavens, it can easily be identified from the distance given in the
Almanac; for the observer may set the sextant to the distance, computed roughly for the estimated time
at the meridian of Greenwich, and direct his sight to the east or west of the moon, according as the
object is marked E. or W. in the Nautical Almanac, and, having found the reflected image of the moon
upon the horizon glass, sweep the instrument to the right or left, and the image will pass over the star or
planet sought, if above the horizon and the weather clear; the star or planet is always one of the brightest,
and is situated nearly in the arc passing through the moon's center, perpendicular to the line connecting
the two horns.
Although all the instruments used in these observations ought to be well adjusted, yet particular
care should be taken of the sextant used in measuring the angular distance of the moon from the sun or
star, since an error of V in this distance will cause an error of nearly 30'' in the longitude deduced
therefrom. When a great angular distance is to be measured it is absolutely necessary to use a telescope,
and its parallelism with respect to the plane of the instrument must be carefully' examine<l; but in
measuring small distances the use of the telescope is not of such great importance, and a sight tube may
then l)e xised, taking care, however, that the eye and point of contact of the objects on the horizon glass
be equally distant from the plane of the instrument. It is always conducive to accuracy to xise a
telescope, and, after a little practice, this is easily done.
While one person is observing the distance of the objects, two others should observe the altitudes.
The chronometer should be under the eye of a fourth person appointed to note the time; the observer
who takes the angular distance gives previous notice to the others to be ready with their altitudes by
the time he has finished his observation, which, being done, the time, altitudes, and distance should be
carefully noted; if other sets of observations are taken it must be done within the space of fifteen
rdinutes, and the mean of all the observations should be worked as a single one.
When a ship is rolling considerably it is difficult to measure the distance of the objects, but when
steady there is much less difficulty, especially in small distances, which are much more easily measured
than large ones, and are not so liable to error from an ill adjustment of the telescope; an observer would
therefore do well to choose those times for observation when the distance of the objects is less than 70°
or 80°. But it must be observed that neither of the objects, if possible, ought to be at a less altitude
than 10°, on account of the uncertainty of the refraction near the horizon, for the horizontal refraction
varies from 33'' to 36^ 40'' by an alteration of 40° in the thermometer; this alteration might cause an
error of 2° in the longitude with an observer who uses the mean refraction.
LUNAR DISTANCES. 289
In measuring the distance of the moon from the sun we must bring the moon's round limb in
contact with the nearer Hml^ of the sun. In measuring the distance of the moon from a planet or fixed
star tlie round limb must be brought in contact with the center of the star or planet, observing that, the
semidiameter of the planet being only a few seconds, the center of it can be estimated sufficiently near
for all the ])urposes of this observation.
In taking the altitude of the moon, the round limb, whether it be the upper or lower, must be
brought to the horizon. In misty weather it is rather difficult to observe the altitude of the stars on
account of their dimness. Sometimes they are so dim that they can not be seen through the telescope
of a sextant, particularly if the mirrors are not well silvered. In this case the telescope must be laid
aside and the altitude taken with a sight tube.
It has been assumed that there were observers enough to measure the altitudes when the distance
was observed, but if that is not the case the altitudes may be estimated in a manner to be explained
hereafter.
The method here given is that of Professor Chauvenet, and involves the use of the tables in this
Appendix. The object of these tables is to give the true correction of a lunar distance in all cases when,
with the apparent distance of the moon from the sun, a planet, or star, the apparent altitudes of the
two objects have also been obtained by observation. They enable us readily to take into account:
First, the parallax of the moon in the latitude of the observer, allowing for the spheroidal figure of the
earth; second, the i)arallax of the sun or a planet; third, the true atmospheric refraction, allowing for
the actual state of the air as shown by the barometer and thermometer; and, fourth, that effect of
refraction which gives the apparent disks of the moon and sun an oval or elliptical figure.
The longitude deduced from a lunar observation, when no attention is paid to the spheroidal figure
of the earth, to the barometer and thermometer, or to the elliptical figure of the disks, may in certain
cases be in error a whole degree. It is true these extreme cases are rare in practice, but cases are
common in which from such neglect the error in the longitude is 10^, 15', or 20', and it is absolutely
necessary to get rid of such errors and to leave no other inaccuracy in the result than that which
unavoidably follows from the observations.
The Observation. — The record of a complete observation embraces:
1. The latitude and approximate longitude of the place of observation.
2. The approximate local time.
3. The time of observation as shown ])y a chronometer, and the error of the chronometer, or its
difference from mean Greenwich time.
4. The apparent distance of the moon's bright limb from a star or planet, or from the nearer limb
of the sun.
5. The apparent altitude of the moon's upper or lower limb above the sea horizon.
6. The apparent altitude of the star, i)lanet, or lower limb of the sun above the sea horizon.
7. The height of the barometer and thermometer.
8. The height of the eye above the level of the sea.
9. The index correction of the sextant.
The index correction of the sextant may be supposed to be previously determined; but, since even
in the best instruments it is not constant, its determination should be considered a necessary part of the
observation.
The error of the chronometer alluded to is that which is obtained by applying the daily rate
(multiplied by the j^rojjer number of days) to the error found before leaving port. The agreement or
disagreement of the error thus found with that found by the lunar observation will be the test of the
accuracv of the chronometer, subject, of course, to the accepted limits of accuracy of the observation
itself.
Preparation' of the Data. — Greenwich Date. — Correct the chronometer time for its error from
Greenwich time and deduce the Greenwich date, i. e., the Greenwich day and hour (mean time), reck-
oning the hours in succession from 0 to 24, beginning at noon.
Xauticdl Almanac. — With the Greenwich date enter the Almanac and take out the moon's semi-
diameter and horizontal parallax; if the sun is observed, take its semidiameter; in the case of a planet,
take its horizontal parallax only.
Apparent Altitude of the Moon. — To the altitude given by the sextant apply the index correction of
the instrument and subtract the dip of the horizon (Table 14).« If the lower limb is observed, add the
semidiameter and augmentation (Table 18) ; if the upper lindj is observed, subtract the augmented semi-
diameter. The result is the apparent altitude of the moon's center, denoted " ([ 's App. Alt."
Apparent Altititde of the Sun, Planet, or Star. — To the observed altitude apply the index correction of
the sextant, and subtract the dip (Table 14) ; and if the sun is used, add its semidiameter when the lower
limb is observed, or subtract it when the upper limb is observed. The result is the apparent altitude
required, denoted by "Q's or jfc's App. Alt."
Apparent Distance. — First, when the sun is used, to the observed distance (corrected for index error
when necessary) add the moon's augmented semidiameter and the sun's semidiameter; second, when a
planet or star is used, add the moon's augmented semidiameter if its nearer limb is observed, but
subtract it if its farther limb is observed. The result is "App. Dist."
Moon's Reduced Par alkLc and Refraction. — Enter Table 19 with the latitude of the place of observa-
tion and the moon's horizontal parallax, and take out the correction, which add to the horizontal
parallax. Call the result the moon's reduced parallax, or " (['s Red. P."
Enter Table I with the moon's apparent altitude, and take out the mean reduced refraction, and
apply to this mean refraction the corrections given in Tables 21 and 22, adding or subtracting these cor-
rections according to the directions in the tallies. The result is the moon's reduced refraction, or ''C's
Red. R."
a The tables designated by their numbers in Arabic notation are to be found in Part II. The tables contained in this
Appendix, which are for exchisive use with lunar-distance observations, are denoted by Roman numbers.
22489—03 19
290 LUNAR DISTANCES.
Subtract the "(['s Red. R." from the "C's Red. P." and mark the result as "C's Red. P. and iJ."
Reduced Parallax and Refraction of Sun, Planet, or Star.c — With the apparent ahitude of the sun,
planet, or star, take from Table I the mean reduced refraction, which correct by Tables 21 and 22. If
the sun is observed, subtract its horizontal parallax (which may always be taken at 8''.5) from its reduced
refraction, and mark the result as "O's Red. P. and jK." If a planet is observed subtract its horizontal
parallax, and mark the result as " >l<:'s Red. P. and i2." If a star is observed, its reduced refraction is
at once the required " -X-'s Red. P. and R."
Computation of the True Distanx-e. — Take from Tables II, III, IV, and V respectively the four
logarithms A, B, C, 'D,f> and place these logarithms each at the head of a colunni, marking the columns
A, B, C, and D; then put the—
log of (t s Red. P. and R. (Table IX) in columns A and B.
log of O's or jfc's Red. P. and R. (Table IX) in columns C and D.
log sin a 's App. Alt. (Table 44) in columns A and D.
log sin O's or sjc's App. Alt. (Table 44) in columns B and C.
log cot App. Dist. (Table 44) in columns A and C.
log cosec App. Dist. (Table 44) in columns B and D.
The sum of the four logs in Col. A is the log (Table IX) of the First Part of (i's Correction, which is
to be marked + when the app. dist. is less than 90°, but — when the app. dist. is greater than 90°.
The sum of the four logs in Col. B is the log (Table IX) of the Second Part of C's Correction, which
is always to be marked — .
The sum of the four logs in Col. C is the log (Table IX) of the First Part of the Q's or >\i:'s Correction,
which is to be marked — when the app. dist. is less than 90°, but + when the ajjp. dist. is greater
than 90°.
The sum of the four logs in Col. D is the log (Table IX) of the Second part of the Q' s or ■}ii' s Correc-
tion, which is always to be marked —•
Combine the first and second parts of the (J 's correction according to the signs prefixed; that is,
take their sum if they have the same sign, but their difference if they have different signs, and prefix the
sign of the greater to the result, which call " C's ivJiole correction."
In the same manner form the "O's or >|<:'s vjhole correction."
Firiit Correction of Distance. — Combine the (i's whole corr. and the O'* or >|<'s whole corr., according
to their signs; the result is the First Correction of Distance, which is to be added to or subtracted from
the apparent distance, according as its sign is -p or — .
Second Correction of Distance. — Enter Table VI with the Apparent Distance and the First Correction
of Distance, and take out the Second Correction of Distance, which is to be applied to the distance
according to the directions in the side columns of the Table.
Correction for the Elliptical Figure of the Moon's Dish, or Contraction of the Ifoon's Semi-diameter. — Enter
Table VII A .with the C's App. Alt. and C's Red. P. and R., and take out the number. With this
number and the (L's whole correction enter Table VII B and take out the required contraction, which is
to be added to the app. dist. when the farther limb is observed, but subtracted when the nearer limb is
observed.
Correction for the Elliptical Figure of the Sun's Disk, or Contraction of the Sun's Semi-diameter. — Enter
Table VIII A with the O's App. Alt. and O's Red. P. and R., and take out the number. With this
number and the O's whole corr. enter Table VIII B and take out the required contraction, which is
always to be sxibtracted from the distance (the nearer limb of the sun being always observed).
Correction for Compression, or for the Spheroidal Figure of the Earth. — Take from the Nautical Alma-
nac for the Greenwich date the declinations of the bodies to the nearest whole degree. With the moon's
declination and apparent distance, take from Table XI A the first part of N, and mark it with the sign ,
in the table if the declination is North; but if the declination is SoutJi, change the sign from + to — or
from — to -p. With the sun's or star's declination and the apparent distance, take from Table XI B the
second part of N, giving it the same sign as the declination. Take the sum, or difference, of the two parts,
according as their signs are the same or different, and to the resulting number prefix the sign of the
greater. The logarithm of this number of seconds, taken from Table IX, with its sign prefixed, is the
required log N. To log N add the log sine of the latitude of the place of observation; the sum is the log
(Table IX) of the required correction for compression. In north latitude add this correction if log N is +,
or subtract it if log N is — ; in south latitude subtract the correction when log N is +> and add it when
log N is — .
All these corrections being applied to the Apparent Distance, the result is the True Distance.
To FixD THE Greenwich Time. — Find in the Nautical Almanac the two distances between which the
true distance falls. Take out the first of these, together with the Prop. Log following it, and the hours
of Greenwich time over it. Find the difference tetween the distance taken from the Almanac and the
true distance, and to the log of this difference (Table IX) add the Prop. Log from the Almanac; the
sum is the log (Table IX) of an interval of time to be added to the hours of Greenwich time taken from
the Almanac. The result is the approximate Greenwich time.
To correct this Greenwich time, take the difference between the two Prop. Logs in the Almanac
which stand against the two distances between which the true distance falls. With this difference and
the interval of time just found enter Table X and take out the seconds, which are to be added to the
approximate Greenwich time when the Prop. Logs are decreasing, but subtracted when the Prop. Logs
are increasing. The result is the true Greenwich time.
By comparing with this the local mean time the longitude will be found; or, if testing the time
shown by chronometer, the difference between the true Greenwich time and the time shown by the
chronometer is the error of the chronometer as determined bv the lunar observation.
a The parallax of a star being zero, its "reduced parallax and refraction " become, of course, merely its " reduced refrac-
tion; " but as no mistake can arise from marking it as " 3|c'8 Red. P. r nd R.," this designation has been retained in order to
give simplicity and uniformity at once to the rules and the tables.
b No interpolation is necessary in taking out these logarithms.
LUXAR DISTANCES.
291
Degree of Dependenxe. — If the error thus determined agrees with that deduced by means of the
rate and original error, it may be accepted as a confirmation of the rate of the chronometer; if otherwise,
more or less doubt is thrown upon the chronometer, according to the degree of accuracy of the lunar
observation itself. An error of 10^^ in the measurement of the distance produces about 20' error in the
Greenwich time; and since, even with the best observers, a single set of distances is subject to a possible
error of 10'^, it may be well to consider the chronometer as still to be trusted so long as it does not
differ from the lunar by more than 20^ Since, however, so much depends upon skill in measuring the
distance, the observer can only form a correct judgment of the degree of dependence to be placed upon
his own observations by repeated trials and a careful comparison of his several results.
Example: In Lat. 35° 30^ N., Long. 30° W., by account, at the local mean time, 1855, September 6,
IS*" 8'" 0% the observed distance of Q'a andC 's nearer limbs was 43° 52^ 10^^; observed alt. C, 49° 32^ 50^^
observed alt. 0, 5° 27^ 10^^; barometer, 29'". 1; thermometer, 75°; height of the eye above the sea, 20"
I. C, 0^ 00'''; required the longitude.
L. M. T., Sept. 6,
Long., D. R.,
G. 31. T., approx.,
Obs. Alt. C,
Dip, Table 14,
C's Aug. S. D.,
(T'sApp. Alt.,
C'sRed. R., Table!
Bar. 29'". 1, Table 21
Ther. 75°, Table 22,
C'sRed. R.,
C'sRed. P.,
C'sRed. P. andR.,
Preparation of the Data.
18" OS-"
+ 2 00
20 08
49'
+
32^ 50^'
4 23
15 01
49
43
28
V
16^^
3
4
1
54
09
23
53
14
C'sS. D.,
Aug. Table 18,
C's Aug. S. D,
Obs. Alt. 0,
Dip,
O'sS. D.,
O's App. Alt,
O'sRedR., Table I,
Bar., Table 21,
Ther., Table 22,
0's Red. R.,
O's Par.,
O's Red. P. aiid R.,
14^ 50^^0|C'aPar., N. A.,
11 .2 Aug., Table 19,
C'sRed. P.,
54^
15 01 .2
5°
27^
10^^
—
4
23
+
15
55
5
38
42
8^
57'^
16
—
28
8
13
8
+
19''^ 4
3 .6
54 23 .0
Obs. Dist. 01 IC, 43° 52^ 10^^
8 05
C's Aug. S. D.,
O'sS. D.,
App. Dist.,
C'sDec, N. A.,
O's Dec, N. A.,
+
15 01
15 55
44 23 06
25° N.
6°N.
log A, Table II, 0. 0021
log ([ 's Red. P. and R., 3. 5043
log sin C 's App. Alt. , 9. 8825
log cot App. Dist. , 0. 0093
flog. Table IX, 3. 3982
\lst Part C 's corr., +41' 4^'
B.
log B, Table III, 9. 9951
log (L 's Red. P. and R., 3. 5043
log sin O's App. Alt., 8. 9929
log cosec App. Dist. , 0. 1552
/log. Table IX, 2. 6475
\2d Part C's corr., - 7' 24'^
C 's whole corr., +34' 18''
log N, Tabs. XIandIX, ( - ) 0. 845
log sin Lat, + 35° 30', ( + ) 9. 764
riog. Table IX, (-) 0.609
\Corr. for Compression, — 4"
Computation of the True Distance.
C.
log C, Table IV, 9. 9949
log O's Red. P. and R., 2. 6857
log sin O's App. Alt, 8. 9929
log cot App. Dist. , 0. 0093
flog. Table IX,
list I
Part O's corr..
1. 6828
-0' 48"
D.
log D, Table V, 9. 9992
log O's Red. P. and R., 2. 6857
log sin C ' s App. Alt , 9. 8825
log cosec App. Dist., 0. 1552
/log. Table IX, 2. 7226
t2d Part O ' s corr. , +8' 48"
O ' s whole corr. , +8' 00"
App. Dist,
Ist Corr.,
2d Corr., Table VI, —
Contraction of d's
S.D., Table VII,
Contraction of O's
S.D., Table VIII,
Corr. for Comp.
True Distance,
44° 23' 06"
+ 42 18
16
0
20
45 04 44
292
LUNAR DISTANCES.
Extract from Nautical Almanac, September, 1855.
GREENWICH MEAN TIME: LUNAR DISTANCES.
to
1 1
' i PL
Star's name and i Midnitrht of '
position. 1 Midnight. ^o^
xv.
p. L.
Of
Diff.
XVIIIh.
p. L.
Of
Diff.
XXI"".
P. L.
of
Diff.
6
Si-N E. '48° 46' 55''
3422 47° 25' 3" 3427
46° 3' 17"
3433
44° 41' 38"
3438
Computation of Greemcich Mean Time.
True Distance,
Distance, N. A., at XVIIl",
Difference,
Approximate interA'al,
Add—
Approx. G. M. T.,
Corr., Table X,
True G. M. T.,
L. M. T.,
Longitude,
45° 04' 44"
46 03 17
58
33
2''
18
09"
04^
20
09
04
2
20
18
09
08
02
00
P. L., 0.3433
log, Table IX, 3.5457
log, Table IX, 3.8890
2 01 02 = 30° 15' 30" W.
Diff. P. logs + 5
Example: In Lat. 55° 20' S., Long. 120° 25' W., by account, on August 29, 1855, at 9'> 40" 00' p. m.,
local mean time, the following distance and altitudes were found, being the mean of six observations
corrected for index error. Observed distance of Fomalhaut and moon's farther limb, 46° 30' 23";
observed alt. C, 6° 26' 10"; observed alt. Fomalhaut, 52° 34' 40"; barometer, 31'°; thermometer, 20°;
height of the eye above the sea, 18".
L. M. T. , August 29, 9" 40"' 00^
Long, by D. K., +8 01 40
Approx. G. M. T.,
Obs, alt. C
Dip, -
C'saug. S. D., +
C's A pp. Alt.,
C 's Red R., Table I,
Bar., Table 21, +
Ther., Table 22, +
(C'sRedR.,
C'sRetl. P.,
C'sRed. P. andR.,
17
41
40
6°
26'
4
16
10"
09
28
6
38
29
7'
48"
16
32
8
60
36
20
51 44
Preparation of the Data.
C'sS.D.,Naut.Al.,
Aug., Table 18, +
\
C's aug S. D.,
Obs. alt. >)«,
Dip,
:!|!:'s Ai>p. Alt.,
*'sRed.R.,TableI,
Bar., Table 21, -f
Ther., Table 22, -j
>|<'s Red. R.,
*'s Red P.,
*'s Red. P. and R.
16' 26". 3
2 .0
16
28
.3
52°
34'
4
40"
09
52
30
31
1'
13"
2
5
1
20
0
>
1
20
C'sPar., N. A.,
Aug., Table 19,
C Red P.,
Obs. Dist. -X- IC,
C's aug., S. D.,
App. Dist.,
C's Dec, N. A.,
>l<:'s Dec, N. A.,
+
60' 11". 8
8 .3
60 20
.1
46°
30'
16
23"
28
46
13
55
4°N.
30° S.
LUNAR DISTANCES.
293
log A, Table II, 0.0274
log C 's Red. P. and R., 3.4919
log sin C ' s App. Alt. , 9. 0632
log cot App. Dist., 9.9813
I log, Table IX, 2.5638
tlst Part C's com, + 6^ 06^^
B.
log B, Table III, 0.0001
log C 's Red. P. and R., 3.4919
log sin sjc's App. Alt., 9.8995
log cosec App. Dist. , 0.1414
flog, Table IX, 3.5329
\2d Part (T's corr., - 56^ 51'^
C's whole corr., — 50 45
log N, Tabs. XI and (-) 1.2.30
IX,
logsinLat., -55°, ( — ) 9.913
flog Table IX,
\Corr. for Comp.,
;+;
1.143
14''
Computation of the True Distance.
C.
log C, Table IV, 9.9999
log )f:'s Red. P. and R., 1.9031
log sin *'s App. Alt., 9.8995
log cot App. Dist., 9.9813
flog. Table IX,
\lst Part >)i:'s corr.
D.
1.7838
log D, Table V, 0.0267
log *'s Red. P. and R., 1.9031
log sin (L 's App. Alt, 9.0632
log cosec App. Dist., 0.1414
flog. Table IX, 1.1344
[2d Part >|c's corr., + 0' 14''
>|<'s whole corr., — 0 47
App. Dist., 46=
13'
55"
1st corr., —
51
32
2dcorr., Table VI, —
22
Contraction of d 's \ ,
S.D., Table VII,i +
17
Corr. for Comp., +
14
True Distance, 45
22
32
Extract from Nautical Almanac, August, 1855.
GREENWICH MEAN TIME: LUNAR DISTANCES.
j3
Star's name and
position.
Midnight.
P. L. P. L.
of XV h. 1 of
Diff. ' Diff.
i
1
XVIII >>.
P. L.
of
Diff.
XXI ^
P. L.
of
Diff.
29
Fomalhaut W.
42° 11' 34"
2.535 ; 43° 51' 59" .2527
i 1
45° 32' 35"
2521
47° 13' 19"
2516
Computation of Greenwich Mean Time.
True Distance,
Dist., N. A., at XV^
Difference,
Approx. interval.
Add—
Approx. G. M. T.,
Corr., Table X,
True G. M. T.,
L. M. T.,
Long.,
45° 22' 32"
43 51 59
1
30 33
2''
15
42"' 01'
17
+
42 01
01
17
9
42 02
40 00
P. L., 0.2527
log, Table IX, 3.7350
Diff. P. logs — 6
loe, Table IX, 3.9877
+ 8 02 02 = 120° 30' 30" W.
Method op Taking a Lunar Observation by One Observer. — Three observers are required to
make the necesssary observations for determining the longitude — one to measure the distance of the
bodies, and the others to take the altitudes. In case of not having a sufficient number of instruments
or observers to take the altitudes, the latter may be calculated, there being given the latitude of the place,
the time, the right ascensions, and the declinations of the objects. These calculations are long, however,
especially in the case of the moon, and a considerable degree of accuracy is required in finding from the
Nautical Almanac the moon's right ascension and declination, which must be liable to some error on
account of the uncertainty of the ship's longitude. The following method of obtaining those altitudes
is far more simple, and sufficiently accurate. This method depends on the supposition that the altitudes
increase or decrease uniformly.
294
LUNAR DISTANCES.
Before measuring the distance of the bodies, take their altitudes, and note the times by a chro-
nometer; then measure the distance and note the time (or measure a number of distances, and note
the corresponding times, and take the means); after having measured the distances, again measure the
altitudes, and note the times; then, from the two observed altitudes of either of the objects, the required
altitude of that object may be found from the following formula, which is based upon simple proportion:
dXe
where x = change of altitude, in minutes, between first altitude and time of measuring the lunar
distance, being positive or negative according as body is rising or falling;
d = difference between first and second altitudes, in minutes;
e = time, in seconds, between first altitude and lunar observations; and
/ = time in seconds, between first and second altitudes.
The change of altitude thus deduced, applied w-ith proper sign to the first altitude, gives the
altitude at time of observing the lunar distance.
Example: Suppose the dista,nces and altitudes of the sun and moon were observed, as in the
following table; it is required to find the altitudes at the time of measuring the mean distance.
Times by chro-
nometer.
2" 03™ 20'
2 04 20
2 05 50
Mean, 2 04 30
Lunar dis-
tance.
40° 00' 00''
40 00 30
40 01 30
40 00 40
Times hy chro-
nometer.
2^ 02
2 06
"00^
10
'.{
Obs. alt.
d's L. L.
20° 46'
21 20
(/, 34
For C-
Time of lunar obs.,
Time of 1st alt..
2" 04"
2 02
30^
00
, 34 X 150
"^ 250~
First altitude,
X,
/ 2 30
\ ISO"
= + 20'.4 = + 20' 24"
20° 46' 00"
+ 20 24
10
250^
For Q.
Time of lunar obs.,
Time of 1st alt.,
Times by chro-
nometer.
2^ 02™ 30"
2 07 00
/ 4 30
1 270'
2'> 04"
2 02
Ob><. alt.
Q's L. L.
40° 20'
39 12
<'
08
30^
30
«,
X 120
270
First altitude,
= -30'.2
Required altitude.
J 2 00
\ 120'
= — 30' 12"
40° 20' 00"
30 12
39 49 48
Required altitude, 21 06 24
To obtain the altitudes by calculation the following formulae may be employed:
tan A = tan d sec t;
smh= ^•OB(A-L)sind
sm A
in which d is the declination; t, the hour angle; L, the latitude; /;, the true altitude of the center of the
object; A, an arc Avhich has the same name or sign as the declination and is numerically in the same
quadrant as t. In the solution, strict regard must be had for the signs.
Example: Required the apparent altitude of the sun's center on December 22, 1879, in Lat. 48° 23'
N., Long. 60° W., at 10" 01™ 14' a. m., app. time.
L. A. T., December 21, 22" 01™ 14»
Long., + 4 00 00
t,
O's Dec.
1" 58™ 46'
23° 27' 16" S.
G. A. T., December 22, 2 01 14
t
d
A
L
29° 41' 30"
— 23 27 16
-26 32 20
+ 48 23 00
sec 0.06113
tan (-) 9.63735
tan (-) 9.69848
74 55 20
h 13 23 58
ref.— par. + 3 50
sin (-) 9.59991
cosec(— ) 0.34989
cos ( + ) 9.41520
sin (+) 9.36500
App. alt. 13 27 48
Page 296] APPENDIX V: TABLE II.
Log. A, for computing the First Correction of the Lunar Distance.
App
alt. of
moon.
Redticed parallax and refraction of moon. 1
41'
42'
48'
44'
45'
46'
4i'
48'
40'
50'
51'
52'
58'
54'
55'
5° 0^
2
4
6
8
.0288
.0286
.0284
.0282
.0281
0295
0293
0291
0289
0287
0301
0299
0297
0294
0308
0306
0304
0302
0300
0298
0296
0295
0293
0291
0289
0288
0286
0284
0282
0281"
0279
0277
0276
0274
0315
0313
0311
0309
0307
0305
0303
0301
0299
0297
0296
0294
0292
0290
0289
0321
0319
0317
0315
0313
0311
0309
0307
0306
0304
0302
0300
0298
0296
0295
0328
0326
0324
0322
0320
0318
0316
0314
0312
0310
0335
0333
0330
0328
0326
0324
0322
0320
0318
0316
0341
0339
0337
0335
0333
0331
0329
0327
0325
0323
0321
0319
0317
0315
0313
0348
0346
0344
0341
0339
0337
0335
0333
0331
0329
0327
0325
0323
0321
0319
0355
0352
0350
0348
0346
0344
0341
0339
0337
0335
0361
0359
0357
0354
0352
0368
0366
0363
0361
0359
5 10
12
14
16
18
5 20
22
24
26
28
.0279
.0277
.0275
.0274
.0272
0285
0284
0282
0280
0278
0292
0290
0288
0286
0285
0350
0348
0346
0344
0341
0339
0337
0335
0333
0331
0329
0327
0326
0324
0322
0320
0318
0316
0315
0313
0356
0354
0352
0350
0348
0346'
0344
0341
0339
0337
0335
0334
0332
0330
0328
0326"
0324
0322
0320
0319
.0270
.0269
.0267
.0265
.0264
0277
0275
0273
0272
0270
0283
028r
0280
0278
0276
0308
0306
0304
0303
0301
0314
0313
0311
0309
0307
0333
0331
0329
0327
0325
0346
0344
5 30
32
34
36
38
.0262
.0261
.0259
.0258
0268
0267
0265
0264
0262
0261
0259
0258
0256
0255
0253
0252
0251
0249
0248
0275
0273
0271
0270
0268
0267
0265
0264
0262
0261
0287
0285
0283
0282
0280
0279
0277
0275
0274
0272
0293
0291
0290
0288
0286
0285
0283
0281
0280
0278
0299
0297
0296
0294
0292
0290
0289
0287
0286
0284
0305
0303
0302
0300
0298
0296
0295
0293
0291
0290
0288
0287
0285
0283
0282
0311
0309
0308
0306
0304
0317
0315
0314
0312
0310
0323
0321
0320
0318
0316
0314
0312
0311
0309
0307
0342
0340
0338
0336
0334
0332
0330
0328
0326
0324
5 40
42
44
46
48
5 50
52
54
56
58
0273
0271
0270
0268
0267
0302
0301
0299
0297
0296
0308
0306
0305
0303
0301
0259
0258
0256
0255
0254
0265
0264
0262
0261
0259
0271
0269
0268
0266
0265
0277
0275
0274
0272
0271
0282
0281
0279
0278
0276
0294
0292
0291
0289
0287
0300
0298
0296
0295
0293
0305
0304
0302
0300
0299
0311
0309
0308
0306
0304
0303"
0.301
0299
0298
0296
0317
0315
0313
0312
0310
0308
0307
0305
0303
0302
0323
0321
0319
0317
0316
6 0
2
4
6
8
0247
0245
0244
0243
0241
0252
0251
0249
0248
0247
0246
0244
0243
0242
0240
0258
0256
0255
0254
0252
0263
0262
0261
0259
0258
0269
0268
0266
0265
0263
0275
0273
0272
0270
0269
0267
0266
0265
0263
0262
0280
0279
0277
0276
0274
0273
0271
0270
0269
0267
"0266
0264
0263
0262
0260
0286
0284
0283
0281
0280
0278
0277
0275
0274
0273
0291
0290
0288
0287
0285
0284
0282
0281
0279
0278
0297
0295
0294
0292
0291
0289
0288
0286
0285
0283
0314
0312
0310
0309
0307
6 10
12
14
16
18
0240
0239
0237
0236
0235
0234
0233
0231
0251
0250
0248
0247
0246
0256
0255
0254
0252
0251
0262
0261
0259
0258
0257
0295
0293
0292
0290
0289
0287
0286
0284
0283
0281
0300
0299
0297
0295
0294
0306
0304
0302
0301
0299
6 20
22
24
26
28
0239
0238
0237
0236
0234
0233
0232
0231
0230
0229
0245
0243
0242
0241
0240
0238
0237
0236
0235
0234
0250
0249
0247
0246
0245
0255
0254
0253
0251
0250
0261
0259
0258
0257
0255
0271
0270
0268
0267
0266
0276
0275
0274
0272
0271
0282
0280
0279
0277
0276
0292
0291
0289
0288
0286
0298
0296
0295
0293
0292
0297
0295
0294
0292
0291
0290
6 30
32
34
36
38
0244
0242
0241
0240
0239
0249
0248
0246
0245
0244
0254
0253
0251
0250
0249
0248
0246
0245
0244
0243
0259
0258
0257
0255
0254
0253
0252
0250
0249
0248
0264
0263
0262
0260
0259
0270
0268
0267
0266
0264
0275
0273
0272
0271
0269
0268
0267
0265
0264
0263
"0262
0260
0259
0258
0257
0280
0278
0277
0276
0274
0285
0284
0282
0281
0279
0290
0289
0287
0286
0284
6 40
42
44
46
48
0227
0226
0225
0224
0223
0232
0231
0230
0229
0228
0238
0236
0235
0234
0233
0232
0231
0230
0229
0227
0243
0241
0240
0239
0238
0258
0257
0255
0254
0253
0252
0250
0249
0248
0247
0263
0262
0260
0259
0258
0257
0255
0254
0253
0252
0273
0272
0270
0269
0268
"0266'
0265
0264
0263
0261
0278
0277
0275
0274
0273
0271
0270
0269
0267
0266
0283 0288
0282 ! 0287
0280 0285
0279 '■ 0284
0278 0283
6 50
52
54
56
58
0222
0221
0220
0219
0218
0227
0226
0225
0224
0223
0237
0236
0235
0233
0232
0242
0241
0239
0238
0237
0247
0246
0244
0243
0242
0276
0275
0274
0272
0271
0281
0280
0279
0277
0276
7 0
0217
0222
0226
0231
0236
0241
0246
0251
0255
0260
0265
0270
0275
APPENDIX V: TABLE II. [Page 297
Log. A, for computing the Mrst Correction of the Lnnar Distance.
App
alt. of
moon.
Reduced parallax and refraction of moon. 1
44'
45'
46'
47'
48' 1 49' 50'
51'
62'
68'
54'
55'
66' j 67'
7° 0^
3
6
9
12
.0222
.0220
.0218
.0217
.0215
0226
0225
0223
0222
0220
0231
0230
0228
0226
0225
0236
0234
0233
0231
0230
0241
0239
0238
0236
0234
0246 0251
0244 0249
0242 i 0247
0241 0245
0239 0244
0255
0254
0252
0250
0248
0260
0258
0257
0255
0253
0265
0263
0261
0260
0258
0270
0268
0266
0264
0262
0275
0273
0271
0269
0267
7 15
18
21
24
27
.0214
.0213
.0211
.0210
.0208
.0207
.0206
.0204
.0203
.0202
0219
0217
0216
0214
0213
0211
0210
0209
0207
0206
0205
0203
0202
0201
0200
0198
0197
0196
0195
0193
0223
0222
0220
0219
0217
0228
0226
0225
0223
0222
0220
0219
0218
0216
0215
0233
0231
0230
0228
0227
0225^
0224
0222
0221
0219
0237
0236
0234
0233
0231
0230
0228
0227
0225
0224
0222
0221
0219
0218
0217
0215
0214
0213
0211
0210
0242
0240
0239
0237
0236
0247
0245
0243
0242
0240
0251
0250
0248
0246
0245
0256
0254
0253
0251
0249
0261
0259
0257
0255
0254
0252
0250
0249
0247
0246
0265
0263
0262
0260
0258
7 30
33
36
39
42
0216
0215
0213
0212
0210
0209
0208
0206
0205
0204
0203
0201
0200
0199
0198
0234
0232
0231
0229
0228
0227'
0225
0224
0222
0221
0239
0237
0235
0234
0232
0231
0229
0228
0227
0225
0243 0248
0241 0246
0240 0244
0238 ! 0243
0237 0241
0257
0255
0253
0252
0250
!
7 45
48
51
54
57
8 0
3
6
9
12
.0200
.0199
.0198
.0196
.0195
.0194
.0193
.0192
0213 0218
0212 0216
0211 0215
0209 0214
0208 0212
0207 0211
0206 1 0210
0204 0208
0203 i 0207
0202 ' 0206
02a5
0234
0232
0231
0229
0240
0238
0237
0235
0234
0232
0231
0229
0228
0227
0244
0242
0241
0239
0238
0236'
0235
0233
0232
0231
0229
0228
0226
0225
0224
0248
0247
0245
0244
0242
0241
0239
0238
0236
0235
0233
0232
0231
0229
0228
0226
0225
0224
0223
0221
0249
0248
0246
8245
0243
0242
0240
0239
0219
0218
0217
0215
0214
0224
0222
0221
0220
0218
0217
0217
0214
0213
0212
0211
0209
0208
0207
0206
0228
0227
0225
0224
0222
8 15
18
21
24
27
8 30
33
36
39
42
8 45
48
51
54
57
0192
0191
0190
0189
0188
0196
0195
0194
0193
0192
0191
0190
0188
0187
0186
0201
0199
0198
0197
0196
0205
0203
0202
0201
0200
0209
0207
0206
0205
0204
0213
0212
0210
0209
0208
0221 0225
0220 0224
0218 0222
0217 0221
0216 0220
0237
0236
0235
0233
0232
0187
0186
0184
0183
0182
0195
0193
0192
0191
0190
0199
0197
0196
0195
0194
0203
0201
0200
0199
0198
0207
0205
0204
0203
0202
0215
0213
0212
0211
0210
0219
0217
0216
0215
0214
0223
0221
0220
0219
0217
0216
0215
0214
0212
9211
0230
0229
022S
0226
0225
0181
0180
0179
0178
0177
0185 0189
0184 0188
0183 ' 0187
0182 1 0186
0181 0185
0193
0192
0191
0190
0189
0197
0196
0195
0193
0192
0201
0200
0198
0197
0196
0205
0203
0202
0201
0200
0208
0207
0206
0205
0204
0212
0211
0210
0209
0208
0220 0224
0219 0223
0218 0221
0216 0220
0215 1 0219
9 0
3
6
9
12
0176
0175
0174
0173
0172
0180 0184
0179 0183
0178 0182
0177 0181
0176 ! 0180
0188
0186
0185
0184
0183
0191
0190
0189
0188
0187
0195
0194
0193
0192
0191
0199
0198
0197
0196
0194
0203
0201
0200
0199
0198
0206
0205
0204
0203
0202
0210
0209
0208
0207
0206
0214 0218
0213 0216
0211 0215
0210 1 0214
0209 1 0213
•
9 15
18
21
24
27
0171
0170
0170
0175
0174
0173
0172
0171
0179
0178
0177
0176
0175
0182
0181
0180
0179
0179
0186
0185
0184
0183
0182
0190
0189
0188
0187
0186
0193
0192
0191
0190
0189
0197
0196
0195
0194
0193
0201
0200
0199
0198
0196
0204
0203
0202
0201
0200
0208 j 0212
0207 1 0211
0206 ! 0209
0205 0208
0204 0207
9 30
33
36
39
42
9 45
48
51
54
57
0170
0170
0169
0168
0167
0174
0173
0172
0171
0170
0178
0177
0176
0175
0174
0173
0172
0171
0170
0169
0181
0180
0179
0178
0177
0185
0184
0183
0182
0181
0180
0179
0178
0177
0176
0188 0192
0187 0191
0186 0190
0185 0189
0184 0188
0195
0194
0193
0192
0191
0190
0189
0188
0187
0186
0199
0198
0197
0196
0195
0194
0193
0192
0191
0190
0203 0206
0201 ! 0205
0200 i 0204
0199 0203
0198 1 0202
1
0166
0165
0164
0163
0163
0169
0169
0168
0167
0166
0176
0176
0175
0174
0173
0183
0182
0182
0181
0180
0187
0186
0185
0184
0183
0197
0196
0195
0194
0193
0201
0200
0199
0198
0197
0203
0202
0201
0200
10 0
0162
0165
0169
0172
0175
0179 0182
0186
0189
0192
0196 0199
Page 298]
APPENDIX V: TABLE II.
Log.
A, for computing the First Correction of the Lunar Distance.
App.
alt. of
moon.
Reduced parallax and refraction of moon. 1
46'
47'
48'
49'
50'
61'
oS'
o8'
54' 55'
56'
0196
57'
68'
10° 0'
.0162
0165
0169
0172
0175
0179
0182
0186
0189 ' 0192
0199
5
.0160
0164
0167
0171
0174
0177
0181
0184 ; 0187 0191
0194 0197
10
.0159
0162
0166
0169
0172
0176
0179
0182 1 0186 0189
0192 0196
15
.0158
0161
0164
0168
0171
0174
0178
0181 ; 0184 i 0187
0191 i 0194
I
20
.0156
0160
^163
0166
0170
0173
0176
0179
0183 i 0186
0189
0192
25
.0155
0158
0162
0160
0165
0168
0171
0175
0178
0181
0180
0184
0188
0191
10 30
.0154
0157
0164
0167
0170
0173
0177
0183
0186
0189
35
.0153
0156
0159
0162
0166
0169
0172
0175
0178 0181
0185 j 0188
40
.0151
0155
0158
0161
0164
0167
0171
0174
0177 0180
0183 i 0186
45
.0150
0153
0157
0160
0163
0166
0169
0172
0175 0179
0182 0185
• 50
.0149
0152
0155
0158
0162
0165
0168
0171 i 0174 i 0177
0180
0183
55
.0148 i 0151
0154
0157
0160
0163
0167
0170 1 0173 i 0176
0179
0177
0182
11 0
.0147 1 0150
0153
0156
0159
0162
0165
0168 ! 0171
0174
0181
5
.0146
0149
0152
0155
0158
0161
0164
0167 1 0170
0173
0176
0179
10
0148
0151
0154
0157
0160
0163
0166
0169
0172
0175
0178
15
0146
0149
0152
0155
0158
0161
0164
0167
0170
0173 1 0176
20
0145
0148
0151
0154
0157
0160
0163
0166
0169
0172 0175
25
11 30
0144
0147
0150
0153
0156
0159
0162 1 0165
0168 i 0171 1 0174
0143
0146
0149
0152
0155
0158
0161 0164
0167
0170 1 0172
35
0142
0145
0148
0151
0154
0157
0160 1 0162
0165
0168 0171
40
0141
0144
0147
0150
0153
0156
0158 0161
0164
0167 0170
45
0140
0143
0146
0149
0151
0154
0157 ! 0160
0163
0166 0169
50
0139
0142
0145
0148
0150
0153
0156 : 0159
0162
0165 0167
55
12 0
0138
0141
0144
0146
0145
0149
0148
0152
0155 0158
0161
0163
0162'
0166
0137
0140
0143
0151
0154 ! 0157
0159
0165
5
0136
0139
0142
0144
0147
0150
0153 0156
0158
0161 0164
10
0135
0138
0141
0143
0146
0149
0152
0154
0157
0160 0163
15
0134
0137
0140
0142
0145
0148
0151
0153
0156
0159 0162
20
0133
0136
0139
0141
0144
0147
0150
0152
0155
0158 1 0160
25
0132
0135
0138
0140
0143
0146
0148
0151
0154
0157 0159
12 30
0131
0134
0137
0139
0142
0145
0147 ! 0150
0153
0155 0158
35
0130
0133
0136
0138
0141
0144
0146 0149
0152
0154 ; 0157
40
0129
0132
0135
0137
0140
0143
0145 ! 0148
0151 1 0153 0156
45
0129
0131
0134
0136
0139
0142
0144 \ 0147
0150
0152 0155
0158
50
0128
0130
0133
0136
0138
0141
0143 0146
0149
0151 ' 0154
0156
1
55
0127
0129
0129
0132
0131
0135
0137
0136
0140
0142
0145
0148
0150 0153
0155
13 0
0126
0134
0139
0141
0144
0147
0149 0152
0154
5
0125
0128
0130
0133
0135
0138
0141
0143
0146
0148 0151
0153
10
0124
0127
0129
0132
0135
0137
0140
0142
0145
0147 0150
0152
15
0123
0126
0129
0131
0134
0136
0139
0141
0144
0146 0149
0151
1
20
0123
0125
0128
0130
0133
0135
0138
0140
0143
0145 0148
0150
25
0122
0124
0127
0129
0132
0131
0134
0133
0137
0136
0139
0142
0144 1 0147
0143 1 0146
0149
1
13 30
0121
0124
0126
0129
0138
0141
0148
35
0120
0123
0125
0128
0130
0133
0135
0138
0140
0142 0145
0147
40
0120
0122
0124
0127
0129
0132
0134 i 0137
0139
0142 0144
0146
45
0121
0124
0126
0128
0131
0133
0136
0138
0141 1 0143
0145
50
0120
0123
0125
0128
0130
0132
0135
0137
0140 ; 0142
0145
55
0120
0122
0124
0127
0129
0132
0131
0134
0133
0136
0136
0139 ! 0141
0144
0143
14 0
0119
0121
0124
0126
0128
0138 0140
!
5
0118
0121
0123
0125
0128
0130
0132
0135
0137 i 0139
0142
10
0117
0120
0122
0124
0127
0129
0132
0134
0136 i 0139
0141
15
0117
0119
0121
0124
0126
0128
0131
0133
0135
0138
0140
20
0116
0118
0121
0123
0125
0128
0130
0132
0135
0137
0139
25
0115
0118
0120
0122
0124
0127
0129
0131
0134
0136
0138
!
14 30
0114
0117
0119
0121
0124
0126
0128
0131
0133 0136 i 0137
i
35
0114
0116
0118
0121
0123
0125
0128
0130
0132
0134
0137
40
0113
0115
0118
0120
0122
0124
0127
0129
0131
0134
0136
\
45
0112
0115
0117
0119
0121
0124
0126
0128
0130
0133
0135
1
50
0112
0114
0116
0118
0121
0123
0125
0127
0130
0132
0134
1
55
0111
0113
0116
0118
0120
0122
0124
0127
0129
0131 0133
15 0
0110
0113
0115
0117
0119
0121
0124
0126
0128
0130 ; 0133
!
APPENDIX V: TABLE 11. [Page 298
Log. A, for computing the First Correction of the Lunar Distance.
App
alt. of
moon.
Reduced parallax and refraction of moon. 1
43'
49'
50'
51'
52' 58'
54'
56'
56'
57'
58'
59'
15° 0'
10
20
30
40
50
16 0
10
20
30
.0110
.0109
.0108
.0107
.0105
0113
0111
0110
0109
0107
dlO'6
0105
0104
0103
0102
0115
0113
0112
0111
0110
0117
0116
0114
0113
0112
0119 0121
0118 1 0120
0116 0119
0115 ' 0117
0114 ' 0116
0124
0122
0121
0119
0118
0126
0124
0123
0121
0120
0128
0127
0125
0124
0122
0130
0129
0127
0126
0124
0133
0131
0129
0128
0126
.0104
.0103
.0102
.0101
.0100
0108
0107
0106
0105
0103
0110
0109
0108
0107
0105
0112
0111
0110
0109
0107
0115
0113
0112
0111
0109
0117
0115
0114
0113
0111
0119
0117
0116
0115
0113
0121
0119
0118
0117
0115
0123
0121
0120
0119
0117
0125
0124
0122
0121
0119
40
50
17 0
10
20
.0098
.0097
.0096
.0095
.0094
0100
0099
0098
0097
0096
0102
0101
0100
0099
0098
0104
0103
0102
0101
0100
0106
0105
0104
0103
0102
0108
0107
0106
0105
0104
0110
0109
0108
0107
0106
0112
0111
0110
0109
0107
0114
0113
0112
0110
0109
0116
0115
0114
0112
0111
0118
0117
0116
0114
0113
30
40
50
18 0
10
0095
0094
0093
0092
0091
0097
0096
0095
0094
0093
0099
0098
0097
0096
0095
0101
0100
0099
0098
0097
0103
0101
0100
0099
0098
0104
0103
0102
0101
0100
0106
0105
0104
0103
0102
0108
0107
0106
0105
0104
0110
0109
0108
0107
0105
0112
0111
0109
0108
0107
0109
0108
0107
0106
0105
0104
20
30
40
50
19 0
10
20
30
40
50
0090
0089
0088
0088
0087
0092
0091
0090
0089
.0088
0094
0093
0092
0091
0090
0096
0095
0094
0093
0092
0097
0096
0095
0094
0093
0099
0098
0097
0096
0095
0101
0100
0099
0098
0097
0103
0102
0101
0099
0098
0104
0103
0102
0101
0100
0106
0105
0104
0103
0102
0086 0087
0085 0087
0084 0086
0083 1 0085
0082 j 0084
0089
0088
0087
0087
0086
0085
0084
0083
0082
0082
0091
0090
0089
0088
0087
0092
0092
0091
0090
0089
0088
0087
0086
0086
0085
0084
0083
0082
0082
0081
0094 0096
0093 0095
0092 : 0094
0091 0093
0090 1 0092
0098
0097
0096
0095
0094
0093
0092
0091
0090
0089
0088
0088
0087
0086
0085
0099
0098
0097
0096
0095
0101
0100
0099
0098
0097
0103
0102
0101
0100
0099
0098
0097
0096
0095
0094
0093
0092
0091
0090
0090
20 0
10
20
30
• 40
50
21 0
10
20
30
0082
0081
0080
0079
0079
0078
0077
0076
0076
0075
0083
0082
0082
0081
0080
0086
0086
0085
0084
0083
0090
0089
0088
0087
0086
0091
0090
0089
0089
0088
0094 i 0096
0093 1 0095
0093 0094
0092 ' 0093
0091 0092
■
0079
0079
0078
0077
0076
0081
0080
0079
0079
0078
0082
0082
0081
0080
0079
0085 1 0087
0085 ' 0086
0084 1 0085
0083 ! 0085
0082 0084
0090 0091
0089 0091
0088 i 0090
0087 0089
0087 i 0088
40
50
22 0
10
20
0074
0074
0073
0072
0072
0076
0075
0074
0074
0073
0077
0076
0076
0075
0074
0079
0078
0077
0076
0076
0075
0074
0074
0073
0072
0080
0079
0079
0078
0077
0076
0076
0075
0074
0074
0082
0081
0080
0079
0079
0078
0077
0076
0076
0075
0083
0082
0081
0081
0080
0084
0084
0083
0082
0081
0086
0085
0084
0083
0083
0087
0086
0086
0085
0084
0089
0088
0087
0086
0086
30
40
50
23 0
10
0071
0070
0070
0069
0068
0072
0072
0071
0070
0070
0074
0073
0072
0072
0071
0079
0079
0078
0077
0076
0081
0080
0079
0078
0078
0082
0081
0081
0080
0079
0083
0083
0082
0081
0080
0085
0084
0083
0082
0082
1
20
30
40
50
24 0
0068
0067
0067
0066
0069
0069
0068
0067
0067
0070
0070
0069
0069
0068
0072
0071
0071
0070
0069
0073
0072
0072
0071
0071
0074
0074
0073
0073
0072
0076
0075
0074
0074
0073
0077
0076
0076
0075
0074
0078
0078
0077
0076
0076
0080
0079
0078
0078
0077
0081
0080
0080
0079
0078
10
20
30
40
50
0066
0066
0065
0065
0064
0067
0067
0066
0066
0065
0069
0068
0068
0067
0066
0070
0069
0069
0068
0068
0071
0071
0070
0069
0069
0073
0072
0071
0071
0070
0074
0073
0072
0072
0071
0075
0074
0074
0073
0072
0076
0076
0075
0074
0074
0078
0077
0076
0076
0075
25 0
0063
0065
0066
0067 j 0068
0069 1 0071
0072 1 0073
0074;
Page 300]
APPENDIX V: TABLE 11.
Log. A, for computing the First Correction of the Lunar Distance.
App.
alt. of
moon.
Reduced parallax and refraction of moon. 1
50'
51'
52'
58' j 54' 1 56'
56' 57' i 58'
59'
80'
1
25° 0'
.0063
0065
0066 ' 0067 0068 0069
0071 0072 0073
0074
1
1
20
.0062
0064
0065 0066 I 0067 0068
0069 0071 0072
0073
40
.0061
0062
0064 1 0065 0066 i 0067
0068 ' 0069 0071 i 0072
26 0
.0060
006f
0063 0064 0065 0066
0067 0068 0069 : 0071
1
20
.0059
0060
0062 1 0063 ' 0064 0065
0066 1 0067
0065 ; 0066
0068 0069
1
40
.0058
0059
0061 0062 0063 0064
0067 0068
1
27 0
.0057
0058
0060 0061 ' 0062 0063
0064 0065 0066 0067
20
.0056
0057
0059
0060 0061 0062
0063 0064 0065 0066
40
.0055
0057
0058
0059 i 0060 0061
0062 0063 0064 ■ 0065
28 0
.0055
0056
0057
0058 0059 0060
0061 0062 j 0063 0064
20
.0054
0055
0056
0057 0058 0059
0060 i 0061 0062 0063
40
.0053
0054
0055 0056 0057 ■ 0058
0059 i 0060 0061 0062
j
29 0
.0052
0053
0054 0055 0056 0057
0058 0059 0060 0061
1
20
.0051
0052
0053 i 0054 0055 0056
0057 0058 1 0059 0060
40
.0050
0051
0052 1 0053 0054 0055
0056 0057 0058 0059
30 0
.0050
0051
0051 0052 j 0053 0054 ; 0055 0056 0057 i 0058
1
20
.0049
0050
0051 1 0052 1 0052 0053
0054 0055 0056 0057
40
.0048
0049
0050 i 0051 0052 0053
0053 0054 0055 0056
31 0
.0047
0048
0049 0050 0051 0052
0053 0053
0054 0055
20
.0047
0047
0048 0049 0050 0051
0052 0053
0054 0054
0055
40
.0046
0047
0048 ^ 0048 0049 0050
0051 : 0052
0053 i 0054
0054
32 0
.0045
0046
0047 1 0048 1 0048 0049
0050 ! 0051
0052
0053
0054
20
.0044
0045
0046 ' 0047 0048 0049 0049 0050 I 0051
0052
0053
1
40
.0044
0045
0045 ; 0046 0047 0048 0049 0049 | 0050
0051
0052
1
33 0
.0043
0044
0045 1 0045 0046 0047 ! 0048 0049
0044 i 0045 0046 0046 , 0047 ! 0048
0049
0050
0051
20
.0042
0043
0049 i 0050
0050
1 1
40
.0042
0043
0043 0044 0045 i 0045 ' 0046 ' 0047 i 0048 ! 0049
0050
34 0
.0041
0042
0043 0043 1 0044 0045 0046 | 0046 ! 0047 - 0048
0049
20
.0040
0041
0042 0043 i 0043 0044 0045 i 0046 0047 0047
0048
40
.0040
.0039
0041
0040
0041 j 0042 0043 0044 \ 0044 | 0045
0041 1 0041 0042 0043 1 0044 j 0044
0046
0047
0047
35 0
0045
0046
0047
20
.0039
0039
0040 0041 0042 0042 j 0043 0044
0044
0045
0046
40
.0038
0039
0039 i 0040 0041 0042 0042 0043 i 0044
0044
0045
36 0
.0037
0038
0039 0040 . 0040 0041 0042 0042 \ 0043
0044 0044
20
.0037
0038
0038 0039 0040
0040
0040
0041 0042 0042 | 0043
0044
0043
40
.0036
0037
0038 1 0038 0039
0040
0041 i 0042 0042
1
1
37 0
.0036
0036
0037 ' 0038 0038 0039 | 0040
0040 0041 0042 ! 0042
20
.0035
0036
0037 0037 0038
0039 0039
0040 ! 0040 0041
0042
40
.0035
0035
0036 0037 0037
0038 0039
0039 0040 0040
0041
38 0
.0034
0035
0035 i 0036 i 0037
0037 0038
0039 0039 0040
0040
20
.0034
0034
0035
0036 1 0036
0037 1 0037
0038 0039 1 0039 0040
40
.0033
0034
0034
0035 0036
0036 0037
0037 0038 0039 0039
39 0
0033
0034
0034 0035 0036 \ 0036
0037 ! 0037 0038 ' 0039
20
0033
0033
0034 i 0035 i 0035
0036
0036
0037 0037 1 0038
40
40 0
0032
0033
0033 ' 0034
0035
0035
0036
0036 1 0037 ' 0037
0032
0032
0033 0033
0034 i 0035
0035 0036 0036 0037
20
0031
0032
0032 0033 0034 0034
0035 0035 0036 0036
40
0031
0031
0032 ; 0032 0033 i 0034
0034 0035 0035 0036
41 0
0030
0031
0031 1 0032 ; 0033 1 0033
0034 1 0034 1 0035 0035
20
0030
0030
0031
0031
0032
0033
0033
0034 I 0034 i
0033 1 0034 ;
0035
40
0029
0030
0030
0031
0032
0032
0033
0034
42 0
1
0029 1
0029
0030
0031
0031
0032
0032 0033 1 0033 j 0034
20
0029
0029
0030
0030
0031
0031
0032 0032 ! 0033 0033
40
0028
0029
0029
0030 0030 1
0031
0031
0032 0032 0033
43 0
1
0028
0027
0028
0028
0029
0028
0029
0029
0030
0029
0030
0031
0031 0032 ! 0032
20
0030
0030
0031
0031 0032
40
0027
0027
0028
0028
0029
0029
0030
0030
0031 0031
44 0
0026
0027
0027.
0028
0028
0029
0029
0030
0030 0031
20
1
0026
0026
0027
0027
0028
0028
0029
0029
0030 ' 0030
40
0026 ;
0026
0026
0027
0027
0027
0028
0028
0029
0029 j 0030
45 0
1 0025 j
0026
0026
0027
0027
0028
0028
0029 , 0029
APPENDIX V: TABLP] II. [Page 301.
Log. A, for computing the First Correction of the Lunar Distance.
App
alt. of
moon.
Reduced parallax and refraction of moon. 1
51'
52'
53'
54'
55'
56'
57'
58'
69'
60'
45° 0^
30
40, 0
30
47 0
30
48 0
30
49 0
30
.0025
. 0025
.0024
.0023
.0023
.0022
.0022
.0021
.0021
.0020
0026
0025
0024
0024
0023
0026
0025
0025
0024
0024
0027
0026
0025
0025
0024
0024
0023
0022
0022
0021
0027
0026
0026
0025
0025
0024
0023
0023
0022
0022
0027
0027
0026
0026
0025
0028
0027
0027
0026
0025
0028
0028
0027
0026
0026
0029
0028
0027
0027
0026
0025'
0025
0024
0024
0023
0029
0028
0028
0027
0026
0023
0022
0022
0021
0021
0023
0023
0022
0022
0021
0024
0024
0023
0023
0022
0025
0024
0024
0023
0022
0022
0021
0021
0020
0020
0025
0024
0024
0023
0023
0022
0022
0021
0021
0020
0020
0019
0019
0018
0018
0017"
0017
0016
0016
0015
0026
0025
0025
0024
0023
50 0
30
51 0
30
52 0
30
53 0
30
54 0
30
.0020
.0019
.0019
.0018
.0018
0020
0020
0019
0019
0018
0018
0017
0017
0016
0016
"0016
0015
0015
0014
0014
0020
0020
0020
0019
0019
0018
0018
0017
0017
0016
0016
0015
0015
0015
0014
0021
0020
0020
0019
0019
0018
0018
0017
0017
0017
0021
0021
0020
0020
0019
0022
0021
0020
0020
0019
0023
0022
0021
0021
0020
0020
0019
0019
0018
0018
0017
0017
0017
0016
0016
0023
0022
0022
0021
0021
0020
0020
0019
0019
0018
.0018
.0017
.0017
.0016
.0016
0019
0018
0018
0017
0017
0019
0018
0018
0018
0017
0019
0019
0018
0018
0017
0017
0016
0016
0016
0015
1
55 0
30
56 0
30
57 0
.0015
. 0015
. 0015
.0014
.0014
0016
0016
0015
0015
0015
0016
0016
0016
0015
0015
0017
0016
0016
0015
0015
0018
0017
0017
0016
0016
1
i
30
58 0
30
59 0
30
.0014
. 0013
.0013
.0012
.0012
0014
0013
0013
0013
0012
0014
0014
0013
0013
0012
0014
0014
0013
0013
0013
0014
0014
0014
0013
0013
0015
0014
0014
0013
0013
0015
0014
0014
0014
0013
0015
0015
0014
0014
0013
0015
0015
0014
0014
0014
0015
0015
0015
0014
0014
60
61
62
63
64
.0012
.0011
.0011
.0010
.0009
.0009
.0008
.0008
. 0007
.0007
0012
0011
0011
0010
0010
0009
0008
0008
0007
0007
0007
0006
0006
0005
0005
000b
0005
0004
0004
0004
0012
0011
0011
0010
0010
0009
0009
0008
0008
0007
0012
0012
0011
0010
0010
0009
0009
0008
0008
0007
0013
0012
0011
0011
0010
0009
0009
0008
0008
0007
0007
0006
0006
0006
0005
0005
0005
0004
0004
0004
0013
0012
0011
0011
0010
0013
0012
0011
0011
0010
0013
0012
0012
0011
0010
0010
0009
0009
0008
0008
0013
0012
0012
0011
0010
0010
0009
0009
0008
0008
0007
0007
0006
0006
0005
0005
0005
0004
0004
0004
0004
0003
0003
0003
0003
0013
0013
0012
0011
0011
0010'
0009
0009
0008
0008
65
66
67
6S
69
0009
0009
0008
0008
0007
0007
0006
0006
0006
0005
0005
0005
0004
0004
0004
0010
0009
0008
0008
0007
0007
0007
0006
0006
0005
0005
0005
0004
0004
0004
0004
0003
0003
0003
0003
0003
0003
0003
0003
0003
i
70
71
72
73
74
.0007
.0006
. 0006
.0005
. 0005 ^
0007
0006
0006
0006
0005
0005
0005
0004
0004
0004
0007
0006
0006
0006
0005
0005
0005
0004
0004
0004
0004
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003"
0007
0007
0006
0006
0005
0005
0005
0004
0004
0004
0004
0003
0003
0003
0003
0007
0007
0006
0006
0006
75
76
77
78
79
. 0005
.0004
.0004
.0004
.0004
.0004
. 0003
.0003
. 0003
.0003
.0003
.0003
.0003
. 0003
.0003
0005
0005
0004
0004
0004
80
81
82
83
84
0004
0003
0003
0003
0003
0004
0003
0003
0003
0003
0004
0003
0003
0003
0003
0003
0003
0003
0003
0003
0004
0003
0003
0003
0003
0003
0003
0003
0003
0003
0004
0003
'0003
0003
0003
85
86
87
88
89
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
90
. 0003 0003
0003
0003
0003
0003
0003
0003 0003
Page 302J APPENDIX V: TABLE III.
Log. B, for computing the First Correction of the Lunar Distance.
App. alt.
of sun
or star.
Reduced refraction and parallax of sun or star.
0' 0"
0' 80"
V 0"
1' 30"
2' 0"
2' 80" 1 8' 0" 1 8' 80"
4' 0"
4' 80"
5' 0"
5' 80"
5° 0'
10
20
30
40
•
50
6 0
20
40
7 0
9. 9976
9. 9977'
9. 9978
9. 9979
9. 9980
9. 9981
'9. 9982
9. 9983
9. 9983
9. 9984
9. 9986
9. 9987
9. 9989
9. 9990
9. 9991
9. 9970
9. 9972
9. 9974
9. 9975
9. 9976
9. 9977
9. 9978
9. 9979
9.99M
9. 9981
9. 9982
9. 9982
9. 9984
"9. 9986
9. 9987
20
40
8 0
20
40
9. 9981
9. 9982
9. 9982
9. 9983
9.9984
9. 9985
9. 9985
9. 9986
9. 9987
9. 9989
9. 9990
9. 9991
9. 9992
9. 9993
9 0
20
40
10
11
9. 9992
9. 9993
9. 9994
9. 9994
9. 9995
9. 9995
9. 9996
9. 9997
9. 9998
9. 9999
9. 9989
9. 9991
9. 9986
9. 9986
9. 9987
9. 9988
9. 9989
12
13
14
15
16
9. 9997
9. 9997
9. 9995
9. 9995
9. 9996
9. 9996
9. 9992
9. 9992
9. 9993
9. 9994
9. 9994
9. 9995
9. 9996
9. 9998
9. 9990
9. 9991
9. 9992
9. 9993
9. 9993
18
20
25
30
50
0.0001
0.0001
0.0001
0.0000
0. 0000
0. 0001
0. 0001
9. 9999
9. 9999
0. 0000
0. 0000
0. 0001
9.9998
9. 9998
9. 9999
0. 0000
0. 0001
9. 9997
9. 9998
9. 9999
0. 0000
0.0001
9. 9995
9. 9996
90
0.0001
0.0002
0. 0002 1 0. 0002
1
App. alt.
of sun
or star.
Reduced refraction and parallax of sun or star. 1
6' 0"
6' 80"
7' 0" 1 7' 30"
8' 0"
8' 30"
0' 0"
0' 80"
10' 0"
10' 80" i 11' 0" 11' 80" 1
5° 0'
10
20
30
40
50
6 0
20
40
7 0
9. 9959
9. 9960
9. 9962
9. 9963
9. 9965
9. 9967
9. 9968
9. 9970
9. 9971
9. 9973
9. 9974
9. 9975
9. 9976
9. 9977
9. 9978
9. 9979
9. 9981
9. 9951
9. 9953
9. 9954
9. 9956
9. 9957
9. 9947
9. 9949
9. 9951
9. 9952
9. 9954
9. 9944
9. 9946
9. 9948
9. 9949
9. 9951
9. 9952
9. 9954
9. 9956
9. 9959
9. 9961
9. 9963
9. 9965
9. 9966
9. 9968
9. 9940
9. 9942
9. 9944.
9. 9946
9. 9948
9. 9949
9. 9951
9. 9954
9. 9956
9. 9958
9. 9960
9. 9962
9. 9964
9. 9937
9. 9939
9. 9941
9. 9943
9. 9944
'9. 9946
9. 9948
9. 9951
9. 9953
9. 9956
9. 9933
9. 9935
9. 9937
9. 9939
9. 9941
9.9943
9. 9945
9. 9948
9. 9951
9. 9953
9. 9929
9. 9932
9. 9934
9. 9936
9. 9938
9. 9926
9. 9928
9. 9931
9. 9933
9. 9935
9. 9922
9. 9925
9. 9927
9. 9929
9. 9932
9. 9919
9. 9921
9. 9924
9. 9965
9. 9966
9. 9968
9. 9969
9. 9971
9. 9958
9. 9960
9. 9962
9. 9964
9. 9966
9.9968
9. 9969
9. 9971
9. 9972
9. 9973
9. 9974
9. 9975
9. 9976
9. 9977
9. 9955
9. 9957
9. 9959
9. 9961
9. 9963
9. 9940
9. 9942
9. 9945
9. 9948
9. 9937
9. 9939
20
40
8 0
20
40
9. 9972
9. 9974
9. 9975
9. 9976
9. 9977
9. 9965
9. 9967
9. 9968
9. 9970
9. 9971
9.9972
9. 9958
9 0
20
40
10
11
9. 9978
9. 9979
9. 9980
9. 9981
9. 9983
12
13
14
15
16
9. 9985
18
20
25
30
50
-^
90
APPENDIX V: TABLE IV. [Page 303
Log. C, for computing the First Correction of the Lunar Distance.
App. alt.
of sun
or star.
Reduced refraction and parallax of sun or star. 1
O'O"
0'30"
I'O" i 1'30"
1
2'0"
2' 30" 3' 0"
3' 80" 4' 0"
4' 80"
5'0"
5' 30"
5° 0'
20
40
6 0
20
9. 9969
40
7
8
9
10
9. 9988
9. 9984
9. 9986
9. 9980
9. 9982
9. 9984
9. 9986
9. 9987
9. 9988
9. 9989
9. 9990
9. 9990
9. 9991
9. 9974
9. 9978
9. 9980
9. 9982
9. 9984
9. 9985
9. 9987
9. 9988
9. 9989
9. 9970
9. 9972
9. 9975
9. 9978
9. 9981
11
12
13
14
15
9. 9995
9. 9993
9. 9994
9. 9994
9. 9990
9. 9991
9. 9992
9. 9993
9. 9993
9. 9994
9. 9994
9. 9994
9. 9995
9. 9996
9. 9989
9. 9990
9. 9991
9. 9991
9. 9992
9. 9987
9. 9988
9. 9989
9. 9990
9. 9991
9. 9982
9. 9984
9. 9985
16
17
18
20
25
9. 9998
9. 9999
9. 9999
9. 9999
0. 0000
0. 0000
9. 9997
9. 9998
9. 9998
'9. 9999
9. 9999
9. 9999
0. 0000
9. 9996
9. 9996
9. 9996
9. 9997
9. 9998
9. 9998
9. 9999
9. 9999
9. 9995
9. 9995
9. 9995
9. 9996
9. 9997
9. 9993 i 9. 9992
9. 9993 9. 9992
9. 9994 9. 9993
9.9994 9.9993
9. 9996
30
40
50
90
0. 0000
0. 0000
0. 0000
0. 0000
0. 0000
0. 0000
9. 9998
9. 9999
9. 9997
\
'
App. alt.
of sun
or star.
Reduced refraction and parallax of sun or star. 1
6'0"
6' 30"
7'0"
7' 30"
8'0"
8' 80"
O'O" 9' 80"
10' 0"
10' 80"
11' 0"
11' 30"
5° 0^
20
40
6 0
20
. 40
7
8
9
10
9. 9962
9. 9964
9. 9966
"9. 9968
9. 9969
9.9973
9. 9976
9. 9979
9. 9956
9. 9959
9. 9961
9. 9963
9. 9949
9. 9953
9. 9955
9. 9958
9. 9960
9. 9962
9. 9964
9. 9969
9. 9972
9. 9975
9. 9946
9. 9949
9. 9952
9. 9955
9. 9957
9. 9960
9. 9962
9. 9966
9. 9970
9. 9942
9. 9946
9. 9949
9. 9952
9. 9955
9. 9957
9. 9959
9. 9964
9. 9968
9. 9938
9. 9942
9. 9946
9. 9949
9. 9952
9. 9954"
9. 9956
9. 9962
9. 9935 ' 9. 9931
9. 9939 9. 9936
9. 9943 9. 9939
9. 9946 9. 9943
9. 9949 i 9. 9946
9. 9927
9. 9932
9. 9936
9. 9940
9. 9943
9. 9946
9. 9924
9. 9929
9. 9933
9. 9937
9. 9920
9. 9925
9. 9930
9. 9916
9. 9922
9. 9965
9. 9967
9. 9971
9. 9974
9. 9977
9. 9951
9. 9954
9. 9960
9. 9949
9. 9951
11
12
13
14
15
9. 9981
9. 9983
9. 9979
16
17
18
20
25
30
40
50
90
APPENDIX V: TABLE V.
[Page 305
Log. D, for computing
tlie First Correction of the Lunar Distance.
A pp.
alt. ot
moon.
Reduced parallax and refraction of moon. 1
45'
46'
47'
48'
49'
60' ! 51'
52' i 68'
54'
55'
56'
67'
58'
8° 0'
.0192
0196
0200
0204
0208
0212 ! 0217 0221 0225
0229
0233
0237
5
.0190
0194
0198
0202
0206
0210 0214 0218 0222
0227 ' 0231
0235
10
.0188
0192
0196
0200
0204
0208 ' 0212
0216 0220
0224 ! 0228
0232
15
.0186
0190
0194
0198
0202
0206 : 0210
0214 0218
0222 0226
0230
20
.0184
. 0182'
0188
0186
0192
0190
0196
0194
0200
0197
0204 0207
020r 0205'
0211 0215
0209 0213
0219 1 0223
0227
25
0217 ; 0221
0225
8 30
.0180
0184
0188
0192
0195
0199 0203
0207 0211
0215 1 0219
0223
35
.0178
0182
0186
0190
0193
0197 0201 1 0205 i 0209
0213 0216
0220
40
.0176
0180
0184
0188
0191
0195 0199 ! 0203 { 0207
0210 0214 0218
45
50
.0174
.0173
0178
0176
0182
0180
0186
0184
0189
0193
0197 I 0201 ! 0205
0195 1 0199' 0202
0208 ' 0212
0206 0210
0216
0214
0188
0191
55
.0171
0175
0178
0182
0186
0189 1 0193 1 0197 0200
0204 0208
0212
9 0
. 0169
0173
0177
0180
0184
0188 0191 0195 0198
0202 0206
0209
5
.0167
0171
0175
0178
0182
0186 0189 I 0193 0197
0200 1 0204
0207
10
15
.0166
0169
0168
0173
0171
0177
0180
0184
0187 1 0191 0195 1 0198
0186 0189 0193 0196
0202
0205
. 0164
0175
0179
0182
0200
0203
20
. 0163
0166
0170
0173
0177
OIHO 0184 0187 0191 ' 0194
0198
0201
25
.0161
0165
0168
0172
0175
0179 0182
0186 0189 0193
0196
0199
9 30
0163
0166
0170
0173
0177 , 0180
0184 , 0187 0191
0194
0198
35
0161
0160
0165
0168
0167
0172
0170
0175 1 0179 ' 0182 0185
0189
0192 0196
40
0174 1 0177 j 0180 t 0184
0187 0191 ' 0194
45
0158
0162
0165
0169
0172 i 0175 0179 • 0182
0185 i 0189 0192
0195
50
0157
0160
0164
0167
0170 ; 0174 ' 0177 0180
0184 ! 0187 0190
0194
55
0156
0159
0162
0165
0169 ; 0172 j 0175 0179
0182 1 0185 0189
0192
10 0
5
0154
0153
0157
0156
0161
0159
0164
0162
0167 i 0171 1 0174 i 0177
0166 j 0169 1 0172 0175
0180 i 0184 0187
0179 0182' 0185
0190
0188
1
10
0151
0155
0158
0161
0164 ' 0167 0171 0174
0177 ' 0180 ' 0183
0187
15
0150
0153
0156
0160
0163 0166 0169 1 0172
0175
0179 0182
0185
20
0149
0152
0155
0158
0161 i 0164 0168 0171
0174
0177 ! 0180
0183
25
10 30
0147
0146
0150
0149
0154
0152
0157
0155
0160 1 0163 0166 0169
0172
0175 1 0179
0182
0J58
0162 1 0165
0168
0171 1 0174
0177
0180
35
0145
0148
0151
0154
0157
0160 0163
0166
0169 i 0172 1 0175
0179
40
0143
0147
0150
0153
0156
0159 0162
0165
0168
0171 1 0174
0177
. -l-^
0142
0145
0148
0151
0154
0157 ; 0160
0163
0166
0169
0172
0175
50
55
0141
0144
0147
0150
0149
0153
0156 ! 0159
0162
0161
0166
0168
0171
0174
0172
0140
0143
0146
0152 0155 0158
0164 1 0167 i 0170
11 0
0139
0142
0145
0147
0150 0153 0156
0159
0162 ■ 0165 1 0168
0171
0
0137
0140
0143
0146
0149 1 0152 0155
0158
0161 ! 0164 1 0167
0170
10
0139
0142
0145
0148 0151 0154
0157 0159 i 0162 0165
0168
15
0138
0137
0141
0140
0144
0143
0147 0150 0152 i 0155 0158 i 0161 0164
0167
20
0145 1 0148 0151
0154 0157
0160 0163
0165
25
0136
0139
0141
0144 ' 0147 0150
0153 0156
0158 ! 0161
0164
11 30
0135
0137
0140
0143 0146 0149
0151 0154
0157 : 0160
0163
35
0133
0136
0139
0142 0145 0147
0150 0153
0156 1 0159
0161
40
45
0132
0135
0138
0137
0141 0143 0146
0140 0142 0145
0149 0152
0154 1 0157
0160
0159
"-
0131
0134
0148 0150 0153 i 0156
50
0130
0133
0136
0138 0141 0144
0147 0149
0152 i 0155
0157
55
0129
0132
0135
0137 0140 0143
0145 0148
0151 ! 0153
0156
12 0
0128
0131
0134
0136 0139 0142
0144 0147 0150 ' 0152
0155
5
10
0127
0126
0130
0132
0135
0138 0140
0137 0139
0143 0146
0142 0145
0148 0151
0154
0129
0131
0134
0147 0150
0152
15
0125
0128
0130
0133 0136 0138
0141 0143 0146 0149
0151
20
0124
0127
0129
0132 0135 0137
0140 0142 0145
0147
0150
25
0123
0126
0128
0131 0133 i 0136
0139 1 0141 0144
0146
0149
12 30
35
0122
0125
0127
0130
0132 ! 0135
0131 1 0134
0138 i 0140 1 0143
0145
0144
0148
0147
0121
0124
0126
0129
0136 i 0139
0141
40
0120
0123
0125
0128 0130
0133
0135 0138
0140
0143
0145
45
0119
0122
0124
0127 0129
0132
0134 0137
0139
0142
0144
0147
50
0118
0121
0123
0126 0128
0131
0133
0136
0138
0141
0143
0146
55
0118
0120
0123
0125 0127
0130
0132
0135
0137
0140
0142
0145
13 0
0117
0119
0122
0124 0126
0129
0131
0134 0136
0139
0141
0143
22489—03-
-20
Page 306] APPENDIX V: TABLE V.
Log. D, for computing the First Correction of the Lunar Distance.
App.
alt. of
moon.
Reduced parallax and refraction of moon.
47'
48'
40'
60'
51'
62'
68'
84'
66'
66'
67'
58'
59'
13° 0'
10
20
30
40
.0117
.0115
.0113
.0112
0119
0117
0116
0114
0112
0122 0124
': 0120 0122
0118 0120
0116 0119
0114 ! 0117
0126
0125
0123
0121
0119
0129
0127
0125
0123
0121
0131
0129
0127
0125
0124
0134
0132
0130
0128
0126
0136
0134
0132
0130
0128
0139
0137
0134
0132
0131
0141
0139
0137
0135
0133
0143
0141
0139
0137
0135
0133
0131
0129
0127
0126
50
14 0
10
20
30
0111
0109
0107
0106
0104
0113
0111
0110
0108
0106
0115
0113
0112
OHO
0109
0117
0116
0114
0112
0111
0120
0118
0116
0114
0113
0122
0120
0118
0117
0115
0124
0122
0121
0119
0117
0115
0114
0112
0111
0109
0126
0125
0123
0121
0119
0118
0116
0114
0113
0111
0110
0108
0107
0105
0104
0102
0101
0100
0098
0097
0129 0131
0127 0129
0125 0127
0123 ! 0125
0121 1 0123
40
50
15 0
10
20
0103
0101
0100
0099
0097
0105
0103
0102
0101
0099
0098
0096
0095
0094
0093
0107
0106
0104
0103
0101
0109
0108
0106
0105
0103
0111
0110
0108
0107
0105
0113
0112
0110
0109
0107
0120
0118
0116
0115
0113
0112'
0110
0108
0107
0106
0122 ! 0124
0120 i 0122
0118 0120
0117 0119
0115 0117
"0113 "0115"
0112 0114
0110 0112
0109 0111
0107 0109
30
40
50
16 0
10
0096
0094
0093
0092
0091
0100
0098
0097
0096
0094
0102
0100
0099
0098
0096
0104
0102
0101
0099
0098
0106 0108
0104 0106
0103 0105
0101 0103
0100 0102
20
30
40
50
17 0
0089
0088
0087
0086
0085
0091
0090
0089
0088
0087
0093 i 0095
0092 1 0094
0091 0092
0089 0091
0088 0090
0097
0096
0094
0093
0092
0099
0097
0096
0095
0093
0100
0099
0098
0096
0095
0104
0103
0101
0100
0099
0097
0096
0095
0094
0092
0106 0108
0105 0106
0103 0105
0102 ! 0104
0100 i 0102
10
20
30
40
50
0084
0083
0085
0084
0083
0082
0081
0087
0086
0085
0084
0083
0089
0088
0086
0085
0084
0091
0089
0088
0087
0086
0092
0091
0090
0089
0087
0094
0093
0091
0090
0089
0096
0094
0093
0092
0091
0090
0087
0085
0083
0081
0079
0077
0075
0073
0071
0099
0098
0096
0095
0094
0101
0099
0098
0097
0096
18 0
20
40
19 0
20
0080
0078
0076
0074
0072
0082 0083
0079 0081
0077 0079
0075 0077
0073 ; 0075
0085
0083
0080
0078
0076
0086 0088
0084 0086
0082 0083
0080 0081
0078 0079
0091
0089
0087
0084
0082
0093
0090
0088
0086
0084
0094
0092
0090
0087
0085
0083
0081
0079
0077
0075
0093
0091
0089
0086
40
20 0
20
40
21 0
0070
0068
0067
0065
0063
0072
0070
0068
0066
0065
0073
0071
0069
0068
0066
0074
0073
0071
0069
0067
0076 0077
0074 0075
0072 0073
0070 0072
0068 0070
0080
0078
0076
0074
0072
0081
0079
0077
0075
0074
0084
0082
0080
0078
0076
0074
0072
0070
0069
0067
0065
0064
0062
0060
0059
20
40
22 0
20
40
0062 0063
0060 0061
0059 0060
0057 0058
0056 0057
0064
0063
0061
0059
0058
0065
0064
0062
0061
0059
0067
0065
0063
0062
0060
0068
0066
0065
0063
0061
0060
0058
0057
0055
0054
0069
0067
0066
0064
0062
0061
0059
0058
0056
0055
0070
0069
0067
0065
0064
"0062
0060
0059
0057
0056
0072
0070
0068
0066
0065
0073
0071
0069
0068
0066
0064
0063
0061
0059
0058
23 0
20
40
24 0
20
0054
0053
0052
0050
0055
0054
0053
0051
0050
0057
0055
0054
0052
0051
0058
0056
0055
0053
0052
0059
0057
0056
0054
0053
0063
0061
0060
0058
0057
40
25 0
20
40
26 0
0049
0047
0046
0045
0044
0050
0048
0047
0046
0045
0051
0049
0048
0047
0046
0044
0043
0042
0041
0040
0039
0052
0050
0049
0048
0046
0045
0044
0043
0042
0040 .
0039
0053
0051
0050
0049
0047
0046
0045
0044
0042
0041
0040
0053
0052
0051
0049
0048
0054
0053
0052
0050
0049
0055
0054
0053
0051
0050
0048
0047
0046
0045
0043
0042;
0056
0055
0053
0052
0051
0049
0048
0047
0045
0044
0043'
0057
0056
0054
0053
0052
0"05"0
0049
0047
0046
0045
0044
20
40
27 0
20
40
0043
0041
0040
0039
0038
0043
0042
0041
0040
0039
0047
0046
0044
0043
0042
0048
0046
0045
0044
0043
0042'
28 0
0037 0038
0041
APPENDIX V: TABLE V. [Page 307
Log. D, for computing tiie First Correction of the Lunar Distance.
App
alt. of
moon.
Reduced parallax and refraction of moon. 1
50'
51' 1 52'
58'
54'
55' 1 56'
67' I 58'
59'
60'
28° 0^
0. 0037
0. 0038
0. 0039
0. 0039
0. 0040
0. 0041 0. 0042
0. 0042 0. 0043
0.0044
30
0. 0036
0. 0036
0. 0037
0. 0038
0. 0038
0. 0039 0. 0040
0. 0040 1 0. 0041
0. 0042
29 0
0. 0034
0. 0035
0. 0035
0. 0036
0. 0037
0.0037 0.0038
0. 0039 1 0. 0039
0. 0040
30
0. 0033
0. 0033
0.0034
0. 0035
0. 0035
0. 0036 0. 0036
0. 0837 0. 0038
0. 0038
30 0
30
0. 0031
0. 0030
0. 0032
0. 0030
0. 0032
0. 0031
0. 0033
0. 0031
0. 0034
0. 0032
0. 0034 0. 0035
0. 0033 1 0. 0033
0.0035 0.0036
a 6034 0.0034
0. 0037
"0.0035
31 0
0. 0028
0. 0029
0. 0029
0. 0030
0. 0031
0. 0031 0. 0032
0. 0032 0. 0033
0. 0033
30
0. 0027
0. 0028
0. 0028
0. 0029
0. 0029
0. 0030 0. 0030
0. 0031 0. 0031
0. 0032
0. 0032
32 0
0. 0026
0. 0026
0. 0027
0. 0027 1 0. 0028
0. 0028 i 0. 0029
0. 0029 1 0. 0030
0. 0030
0. 0031
30
0. 0024
0. 0025
0. 0024
0. 0025
0. 0026
0. 002(i
0. 0027 0. 0027
0. 0025 0. 0026
0. 0028 1 0. 0028
0. 0026 ! 0. 0027
0. 0029 0. 0029
0.0027 0.0028
33 0
0. 0023
0. 0024
0. 0025
0. 0025
30
0. 0022
0. 0022
0. 0023
0. 0023
0. 0024
0. 0024 0. 0025
0. 0025 ! 0. 0025
0.0026 0.0026
34 0
0. 0021
0. 0021
0. 0022
0. 0022
0. 0022
0. 0023 0. 0023
0. 0024
0. 0024
0.0024 0.0025
30
0. 0020
0. 0020
0. 0020
0. 0021
0. 0021
0. 0022 0. 0022
0. 0022
0. 0023
0.0023 0.0023
35 0
0.0018
0. 0019
0. 0019
0. 0020
0.0018
0. 0020
0. 0019
0. 0020
0. 0019
0. 0021
0.0019
0.0021
"0. 0020
0. 0021
0. 0020
0.0022 0.0022
0.0020 0.0021
30
0. 0017
0. 0018
0. 0018
3(5 0
0. 0016
0.0017
0.0017
0.0017
0. 0018
0. 0018
0. 0018
0.0019
0. 0019
0.0019 0.0019
30
0.0015
0.0016 0.0016
0.0016
0. 0016
0. 0017
0. 0017
0. 0017
0.0018
0.0018 0.0018
37 0
0. 0014
0.0014
0.0015
0. 0015
0. 0015
0. 0016
0. 0016
0. 0016
0. 0016
0.0017 0.0017
30
0. 0013
0. 0013
0.0012
0.0014
0. 0013
0.0014
0. 0014
0.0013
0. 0014
0. 0013
0.0015
0. 0014
0. 0015
6. 0014
0. 0015
0. 0014
0.0015 0.0016
0.0014 0.0014
38 0
0. 0012
0. 0013
30
0.0011
0.0011
0. 0012
0.0012
0.0012
0. 0012
0. 0012
0. 0013
0. 0013
0. 0013 0. 0013
39 0
0. 0010
0. 0010
0. 0011
0. 0011
0. 0011
0. 0011
0.0011
0.0012
0.0012
0.0012 0.0012
30
0.0009
0. 0010
0.0010
0. 0010
0. 0010
0. 0010
0.0010
0.0011
0.0011 0.0011
40
0.0008
0.0009
0. 0009
0. 0009
0. 0007
0. 0009
0. 0007
0. 0009
0. 0007
0. 0009
0. 0010
070607
0. 0010
0. 0008
0. 0010
41
0.0007
0.0007
0. 0007
0. 0007
0. 0008 1 1
42
0. 0005
0. 0005
0. 0005
0. 0005
0. 0005
0. 0005
0. 0005
0. 0005
0. 0005 ' 0. 0006
43
0. 0003
0. 0003
0. 0003
0. 0003
0. 0003
0. 0003
0. 0003
0. 0003
0.0003 0.0004
44
0.0001
0.0001
0.0001
0. 0001
0. 0001
0. 0001
0. 0002
0. 0002
0.0002 0.0002
45
0.0000
9. 9998
0.0000
0. 0000
0. 0000
9. 9998
0. 0000
9. 9998
0.0000
9. 9998
0. 0000
9. 9998
0.0000
0. 0000 0. 0000
46
9. 9998
9. 9998
9. 9998 9. 9998 I 9. 9998
47
9. 9997
9. 9997
9. 9997
9. 9997
9. 9996
9. 9996
9. 9996
9. 9996 i 9. 9996 9. 9996
48
9. 9995
9. 9995
9. 9995
9. 9995
9. 9995
9. 9995
9. 9995
9. 9995 9. 9994 . 9. 9994
49.
9. 9994
9. 9994
9. 9994
9. 9993
9. 9993
9. 9993
9. 9993
9. 9993 I 9. 9993 1 9. 9993
50
9. 9992
9. 9992
9. 9992
9. 9991
9. 9992
979991
9. 9992
9. 9992
9. 9992
9. 9990
9. 9991 i 9. 9991 9. 9991
9. 9990 9. 9990 i 9. 9990 1
51
9. 9991 9. 9991
9. 9990 9. 9990
52
9. 9990 9. 9990
9. 9990
9. 9989
9.9989 9.9989
9. 9989
9. 9989 9. 9988 i 9. 9988
53
9. 9989 9. 9988
9. 9988
9. 9988
9.9988 9.9988
9. 9987
9. 9987 9. 9987
9. 9987
54
9. 9988
9. 9987
9. 9987
9. 9987
9. 9987
9. 9986
9. 9986
9. 9986 9. 9986
9. 9985
55
9. 9986
9. 9986
9. 9986
9. 9986
9. 9984"
9. 9985
9. 9984
9. 9985
9. 9984
9. 9985
9. 9984
9. 9984 9. 9984
9. 9983 9. 9983
9. 9984
9. 9983 1
56
9. 9985
9. 9985
9. 9985
57
9. 9984
9. 9984
9. 9984
9. 9983
9. 9983
9. 9983
9. 9982
9. 9982 9. 9982
9. 9981 '
58
9. 9983
9. 9983
9. 9983
9. 9982
9. 9982
9. 9982
9. 9981
9. 9981 9. 9981
9. 9980
59
9. 9982
9. 9982
9.9981
9.9981
9. 9981
9. 9980
9. 9980
9. 9980 9. 9979
9. 9979
60
9. 9981
9. 9981
9. 9980
9. 9980
9.9979
9. 9980
9. 9979
9. 9979
9. 9979
9.9978
9. 9979
9. 9978
9. 9978
9. 9977
9. 9978 1
9. 9977
61
9. 9980
9. 9980
9. 9980
9. 9978
62
9. 9979
9. 9979
9. 9979
9. 9978
9. 9978
9. 9977
9. 9977
9. 9977
9. 9976
9. 9976
63
9.9979
9. 9978
9. 9978
9. 9977
9. 9977
9. 9976
9. 9976
9. 9976
9. 9975
9. 9975
64
9. 9978
9. 9977
9. 9977
9. 9976
9: 9976
9. 9976
9. 9975
9. 9975
9. 9974
9. 9974
65
9. 9977
9. 9976
9. 9977
9.9976
9. 9976
9. 9975
9. 9976
9. 9975
9. 9975
9. 9974
9. 9975
9.9974
9. 9974
9.9974 9.9973
9. 9972
66
9. 9973
9. 9973
9. 9973
9. 9972
67
9. 9976
9. 9975
9. 9975
9. 9974
9. 9974
9. 9973
9. 9973
9. 9972
9. 9972
9. 9971
68
9. 9975
9. 9974
9. 9974
9. 9973
9.9973 9.9972
9. 9972
9. 9971
9. 9971
9. 9970 1
69
9. 9974
9. 9974
9. 9973
9. 9973
9. 9972
9. 9972
9. 9971
9. 9971
9. 9970
9. 9970
70
72
9. 9974
9. 9973
9. 9972
9. 9973
9. 9971
9. 9972
9. 9971'
9. 9972
9. 9970
9. 9971
9. 9970
9. 9970
9. 9969
9. 9970
9. 9969
9. 9969
9. 9968
9. 9972
9. 9969 9. 9968
74
9. 9971
9. 9971
9. 9970
9. 9970
9. 9969
9. 9969
9. 9968
9. 9968 ' 9. 9967
9. 9966
76
9. 9971
9. 9970
9. 9969
9. 9969
9. 9968
9. 9968
9. 9967
9. 9966 ; 9. 9966
9. 9965
78
9. 9970
9. 9969
9. 9969
9. 9968
9. 9967
9. 9967
9. 9966
9. 9966 9. 9965
9. 9964
80
9. 9969
9. 9969
9. 9968
9. 9967
9. 9967 { 9. 9966
9. 9965
9. 9964
9. 9965 9. 9964
9. 9964
9. 9962
90
9. 9968
9. 9967
9.9966 9.9966
9. 9965
9. 9964
9. 9963
9. 9963
Page 308J
APPENDIX V:
lABLE
VI.
Second Correction of the Lunar Distance.
Appar-
ent dis-
tance.
First correction of distance.
Appar-
3'
V
10
12'
14'
16'
18' 20'
21'
22'
28'
24'
26'
26'
27'
28'
ent dis-
tance.
Sub.
II
II
II
II
//
II
// II
II
It
II
//
II
II
II
II
Add.
15° (y
0
2
3
5
6
8
11 13
14
16 i 17
19
20
22
24
26
30
0
2
3
0
6
8
10 13
14
15 1 17
18
20
21
23
25
16 0
0
3
\
6
8
10 i 12
13
15
16
18
19
21
22
24
30
0
3
6
8
10 12
13
14
16
17
18
20
21
23
17 0
0
0
3
3
4
4
6
5
7
9 11
13
14
15
16
18
19
21
22
30
7
9 11
12
13
15
16
17
19
20
22
18 0
0
3
4
5
7
9 11
12
13
14
15
17
18
20
21
30
0
3
4
5
7
8 , 10
12
13
14
15
16
18
19
20
19 0
0
3
4
5
6
8
10
11
12
13
15
16
17
18
20
30
0
2
4
5
5
6
6
8
10
11
12
13
14
15
17
18
17-
19
19
20 0
0
2
3
8
10
11
12
13
14
15
16
21
0
2
3
4
6
7
9
10
11
12
13
14
15
17
18
22
0.
2
3
4
6
7
9
10
10
11
12
14
15
16
17
23
0
2
3
4
5
7
8
9
10
11
12
13
14
15
16
24
0
2
2
3
3
4
4
5
5
6
8
9
9
10
U
12
13
14
15
15
25
0
6
7
8
9
10
11
12
13
14
26
0
2
3
4
5
6 1 7
8
9
9
10
11
12
13
14
27
0
2
2
3
4
6 7
8
8
9
10
11
12
12
13
28
0
2
2
3
4
5 7
<
8
9
9
10
11
12
13
29
0
"
2
2
2
2
3
3
4
5
6
7
8
8
9
10
11
11
12
30
0
4
5
6
1
7
8
9
9
10
11
12
31
0
2
3
4
5
6
6
7
8
8
9
10
11
11
32
0
2
3
4
5
6
6
7
7
8
9
9
10
11
33
0
2
3
3
4
5
6
7
7
8
8
9
10
11
34
0
— j-
2
2
3
3
4
5
6
6
7
"■
8
9
9
10
35
0
2
3
4 ; 5
5
6
7
7
8
8
9
10
36
0
2
2
3
4 5
5
6
6
(
8
8
9
9
37
0
2
2
3
4
5
5
6
6
/
7
8
8
9
38
0
2
2
3
4
4
5
5
6
6
/
8
8
9
39
Oj 1
2
2
2
2
3
3
4
5
5
6
6
6
7
7
7
7
8
8
8
"140°"
40
0
1
2
3
3
4
5
5
6
8
42
0
0
2
2
3
4
4
5
5
6
6
7
/
8
138
44
0
0
1
2
2
3
4
4
4
5
5
6
6
7
7
136
46
0
0
2
2
3
3
4
4
4
5
5
6
6
7
134
48
50
0
6
0
0
~1
2
2
3
3
3
4
4
5
5
5
6
6
132
"130
2
2
3
3
4
4
4
5
5
5
6
52
0
0
2
2
3
3
3
4
4
4
5
5
5
128
54
0
0
1
2
2
3
3
3
3
4
4
4
5
5
126
56
0
0
2
2
2
3
3
3
3
4
4
4
5
124
58
0
0
0
0
2
2
2
3
3
3
3
4
4
4
122
120
60
0
2
2
2
2
3
3
3
3
4
4
62
0 0
0
2
2 2
2
2
3
3
3
3
4
118
64
0 0
0
2 i . 2
2
2
2
3
3
3
3
116
66
0 0
0
2 1 2
2
2
2
2
3
3
3
114
68
0
0
0
0
0
0
— j-
1 i 2
2
2
2
2
2
2
3
3
112
70
0
1 1 i 1
2
2
2
2
2
2
110
74
0 1 0
0
0
0
1 1
1
1
1
2
2
2
2
106
78
0 0
0
0
0
0
1 1
1
1
1
1
1
1
1
102
82
0 0
0
0
0
0
0
0 ! 1
1
1
1
1
1
1
1
98
86
0
0
0
0
7'
0
0
10'
0
0
12'
0
0
0
0
0
0
0
0
0
0
0
0
94
90
0
0
0
0
0
0
'0
0
0
0
0
0
90
Appar-
ent dis-
tance.
3'
14'
16'
18'
20'
21'
22'
28'
24'
25'
26'
27'
28'
Appar-
ent dis-
tan<'c.
First correction ol
distance.
APPENDIX V: TABLE VI. [Page 309
Second Correction of the Lxinar Distance.
Appar-
ent dis-
tance.
First correction of distance.
Appar-
ent dis-
tance.
29'
80'
81'
II
31
30
29
28
27
27"
26
25
24
24
23
22
21
20
19
18
17
16
16
15
14
14
13
13
12
82'
II
33
32
31
30
29
28
28
27
26
25
25
23
22
21
20
19
18
18
17
16
15
15
14
14
13
88'
84'
85'
86'
37'
88'
89'
40'
41'
42'
48'
44'
Sub.
15° 0'
30
16 0
30
17 0
27
26
26
25
24
'23
23
22
21
21
20
19
18
17
16
16
15
14
14
13
13
12
12
11
11
29
28
27
27
26
25'
24
23
23
22
22
20
19
19
18
17'
16
15
15
14
14
13
13
12
12
II
35
34
33
32
31
30
29
28
28
27
II
38
36
35
34
33
32
31
30
29
28
II
40
39
37
36
35
34
33
32
31
30
II
42
41
39
38
37
II
45
43
42
40
39
II
47
45
44
43
41
II
50
48
46
45
43
II
52
50
49
47
46
II
55
53
51
50
48
II
57
56
54
52
50
II
60
58
56
54
53
63
61
59
57
55
Add.
30
18 0
30
19 0
30
36
35
34
33
32
38
37
36
35
34
40
39
38
37
36
42
41
40
39
37
36
35
33
31
30
44
43
42
41
39
38'
36
35
33
31
47
45
44
43
41
49
47
46
45
43
51
50
48
47
46
54
52
50
49
48
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
26
25
24
22
21
20
19
19
18
17
16
16
15
15
14
28
26
25
24
23
29
28
26
25
24
31
29
28
27
25
24
23
22
21
20
33
31
30
28
27
35
33
31
30
28
40
38
36
35
33
42
40
38
36
35
44
42
40
38
36
46
44
42
40
38
22
21
20
19
18
23
22
21
20
19
26
25
23
22
22
27
26
25
24
23
28
27
26
25
24
30
29
27
26
25
24
23
22
22
21
31
30
29
28
26
33
32
30
29
28
35
33
32
30
29
36
35
33
32
30
17
17
16
16
15
19
18
17
16
16
20
19
18
17
17
21
20
19
18
18
22
21
20
19
19
23
22
21
20
20
25
24
23
23
22
27
26
25
24
23
28
27
26
25
24
29
28
27
26
25
35
36
37
38
39
10
10
10
9
9
9
8
8
7
7
6
6
5
5
5
4
4
4
3
3
3
2
2
i
1
11
11
10
10
10
9
9
8
8
7
7
6
6
5
5
5
4
4
4
3
3
2
2
1
1
0
12
12
11
11
10
10
9
9
8
8
7
7
6
6
5
13
12
12
11
11
11
10
9
9
8
8
7
6
6
6
14
13
13
12
12
14
14
13
13
12
15
15
14
14
13
16
16
15
14
14
17
16
■ 16
15
15
18
17
17
16
16
19
18
18
17
16
20
19
19
18
17
21
20
19
19
18
22
21
20
20
19
23
22
21
.21
20
24
23
22
22
21
140°
138
136
134
, 132
40
42
4-f
46
48
11
11
10
9
9
8
7
7
6
6
12
11
10
10
9
13
12
11
10
10
13
13
12
11
10
14
13
12
12
11
15
14
13
12
11
16
15
14
13
12
17
16
14
13
13
17
16
15
14
13
18
17
16
15
14
19
18
17
16
15
-20
19
17
16
15
50
52
54
56
58
60
62
64
66
68
70
74
78
82
86
8
8
7.
7
6
9
8
8
7
7
9
9
8
8
7
10
9
9
8
7
11
10
9
9
8
11
10
10
9
8
10
9
9
12
11
11
10
9
13
12
11
10
10
14 1 14
13 13
12 12
11 11
10 11
130
128
126
124
122
5
4
4
4
3
5
5
4
4
4
5
5
5
\
6
6
5
4
4
6
6
5
5
4
7
6
6
5
5
6
6
5
5
7
7
6
6
5
8 i 8
7 1 7
6 7
6 6
5 6
8
8
7
7
6
9
8
8
7
6
9
9
8
7
7
10
9
8
8
7
120
118
116
114
112
3
2
2
1
1
3
3
2
1
1
3
3
2
1
1
4
3
2
1
1
4
3
2
2
1
4
3
2
2
1
4
3
3
9
5
4
3
2
1
5
4
3
2
1
5
4
3
2
1
5
4
3
2
1
6
4
3
2
1
6
5
3
2
1
6
5
4
2
1
0
110
106
102
98
94
90°
0
0
0
0
0
0
0
0
0
0
0
0
0
0
90°
Appar-
ent dis-
tance.
29'
30
81'
82'
33'
84'
86'
86'
87'
38'
89'
40'
41'
42'
48'
44'
Appar-
ent dis-
tance.
First correction of distance.
Page 310]
APPENDIX V: TABLP: YI.
Second Correction of the Lunar Distance
Appar-
ent dis-
tance.
First correction of distance.
Appar-
ent dis-
tance.
45'
46'
47' 1 48'
49'
50'
51'
52'
68'
64'
55'
56'
57'
68'
69'
60'
Sub.
15° 0'
66
II
69
//
72
II
75
78
II
81
II
85
II
88
91
II
95
99
II
102
II
106
110
113
II
117
Add.
30
64
67
70
72
76
79
82
85
88
92
95
99
102
106
110
113
16 0
62
64
67 L 70
65 '68
73
76
79
82
85
89
92
95
99
102
106
110
30
60
62
71
74
77
80
83
86
89
92
96
99
103
106
17 0
58 ! 60
56 59
63
61
66
69
71
69
74
77
80
83
86
90
93
96
99
103
100
30
64
66
72
75
78
81
84
87
90
93
96
18 0
54 57
59 1 62
64
67
70
73
75
78
81
84
87
90
94
97
30
53 55
58 ; 60
63
65
68
71
73
76
79
82
85
88
91
94
19 0
51 54
56 1 58
61
63
66
69
71
74
77
79
82
85
88
91
30
50 , 52
49 51
54 57
53 55
59
62
64
62
67
65
69
72
75
77
80
83
86
83
89
86
20
58
60
67
70
73
75
78
81
21
46 48
50 52
55
57
59
61
64
66
69
71
74
76
79
82
22
44 ; 46
48 j 50
52
54
56
58
61
63
65
68
70
73
75
78
23
42 44
45
47
49
51
53
56
58
60
62
64
67
69
72
74
24
40 41
38 40
43
41
45
43
47
45^
49
47
51
49
53
55
57
59
61
59
64
61
66
63
68
65
71
67
25
51
53
55
57
26
36 38
40
41
43
45
47
48
50
52
54
56
58
60
62
64
27
35 36
38
39
41
43
45
46
48
50
52
54
56
58
60
62
28
33 35
36 j 38
39
41
43
44
46
48
50
51
53
55
57
59
29
32 33
31 32
35 36
33 i 35
38
39
41
43
44 1 46
48
49
51
53
55
53
57
30
36
38
39
41
42 44
46
47
49
51
54
31
29 31
32 ' 33
35
36
38
39
41 42
44
46
47
49
51
52
32
28 30
31 1 32
34
35
36
38
39 1 41
42
44
45
47
49
50
33
27 28
30 31
32
34
35
36
38
39
41
42
44
45
47
48
34
26
27
26
29 1 30
28 29
31
30
32
34
35
36
38
39
41
42
44
45
43
47
45
35
25
31
32
34
35
36
38
39
40
42
36
24 25
27 28
29
30
31
32
34 35
36
38
39
40
42
43
37
23 25
26 27
28
29
30
31
33
34
35
36
38
39
40
42
38
23 24
25
26
27
28
29
30
31
33
34
35
36
38
39
40
39
22 1 23
24
25
26
27
26
28
29
30
31
33
34
35
36
38
39
37
40
21 22
23
24
25
27
28
29
30
31
33
34
35
36
140°
42
20 21
21
22
23
24
25
26
27
28
29
30
31
33
34
35
138
44
18
19
20
21
22
23
24
24
25 26
27
28
29
30
31
33
136
46
17
18
19
19
20
21
22
23
24
25
26
26
27
28
29
30
134
48
16
15
17
16
17
16
18
17
19
20
20
21
22
23
24
25
26
26
27
28
132
50 '
18
18
19
20
21
21
22
23
24
25
25
26
130
52
14
14
15
16
16
17
18
18
19
20
21
21
22
23
24
25
128
54
13
13
14
15
15
16
16
17
18
18
19
20
21
21
22
23
126
56
12
12
13
14
14
15
15
16
17
17
18
18
19
20
20
21
124
58
11
10
12
11
12
11
13
12
13
14
14
15
15
16
16
17
18
18
19
20
122
60
12
13
13
14
14
15
15
16
16
17
18
18
120
62
9
10
10
11
11
12
12
13
13
14
14
15
15
16
16
17
118
64
9
9
9
10
10
11
11
12
12
12
13
13
14
14
15
15
116
66
8
8
9
9
9
10
10
11
11
11
12
12
13
13
14
14
114
68
7
. 6
7
7
8
8
8
9
9
10
10
10
9
11
11
11
12
12
13
112
70
7
7
8
8
8
9
9
10
10
10
11
11
11
110
74
5
5
6
6
6
6
7
7
7
• 7
8
8
8
8
9
9
106
78
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
7
102
82
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
98
86
1
0
45'
1
0
46'
1
1
1
2
2
2
2
2
2
2
2
2
2
2
94
90°
90°
Appar-
ent dis-
tance.
0
47'
0
0
0
0
0
0
0
0
0
0
0
0
0
48'
49'
50'
61'
62'
68'
64'
65'
56'
57'
68'
59'
60'
Appar-
ent dis-
tance.
First
correc
tion of distan
ce.
APPENDIX V: TABLE VII.
[Page 311
For finding the Correction of the Lunar Distance for the Contraction of the Moon
'9 Semidiameter. 1
TABLE VII A.— GIVING THE ARGUMENT FOR TABLE VII B.
Red.
P. and
R. of
moon.
Apparent altitude of moon.
6°
5i°
6°
64°
7°
7i° 8=
8i'
9°
|9ic
ic
' 11<:
12
' 18'
» 14°| 15<=
10°
17°
18°
20°
25°
80°
40°
60°
iV
65
56
[
42
63
54
47
41
43
62
53
46
40
35
44
60
51
45
39
34
30
27
45
58
50
43
42
38
37
33
33
30
29
26
26
24
23
21
21
20
19
17
l5
1 1
0
46
57 149
47
56
48
41
36
32
28
25
23
20
19
17
14
12
10
48
54
46
40
35
31
28
25
22
20
;i8
17
14
12
10
9
8
7
6
49
53
45
39
35
30
27
24
22
19
18
16
14
12
10
9
8
7
6
6
5
3
50
52
44138
34
30
26
24
21
19
il7
16
13
11
10
9
8
7
6
5
5
3
3
2
51
50
43 38
33
29
26
23
21
19
17
15 13
11 10
8
7
7
6
5
5
3
2
2
2
52
49
42 37
32
28
25
23
20
18
17
15 13
11 9
8! 7
7
6
5
4
3
2
2
2
53
48
41:36
32
28
25
22
20
18
16
15 12
11
9
8- 7
6
6
5
4
3
2
2
2
54
47
41135
31
27
24
22
19
18
16
15 12
10
9
8; 7
6
6
5
4
3
2
2
2
55
35
30
27
26
24
23
21
21
19
19
17
17
16
15
14 12
10
10
9
9
81 7
6
6i
6
5
5
5
4
4
3
3
2
2
2
2
2
2
56
1
14
12
8
7
57
18
17
15
14
12
10
9
7
7
6
5
5
4
3
2
2
2
58
13111
10
8
7
7
6
5
5
4
3
2
2
2
59
8
7
6
6
5
5
4
3
2
2
2
60
1
\
4
3
2
2
2
1
AB
LE
VII B.— CONTRACTION OF MOON'S SEMI-DIAMETER.
<u O c
I'll
Argument, number from Table VII A.
"1
tj6
i
8 i
//
10
12
ir
16
II
18
II
20
22
II
24
II
26
II
28
II
SO
II
32
//
34!
i_
II
36
II
38
II
40
n
44
II
48
II
52
II
56
II
60 64
II 1 //
,
0
0 (
) 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
01
0
0! 0
• 5
0 (
) 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0 (
)'0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15
0 (
) 0
0
0
1
1
1
1
1
1
1
11
1
1
1
2
2
2
2
2
2
2
3
3
3
20
0 (
0 (
)!0
) 1
y
1
1 ■
1
1
1
1
1
2
1
2
2
2
2
2
2
2
2
3
2
3
2
3
3
3
3
3!
3
3
3
4
3
4
4
4
4
5
4
5
4
5
5
6
5
6
22
24
0 Oil
1
1
2
2
2
2
3
3
3
3
3
4
41
4
4
5
6
6
6
6
7
7
26
0
L 1
1
2
2
2
2
3
3
3
4
4
4
4
5!
5
5
5
6
6
7
8
8
9
28
0
I 1
2
2
2
3
3
3
3
4
4
4
5
5
5i
6
6
6
7
8
8
9
9
10
30
0
I 1
I 1
1 1
2
2
2
2
2
3
3
3
3
3
4
4
4
4
5
4
5
5
5
5
6
5
6
6
7
6
1 :
6
7
7
8
7
8
8
9
9
10
9
11
10
11
11
12
12
13
32
34
0
I 1
2
2
3
3
4
4
5
5
6
6
6
7
7
8
8
9
9
10
11
12
13
14
15
36
I 2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
12
13
15
16
17
38
1 2
21
3i
3
4
5
5
6
6
7
8
8
9
9
10
10
11
12
13
14
15
16
17
18
40
I 2
3
31
4
4
5
6
6
7
8
8
9
9
10
11
12
12
13
14
15
17
,18
19
20
42
I 2
3
41
4
5
6
6
7
8
8
9
10
11
11
12
13
13
14
16
17
18
20
21
23
44
2 2
3
4
5
5
6
7
8
9
9
10
11
12
12
13
14
15
15
17
19
20
22
23
45
2 2
3
4
5
6
6 7
8
9
10 11
11
12
13
14
15
15
16' 18
19
21
23
24
46
2 3
3
4i
5
6
7 7
8
9
10 11
12
13
14
14
15
16
17! 19
20
22
24
47
2 3
4
4
5
6
7
8
9
10
11 11
12
13
14
15
16
17
18 i 19
21
23
25
48
2 3
4
5
6
6
7
8
9
10
11 12
13
14
15
16
17
18
18
20
22
24
26
49
2 3
4
5!
6
7
8
9
10
11
12 12
13
14
15
16
17
18
19
21
23
25
-
50
2 3
4
5
6
7
8 9
10
11
12
13
14
15
16
17
18
19
20
22
24
26
51
2 3
4
5
6
7
8
9
10
11
12
1-1 i
15
16
17
18
19
20
21
23
25
27
52
2 3
4
5
6
8
9
10
11
12
13
14!
15
16
17
18
19
21
22
24
26
53
2 3
4
6
7
8
9
10
11
12
13
15
16
17
18
19
20
21
22
25
27
54
2 3
5
6
7
8
9
10
12
13
14
15
16
17
19
20
21
22
23
26
55
2 4
5
6
7
8
10
11
12
13
15
16
17
18
19
21
22
56
i 4
5
6
8
9
10
11
13
14
15
16
57
4
5
7
1
When the nearer limb is obser\-ed, suhstract this correction; when ihe farther, add.
Page 312j APPENDIX V: TABLE VIII.
For finding the Correction of the Lunar Distance for the Contraction of the Sun's Semidiameter.
TABLE VIII A.— GIVING THE ARGUMENT FOR TABLE VIII B.
Red. P.
and R.
of sun.
Apparent altitude of sun. 1
5° I 5i°
6°
6i°
JO
7i°
8°
8i°
»"
9*°
10°
11°
12°
18°
14°
15°
16°
17°
18°
20°
25°
80°
40°
50°
V (/'
30
2 0
30
3 0
30
4 0
30
5 0
30
55
59
62
66
69
73
51
55
59
50
54
58
62
49"
53
58
62
66
70
74
79
47
52
56
61
65
70
50
47
52
50
55
60
65
70
75
47
52
57
63
68
74
•
49
54
60
66
71
45
51
57
62
68
74
49
55
61
67
74
I5"
52
59
66
72
-
48
55
63
70
44
51"
59
66
74
46
54
62
70
40
49
57
65
42
51
60
68
35
44
•53
62
37
47
57
67
30
42
53
34
46
59
22
24
46
18
29
6 0
30
7 0
30
8 0
55; 57
59 62
64 67
69 72
73 77
30
9 0
30
10 0
30
63 66
66! 70
70I74
74 78
771
74 78
79
i
11 0
30
76
80
81
i
TABLE VIII B.— CONTRACTION OF SUN'S SEMIDIAMETER.
Whole
correction
of sun.
Argument, number from Table VIII A.
20
24
28
82
36
40
44 1 46 1 48 j 50 52
54
56
58 60
62
64
66
68
70
72
0
0
1
2
2
3
4
5
5
6
7
8
9
10
11
74
II
0
0
1
2
2
3
4
5
5
6
7
8
9
10
11
12
13
14
16
17
18
20
21
23
24
26
28
76
0
0
1
1
2
3
4
4
5
6
7
8
9
10
11
12
13
14
15
16
18
19
21
22
24
25
27
29
78
0
0
1
1
2
3
4
4
5
6
7
t
8
9
10
11
12
14
15
16
17
19
20
22
23
25
26
28
30
0 0
1 0
2 0
\ 30
3 0
0
1
0
1
0
1
2
0
1
2
0
1
2
3
0
0
2
3
4
// j />
01 0
0 0
2; 2
3! 2
4 4
•
ff ] It
Oi 0
0: 0
2! 1
2 2
3; 3
0
0
1
2
3
n
0
0
1
2
3
4
5
6
7
8
9
11
12
13
15
0
0
1
2
3
4
5
?
8
9
10
12
13
14
It
0
0
1
2
3
4
5
6
7
8
9
10
11
12
14
//
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
0
0
1
2
3
4
5
5
6
7
8
9
10
12
13
0
0
1
2
3
3
5
5
6
7
8
9
10
11
13
II
0
0
1
2
2
3
4
5
6
7
8
9
10
11
12
0
0
1
2
2
3
4
5
6
7
8
9
10
11
12
II
0
0
1
2
2
3
4
5
6
6
7
8
9
10
11
30
4 0
20
40
5 0
—
—
—
—
5
7
5
6
7
9
10
5 ; 4
6 6
7 7
8 8
9( 9
4
6
7
8
9
20
40
6 0
20
40
1
!
11
12
10 10
]2lll
13 12
14 14
16 15
7 0
20
40
8 0
20
1
1
1
18
17
19
16
18
20
21
16
17
19
21
15
17
18
20
22
15
16
18
19
21
14
16
17
19
20
22^
24
14
15
17
18
20
21
23
25
13
15
16
17
19
20
22
24
25
13
14
16
17
18
20
21
23
25
26
13
14
15
16
18
19
21
22
24
26
28
12
13
15
16
17
19
20
22
23
25
27
28
40
9 0
20
40
10 0
j
!
23
23
20
40
11 0
20
1
Subtract this correction from the distance.
APPENDIX V: TABLE IX.
[Page 313
Lo
garithms of Smal
Arcs in Space or Time.
Arc.
0"
1"
2"
3"
4"
5"
6"
7" i 8"
1
9"
O t II
0" 0™ 0'
0.0000
0. 3010
0. 4771
0. 6021
0.6990
0. 7782
0. 8451 0. 9031 0. 0542
0 10
1.0000
1.0414
1.0792
1.1139
1. 1461
1. 1761
1. 2041
1.2304 1.2553
1. 2788
0 20
1. 3010
1. 3222
1. 3424
1.3617
1. 3802
1. 3979
1.4150
1. 4314 1 1. 4472
1.4624
0 30
1.4771
1. 4914
1.5051
1.5185
1.5315
1. 5441
1. 5563
1.5682
1.5798
1.5911
0 40
1. 6021
1.6128
1.6232
1. 6335
1.6435
1.6532
1. 6628
1.6721
1.6812
1.6902
0 50
0 10
1.6990
1. 7782
1. 7076
1. 7853
1. 7160
1. 7243
1. 7324
1. 7404
1. 7482
1.8195
1. 7559
1. 8261
1. 7634
1.8325
1. 7709
1. 7924
1. 7993
1.8062 1 1.8129
1. 8388
1 10
1. 8451
1.8513
1. 8573
1. 8633
1.8692 1.8751
1.8808
1. 8865
1. 8921
1. 8976
1 20
1. 9031
1.9085
1.9138
1.9191
1.9243 1 1.9294
1. 9345
1. 9395 1. 9445
1.9494
1 30
1. 9542
1.9589
1.9638
1. 9685
1.9731 1.9777
1. 9823
1.9868 1 1.9912
1. 9956
1 40
2. 0000
2. 0043
2. 0086
2. 0128
2.0170 2.0212
2. 0253
2. 0294 ! 2. 0334
2. 0374
1 50
2. 0414
2. 0453
2. 0492
2. 0531
2. 0569 2. 0607
2.0645
2. 0682
2. 0719
2. 1072
2. 0755
0 2 0
2.0792 ! 2.0828
2. 0864
2. 0899
2.0934 2.0969
2.1004
2. 1038
2. 1106
2 10
2.1139 2.1173
2. 1206
2. 1239
2. 1271 2. 1303
2. 1,335
2. 1367 2. 1399
2. 1430
2 20
2. 1461 2. 1492
2. 1523
2. 1553
2.1584 2.1614
2. 1644
2. 1673 2. 1703
2. 1732
2 30
2.1761 2.1790
2. 1818
2. 1847
2. 1875 1 2. 1903
2. 1931
2. 1959 2. 1987
2. 2014
2 40
2.2041 2.2068
2. 2095
2.2122
2. 2148 2. 2175
2. 2201
2. 2227 2. 2253
2. 2279
2 50
2. 2304 2. 2330
2. 2.355
2. 2380
2. 2405 2. 2430
2. 2455
2. 2480 2. 2504
2. 2529
0 3 0
2. 2553
2. 2577
2. 2601
2. 2625
2. 2648 1 2. 2672
2. 2695
2. 2718 2. 2742
2. 2765
3 10
2. 2788
2. 2810
2. 2833
2. 2856
2. 2878 2. 2900
2. 2923
2. 2945 2. 2967
2. 2989
3 20
2. 3010
2. 3032
2. 3054
2. 3075
2. 3096 2. 3118
2. 3139
2.3160 2.3181
2. 3201
3 30
2. 3222
2. 3243
2. 3263
2. 3284
2.3304 2.3324
2. 3345
2. 3365 : 2. 3385
2. 3404
3 40
2. 3424
2. .3444
2. 3464
2. 3483
2.3502 ! 2.3522
2. 3541
2. 3560 5 2. 3579
2. 3598
3 50
0 4 0
2. 3617
2. 3636
2. 3655
2. 3674
2. 3692
2. 3874
2.3711
2. 3729
2. 3747
2. 3766
2. 3945
2. 3784
2. 3962
2. 3802
2. 3820
2. 3838
2. 3856
2. 3892
2. 3909
2. 3927
4 10
2. 3979
2. 3997
2. 4014
2. 4031
2. ':048 1 2.4065
2. 4082
2. 4099 2. 4116
2. 4a 33
4 20
2. 4150
2. 4166
2.4183
2. 4200
2.4216 ' 2.4232
2. 4249
2. 4265 2. 4281
2. 4298
4 30
2. 4314
2. 43.30
2. 4.346 2. 4362
2.4378 2.4393
2. 4409
2. 4425 2. 4440
2. 4456
4 40
2. 4472
2. 4487
2.4502 ' 2.4518
2.4533 2.4548
2. 4564
2. 4579 2. 4594
2. 4609
4 50
0 5 0
2. 4624
2. 4639
2.4654 i 2.4669
2.4683 2.4698
2.4713
2. 4728
2. 4742
2. 4886
2. 4757
2. 4900
2. 4771
2. 4786
2. 4800
2. 4814
2.4829 2.4843
2. 4857
2. 4871
5 10
2. 4914
2. 4928
2. 4942
2. 4955
2.4969 \ 2.4983 ' 2.4997
2.5011
2. 5024
2. 5038
5 20
2. 5051
2. 5065
2. 5079
2.5092
2.5105 2.5119 i 2.5132
2. 5145
2.5159
2.5172
5 30
2.5185 2.5198
2.5211
2. 5224
2. 5237 2. 5250
2. 5263
2. 5276
2. 5289
2. 5302
§ 40
2.5315 2.5328
2. 5340
2. 5353
2. 5366 2. 5378
2. 5391
2. 5403
2. 5416
2. 5428
5 50
2. 5441
2. 5453
2. 5575
2. 5465
2. 5587
2. 5478
2. 5599
2. 5490
2.5611
2. 5502
2. 5514
2. 5527
2. 5539
2.5551
0 6 0
2. 5563
2.5623 2.5635
2. 5(547
2. 5658
2. 5670
6 10
2.5682 1 2.5694
2. 5705
2.5717
2.5729 2.5740 2.5752
2. 5763
2. 5775
2. 5786
6 20
2.5798 ! 2.5809
2. 5821
2. 5832
2.5843 2.5855 i 2.5866
2. 5877
2. 5888
2. 5899
6 30
2.5911 2.5922
2. 5933
2. 5944
2. 5955
2. 5966
2. 5977
2. 5988 ! 2. 5999
2. 6010
6 40
2.6021 i 2.6031
2. 6042
2. 6053
2. 6064
2. 6075
2. 6085
2.6096 2.6107
2.6117
6 50
0 7 0
2. 6128
2. 6138
2. 6149
2.6160
2. 6170
2. 6180
2.6191
2.6201 2.6212
2. 6222
2. 6232
2. 6243
2. 6253
2. 6263
2. 6274
2.6284 1 2.6294
2. 6304 2. 6314
2. 6325
7 10
2.6335 I 2.6345
2. 6355
2. 6365
2. 6375
2.6385 2.6395
2. 6405 1 2. 6415
2. 6425
7 20
2.6435 i 2.6444
2. 6454
2. 6464
2. 6474
2.6484 2.6493
2. 6.503 1 2. 6513
2. 6522
7 30
2. 6532
2. 6542
2. 6551
2. 6561
2. a571
2.6580 2.6590
2. 6599 2. 6609
2. 6618
7 40
2. 6628
2. 6637
2.6646
2. 6656
2. 6665
2.6675 2.6684
2. 6693 2. 6702
2. 6712
7 50
0 8 0
2. 6721
2. 6812
2. 6730
2. 6821
2. 6739
2. 6830
2. 6749
2. 6758
2.6767 2.6776
2.6857 1 2.6866
2. 6785 1 2. 6794
2. 6803
2. 6839
2. 6848
2. 6875
2. 6884
2. 6893
8 10
2. 6902
2. 6911
2. 6920
2. 6928
2. 6937
2.6946 ! 2.6955
2. 6964
2. 6972
2. 6981
8 20
2. 6990
2. 6998
2. 7007
2. 7016
2. 7024
2. 7033 ! 2. 7042
2. 7050
2. 7059
2. 7067
8 30
2. 7076
2. 7084
2. 7093
2. 7101
2.7110
2.7118 1 2.7126
2. 7135
2. 7143
2. 7152
8 40
2.7160 1 2.7168
2.7177
2. 7185
2. 7193
2.7202 1 2.7210
2. 7218
2. 7226
2. 7235
8 50
2. 7243 2. 7251
2. 7259
2. 7267
2. 7275
2.7284 2.7292
2. 7300
2. 7308
2. 7316
0 9 0
2. 7324 2. 7332
2. 7340
2. 7348
2. 7356
2. 7364 2. 7372
2. 7380
2. 7388
2.7396
9 10
2. 7404 2. 7412
2. 7419
2. 7427
2. 7435
2.7443 2.7451
2. 7459
2. 7466
2. 7474
9 20
2. 7482 2. 7490
2. 7497
2. 7505
2. 7513
2.7520 2.7528
2. 7536
2. 7543
2. 7551
9 30
2. 7559 2. 7566
2. 7574
2. 7582
2. 7589
2.7597 2.7604
2. 7612
2. 7619
2. 7627
9 40
2.7634 1 2.7642
2. 7649
2. 7657
2. 7664
2. 7672 ! 2. 7679
2. 7686
2. 7694
2. 7701
9 50
2.7709 2.7716
2. 7723
2. 7731
2. 7738
2. 7745 1 2. 7752
2. 7760
2. 7767
2. 7774
Page 314]
APPENDIX V: TABLE IX.
\
Logarithms of Small Arcs in
Space or
Time.
Arc.
0"
1"
2"
8"
4"
6"
6"
7"
8"
9"
O '
0" 10°
n
' 0"
2. 7782
2. 7789
2. 7796
2.7803
2. 7810
2. 7818
2. 7825
2. 7832
2. 7839
2. 7846
10
10
2.7853
2. 7860
2. 7868
2.7875.
2. 7882
2. 7889
2. 7896
2. 7903
2. 7910
2. 7917
10
20
2. 7924
2. 7931
2. 7938
2. 7945
2. 7952
2. 7959
2. 7966
2. 7973
2. 7980
2. 7987
10
30
2. 7993
2.8000
2. 8007
2. 8014
2. 8021
2. 8028
2.8035
2. 8041
2.8048
2. 8055
10
40
2.80Q2
2. 8069
2. 8075
2. 8082
2. 8089
2.8096
2. 8102
2.8109
2. 8116
2. 8122
10
50
2. 8129
2. 8136
2. 8142
2. 8149
2. 8156
2. 8162
2. 8169
2. 8176
2.8241"
2. 8182
2. 8189
0 11
0
2. 8195
2. 8202
2. 8209
2. 8215
2. 8222
2. 8228
2. 8235
2. 8248
2. 8254
11
10
2. 8261
2. 8267
2. 8274
2. 8280
2. 8287
2. 8293
2.8299
2. 8306
2. 8312
2. 8319
11
20
2. 8325
2. 8331
2. 8338
2. 8344
2. 8351
2. 8357
2. 8363
2. 8370
2. 8376
2. 8382
11
30
2. 8388
2. 8395
2. 8401
2. 8407
2. 8414
2. 8420
2.8426
2. 8432
2. 8439
2.8445
11
40
2. 8451
2. 8457
2. 8463
2. 8470
2.8476
2. 8482
2. 8488
2. 8494
2.8500
2. 8506
11
50
2. 8513
2.8519
2. 8525
2. 8531
2. 8537
2. 8543
2. 8549
2. 8555
2. 8561
2. 8567
0 12
0
2. 8573
2. 8579
2.8585
2. 8591
2. 8597
2. 8603
2. 8609
2. 8615
! 2. 8621
2. 8627
12
10
2. 8633
2. 8639
2.8645
2. 8651
2. 8657
2. 8663
2. 8669
2. 8675
2. 8681
2. 8686
12
20
2. 8692
2. 8698
2.8704 2.8710
2. 8716
2. 8722
2. 8727
2. 8733
2. 8739
2. 8745
12
30
2. 8751
2. 8756
2. 8762
2. 8768
2. 8774
2. 8779
2. 8785
2. 8791
2. 8797
2. 8802
12
40
2. 8808
2. 8814
2. 8820
2. 8825
2. 8831
2. 8837
2. 8842
2.8848
2. 8854
2. 8859
12
50
2.8865
2. 8871
2.8876 1 2.8882
2. 8887
2. 8893
2.8899
2.8904
2. 8910
2. 8915
0 13
0
2. 8921
2. 8927
2. 8932
2. 8938
2. 8943
2. 8949
2. 8954
2. 8960
2. 8965
2. 8971
13
10
2. 8976
2. 8982
2. 8987
2. 8993
2. 8998
2.9004
2. 9009
2. 9015
2. 9020
2. 9025
13
20
2. 9031
2. 9036
2.9042
2. 9047
2. 9053
2. 9058
2.9063
2. 9069
2. 9074
2. 9079
13
30
2. 9085
2. 9090
2. 9096 2. 9101
2. 9106
2.9112
2.9117
2.9122
2. 9128
2. 9133
13
40
2. 9138
2. 9143
2. 9149 2. 9154
2. 9159
2. 9165
2. 9170
2. 9175
2. 9180
2. 9186
13
50
2. 9191
2. 9196
2.9201 2.9206 i 2.9212
2.9217
2. 9222
2. 9227
2. 9232 ! 2. 9238 |
0 14
0
2. 9243
2. 9248
2.9253 2.9258 ; 2.9263
2. 9269
2. 9274
2. 9279
2. 9284
2. 9289
14
10
2. 9294
2. 9299
2.9304 : 2.9309 2.9315
2. 9320
2. 9325
2. 9330
2. 9335
2. 9340
14
20
2. 9345
2. 9350
2. 9355
2.9360 ' 2.9365
2. 9370
2. 9375
2. 9380
2. 9385
2. 9390
14
30
2. 9.395
2. 9400
2. 9405
2.9410 2.9415
2. 9420
2. 9425
2. 9430
2.9435
2. 9440
14
40
2. 9445
2. 9450
2. 9455
2.9460 2.9465
2. 9469
2. 9474
2. 9479
2. 9484
2. 9489
14
50
2. 9494
2. 9499
2. 9504
2.9509 2.9513
2. 9518
2. 9523
2. 9528
2. 9533 ! 2. 9538
0 15
0
2. 9542
2. 9547
2. 9552
2.9557 j 2.9562
2. 9566
2. 9571
2. 9576
2. 9581 2. 9586
15
10
2. 9590
2. 9595
2.9600 1 2.9605 i 2.9609
2. 9614
2. 9619
2. 9624
2. 9628
2. 9633
15
20
2. 9638
2. 9643
2.9647 2.9652 1 2.9657
2. 9661
2. 9666
2. 9671
2. 9675
2. 9680
15
30
2. 9685
2. 9689
2.9694 2.9699 2.9703
2. 9708
2.9713
2.9717
2. 9722
2. 9727
15
40
2. 9731
2. 9736
2. 9741 2. 9745 2. 9750
2. 9754
2. 9759
2. 9763
2. 9768
2. 9773
15
50
2. 9777
2. 9823
2. 9782
2. 9786
2.9791 2.9795
2. 9800
2. 9805
2. 9809
2. 9814
2.9818
0 16
0
2. 9827
2. 9832
2.9836 2.9841
2. 9845
2. 9850
2. 9854
2. 9859
2. 9863
16
10
2. 9868
2. 9872
2. 9877
2.9881 2.9886
2. 9890
2. 9894
2. 9899
2. 9903
2. 9908
16
20
2. 9912
2. 9917
2. 9921
2.9926 2.9930
2. 9934
2. 9939
2. 9943
2. 9948
2. 9952
16
30
2. 9956
2. 9961
2. 9965
2.9969 2.9974
2. 9978
2. 9983
2. 9987
2. 9991
2. 9996
16
40
3. 0000
3.0004
3. 0009
3. 0013 3. 0017
3. 0022
3. 0026
3.0030
3. 0035
3.0039
16
50
3.0043
3.0048
3. 0052
3. 0056 3. 0060
3. 0065
3. 0069
3. 0073
3. 0077
3. 0082
0 17
0
3. 0086
3. 0090
3.0095
3. 0099 3. 0103
3. 0107
3.0111
3.0116
3.0120
3. 0124
17
10
3. 0128
3. 0133
3. 0137
3.0141 , 3.0145
3. 0149
3. 0154
3.0158
3. 0162
3. 0166
17
20
3. 0170
3. 0175
3. 0179
3.0183 1 3.0187
3. 0191
3. 0195
3. 0199
3. 0204
3. 0208
17
30
3. 0212
3. 0216
3. 0220
3. 0224 3. 0228
3. 0233
3. 0237
3. 0241
3. 0245
3. 0249
17
40
3. 0253
3. 0257
3. 0261
3.0265 i 3.0269
3. 0273
3. 0278
3. 0282
3. 0286
3. 0290
17
50
3. 0294
3. 0298
3. 0302
3. 0342
3. 0306
3. 0346
3. 0310
3. 0314
3. 0318
3. 0322
3. 0326
3. 0366
3. 0330
0 18
0
3. 0334
3. 0338
3. 0350
3. 0354
3. 0358
3. 0362
3. 0370
18
10
3. 0374
3. 0378
3. 0382
3.0386 i 3.0390
3. 0394
3. 0398
3. 0402
3. 0406
3.0410
18
20
3. 0414
3. 0418
3. 0422
3. 0426 3. 0430
3. 0434
3. 0438
3. 0441
3. 0445
3.0449
18
30
3. 0453
3. 0457
3. 0461
3. 0465
3. 0469
3. 0473
3. 0477
3. 0481
3. 0484
3. 0488
18
40
3. 0492
3. 0496
3. 0500
3.0504
3.0508
3. 0512
3. 0515
3. 0519
3. 0523
3. 0527
18
50
3. 0531
3. 0535
3. 0538
3. 0542
3. 0546
3. 0550
3. 0554
3. 0558 3. 0561
3. 0565
0 19
0
3. 0569
3. 0573
3. 0577
3. 0580
3. 0584
3. 0588
3. 0592
3.0596 3.0599
3. 0603
19
10
3. 0607
3. 0611
3. 0615
3. 0618
3. 0622
3. 0626
3. 0630
3. 0633
3. 0637
3. 0641
19
20
3. 0645
3. 0648
3. 0652
3. 0656 3. 0660
3. 0663
3. 0667
3. 0671
3.0674
3. 0678
19
30
3. 0682
3. 0686
3. 0689
3. 0693 3. 0697
3.0700
3. 0704
3. 0708
3. 0711
3. 0715
19
40
3.0719
3. 0722
3. 0726
3. 0730 3. 0734
3. 0737
3. 0741
3. 0745
3. 0748
3. 0752
19
50
3. 0755
3. 0759
3. 0763
3. 0766 3. 0770
3. 0774
3. 0777
3. 0781
3. 0785
3. 0788
APPENDIX V: TA.BLE IX.
[Page 315
Logarithms of Small Arcs in Space or
Time.
Arc.
0"
1"
2" 8"
4"
5"
6"
7"
8"
9"
O '
0" 20"
0'
3. 0792
3. 0795
3.0799 3.0803
3.0806
3. 0810
3. 0813
3. 0817
3. 0821
3. 0824
20
10
3. 0828
3. 0831
3.0835 3.0839
3.0842
3. 0846
3. 0849
3. 0853
3. 0856
3. 0860
20
20
3. 0864
3. 0867
3.0871 3.0874
3. 0878
3. 0881
3. 0885
3. 0888
3. 0892
3. 0896
20
30
3. 0899
3. 0903
3.0906 3.0910
3.0913 i 3.0917
3. 0920
3. 0924
3. 0927
3. 0931
20
40
3. 0934
3. 0938
3.0941 3.0945
3.0948 j 3.0952
3. 0955
3. 0959
3. 0962
3. 0966
20
50
3. 0969
3. 0973
3.0976 3.0980
3.0983 1 3.0986
3. 0990
3. 0993
3. 0997
3. 1000
0 21
0
3. 1004
3. 1007
3.1011 : 3.1014
3. 1017 3. 1021
3. 1024
3. 1028
3. 1031
3. 1035
21
10
3. 1038
3. 1041
3.1045 ' 3.1048
3. 1052 3. 1055
3. 1059
3. 1062
3. 1065
3. 1069
21
20
3. 1072
3. 1075
3. 1079 ■ 3. 1082
3. 1086 3. 1089
3. 1092
3. 1096
3. 1099
3. 1103
21
30
3. 1106
3.1109
3. 1113
3.1116
3. 1119 3. 1123
3. 1126
3. 1129
3. 1133
3. 1136
21
40
3. 1139
3. 1143
3. 1146
3. 1149
3. 1153 3. 1156
3.1159
3. 1163
3. 1166
3. 1169
21
50
3. 1173
3. 1176
3. 1179
3.1183
3. 1186 1 3. 1189
3. 1193 .
3.1196
3. 1199
3. 1202
0 22
0
3. 1206
3. 1209
3.1212
3. 1216
3. 1219 3. 1222
3. 1225
3. 1229
3. 1232
3. 1235
22
10
3. 1239
3.1242
3. 1245
3. 1248
3.1252 3.1255
3. 1258
3. 1261
3. 1265
3. 1268
22
20
3. 1271
3. 1274
3. 1278
3. 1281
3. 1284
3. 1287
3.1290
3. 1294
3. 1297
3.1300
22
30
3. 1303
3. 1307
3. 1310
3. 1313
3. 1316
3. 1319
3. 1323
3. 1326
3. 1329
3. 1332
22
40
3. 1335
3. 1339
3. 1342
3. 1345
3. 1348
3. 1351
3. 1355
3.1358
3. 1361
3. 1364
22
50
3. 1367
3. 1370
3. 1374
3. 1377
3.1380
3. 1383
3. 1.386
3. 1389
3. 1392
3. 1396
0 23
0
3. 1399
3. 1402
3. 1405
3. 1408
3. 1411
3.1414
3. 1418
3. 1421
3. 1424
3. 1427
23
10
3. 1430
3. 1433
3. 1436
3.1440
3. 1443
3. 1446
3. 1449
3. 1452
3. 1455
3. 1458
23
20
3. 1461
3.1464
3. 1467
3. 1471
3. 1474
3. 1477
3. 1480
3. 1483
3. 1486
3. 1489
23
30
3. 1492
3. 1495
3. 1498
3. 1501
3. 1504
3. 1508
3. 1511
3.1M4
3. 1517
3. 1520
23
40
3. 1523
3. 1526
3. 1529
3. 1532
3. 1535
3. 1538
3. 1541
3. 1544
3. 1547
3. 1550
2a
50
3. 1553
3. 1556
3. 1559
3. 1562 3. 1565
3. 1569
3. 1572
3. 1575
3.1578 3.1581
0 24
0
3. 1584
3. 1587
3. 1590
3.1593 3.1596
3. 1599
3. 1602
3. 1605
3. 1608 1 3. 1611
24
10
3. 1614
3.1617
3. 1620
3.1623 3.1626
3. 1629
3. 1632
3. 1635
3. 1638 3. 1641
24
20
3. 1644
3. 1647 i 3. 1649
3.1652 1 3.1655
3. 1658
3. 1661
3. 1664
3. 1667 ! 3. 1670
24
30
3. 1673
3.1676 3.1679
3. 1682 : 3. 1685
3. 1688
3. 1691
3. 1694
3. 1697 ! 3. 1700
24
40
3. 1703
3. 1706 i 3. 1708
3.1711 i 3.1714
3. 1717
3. 1720
3. 1723
3. 1726 ! 3. 1729
24
50
3. 1732
3.1735 3.1738
3. 1741
3. 1744
3. 1746
3. 1749
3. 1752
3. 17.55
3. 1758
0 25
0
3.1761
3. 1764 [ 3. 1767
3. 1770
3. 1772
3. 1775
3. 1778
3. 1781
3. 1784
3. 1787
25
10
3. 1790
3. 1793 I 3. 1796
3. 1798
3. 1801
3. 1804
3. 1807
3. 1810
3. 1813
3.1816
25
20
3. 1818
3.1821 i 3.1824
3. 1827
3. 1830
3. 1833
3. 1836
3. 1838
.3. 1841
3.1844
25
30
3. 1847
3. 1850 1 3. 1853
3. 1855
3. 1858
3. 1861
3.1864
3. 1867
3. 1870 1 3. 1872
25
40
3. 1875
3. 1878
3. 1881
3. 1884 3. 1886
3. 1889
3. 1892
3. 1895
3. 1898 i 3. 1901
25
50
3. 1903
3.1906
3. 1909
3. 1912 3. 1915
3.1917
3. 1920
3. 1923
3. 1926 ! 3. 1928
0 26
0
3. 1931
3. 1934
3. 1937
3.1940 3.1942
3.1945
3. 1948
3. 1951
3. 19.53 3. 1956
26
10
3. 1959
3. 1962
3. 1965
3.1967 3.1970
3. 1973
3. 1976
3. 1978
3. 1981
3. 1984
26
20
3. 1987
3. 1989
3. 1992
3.1995 3.1998
3. 2000
3. 2003
3. 2006
3. 2009
3. 2011
26
30
3. 2014
3. 2017
3. 2019
3.2022 3.2025
3. 2028
3. 2030
3. 2033
3. 2036
3. 2038
26
40
3. 2041
3.2044 1 3.2047
3.2049 3.2052
3. 2055
3. 2057
3. 2060
3. 2063
3. 2066
26
50
3. 2068
3.2071 3.2074
3.2076 ! 3.2079
3. 2082
3. 2084
3. 2087
3. 2090
3. 2092
0 27
0
3. 2095
3.2098 3.2101
3.2103 j 3.2106
3. 2109
3.2111
3. 2114
3.2117
3.2119
27
10
3. 2122
3.2125 ; 3.2127
3.2130 1 3.2133
3. 2135
3. 2138
3. 2140
3. 2143
3. 2146
27
20
3. 2148
3.2151 i 3.2154
3.2156
3.2159
3. 2162
3.2164
3. 2167
.3. 2170
3. 2172
27
30
3. 2175
3.2177 1 3.2180
3.2183
3. 2185
3. 2188
.3. 2191
3. 2193
3. 2196
3. 2198
. 27
40
3. 2201
3.2204 1 3.2206
3. 2209
3. 2212
3. 2214
3.2217
3. 2219
3. 2222
3. 2225
27
50
3. 2227
3. 2230
3. 2232
3. 2235
3. 2238
3.2240
3. 2243
3. 2269
3. 2245
3. 2248
3. 2250
0 28
0
3. 2253
3. 2256
3. 2258
3. 2261
3. 2263
3. 2266
3. 2271
3. 2274
3. 2276
28
10
3. 2279
3. 2281
3. 2284
3. 2287
3. 2289
3. 2292
3. 2294
3. 2297
3. 2299
3. 2302
28
20
3.2304
3. 2307
3. 2310
3. 2312
3. 2315
3.2317
3. 2320
3. 2322
3. 2325
3. 2327
28
30
3. 2330
3. 2333
3. 2335
3. 2338
3.2340
3. 2343
3. 2345
3. 2348
3. 23.50
3. 2353
28
40
3. 2355
3. 2358
3. 2360
3. 2363
3. 2365
3. 2368
3. 2370
3. 2373
3. 2375
3. 2378
28
50
3. 2380
3. 2383
3. 2385
3. 2388
3.2390 I .3.2393
3. 2395
3. 2398
3. 2400
3.2425
3. 2403
0 29
0
3. 2405
3. 2408
3. 2410
3. 2413
3.2415 1 3.2418
3. 2420
3. 2423
3. 2428
29
10
3. 2430
3. 2433
3.2435
3. 2438
3. 2440
3.2443
3. 2445
3. 2448
3. 2450
3. 2453
29
20
3. 2455
3. 2458
3.2460
3. 2463
3. 2465
3. 2467
3. 2470
3. 2472
3. 2475
3. 2477
29
30
3. 2480
3. 2482
3. 2485
3. 2487
3. 2490
3. 2492
3. 2494
3. 2497
3. 2499
3. 2502
29
40
3.2504
3. 2507
3. 2509
3. 2512
3. 2514
3. 2516
3. 2519
3. 2521
3. 2524
3. 2526
29
50
3. 2529
3. 2531
3. 2533
3. 2536
3. 2538
3. 2.541
3. 2.543
3. 2545
3.2548
3. 2550
Page
316J
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or Time.
Arc.
«"
1"
2"
8"
4"
5" 6"
7"
8" 1 a"
o /
0" 30™
II
0»
3.2553
3.2555
3.2558
3.2560
3. 2562
.3.2565 ' 3.2567
3. 2570
3. 2572 3. 2574
30
10
20
3. 2577
3. 2579
3. 2582
3. 2584
3. 2586
.3.2589 3.2591
3. 2594
3. 2,596 ' 3. 2598
30
3. 2601
3. 2603
3.2605
3. 2608
3. 2610
3.2613 1 3.2615
3.2617
3. 2620 3. 2622
30
30
3. 2625
3. 2627
3. 2629
3. 2632
3. 2634
3.2636 : 3.2639
3. 2641
3. 2643 3. 2646
30
40
3. 2648 <
3. 2651
3. 2653
3. 2655
3. 2658
3.2660 ; 3.2662
3. 2665
3. 2667 3. 2669
30
50
3. 2672
3. 2674
3. 2676
3. 2679
3. 2681
3.2683 ; 3.2686
3. 2688
3. 2690 1 3. 2693
0 31
0
3. 2695
3. 2697
3.2700
3.2702
3. 2704 j 3. 2707
3. 2709
3.2711
3.2714; 3.2716
31
10
3.2718
3. 2721
3. 2723
3. 2725
3. 2728 3. 27.30
3. 27.32
3. 2735
3. 2737 : 3. 2739
31
20
3. 2742
3. 2744
3. 2746
3. 2749
3.2751 3.2753
3. 2755
3. 2758
3. 2760
3. 2762
31
30
3. 2765
3. 2767
3. 2769
3. 2772
3.2774 3.2776
3. 2778
3. 2781
3. 2783
3. 2785
31
40
3. 2788
3. 2790
3. 2792
3. 2794
3.2797 i 3.2799
3. 2801
3. 2804
3. 2806
3. 2808
31
50
3. 2810
3. 2813
3.2835
3.2815 \ 3.2817
3.2838 ; 3.2840
3. 2819 1 3. 2822
3. 2824
3. 2826
3.2828 3.2831 |
0 32
0
3. 2833
3.2842 ' 3.2844
3. 2847
.3:2849
3. 2851
3. 2853
32
10
3. 2856
3. 2858
.3.2860 1 3.2862
3.2865 .3.2867 3.2869
3. 2871
3. 2874
3. 2876
32
20 3. 2878
3. 2880
3. 2882 3. 2885
3.2887 1 3.2889
3. 2891
3. 2894
3. 2896
3. 2898
32
30
3.2900
3. 2903
3. 2905 3. 2907
.3.2909 3.2911
3. 2914
3. 2916
3. 2918
3. 2920
32
40
3. 2923
3. 2925
3. 2927 3. 2929
3. 2931 3. 2934
3. 2936
3. 2938
3. 2940
3. 2942
32
50
3. 2945
3. 2947
3. 2949 3. 2951
3. 2953 3. 2956
3. 2958
3. 2960
3. 2982
3. 2962 \ 3. 2964 |
0 33
0
3. 2967"
3. 2969
3.2971 ! 3.2973
3.2975 i 3.2978
3. 2980
3.2984
3. 2986
33
10
3. 2989
3. 2991
3.2993 j 3.2995
3. 2997
3.2999 3.3002
3. 3004
3. 3006
3. 3008
33
20
3. 3010
3. 3012
3.3015 3.3017
3. 3019
3.3021 1 .3.3023
3. 3025
3. 3028
3. 30,30
33
30
3.3032
3. 3034
3.3036 ' 3.3038
3. 3041
3.3043 ' 3.3045
3. 3047
3. 3049
3. 3051
33
40
3. 3054
3. 3056
3.3058 3.3060
3. 3062
3.3064 3. .3066
3. 3069
3. 3071
3. 3073
33
50
3. 3075
3. 3077
3.3079 ' .3.3081
3. 3084
3.3086 3.3088
3. 3090
3.3092 3,3094 |
0 34
0
3. 3096
3. 3098
3.3101 3.3103
3. 3105
3.3107 3.3109
3.3111
3. 3113
3.3115
34
10
3. 3118
3. 3120
.3.3122 ! 3.3124
3.3126
3.3128 3.3130
3. 3132
3. 3134
3.3137
34
20
3. 3139
3. 3141
3.3143 1 3.3145
3. 3147
.3.3149 3.3151
.3.31,53
3. 3156
3. 31.58
34
30
3. 3160
3. 3162
.3.3164 j 3.3166
.3. 3168 •
3.3170 3.3172
3.3174
.3.3176
,3.3179
34
40
3.3181
3.3183
3.3185 ! 3.3187
3. 3189
3. .3191 ' 3.3193
3. 3195
3. 3197 ! .3. 3199
34
50
3. 3201
3. 3204
3.3206 i 3.3208
3. 3210
3. 3230
3. 3212
3. 3233
3. 3214
3. 3216
3. 3218 ! 3. 3220
0 35
0
3". 3222
3. 3224
3. 3226
3. 3228
3. 3235
3. 3237
3. .3239 ! 3. 3241
35
10
3. 3243
3. 3245
3. 3247
3. 3249
3. 3251
.3.3253 ' 3.3255
3. 3257
3. 32,59 3. 3261
35
20
3. 3263
3. 3265
3. 3267
3. 3269
3. 3272
3.3274 i 3.3276
3. 3278
3. 3280 3. 3282
35
30
3. 3284
3. 3286 ■
3. 3288
3. 3290
3. 3292
3.3294 3.3296
3. 3298
3. 3300 ! 3. 3302
35
40
3. 3304
3. 3306
3. 3308
3. 3310
3.3,312 3.3314 \ 3. .331 6
3. .3318
3. 3320 1 3. 3322
35
50
3. 3324
3. 3326
3. 3328
3. 3330
3. 3332
3.3334 : 3.3336
3.3355 3.3357'
3. 3339
3. 33,59
3.3.341 3. .3343
3. 3361 3. 3363
0 36
0
3. 3345
3. 3347
"3: 3349
3. 3351
3.3353'
36
10
3. 3365
3. 3367
3. 3.369
3. 3371
3. 3373
3. 3375 3. 3377
3. 3379
3. 3381 j 3. 3383
36
20
3. 3385
3. 3387
3. 3389
3. 3391
3. 3393
3.3.395 ! 3. .3397
3. .3398
3. 3400 : 3. 3402
36
30
3. 3404
3. 3406
3. 3408
3. 3410
3.3412 1 .3.3414 | 3.3416
3. 3418
3. 3420 I 3. 3422
36
40
3. 3424
3. 3426
3. 3428
3. 34.30
3.3432 3. .3434 .3.34.36
3. 3438
3. 3440 3. 3442
36
50
3. 3444
3. 3446
3.3448
3.3450 3.3452 ' 3.3454 ! 3.3456
3. 3458
3. 3460 ' 3. 3462
0 37
0
3. 3464
3. 3465
3.3467
3. 3469
3. .3471 ! 3.3473 3. .3475
3. 3477
3. 3479 3. 3481
37
10
3. 3483
3. 3485
3. 3487
3. 3489
3. 3491
3. 3493 3. 3495
3. M97
3. 3499 : 3. 3.501
37
20
3. 3502
3. 3504
3. 3506
3. 3508
3. 3510
3. ,3512 3. 3514
3. 3516
3. ,3518 1 3. 3.520
37
30
3. 3522
3. 3524
3. 3526
3. 3528
3. 35.30
.3.35.31 3.3.533
3. 3535
3. 3.537 1 3. 3.5.39
37
40
3. 3541
3. 3543
3. 3545
3. 3547
3. 3549
3. 3.551
3. 3553
3. ,3555
3. 3556
3. 3,558
37
50
3. 3560
3. 3562
3. 3564
3.3566
3. 3568
3. 3570
3. 3572
3. 3574
3. 3576
3. 3577
0 38
0
3. 3579
3.3581
3. 3583
3. 3585
3. 3587
3. .3589
3. 3591
3. 3593
3. 3595
3. 3596
38
10
3. 3598
3. 3600
3. 3602
3.3604
3. 3606
3. 3608
3. .3610
3. 3612
3. .3614
3. .3615
38
20
3. 3617
3.3619
3. 3621
3. 3623
3. .3625
3. ,3627
3. 3629
3. 3630
3. 3632
3. 3634
38
30
3. 3636
3. 3638
3. 3640
3. 3642
3. 3644
3. 3646
3. 3647
3. 3649
3. 3651
3. 3653
38
40
3. 3655
3. 3657
3. 3659
3. 3660
3. 3662
3. 3664
3. .3666
3. ,3668
3. .3670
3. 3672
38
50
3. 3674
3. 3675
3. 3677
3. 3679
3. 3681
3. 3683
3. ,3685
3. .3687
"3.:3705
3. 3688
3. 3690
0 39
0
3. 3692
3. 3694
3. 3696
3. 3698
3. 3700
3. 3701
3. 3703
3. 3707
3. 3709
39
10
3.3711
3. 3713
3. 3714
3. 3716
3. 3718
3. 3720
3. 3722
3. 3724
3. 3725
3. 3727
39
20
3. 3729
3. 3731
3. 3733
3. 37.35
3. 3736
3. 3738
3. 3740
3. 3742
3.3744
3. 3746
39
30
3. 3747
3.3749
3. 3751
3. 3753
3. 3755
3. 3757
3. 37.58
3. 3760
3. 3762
3. 3764
39
40
3. 3766
3. 3768
3. 3769
3. 3771
3. 3773
3. 3775
3. 3777
3. 3779
3. 3780
3. 3782
39
50
3. 3784
3. 3786
3. 3788
3. 3789
3. 3791
3. 3793
3. 3795
3. 3797
3. 3798 ■ 3. 3800 1
APPENDIX
V: TABLE IX.
[Page 317
Logarithms of Small Arcs in Space or Time.
Arc.
0"
1"
2"
8"
4"
5" ' 6"
7"
8" S"
c /
Qh 40.T
II
0»
3. 3802
3. 3804
3. 3806
3. 3808
3. 3809
3. 3811
3. 3813
3. 3815
j
3.3817^ 3.3818
40
10
3. 3820
3. 3822
3. 3824
3. 3826
3. 3827
3. 3829
3. 3831
3. 3833
3. 3835 1 3. 3836
40
20
3. 3838
3. 3840
3. 3842
3. 3844
3. 3845
3. 3847
3. 3849
3. 3851
3.3852 3.3854
40
30
3. 3856
3. 3858
3. 3860
3. 3861
3. .3863
3. 3865
3. 3867
3. 3869
3.3870 3.3872
40
40
3. 3874
3. 3876
3. 3877
3. 3879
3. 3881
3. 3883
3. 3885
3. 3886
3. 3888 1 3. 3890
40
50
3. 3892
3. 3893
3. 3895
3. 3897
3. 3899
3. 3901
3. 3902
3. 3904
3. 3906
3. 3908
0 41
0
3. 3909
3.3911
3. 3913
3. 3915
3. 3916
3.3918 3.3920
3. 3922
3. 3923
3. 3925
41
10
3. 3927
3. 3929
3. 3930
3. 3932
3. 3934
3.3936 3.3938
3. 3939
3. 3941
3. 3943
41
20
3. 3945
3. 3946
3. 3948
3. 3950
3. 3952
3.3953 3.3955
3. 3957 3. 3959
3. 3960
41
30
3. 3962
3. 3964
3. 3965
3. 3967
3. 3969
3. 3971
3. 3972
3. 3974
3. 3976
3. 3978
41
40
3. 3979
3. 3981
3. 3983
3. 3985
3. 3986
3. 3988
3. 3990
3. 3992
3. 3993
3. 3995
41
50
0
3. 3997
3. 4014
3. 3998
3. 4016
3.4000
3. 4017
3.4002
3. 4019
3. 4004
3. 4021
3. 4005
3. 4023
3. 4007
3. 4024
3. 4009
3.4011
3. 4028
3.4012
0 42
3. 4026
3. 4029
42
10
3. 4031
3. 4033
3. 4035
3.4036
3.4038
3. 4040
3. 4041
3. 4043
3. 4045 1 3. 4047
42
20
3. 4048
3. 4050
3. 4052
3. 4053
3. 4055
3. 4057
3. 4059
3. 4060
3. 4062 1 3. 4064
42
30
3. 4065
3. 4067
3. 4069
3. 4071
3. 4072
3. 4074
3. 4076
3. 4077
3. 4079 i 3. 4081
42
40
3. 4082
3. 4084
3. 4086
3. 4087
3. 4089
3. 4091
3. 4093
3. 4094
3. 4096 3. 4098
42
50
3. 4099
3.4101
3. 4103
3. 4104
3. 4106
3. 4108
3. 4109
"3. 4126
3.4111
3.4113 3.4115
0 43
0
3.4116
3.4118
3. 4120
3.4121
3.4123 ! 3.4125
3. 4128
3. 4130
3. 4131
43
10
3. 4133
3. 4135
3.4136
3. 4138
3. 4140 3. 4141
3. 4143
3. 4145
3. 4146
3. 4148
43
20
3. 4150
3. 4151
3. 4153
3. 4155
3. 4156 3. 4158
3. 4160
3. 4161
3. 4163
3. 4165
43
30
3. 4166
3. 4168
3. 4170
3.4171
3.4173 3.4175
3.4176
3.4178
3. 4180
3.4181
43
40
3. 4183
3. 4185
3. 4186
3. 4188
3.4190 3.4191
3. 4193
3. 4195
3. 4196
3. 4198
43
50
3. 4200
3. 4201
3. 4203
3. 4205
3. 4206
3. 4208
3. 4224
3. 4209
3.4226
3. 4211
3. 4228
3. 4213
3. 4214
0 44
0
3. 4216
3.4218
3.4219
3. 4221
3. 4223
3. 4229
3. 4231
44
10
3. 4232
3. 4234
3. 4236
3. 4237
3.4239 1 3.4241
3. 4242
3. 4244
3. 4246
3. 4247
44
20
3. 4249
3. 4250
3. 4252
3. 4254
3. 4255 3. 4257
3. 4259
3. 4260
3. 4262
3. 4263
44
30
3. 4265
3. 4267
3. 4268
3. 4270
3. 4272 3. 4273
3. 4275
3. 4276
3. 4278
3. 4280
44
40
3. 4281
3. 4283
3. 4285
3. 4286
3. 4288 3. 4289
3. 4291
3. 4293
3. 4294
3. 4296
44
0 45
50
0
3. 4298
3. 4314
3. 4299
3. 4315
3. 4301
3. 4302
3. 4318
3. 4304
3. 4320
3. 4306
3.4322
3. 4307
3. 4309
3. 4310
3. 4326"
3.4312
3. 4328
3.4317
3. 4323
3. 4325
45
10
3. 4330
3. 4331
3. 4333
3. 4334
3. 4336
3. 4338
3. 4339
3. 4341
3. 4342
3. 4344
45
20
3. 4346
3. 4347
3. 4349
3. 4350
3. 4352
3. 4354
3. 4355
3. 4357
3. 4358
3. 4360
45
30
3. 4362
3. 4363
3. 4365
3. 4366
3. 4368
3. 4370
3. 4371
3. 4373
3. 4374
3. 4376
45
.40
3. 4378
3. 4379
3. 4381
3. 4382
3. 4384
3. 4385
3. 4387
3. 4389
3. 4390 i .3. 4392 |
45
0 46
50
0
3. 4393
3. 4395
3.4411
3. 4396
3. 4412'
3. 4398
3.4414
3.4400
3. 4415
3. 4401 3. 4403
3.4417 1 3.4419
3. 4404
3. 4406
3. 4408
3. 4409
3. 4420
3. 4422
3. 4423
46
10
3. 4425
3. 442(>
3.4428
3. 4429
3. 4431
3.4433 1 3.4434
3.4436
3. 4437
3. 4439
46
20
3. 4440
3. 4442
3.4444
3. 4445
3. 4447
3.4448 i 3.4450
3. 4451
3. 4453
3. 4454
46
30
3. 4456
3. 4458
3. 4459
3. 4461
3. 4462
3.4464 .3.4465
3.4467
3. 4468
3. 4470
46
40
3. 4472
3. 4473
3. 4475
3. 4476
3. 4478
3.4479 3.4481
3. 4482
3. 4484
3. 4486
46
50
3. 4487
3. 4489
3. 4490
3. 4492
3. 4493
3.4495 3.4496
3. 4498
3. 4499
3. 4501
0 47
0
3. 4502
3. 4504
3. 4506
3. 4507
3. 4509
3.4510
3. 4512
3.4513
3. 4515
3. 4516
47
10
3. 4518
3. 4519
3. 4521
3. 4522
3. 4524
3. 4526
3. 4527
3. 4529
3. 4530
3. 45.32
47
20
3. 4533
3. 4535
3. 4536
3. 4538
3. 4539
3. 4541
3. 4542
3. 4544
3.4545
3. 4547
47
30
3. 4548
3. 4550
3. 4551
3. 4553
3. 4555
3. 4556
3. 4558
3.4559
3. 4561
3. 4562
47
40
3. 4564
3. 4565
3. 4567
3. 4568
3. 4570
3. 4571
3. 4573
3. 4574
3.4576
3. 4577
47
50
3. 4579
3. 4580
3. 4582
3. 4583
3.4585 1 3.4586
3. 4588
3. 4589
3. 4591
3. 4592
0 48
0
3. 4594
3. 4595
3. 4597
3. 4598
3. 4600
3. 4601
3. 4603
3. 4604
3. 4606 i 3. 4607 |
48
10
3. 4609
3. 4610
3. 4612
3. 4613
3. 4615
3.4616
3. 4618
3. 4619
3. 4621
3. 4622
48
20
3. 4624
3. 4625
3. 4627
3. 4628
3. 4630
3. 4631
3. 4633
3. 4634
3. 4636
3. 4637
48
30
3. 4639
3. 4640
3. 4642
3. 4643
3. 4645
3. 464(5
3. 4648
3.4649
3. 4651
3. 4652
48
40
3. 4654
3. 4655
3. 4657
3. 4658
3. 4660
3. 4661
3. 4663
3.4664
3. 4666
3. 4667
48
50
3. 4669
3. 4670
3. 4672
3. 4673
3. 4675
3.4676 1 3.4678
3. 4679
3. 4681
3. 4682
0 49
0
3. 4683
3. 4685
3. 4686
3. 4688
3. 4689
3. 4691
3. 4692
3. 4694
3.4695
3. 4697
49
10
3. 4698
3. 4700
3. 4701
3.4703
3. 4704
3. 4706
3. 4707
3.4709
3. 4710
3.4711
49
20
3. 4713
3. 4714
3. 4716
3.4717
3. 4719
3. 4720
3. 4722
3. 4723
3. 4725
3. 4726
49
30
3. 4728
3. 4729
3. 4730
3. 4732
3. 4733
3. 4735
3. 4736
3. 4738
3. 4739
3. 4741
49
40
3. 4742
3. 4744
3. 4745
3. 4747
3. 4748
3. 4749
3. 4751
3. 4752
3. 4754
3. 4755
49
50
3. 4757
3. 4758
3. 4760
3. 4761
3. 4763
3. 4764
3. 4765
3. 4767
3. 4768
3. 4770
Page 318]
APPENDIX V: TABLE
IX.
Logarithms of Small Arcs in Space or Time.
7"
Arc.
0"
1"
2" 8" *"
5"
6"
8"
9"
O 1
0" 50"
0»
3. 4771
3. 4773
3. 4774
3. 4776
3. 4777
3. 4778
3. 4780
1
3. 4781 ' 3. 4783
3. 4784
50
10
3. 4786
3. 4787
3. 4789
3. 4790
3. 4791
3. 4793
3. 4794
3. 4796 i 3. 4797
3. 4799
50
20
3. 4800
3. 4802
3. 4803
3.4804
3. 4806
3. 4807
3. 4809
3. 4810
3. 4812
3. 4813
50
30
3. 4814
3. 4816
3.4817
3. 4819
3. 4820
3. 4822
3. 4823
3. 4824
8. 4826
3. 4827
50
40
3. 4829
► 3. 4830
3. 4832
3. 4833
3. 4834
3. 4836
3. 4837
3. 4839
8. 4840
3. 4842
50
50
3. 4843
3. 4844
3. 4846
3. 4847
3.4849
3. 4850
3. 4852
3. 4858
3. 4854
3. 4856
0 51
0
3.4857
3. 4859
3.4860
3. 4861
3. 4863
3. 4864
3. 4866
3. 4667
3. 4869
8. 4870
51
10
3. 4871
3. 4873
3. 4874
3. 4876
3. 4877
3. 4878
3. 4880
8. 4881
3. 4883
8. 4884
51
20
3. 4886
3. 4887
3. 4888
3.4890
3. 4891
3. 4893
3. 4894
8. 4895
3. 4897
8. 4898
51
30
3. 4900
3. 4901
3. 4902
3. 4904
3. 4905
3. 4907
3. 4908
8. 4909
3. 4911
8. 4912
51
40
3. 4914
3. 4915
3. 4916
3. 4918
3.4919
3. 4921
3. 4922
3. 4923
3. 4925
3. 4926
51
50
3. 4928
3. 4929
3. 4930
3. 4932
3. 4933
3. 4935
3. 4936
3. 4987
3. 4939
3. 4940
0 52
0
3. 4942
3. 4943
3. 4944
3. 4946
3. 4947
3. 4949
3. 4950
8. 4951
3. 4953
8. 4954
52
10
3. 4955
3. 4957
3. 4958
3. 4960
3. 4961
3. 4962
3. 4964
3. 4965
3. 4967
8.4968
.52
20
3. 4969
3. 4971
3. 4972
3. 4973
3. 4975
3. 4976
3. 4978
3. 4979
3. 4980
8. 4982
52
30
3. 4983
3. 4984
3. 4986
3.4987 1 3.4989
3. 4990
3. 4991
3. 4998
3. 4994
8. 4995
52
40
3.4997
3. 4998
3. 5000
3.5001 ! 3.5002
3. 5004
3. 5005
3. 5006
3. 5008
8. 5009
52
50
3.5011
3. 5012
3. 5013
3. 5015
3. 5016
3. 5030
3. 5017
3.5031
3. 5019
3.5032
3. 5020
3.5034
3. 5022
3.5035
8. 5023
0 53
0
3. 5024
3. 5026
3. 5027
3. 5028
8. 5037
53
10
3. 5038
3. 5039
3.5041
3. 5042
3. 5043
3. 5045
3. 5046
3. 5047
3. 5049
8. 5050
53
20
3. 5051
3. 5053
3. 5054
3. 5056
3. 5057
3. 5058
3. 5060
3.5061 13.5062
3. 5064
53
30
3. 5065
3. 5066
3. 5068
3. 5069
3. 5070
3. 5072
3. 5073
3. 5075
3. 5076
8. 5077
53
40
3. 5079
3. 5080
3.5081
3. 5083
3. 5084
3. 5085
3. 5087
3. 5088
8. 5089
8. 5091
53
50
3. 5092
3. 5093
3. 5095
3. 5096
3. 5097
3. 5099
3. 5100
3. 5101
3.5103
8. 5104
0 54
0
3. 5105
3. 5107
3. 5108
3. 5109
3.5111
3.5112
3.5113
3.5115
5.5116
8.5117
54
10
3.5119
3.5120
3.5122
3.5123
3. 5124
3. 5126
3. 5127
3.5128
8.5180
8. 5131
54
20
3. 5132
3. 5134
3.5135
3. 5136
3. 5138
3. 5139
3. 5140
3.5141
8.5143
3. 5144
54
30
3. 5145
3. 5147
3.5148
3. 5149
3. 5151
3. 5152
3. 5153
3. 5155
3.5156
8.5157
54
40
3. 5159
3. 5160
3. 5161
3.5163
3. 5164
3. 5165
3. 5167
3. 5168
3. 5169
3.5171
54
50
3.5172
3. 5173
3. 5175
3.5176
3.5177
3. 5179
3. 5180
3.5181
3. 5183
3.5184
0 55
0
3. 5185
3. 5186
3. 5188
3. 5189
3. 5190
3. 5192
3. 5193
3. 5194
3. 5196
3. 5197
55
10
3. 5198
3. 5200
3. 5201
3. 5202
3. 5204
3. 5205
3. 5206
3. 5207
3. 5209
3. 5210
55
20
3. 5211
3.5213
3.5214
3. 5215
3. 5217
3. 5218
3. 5219
8. 5221
8. 5222
3. 5228
55
30
3. 5224
3. 5226
3. 5227
3. 5228
3. 5230
3. 5231
3. 5232
3. 5234
3. 5235
3. 5286
55
40
3. 5237
3. 5239
3. 5240
3. 5241
3. 5243
3. 5244
3. 5245
3. 5247
3. 5248
3. 5249
55
50
3. 5250
3. 5252
3. 5253
3.5254 3.5256
3. 5257
3. 5258
3. 5271
3. 5260
3. 5272
8. 5261
3. 5274
3. 5262
0 56
0
3. 5263
3. 5265
3. 5266
3.5267 1 3.5269
3. 5270
3. 5275
56
10
3. 5276
3. 5278
3. 5279
3. 5280
3. 5281
3. 5283
3. 5284
3. 5285
3. 5287
3. 5288
56
20
3. 5289
3. 5290
3. 5292
3. 5293
3. 5294
3. 5296
3. 5297
8. 5298
3. 5299
8. 5801
56
30
3. 5302
3. 5303
3. 5305
3. 5306
3. 5307
3. 5308
3. 5310
3. 5311
3. 5312
3. 5314
56
40
3. 5315
3. 5316
3. 5317 3. 5319
3. 5320
3. 5321
3. 5322
3. 5324
3. 5325
3. 5326
56
50
3. 5328
3. 5329
3. 5330 3. 5331 3. 5333
3. 5334
3. 5835
3. 5336
3. 5388
3. 5339
0 57
0
3. 5340
3. 5342
3.5343 1 3.5344 3.5345
3. 5347
3. 5348
3. 5849
3. 5850
8. 5352
57
10
3. 5353
3. 5854
3. 5355
3. 5357
3. 5358
3. 5359
3. 5361
3. 5862
3. 5363
3. 5364
57
20
3. 5366
3. 5367
3. 5368
3. 5369
3. 5371
3. 5372
3. 5373
3. 5374
3. 5376
3. 5377
57
30
3. 5378
3. 5379
3. 5381
3. 5382
3. 5383
3. 5384
3. 5386
3. 5387
3. 5388
8. 5390
57
40
3. 5391
3. 5392
3. 5393
3. 5395
3. 5396
3. 5397
3. 5398
3. 5400
3. 5401
3. 5402
57
50
3. 5403
3. 5405
3.5406
3. 5407
3. 5408
3. 5421
3.5410
3. 5422
3. 5411
3.5428
3. 5412
8. 5425
3. 5413
375426
3. 5415
0 58
0
3. 5416
3. 5417
3.5'418 ; 3.5420
3. 5427
58
10
3. 5428
3. 5429
3.5431 1 3.5432
3. 5433
3. 5434
3. 5436
3. 5437
3. 5438
8. 5489
58
20
3. 5441
3. 5442
3.5443 j 3.5444
3.5446
3. 5447
3. 5448
3. 5449
3. 5451
3. 5452
58
30
3. 5453
3. 5454
.3.5456 i 3.5457
3. 5458
3. 5459
3. 5460
3. 5462
3. 5463
3. 5464
58
40
3. 5465
3. 5467
3.5468 i 3.5469 3.5470
3. 5472
3. 5473
3. 5474
8. 5475
3.5477
58
50
3. 5478
3. 5479
3.5480 1 3.5481 3.5483
3. 5484
3. 5485
3. 5486
8. 5488
3. 5489
0 59
0
3. 5490
3. 5491
3.5492 j 3.5494 3.5495
3. 5496
3. 5497
3. 5499 8. 5500
3. 5501
59
10 3. 5502
3. 5504
3.5505 i 3.5506 3.5507
3. 5508
3. 5510
3.5511
3. 5512
3.5518
59
20 3.5514
3. 5516
3. 5517
3. 5518 3. 5519
3. 5521
3. 5522
8. 5528
3. 5524
3. 5525
59
30
3. 5527
3. 5528
3. 5529
3. 5530 3. 5532
3. 5533
3. 5534
3. 5535
8. 5536
3. 5538
59
40
3. 5539
3. 5540
3.5541
3.5542 1 3.5544
3. 5545
3. 5546
3. 5547
8. 5549
3. 5550
59
50
3. 5551
3. 5552
3. 5553
3.5555 1 3.5556
3. 5557
3. 5558
3. 5559
3. 5561
3. 5562
APPENDIX
Y: TABl^E IX.
[Page 319
Logarithms of Small Arcs in Space or Time.
Are.
0"
1"
2"
3"
4"
5"
6"
7"
8" j 9"
0 /
Ih 0"
0^
3. 5563
3. 5564
3. 5565
3. 5567
3. 5568
3. 5569
3. 5570
3. 5571
3. 55^3
3. 5574
0
10
3. 5575
3. 5576
3. 5577
3. 5579
3. 5580 '
3. 5581
3. 5582
3. 5583
3. 5585
3. 5586
0
20
3. 5587
3. 5588
3. 5589
3. 5591
3. 5592
3. 5593
3. 5594
3. 5595
3. 5597
3. 5598
0
30
3. 5599
3. 5600
3. 5601
3. 5603
3. 5604
3. 5605
3. 5606
3. 5607
3. 5609
3. 5610
0
40
3. 5611
3. 5612
3. 5613
3. 5615
3.5616
3.5617
3. 5618
3. 5619
3. 5621
3. 5622
0
50
3. 5623
3. 5624
3. 5625
3. 5626
3. 5628
3. 5629
3. 5630
3. 5631
3. 5632
3. 5634
. 1 1
0
3. 5635
3. 5636
3. 5637
3. 5638
3. 5640
3. 5641
3. 5642
3. 5643
3. 5644
3. 5645
10
3. 5647
3. 5648
3. 5649
3. 5650
3. 5651
3. 5653
3. 5654
3. 5655
3. 5656
3. 5657
20
3. 5658
3. 5660
3. 5661
3. 5662
3. 5663
3. 5664
3. 5666
3. 5667
3. 5668
3. 5669
30
3. 5670
3. 5671
3. 5673
3. 5674
3. 5675
3. 5676
3. 5677
3. 5678
3. 5680
3. 5681
40
3. 5682
3. 5683
3. 5684
3. 5686
3. 5687
3. 5688
3. 5689
3. 5690
3. 5691
3. 5693
50
3. 5694
3. 5695
3. 5696
3. 5697
3. 5698
3. 5700
3. 5701
3. 5702
3. 5703 i 3. 5704
1 2
0
3. 5705
3. 5707
3. 5708
3. 5709
3.5710
3.5711
3.5712
3. 5714
3.5715 3.5716
2
10
3.5717
3.5718
3. 5719
3. 5721
3. 5722
3. 5723
3. 5724
3. 5725
3. 5726 ] 3. 5728
2
20
3. 5729
3. 5730
3. 5731
3. 5732
3. 5733
3. 5735
3. 5736
3. 5737
3. 5738 ! 3. 5739
2
30
3. 5740
3. 5741
3. 5742
3. 5744
3. 5745
3. 5746
3. 5747
3. 5748
3. 5750 1 3. 5751
2
40
3. 5752
3. 5753
3. 5754
3. 5755
3. 5756
3. 5758
3. 5759
3. 5760
3. 5761 3. 5762
2
50
3. 5763
3. 5765
3. 5766
3. 5767
3. 5768
3. 5769
3. 5770
3. 5771
3.5773 3.5774
1 3
0
3. 5775
3. 5776
3.5777
3. 5778
3. 5780
3. 5781
3. 5782
3. 5783
3. 5784 i 3. 5785
3
10
3. 5786
3. 5788
3. 5789
3. 5790
3. 5791
3. 5792
3. 5793
3. 5794
3. 5796
3. 5797
3
20
3. 5798
3. 5799
3. 5800
3. 5801
3. 5802
3. 5804
3. 5805
3.5806
3. 5807
3. 5808
3
30
3. 5809
3. 5810
3. 5812
3. 5813
3. 5814
3.5815
3. 5816
3. 5817
3. 5818
3. 5819
3
40
3. 5821
3. 5822
3. 5823
3. 5824
3. 5825
3. 5826
3. 5827
3.5829
3. 5830
3. 5831
3
50
3. 5832
3. 5833
3. 5834
3. 5835
3. 5837
3. 5838
3. 5839
3. 5840
3. 5841
3. 5842
1 4
0
3. 5843
3. 5844
3. 5846
3. 5847
3. 5848
3. 5849
3. 5850
3. 5851
3. 5852 1 ;i 5853
4
10
3. 5855
3. 5856
3. 5857
3. 5858
3. 5859
3. 5860
3. 5861
3. 5862
3. 5864 1 3. 5865
4
20
3. 5866
3. 5867
3. 5868
3. 5869
3. 5870
3. 5871
3. 5873
3. 5874
3. 5875 3. 5876
4
30
3. 5877
3. 5878
3. 5879
3. 5880
3. 5882
3. 5883
3. 5884
3. 5885
3.5886 3.5887
4
40
3. 5888
3. 5889
3. 5891
3. 5892
3. 5893
3. 5894
3. 5895
3. 5896
3. 5897 1 3. 5898
4
50
3. 5899
3. 5901
3. 5902
3^. 5903
3.5904
3. 5905
3. 5906
3. 5907
3. 5908
3. 5910
1 5
0
3.5911
3. 5912
3. 5913
3. 5914
3. 5915
3. 5916
3.5917
3. 5918
3. 5920
3. 5921
5
10
3. 5922
3. 5923
3. 5924
3. 5925
3. 5926
3. 5927
3. 5928
3. 5930
3. 5931
3. 5932
5
20
3. 5933
3.5934
3. 5935
3. 5936
3. 5937
3. 5938
3. 5940
3. 5941
3. 5942
3. 5943
5
30
3. 5944
3. 5945
3. 5946
3. 5947
3. 5948
3. 5949
3. 5951
3. 6952
3. 5953
3. 5954
5
.40
3. 5955
3. 5956
3. 5957
3. 5958
3. 5959
3. 5960
3. 5962
3. 5963
3.5964
3. 5965
5
50
3. 5966
3. 5967
3. 5968 3. 5969
3. 5970
3. 5971
3. 5973
3. 5974
3. 5975
3. 5976
1 6
0
3. 5977
3. 5978
3. 5979
3. 5980
3. 5981
3. 5982
3. 5984
3. 5985
3. 5986
3. 5987
6
10
3. 5988
3. 5989
3. 5990
3. 5991
3. 5992
3. 5993
3. 5994
3. 5996
3. 5997
3. 5998
6
20
3. 5999
3. 6000
3. 6001
3. 6002
3. 6003
3.6004
3. 6005
3. 6006
3. 6008
3. 6009
6
30
3. 6010
3. 6011
3. 6012
3. 6013
3. 6014
3. 6015
3. 6016
3. 6017
3. 6018
3. 6020
6
40
3. 6021
3. 6022
3. 6023
3. 6024
3. 6025
3. 6026
3. 6027
3. 6028
3. 6029
3. 6030
6
50
3. 6031
3. 6033
3. 6034
3. 6035
3. 6036
3. 6037
3. 6038
3. 6039
3. 6040
3. 6041
1 7
0
3.6042
3. 6043
3. 6044
3. 6046
3. 6047
3.6048
3. 6049
3. 6050
3. 6051
3. 6052
7
10
3. 6053
3. 6054
3. 6055
3. 6056
3. 6057
3. 6058
3. 6060
3. 6061
3. 6062
3. 6063
7
20
3. 6064
3. 60a5
3. 6066
3. 6067
3. 6068
3. 6069
3. 6070
3. 6071
3. 6072
3. 6073
7
30
3. 6075
3. 6076
3. 6077
3. 6078
3. 6079
3. 6080
3. 6081
3. 6082
3. 6083
3. 6084
7
40
3. 6085
3. 6086
3. 6087
3. 6088
3. 6090
3. 6091
3. 6092
3. 6093
3. 6094 3. 6095
7
50
3. 6096
3. 6097
3. 6098
3. 6099
3.6100
3. 6101
3. 6102
3. 6103
3. 6104 j 3. 6106
1 8
0
3. 6107
3. 6108
3.6109 ; 3.6110
3.6111
3.6112
3.6113
3.6114
3.6115 i 3.6116
8
10
3. 6117
3.6118
3.6119 i 3.6120
3. 6121
3. 6123
3. 6124
3.6125
3.6126 3.6127
8
20
3. 6128
3.6129
3.6130 1 3.6131
3. 6132
3. 6133
3. 6134
3. 6135
3. 6136
3. 6137
8
30
3. 6138
3. 6139
3.6141 i 3.6142
3. 6143
3. 6144
3. 6145
3. 6146
3. 6147
3. 6148
8
40
3. 6149
3. 6150
3.6151 i 3.6152
3. 6153
3. 6154
3. 6155
3. 6156
3. 6157
3. 6158
8
50
3. 6160
3. 6161
3.6162 i 3.6163
3. 6164
3. 6165
3. 6166
3. 6167
3. 6168
3. 6169
3. 6179
1 9
0
3.6170
3.6171
3. 6172
3. 6173
3. 6174
3. 6175
3. 6176
3. 6177
3. 6178
9
10
3. 6180
3. 6182
3. 6183
3. 6184
3. 6ia5
3. 6186
3. 6187
3. 6188
3. 6189
3. 6190
9
20
3. 6191
3.6192
3. 6193
3. 6194
3. 6195
3. 6196
3. 6197
3.6198
3. 6199
3. 6200
9
30
3. 6201
3. 6202
3. 6203
3. 6204
3.6206
3. 6207
3. 6208
3. 6209
3.6210 3.6211
9
40
3. 6212
3. 6213
3. 6214
3. 6215
3. 6216
3. 6217
3. 6218
3. 6219
3. 6220 3. 6221
9
50
3. 6222
3. 6223
3.6224 1 3.6225
3. 6226
3. 6227
3. 6228
3. 6229
3. 6230 3. 6231
Page 320J
APPENDIX
V: TABLE IX.
Logarithm
;! of Small Arcs in Space or
Time.
Are.
0"
1"
3. 6235
8"
4" 5"
6"
«"
8" 1 9"
O '
1" 10"
0*
3. 6232
3. 6234
3. 6236
3. 6237 3. 6238 i 3. 6239
3. 6240
3. 6241 1 3. 6242
10
10
3. «)243
3. 6244
3. 6245
3. 6246
3. 6247
3. 6248
3. 6249
3. 6250
3. 6251 3. 6252
10
20
3. (5253
3. 6254
3. 6255
3. 6256
3. 6257
3. 6258
3. 6259
3. 6260
3. 6261 1 3. 6262
10
30
3. 6263
3.6264
3. 6265
3. 6266
3. 6268
3. 6269
3. 6270
3. 6271
3. 6272 ! 3. 6273
10
40
3. 6274
»3. 6275
3. 6276
3. 6277
3.6278
3. 6279
3. 6280
3. 6281
3. 6282 3. 6283
10
50
3. 6284
3. 6285
3. 6286
3. 6287
3. 6297
3. 6288
3. 6298
3. 6289
3. 6299
3.6290
376300
3. 6291
3. 6301
3. 6292 3. 6293
3.6302 1 3.6303
1 11
0
3. 6294
3. 6295
3.6296
11
10
3. 6304
3. 6305
3. 630()
3. 6307
3. 6308
3. 6309
3. 6310
3.6311
3. 6312 3. 6313
11
20
3. 6314
3. 6315
3.6316
3. 6317
3. 6318
3. 6320
3. 6321
3. 6322
3. 6323 3. 6324
11
30
3. 6325
3. 6326
3. 6327
3. 6328
3. 6329
3. 6330
3. 6331
3. 6332
3. 6333 3. 6334
11
40
3. 6335
3. 6336
3. 6337
3. 6338
3. 6339
3. 6340
3. 6341
3. 6342
3. 6343 i 3. 6344
11
50
3. 6345
3. 6346
3. 6347
3. 6348
3. 6349
3. 6350
3. 6351
3. 6352
3. 6353 ! 3. 6354
1 12
0
3. 6355
"3.6356
3. 6357
3. 6358
3. 6359
3. 6360
3. 6361
3.6362
3. 6363 1 3. 6364
12
10
3. 6365
3. 6366
3. 6367
3. 6368
3. 6369
3. 6370
3. 6371
3. 6372
3. 6373 i 3. 6374
12
20
3. 6375
3. 6376
3. 6377
3. 6378
3. 6379
3. 6380
3. 6381
3. 6382
3. 6383
3. 6384
12
30
3. 6385
3. 6386
3. 6387
3. 6388
3. 6389
3. 6390
3. 6391
3. 6392
3. 6393
3. 6394
12
40
3. 6395
3. 6396
3. 6397
3. 6398
3. 6399
3. 6400
3. 6401
3. 6402
3. 6403
3. 6404
12
50
3.6405
3. 6406
3. 6407
3. 6408
3. 6418
3. 6409
3.6419
3.6410
3.6411
3. 6412
3. 6422
3. 6413
3. 6423
3. 6414
3.6424 "
1 13
0
3. 6415
3. 6416
3. 6417'
3. 6420
3. 6421
13
10
3. 6425
3. 6426
3. 6427
3. 6428
3. 6429
3. 6430
3. 6431
3. 6432
3. 6433
3. 6434
13
20
3. 6435
3. 6436
3. 6437
3. 6437
3. 6438 3. 6439
3. 6440
3. 6441
3. 6442 3. 6443
18
30
3. 6444
3. 6445
3. 644(5
3.64-17
3.6448
3. 6449
3.6450 1 3.6451
3. 6452 i 3. 6453
13
40
3. 6454
3. 6455
3. 6456
3. 6457
3. 6458
3. 6459
3. 6460
3. 6461
3.6462 3.6463
13
50
3. 6464
3. 6465
3. 6466
3. 6467
3. 6468
3.6469
3. 6470
3.6471
3. 6472 3. 6473
1 14
. 0
3. 6474
3. 6475
3. 6476
3. 6477
3. 6478
3. 6479
3. 6480
3. 6481
3. 6482 1 3. 6483
14
10
3. 6484
3. 6485
3. 6486
3. 6487
3. 6488
3. 6488
3. 6489
3. 6490
3. 6491 I 3. 6492
14
20
3. 6493
3. ^494
3. 6495
3. 6496
3. 6497
3. 6498
3.6499
3. 6500
3. 6501 ! 3. 6502
14
30
3. 6503
3. 6504
3. 6505
3. 6506
3. 6507
3. 6508
3. 6509
3. 6510
3.6511 1 3.6512
14
40
3. 6513
3. 6514
3. 6515
3. 6516
3. 6517
3. 6518
3.6519
3. 6520
3. 6521 i 3. 6521
14
50
3. 6522
3. 6523
3. 6524
3. 6525
3. 6.526
3. 6527
3. 6528
3. 6538
3. 6529
3. 6539
3. 6530
"3. 6540
3. 6531
1 15
0
3. 6532 "
3. 6533
3. 6534
3. 6535
3. 6536
3. 6537^
3. 6541
15
10
3. 6542
3. 6543
3. 6544
3. 6545
3. 6546
3. 6547
3. 6548
3. 6549
3.6549 3.6550 1
15
20
3. 6551
3. 6552
3. 6553
3. 6554
3.6555 i 3.6556
3. 6557
3. 6558
3.6559 3.6560 |
15
30
3. 6561
3. 6562
3. 6563
3. 6564
3. 6565
3. 6566
3. 6567
3. 6568
3. 6569
3. 6570
15
40
3. 6571
3. 6572
3. 6572
3. 6573
3. 6574
3. 6575
3. 6576
3. 6577
3. 6578
3. 6579
15
50
3. 6580
3. 6581
3. 6591
3. 6582
3. 6592
3. 6583
3. 6584
3. 6585
3. 6586
3. 6587
3. 6588
3. 6589
1 16
0
3. 6590
3. 6593
3. 6593"
3. 6594
3. 6595
3. 6596
3.6597
3. 6598
16
10
3. 6599
3. 6600
3. 6601
3. 6602
3. 6603
3. 6604
3. 6605
3. 6606
3. 6607 ! 3. 6608 |
16
20
3. 6609
3. 6610
3.6611
3.6611
3. 6612
3. 6613
3. 6614
3. 6615
3. 6616
3. 6617
16
30
3. 6618
3. 6619
3. 6620
3. 6621
3. 6622
3. 6623
3. 6624
3. 6625
3. 6626
3. 6627
16
40
3. 6628
3. 6629
3. 6629
3. 6630
3. 6631
3. 6632
3. 6633
3. 6634
3. 6635
3. 6636
16
50
3. 6637
3. 6638
3. 6639
3. 6640
3. 6641
3. 6642
3. 6643
3. 6644
3. 6645
3. 6645
1 17
0
3. 6646^
3. 6647
3.6648
3. 6649
3. 6650 3. 6651
3. 6652
3. 6653
3. 6654
3. 6655
17
10
3. 6656
3. 6657
3. 6658
3. 6659
3. 6660 3. 6660
3. 6661
3. 6662
3. 6663
3. 6664
17
20
3. 6665
3. 6666
3. 6667
3. 6668
3.6669 j 3.6670
3. 6671
3. 6672
3. 6673
3. 6674
17
30
3. 6675
3. 6675
3. 6676
3. 6677
3.6678 ' 3.6679
3. 6680
3. 6681
3. 6682
3. 6683
17
40
3. 6684
3. 6685
3. 6686
3. 6687
3. 6688
3. 6689
3. 6689
3. 6690
3. 6691
3. 6692
17
50
3. 6693
3. 6694
"3.6703
3. 6695
3. 6704
3. 6696
3. 6697
3. 6698
"3. 6707"
3. 6699
3. 6700
3. 6701
3. 6710
3. 6702
3.6711
1 18
0
3. 6702
3. 6705
3. 6706
3. 6708
3. 6709
18
10
3. 6712
3. 6713
3. 6714
3. 6715
3.6715
3.6716
3.6717
3. 6718
3. 6719
3. 6720
18
20
3. 6721
3. 6722
3. 6723
3. 6724
3. 6725
3. 6726
3. 6727
3. 6727
3. 6728
3. 6729
18
30
3. 6730
3. 6731
3. 6732
3. 6733
3. 6734
3. 6735
3. 6736
3. 6737
3. 6738
3. 6738
18
40
3. 6739
3. 6740
3. 6741
3. 6742
3. 6743
3. 6744
3. 6745
3. 6746
3. 6747
3. 6748
18
50
3. 6749
3. 6750
3.6759
3. 6750
3. 6760
3. 6751
3. 6761
3. 6752
3. 6753
3. 6754
3. 6755
3. 6756
3. 6757
1 19
0
3. 6758
3. 6761
3. 6762
3. 6763
3. 6764"
3. 6765
3.6766
19
10
3. 6767
3. 6768
3. 6769
3. 6770
3. 6771
3. 6772
3. 6772
3. 6773
3. 6774
3. 6775
19
20
3. 6776
3. 6777
3. 6778
3. 6779
3. 6780
3. 6781
3. 6782
3. 6782
3. 6783
3. 6784
19
30
3. 6785
3. 6786
3. 6787
3. 6788
3. 6789
3. 6790
3. 6791
3. 6792
3. 6792
3. 6793
19
40
3. 6794
3. 6795
3. 6796
3. 6797
3. 6798
3. 6799
3. 6800
3. 6801
3. 6802
3. 6802
19
50
3. 6803
3. 6804
3. 6805
3. 6806
3. 6807
3. 6808
3. 6809
3. 6810
3. 6811
3. 6812
APPENDIX V: TABLE IX.
[Page 321 |
Logarithms of Small Arcs in
Space or
Time.
Arc.
0"
1"
2"
3"
4"
5"
6"
7"
8"
9"
o /
1» 20'"
0«
3. 6812
3. 6813
3. 6814
3. 6815
3. 6816
3. 6817
3. 6818
3. 6819
3. 6820
3. 6821
20
10
3. 6821
3. 6822
3. 6823
3. 6824
3. 6825
3. 6826
3. 6827
3. 6828
3. 6829
3. 6830
20
20
3. 6830
3. 6831
3. 6832
3. 6833
3. 6834
3. 6835
3. 6836
3. 6837
3. 6838
3. 6839
20
30
3. 6839
3. 6840
3. 6841
3. 6842
3. 6843
3. 6844
3. 6845
3. 6846
3. 6847
3. 6848
20
40
3. 6848
3. 6849
3. 6850
3. 6851
3. 6852
3. 6853
3. 6854
3. 6855
3. 6856
3. 6857
20
50
3. 6857
3. 6858
3. 6859
3. 6860
3. 6861
3. 6862
3. 6863
3. 6864
3. 6865
3.6865
1 21
0
3. 6866
3. 6867
3. 6868
3. 6869
3. 6870
3. 6871
3. 6872
3. 6873
3. 6874
3. 6874
21
10
3. 6875
3. 6876
3. 6877
3. 6878
3. 6879
3. 6880
3. 6881
3. 6882
3. 6882
3. 6883
21
20
3. 6884
3. 6885
3. 6886
3. 6887
3. 6888
3. 6889
3. 6890
3. 6890
3. 6891
3. 6892
21
30
3. 6893
3. 6894
3. 6895
3. 6896
3. 6897
3. 6898
3. 6898
3. 6899
3. 6900
3. 6901
21
40
3. 6902
3. 6903
3. 6904
3. 6905
3. 6906
3. 6906
3. 6907
3. 6908
3.6909
3. 6910
21
50
3.6911
3. 6912
3. 6913
3. 6913
3.6914
3. 6923
3. 6915
3. 6916
3.6917
3. 6918
3. 6927
3. 6919
1 22
0
3. 6920
3. 6921
3. 6921
3. 6922
3. 6924
3. 6925
3. 6926
3. 6928
22
10
3. 6928
3. 6929
3. 6930
3. 6931
3. 6932
3. 6933
3. 6934
3. 6935
3. 6936
3. 6936
22
20
3. 6937
3. 6938
3. 6939
3. 6940
3. 6941
3. 6942
3. 6943
3. 6943
3. 6944
3. 6945
22
30
3. 6946
3. 6947
3. 6948
3. 6949
3. 6950
3. 6950
3. 6951
3. 6952
3. 6953
3. 6954
22
40
3. 6955
3. 6956
3. 6957
3. 6957
3. 6958
3. 6959
3. 6960
3. 6961
3. 6962
3. 6963
22
50
3.6964
3.6964
3. 6965
3. 6966
3. 6967
3. 6968
3. 6969
3. 6970
3. 6971
3. 6971
1 23
0
3. 6972
3. 6973
3. 6974
3. 6975
3. 6976
3. 6977
3. 6978
3. 6978
3. 6979
3. 6980
23
10
3. 6981
3. 6982
3. 6983
3. 6984
3. 6984
3. 6985
3. 6986
3. 6987
3. 6988
3. 6989
23
20
3. 6990
3. 6991
3. 6991
3. 6992
3. 6993
3. 6994
3. 6995
3. 6996
3. 6997
3. 6998
23
30
3. 6998
3. 6999
3.7000
3.7001
3.7002
3. 7003
3. 7004
3. 7004
3.7005
3. 7006
23
40
3. 7007
3. 7008
3.7009
3. 7010
3. 7010
3. 7011
3. 7012
3. 7013
3. 7014
3. 7015
23
50
3. 7016
3. 7017
3, 7017
3. 7026
3. 7018
3. 7019
3. 7020
3. 7021
3. 7022
3. 7023
3. 7023
1 24
0
3. 7024
3. 7025
3. 7027
3. 7028
3. 7029
3.7029
3. 7030
3. 7031
3. 7032
24
10
3. 7033
3. 7034
3. 7035
3. 7035
3. 7036
3. 7037
3. 7038
3. 7039
3. 7040
3. 7041
24
20
3. 7042
3. 7042
3. 7043
3. 7044
3.7045
3. 7046
3. 7047
3. 7048
3. 7048
3. 7049
24
30
3. 7050
3. 7051
3. 7052
3. 7053
3. 7054
3. 7054
3. 7055
3. 7056
3. 7057
3. 7058
24
40
3. 7059
3.7060
3. 7060
3. 7061
3. 7062
3. 7063
3. 7064
3. 7065
3. 7065
3. 7066
24
50
3. 7067
3. 7068
3. 7069
3. 7070
3. 7071
3. 7071
3. 7072
3. 7073
3. 7074
3. 7075
1 25
0
3. 7076
3. 7077
3. 7077
3. 7078
3. 7079
3. 7080
3. 7081
3. 7082
3. 7083
3. 7083
25
10
3. 7084
3. 7085
3. 7086
3. 7087
3. 7088
3. 7088
3. 7089
3. 7090
3.7091
3. 7092
25
20 3. 7093
3. 7094
3. 7094
3.7095
3. 7096
3. 7097
3. 7098
3.7099
3.7099
3.7100
25
30
3. 7101
3. 7102
3. 7103
3. 7104
3. 7105
3. 7105
3. 7106
3. 7107
3. 7108
3. 7109
25
.40
3. 7110
3. 7110
3.7111
3. 7112
3. 7113
3. 7114
3. 7115
3.7116
3. 7116
3.7117
25
50
3.7118
3. 7119
3. 7120
3. 7121
3. 7121
3. 7122
3. 7123
3. 7124
3. 7125
3. 7126
1 26
0
3. 7126
3. 7127
3. 7128
3. 7129
3. 7130
3. 7131
3. 7132
3. 7132
3. 7133
3. 7134
26
10
3. 7135
3. 7136
3. 7137
3. 7137
3. 7138
3. 7139
3.7140
3. 7141
3. 7142
3. 7142
26
20
3. 7143
3. 7144
3. 7145
3. 7146
3. 7147
3. 7147
3. 7148
3. 7149
3. 7150
3. 7151
26
30
3. 7152
3. 7153
3. 7153
3. 7154
3. 7155
3. 7156
3. 7157
3. 7158
3. 7159
3. 7159
26
40
3. 7160
3. 7161
3. 7162
3. 7163
3. 7163
3. 7164
3. 7165
3. 7166
3. 7167
3. 7168
26
50
3. 7168
3. 7169
3. 7170
3.7171
3. 7172
3. 7173
3. 7173
3. 7182
3. 7174
3. 7175
3. 7176
1 27
0
3.7177
3. 7178
3. 7178
3. 7179 1 3. 7180
3. 7181
3. 7183
3. 7183
3. 7184
27
10
3.7185
3. 7186
3. 7187
3.7188 1 3.7188
3. 7189
3. 7190
3. 7191
3. 7192
3. 7192
27
20
3. 7193
3. 7194
3. 7195
3. 7196 I 3. 7197
3.7197
3. 7198
3. 7199
3. 7200
3. 7201
27
30
3. 7202
3. 7202
3. 7203
3. 7204
3. 7205
3.7206
3. 7207
3. 7207
3. 7208
3. 7209
27
40
3. 7210
3. 7211
3. 7212
3.7212
3. 7213
3. 7214
3. 7215
3. 7216
3. 7216
3. 7217
27
50
3. 7218
3. 7219
3. 7220
3. 7221
3. 7221
3. 7222
3. 7223
3. 7224
3. 7225
3. 7226
1 28
0
3. 7226
3. 7227
3. 7228
3.7229
3. 7230
3. 7230
3. 7231
3. 7232
3. 7233
3. 7234
28
10
3. 7235
3. 7235
3. 7236
3. 7237
3. 7238
3. 7239
3. 7239
3. 7240
3. 7241
3. 7242
28
20
3. 7243
3. 7244
3. 7244
3. 7245
3. 7246
3. 7247
3. 7248
3. 7248
3. 7249
3. 7250
28
30
3. 7251
3. 7252
3. 7253
3. 7253
3. 7254
3. 7255
3. 7256
3. 7257
3. 7257
3. 7258
28
40
3. 7259
3. 7260
3. 7261
3. 7262
3. 7262
3. 7263
3. 7264
3. 7265
3. 7266
3. 7266
28
50
3. 7267
3. 7268
3. 7269
3. 7270
3. 7278
3. 7271
3. 7279
3. 7271
3. 7272
3. 7273
3. 7274
3. 7275
1 29
0
3. 7275
3. 7276
3. 7277
3. 7279
3. 7280
3. 7281
3. 7282
3. 7283
29
10
3. 7284
3. 7284
3. 7285
3. 7286
3. 7287
3. 7288
3. 7288
3. 7289
3. 7290
3. 7291
29
20
3. 7292
3. 7292
3. 7293
3. 7294
3. 7295
3.7296
3. 7297
3. 7297
3. 7298
3. 7299
29
30
3. 7300
3. 7301
3. 7301
3. 7302
3. 7303
3. 7304
3. 7305
3. 7305
3. 7306
3. 7307
29
40
3. 7308
3. 7309
3. 7309
3. 7310
3. 7311
3. 7312
3. 7313
3. 7313
3. 7314
3. 7315
29
50
3.7316
3. 7317
3. 7317
3. 7318
3. 7319
3. 7320
3. 7321
3. 7322
3. 7322
3. 7323
22489—03-
-21
Page 322] APPENDIX V: TABLE
[X.
Logarithms of Small Arcs in
Space or
Time.
Arc.
0" i X"
2"
8"
4"
5"
6"
7"
8" 9" 1
O I II
1" 30"' 0"
3. 7324
3. 7325
3. 7326
3. 7326
3. 7327
3. 7328
3.7329
3. 7330
3. 7330
3.7331
30 10
3. 7332
3. 7333
3. 7334
3. 7334
3. 7335
3. 7336
3. 7337
3. 7338
3. 7338
3. 7339
30 20
3. 7340
3. 7341
3. 7342
3. 7342
3. 7343
3.7344
3. 7345
3. 7346
3.7346
3. 7347
30 30
3. 7348
3. 7349
3. 7350
3. 7350
3. 7351
3. 7352
3. 7353
3. 7354
3. 7354
3. 7355
30 40
3.7356
►3. 7357
3.7358
3, 7358
3. 7359
3.7360
3. 7361
3. 7362
3. 7362
3. 7363
30 50
3. 7364
3.7365
3. 7366
3. 7366
3. 7367
3. 7368
3. 7369
3. 7370
3. 7370
3. 7371
1 31 0
3. 7372
3. 7373
3. 7374
3. 7374
3. 7375
3. 7376
3. 7377
3. 7377
3. 7378
3. 7379
31 10
3. 7380
3. 7381
3. 7381
3. 7382
3. 7383
3. 7384
3.7385
3. 7385
3. 7386
3. 7387
31 20
3. 7388
3. 7389
3. 7389
3. 7390
3. 7391
3. 7392
3. 7393
3. 7393
3. 7394
3. 7395
31 30
3. 7396
3. 7397
3. 7397
3. 7398
3. 7399
3.7400
3.7400
3. 7401
3. 7402
3. 7403
31 40
3. 7404
3. 7404
3. 7405
3. 7406
3.7407
3. 7408
3. 7408
3. 7409
3. 7410
3. 7411
31 50
3. 7412
3. 7412
3. 7413
3. 7414
3. 7415
3. 7415
3. 7416
3. 7417
3. 7418
3. 7419
1 32 0
3. 7419
3. 7420
3. 7421
3. 7422
3. 7423
3. 7423
3. 7424
3. 7425
3. 7426
3. 7426
32 10
3. 7427
3. 7428
3. 7429
3. 7430
3. 7430
3. 7431
3. 7432
3. 7433
3. 7434
3. 7434
32 20
3.7435
3. 7436
3. 7437
3. 7437
3. 7438
3. 7439
3. 7440
3. 7441
3. 7441
3. 7442
32 30
3. 7443
3.7444
3.7444
3. 7445
3. 7446
3. 7447
3.7448
3. 7448
3. 7449
3. 7450
32 40
3. 7451
3. 7452
3.7452
3. 7453
3. 7454
3. 7455
3. 7455
3. 7456
3. 7457
3.7468
32 50
3. 7459
3. 7459
3.7460
3. 7461
3. 7462
3. 7462
3. 7463
3.7464
3.7465
3. 7466
1 33 0
3. 7466
3. 7467
3. 7468
3. 7469
3. 7469
3. 7470
3. 7471
3. 7472
3. 7473
3. 7473
33 10
3. 7474
3. 7475
3. 7476
3. 7476
3. 7477
3. 7478
3. 7479
3. 7480
3. 7480
3. 7481
33 20
3. 7482
3. 7483
3. 7483
3. 7484
3. 7485
3. 7486
3. 7487
3. 7487
3. 7488
3. 7489
33 30
3. 7490
3. 7490
3. 7491
3. 7492
3. 7493
3. 7493
3. 7494
3. 7495
3. 7496
3. 7497
33 40
3. 7497
3. 7498
3. 7499
3.7500
3.7500
3. 7501
3. 7502
3. 7503
3. 7504
3. 7504
33 50
3. 7505
3. 7506
3. 7507
3. 7507
3. 7508
3. 7509
3. 7510
3. 7510
3. 7511
3. 7512
1 34 0
3. 7513
3. 7514
3. 7514
3. 7515
3. 7516
3. 7517
3. 7517
3. 7518
3. 7519
3. 7520
34 10
3. 7520
3. 7521
3. 7522
3. 7523
3. 7524
3. 7524
3. 7525
3. 7526
3. 7527
3. 7527
34 20
3. 7528
3. 7529
3. 7530
3. 7530
3. 7531
3. 7532
3. 7533
3. 7534
3. 7534
3. 7535
34 30
3. 7536
3. 7537
3. 7537
3. 7538
3. 7539
3. 7540
3. 7540
3. 7541
3. 7542
3. 7543
34 40
3. 7543
3. 7544
3. 7545
3. 7546
3. 7547
3. 7547
3. 7548
3. 7549
3. 7550
3. 7550
34 50
3. 7551
3. 7552
3. 7553
3. 7553
3. 7554
3. 7555
3. 7556
3. 7556
3. 7557
3. 7558
1 35 0
3. 7559
3. 7560
3.7560
3. 7561
3. 7562
3. 7563
3. 7563
3. 7564
3. 7565
3. 7566
35 10
3. 7566
3. 7567
3. 7568
3. 7569
3. 7569
3. 7570
3. 7571
3. 7572
3. 7572
3. 7573
35 20
3. 7574
3. 7575
3. 7575
3. 7576
3. 7577
3. 7578
3. 7579
3. 7579
3. 7580
3. 7581
35 30
3. 7582
3. 7582
3. 7583
3. 7584
3. 7585
3. 7585
3. 7586
3. 7587
3. 7588
3. 7588
35 40
3. 7589
3. 7590
3. 7591
3. 7591
3. 7592
3. 7593
3. 7594
3. 7594
3. 7595
3. 7596
35 50
3. 7597
3. 7597
3. 7598
3. 7599
3. 7600
3. 7600
3. 7601
3. 7602
3. 7603
3. 7603
1 36 0
3. 7604
3. 7605
3. 7606
3. 7606
3. 7607
3. 7608
3. 7609
3. 7609
3. 7610
3. 7611
36 10
3. 7612
3. 7613
3. 7613
3. 7614
3. 7615
3. 7616
3. 7616
3. 7617
3. 7618
3. 7619
36 20
3. 7619
3. 7620
3. 7621
3. 7622
3. 7622
3. 7623
3. 7624
3. 7625
3. 7625
3. 7626
36 30
3. 7627
3. 7628
3. 7628
3. 7629
3. 7630
3. 7631
3. 7631
3. 7632
3. 7633
3. 7634
36 40
3. 7634
3. 7635
3. 7636
3. 7637
3. 7637
3. 7638
3. 7639
3. 7640
3. 7640
3. 7641
36 50
3. 7642
3. 7643
3. 7643
3.7644
3. 7645
3. 7645
3. 7646
3. 7647
3. 7648
3.7648
1 37 0
3. 7649
3. 7650
3. 7651
3.7651
3. 7652
3. 7653
3. 7654
3. 7654
3.7655
3. 7666
37 10
3. 7657
3.7667
3. 7658
3. 7659
3. 7660
3. 7660
3. 7661
3. 7662
3. 7663
3. 7663
37 20
3. 7664
3. 7665
3. 7666
3. 7666
3. 7667
3. 7668
3. 7669
3. 7669
3. 7670
3. 7671
37 30
3. 7672
3. 7672
3. 7673
3. 7674
3. 7675
3. 7675
3. 7676
3. 7677
3. 7677
3. 7678
37 40
3. 7679
3. 7680
3. 7681
3. 7681
3. 7682
3. 7683
3. 7683
3. 7684
3. 7685
3. 7686
37 50
3. 7686
3. 7687
3. 7688
3. 7689
3. 7689
3. 7690
3. 7691
3. 7692
3. 7692
3. 7693
1 38 0
3. 7694
3. 7695
3. 7695
3. 7696
3. 7697
3. 7697
3. 7698
3. 7699
3. 7700
3. 7700
38 10
3. 7701
3. 7702
3. 7703
3. 7703
3. 7704
3. 7705
3. 7706
3. 7706
3. 7707
3. 7708
38 20
3. 7709
3. 7709
3. 7710
3. 7711
3. 7711
3. 7712
3. 7713
3. 7714
3. 7714
3.7715
38 30
3. 7716
3. 7717
3. 7717
3. 7718
3. 7719
3. 7720
3. 7720
3. 7721
3. 7722
3. 7722
38 40
3. 7723
3. 7724
3. 7725
3. 7725
3. 7726
3. 7727
3. 7728
3. 7728
3. 7729
3. 7730
38 50
3. 7731
3. 7731
3. 7732
3. 7733
3. 7733
3. 7734
3. 7735
3. 7736
3. 7736
3. 7737
1 39 0
3. 7738
3. 7739
3. 7739
3. 7740
3. 7741
3. 7742
3. 7742
3. 7743
3. 7744
3. 7744
39 10
3. 7745
3. 7746
3. 7747
3. 7747
3. 7748
3. 7749
3. 7750
3. 7750
3. 7751
3. 7752
39 20
3. 7752
3. 7753
3. 7754
3. 7755
3. 7755
3. 7756
3. 7757
3. 7758
3. 7758
3. 7759
39 30
3. 7760
3. 7760
3. 7761
3. 7762
3. 7763
3. 7763
3. 7764
3. 7765
3. 7766
3. 7766
39 40
3. 7767
3. 7768
3. 7768
3. 7769
3. 7770
3. 7771
3. 7771
3. 7772
3. 7773
3. 7774
39 50
3. 7774
3. 7775
3. 7776
3. 7776
3. 7777
3. 7778
3. 7779
3. 7779
3. 7780
3. 7781
APPENDIX V: TABLE IX.
[Page 323
Logarithms of Small Arcs in
I Space or Time.
Arc. 1
0"
1"
2"
8"
4"
5"
6"
7"
8"
9"
0 /
Ih 40.n
II
0^
3. 7782
3. 7782
3. 7783
3. 7784
3. 7784
3. 7785
3. 7786
3. 7787
3. 7787
3. 7788
40
10
3. 7789
3. 7789
3. 7790
3. 7791
3. 7792
3. 7792
3. 7793
3. 7794
3. 7795
3. 7795
40
20
3. 7796
3. 7797
3. 7797
3. 7798
3. 7799
3. 7800
3. 7800
3. 7801
3. 7802
3. 7802
40
30
3. 7803
3. 7804
3. 7805
3. 7805
3. 7806
3. 7807
3. 7807
3. 7808
3. 7809
3. 7810
40
40
3.7810
3. 7811
3. 7812
3. 7813
3. 7813
3. 7814
3. 7815
3. 7815
3. 7816
3. 7817
40
50
3. 7818
3. 7818
3. 7819
3. 7826
3. 7820
3. 7820
3. 7828
3. 7821
3. 7822
3. 7823
3. 7823
3. 7824
1 41
0
3. 7825
3. 7825
3. 7827
3. 7828
3. 7829
3. 7830
3. 7830
3. 7831
41
10
3. 7832
3. 7833
3. 7833
3. 7834
3. 7835
3. 7835
3. 7836
3. 7837
3. 7838
3. 7838
41
20
3. 7839
3. 7840
3. 7840
3. 7841
3.7842
3. 7843
3. 7843
3. 7844
3. 7845
3. 7845
41
30
3. 7846
3. 7847
3. 7848
3. 7848
3. 7849
3. 7850
3. 7850
3. 7851
3. 7852
3. 7853
41
40
3. 7853
3. 7854
3. 7855
3. 7855
3. 7856
3. 7857
3. 7858
3.7858
3. 7859
3. 7860
41
50
3. 7860
3. 7861
3. 7862
3. 7863
3. 7863
3. 7864
3. 7865
3. 7865
3. 7866
3. 7867
1 42
0
3. 7868
3. 7868
3. 7869
3. 7870
3. 7870
3. 7871
3. 7872
3. 7872
3. 7873
3. 7874
42
10
3. 7875
3. 7875
3. 7876
3. 7877
3. 7877
3. 7878
3. 7879
3. 7880
3. 7880
3. 7881
42
20
3. 7882
3. 7882
3. 7883
3. 7884
3. 7885
3. 7885
3. 7886
3. 7887
3. 7887
3. 7888
42
30
3. 7889
3. 7889
3. 7890
3. 7891
3. 7892
3. 7892
3. 7893
3. 7894
3. 7894
3. 7895
42
40
3. 7896
3. 7897
3. 7897
3. 7898
3. 7899
3. 7899
3. 7900
3. 7901
3. 7901
3. 7902
42
50
3. 7903
3. 7904
3. 7904
3. 7905
3. 7906
3. 7906
3. 7907
3. 7908
3. 7908
3. 7909
1 43
0
3. 7910
3. 7911
3. 7911
. 3. 7912
3. 7913
3.7913
3. 7914
3. 7915
3. 7916
3. 7916
43
10
3. 7917
3. 7918
3. 7918
3. 7919
3. 7920
3. 7920
3. 7921
3. 7922
3. 7923
3. 7923
43
20
3. 7924
3. 7925
3. 7925
3. 7926
3. 7927
3. 7927
3. 7928
3. 7929
3. 7930
3. 7930
43
30
3. 7931
3. 7932
3. 7932
3. 7933
3. 7934
3. 7934
3. 7935
3. 7936
3. 7937
3. 7937
43
40
3. 7938
3. 7939
3. 7939
3. 7940
3. 7941
3. 7941
3. 7942
3. 7943
3. 7943
3. 7944
43
50
3. 7945
3. 7946
3. 7946
3. 7947
3. 7948
3. 7948
3. 7949
3. 7950
3. 7950
3. 7951
1 44
0
3. 7952
3. 7953
3. 7953
3. 7954
3. 7955
3. 7955
3. 7956
3. 7957
3. 7957
3. 7958
44
10
3. 7959
3. 7959
3. 7960
3. 7961
3. 7962
3. 7962
3. 7963
3. 7964
3. 7964
3. 7965
44
20
3. 7966
3. 7966
3. 7967
3. 7968
3. 7969
3. 7969
3. 7970
3. 7971
3. 7971
3. 7972
44
30
3. 7973
3. 7973
3. 7974
3. 7975
3. 7975
3. 7976
3. 7977
3. 7978
3. 7978
3. 7979
44
40
3. 7980
3. 7980
3. 7981
3. 7982
3. 7982
3. 7983
3. 7984
3. 7984
3. 7985
3. 7986
44
50
3. 7987
3. 7987
3. 7988
3. 7989
3. 7989
3. 7990
3. 7991
3. 7991
3. 7992
3. 7993
1 45
0
3. 7993
3. 7994
3. 7995
3. 7995
3. 7996
3. 7997
3. 7998
3. 7998
3. 7999
3.8000
45
10
3. 8000
3. 8001
3. 8002
3. 8002
3. 8003
3. 8004
3. 8004
3.8005
3. 8006
3.8006
45
20
3. 8007
3. 8008
3. 8009
3. 8009
3. 8010
3.8011
3. 8011
3. 8012
3. 8013
3. 8013
45
30
3. 8014
3. 8015
3. 8015
3. 8016
3. 8017
3. 8017
3.8018
3. 8019
3. 8020
3. 8020
45
•40
3. 8021
3. 8022
3. 8022
3. 8023
3. 8024
3. 8024
3. 8025
3. 8026
3. 8026
3. 8027
45
50
3. 8028
3. 8028
3. 8029
3. 8030
3. 8030
3. 8031
3. 8032
3. 8033
3. 8033
3. 8034
1 46
0
3. 8035
3. 8035
3. 8036
3. 8036
3. 8037
3. 8038
3. 8039
3. 8039
3. 8040
3. 8041
46
10
3. 8041
3. 8042
3. 8043
3. 8043
3. 8044
3. 8045
3. 8045
3. 8046
3. 8047
3. 8048
46
20
3. 8048
3. 8049
3. 8050
3. 8050
3. 8051
3. 8052
3. 8052
3. 8053
3. 8054
3. 8054
46
30
3. 8055
3. 8056
3. 8056
3. 8057
3. 8058
3. 8058
3. 8059
3. 8060
3. 8060
3. 8061
46
40
3. 8062
3. 8062
3. 8063
3. 8064
3. 8065
3. 8065
3. 8066
3.8067
3. 8067
3. 8068
46
50
3. 8069
3. 8069
3. 8070
3. 8071
3. 8071
3. 8078
3. 8072
3. 8073
3. 8073
3. 8074
3. 8075
1 47
0
3. 8075
3. 8076
3. 8077
3. 8077
3. 8079
3. 8079
3. 8080
3. 8081
3. 8081
47
10
3. 8082
3. 8083
3. 8083
3. 8084
3. 8085
3. 8085
3. 8086
3. 8087
3. 8088
3. 8088
47
20
3. 8089
3. 8090
3. 8090
3. 8091
3. 8092
3. 8092
3. 8093
3. 8094
3. 8094
3. 8095
47
30
3. 8096
3. 8096
3. 8097
3.8098
3. 8098
3.8099
3. 8099
3. 8100
3. 8101
3. 8102
47
40
3. 8102
3. 8103
3. 8104
3. 8104
3. 8105
3. 8106
3. 8106
3. 8107
3. 8108
3. 8108
47
50
3. 8109
3.8110
3. 8110
3.8111
3. 8112
3.8112
3. 8113
3. 8114
3.8114
3.8115
1 48
0
3.8116
3. 8116
3.8117
3.8118
3.8118
3.8119
3. 8120
3. 8120
3.8121
3. 8122
48
10
3. 8122
3. 8123
3. 8124
3. 8124
3. 8125
3. 8126
3. 8126
3. 8127
3. 8128
3. 8128
48
20
3. 8129
3.8130
3. 8130
3. 8131
3. 8132
3.8132
3. 8133
3. 8134
3. 8134
3. 8135
48
30
3. 8136
3.8136
3. 8137
3. 8138
3. 8138
3. 8139
3. 8140
3. 8140
3. 8141
3. 8142
48
40
3. 8142
3. 8143
3.8144
3. 8144
3. 8145
3. 8146
3. 8146
3. 8147
3. 8148
3. 8148
48
50
3. 8149
3. 8150
3. 8150
3. 8151
3. 8152
3. 8152
3. 8153
3. 8154
3. 8154
3. 8155
1 49
0
3.8156
3. 8156
3. 8157
3. 8158
3. 8158
3. 8159
3. 8160
3. 8160
3. 8161
3. 8162
49
10
3. 8162
3. 8163
3. 8164
3. 8164
3. 8165
3. 8166
3. 8166
3. 8167
3. 8168
3. 8168
49
20
3. 8169
3. 8170
3. 8170
3. 8171
3. 8172
3. 8172
3.8173
3. 8174
3. 8174
3. 8175
49
30
3. 8176
3.8176
3. 8177
3.8178
3. 8178
3.8179
3. 8180
3. 8180
3. 8181
3. 8182
49
40
3. 8182
3. 8183
3. 8184
3. 8184
3. 8185
3. 8185
3. 8186
3. 8187
3. 8188
3. 8188
49
50
3. 8189
3. 8190
3. 8190
3. 8191
3. 8191
3. 8192
3. 8193
3. 8193
3. 8194
3. 8195
Page 324]
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or
Time.
Arc.
0"
1"
2"
8"
4"
6"
6"
7"
8"
9"
O 1
1" 50™
II
0»
3. 8195
3. 8196
3. 8197
3. 8197
3. 8198
3. 8199
3. 8199
3.8200
3. 8201
3. 8201
50
10
3. 8202
3. 8203
3. 8203
3. 8204
3. 8205
3. 8205
3. 8206
3. 8207
3. 8207
3. 8208
50
20
3.8209
3. 8209
3.8210
3.8211
3. 8211
3. 8212
3. 8213
3. 8213
3. 8214
3. 8214
50
30
3. 8215
3. 8216
3. 8216
3. 8217
3. 8218
3. 8218
3. 8219
3. 8220
3. 8220
3. 8221
50
40
3. 8222
•3. 8222
3. 8223
3. 8224
3. 8224
3. 8225
3. 8226
3. 8226
3. 8227
3. 8228
50
50
3. 8228
3. 8229
3. 8230
3. 8236
3. 8230
3. 8231
3. 8231
3. 8232
3. 8233
3. 8239
3. 8233
3. 8240
3. 8234
3. 8241
1 51
0
3. 8235
3. 8235
3. 8237
3. 8237
3. 8238
3. 8239
51
10
3. 8241
3. 8242
3. 8243
3. 8243
3. 8244
3. 8245
3. 8245
3. 8246
3. 8246
3. 8247
51
20
3. 8248
3. 8248
3. 8249
3. 8250
3. 8250
3. 8251
3. 8252
3. 8252
3. 8253
3. 8254
51
30
3. 8254
3. 8255
3. 8256
3. 8256
3. 8257
3. 8258
3. 8258
3. 8259
3. 8259
3. 8260
51
40
3. 8261
3. 8261
3. 8262
3. 8263
3. 8263
3.8264
3.8265
3. 8265
3. 8266
3, 8267
51
50
3. 8267
3. 8268
3. 8269
3. 8269
3. 8270
3. 8270
3. 8271
3. 8272
3. 8272
3. 8273
1 52
0
3. 8274
3. 8274
3. 8275
3. 8276
3. 8276
3. 8277
3. 8278
3. 8278
3. 8279
3. 8280
52
10
3. 8280
3. 8281
3. 8281
3. 8282
3. 8283
3. 8283
3. 8284
3. 8285
3. 8285
3. 8286
52
20
3. 8287
3. 8287
3. 8288
3. 8289
3. 8289
3. 8290
3. 8290
3. 8291
3. 8292
3. 8292
52
30
3.8293
3. 8294
3. 8294
3. 8295
3. 8296
3. 8296
3. 8297
3. 8298
3. 8298
3. 8299
52
40
3. 8299
3.8300
3. 8301
3. 8301
3. 8302
3. 8303
3. 8303
3. 8304
3. 8305
3. 8305
52
50
3. 8306
3. 8307
3. 8307
3. 8308
3. 8308
3. 8309
3. 8310
3. 8310
3. 8311
3. 8312
1 53
0
3. 8312
3. 8313
3. 8314
3. 8314
3. 8315
3. 8315
3. 8316
3. 8317
3. 8317
3. 8318
53
10
3. 8319
3. 8319
3. 8320
3. 8321
3. 8321
3. 8322
3. 8323
3. 8323
3. 8324
3. 8324
53
20
3. 8325
3. 8326
3. 8326
3. 8327
3. 8328
3. 8328
3. 8329
3. 8330
3. 8330
3. 8331
53
30
3. 8331
3. 8332
3. 8333
3. 8333
3. 8334
3. 8335
3. 8335
3. 8336
3. 8337
3. 8337
53
40
3. 8338
3. 8338
3. 8339
3. 8340
3. 8340
3. 8341
3. 8342
3. 8342
3. 8343
3. 8344
53
1 54
50
0
3. 8344
3. 8345
3. 8345
3. 8346
3. 8347
3. 8347
3. 8348
3. 8349
3. 8349
3. 8350
3. 8351
3. 8351
3. 8352
3. 8352
3. 8353
3. 8354
3. 8354
3. 8355
3. 8356
3. 8356
54
10
3. 8357
3. 8358
3. 8358
3. 8359
3. 8359
3. 8360
3. 8361
3. 8361
3. 8362
3. 8363
54
20
3. 8363
3. 8364
3. 8365
3. 8365
3. 8366
3. 8366
3.8367
3. 8368
3. 8368
3. 8369
54
30
3. 8370
3. 8370
3. 8371
3. 8371
3. 8372
3. 8373
3. 8373
3. 8374
3. 8375
3. 8375
54
40
3. 8376
3. 8377
3. 8377
3. 8378
3. 8378
3. 8379
3. 8380
3. 8380
3. 8381
3. 8382
54
50
3. 8382
3. 8383
3. 8383
3. 8384
3. 8385
3. 8391
3. 8385
3. 8392
3. 8386
3. 8387
3. 8393
3. 8387
3. 8388
1 55
0
3. 8388
3. 8389
3. 8390
3. 8390
3. 8392
3. 8394
3. 8394
55
10
3. 8395
3. 8395
3. 8396
3. 8397
3. 8397
3. 8398
3. 8399
3. 8399
3. 8400
3. 8400
55
20
3. 8401
3. 8402
3. 8402
3. 8403
3. 8404
3. 8404
3. 8405
3. 8405
3. 8406
3. 8407
55
30
3. 8407
3. 8408
3. 8409
3. 8409
3. 8410
3. 8410
3. 8411
3. 8412
3. 8412
3.8413
55
40
3. 8414
3. 8414
3. 8415
3. 8415
3. 8416
3. 841/
3. 8417
3. 8418
3. 8419
3. 8419
55
50
3. 8420
3. 8420
3. 8421
3. 8422
3. 8422
3. 842S
3. 8424
3. 8424
3. 8425
3. 8425
1 56
0
3. 8426
3. 8427
3. 8427
3. 8428
3. 8429
3. 8429
3. 8430
3. 8430
3. 8431
3. 8432
56
10
3. 8432
3. 8433
3. 8434
3. 8434
3.8435
3. 8435
3. 8436
3. 8437
3. 8437
3. 8438
56
20
3. 8439
3. 8439
3. 8440
3. 8440
3. 8441
3. 8442
3.8442
3. 8443
3. 8444
3. 8444
56
30
3. 8445
3.8445
3. 8446
3. 8447
3. 8447
3.8448
3. 8448
3. 8449
3. 8450
3. 8450
56
40
3. 8451
3. 8452
3. 8452
3. 8453
3. 8453
3. 8454
3. 8455
3. 8455
3. 8456
3. 8457
56
50
3. 8457
3. 8458
3. 8458
3. 8459
3. 8460
3. 8460
3. 8461
3. 8462
3. 8462
3. 8463
1 57
0
3. 8463
3. 8464
3.8465
3. 8465
3. 8466
3. 8466
3. 8467
3. 8468
3. 8468
3. 8469
57
10
3. 8470
3. 8470
3. 8471
3. 8471
3. 8472
3. 8473
3. 8473
3. 8474
3. 8474
3. 8475
57
20
3. 8"476
3. 8476
3. 8477
3. 8478
3. 8478
3. 8479
3. 8479
3. 8480
3. 8481
3. 8481
57
30
3. 8482
3. 8483
3. 8483
3. 8484
3. 8484
3. 8485
3. 8486
3. 8486
3. 8487
3. 8487
57
40
3. 8488
3. 8489
3. 8489
3. 8490
3. 8491
3. 8491
3. 8492
3. 8492
3. 8493
3. 8494
57
50
3. 8494
3. 8495
3. 8495
3. 8496
3. 8497
3.8503'
3. 8497
3. 8498
3. 8499
3. 8499
3. 8500
1 58
0
3. 8500
3. 8501
3. 8502
3. 8502
3. 8503
3. 8504
3. 8505
3. 8505
3. 8506
58
10
3. 8506
3. 8507
3; 8508
3. 8508
3. 8509
3. 8510
3. 8510
3. 8511
3. 8511
3. 8512
58
20
3. 8513
3. 8513
3. 8514
3. 8514
3. 8515
3. 8516
3. 8516
3.8517
3. 8517
3. 8518
58
30
3. 8519
3. 8519
3. 8520
3. 8521
3. 8521
3. 8522
3. 8522
3. 8523
3. 8524
3. 8524
58
40
3. 8525
3. 8525
3. 8526
3. 8527
3. 8527
3. 8528
3. 8528
3. 8529
3. 8530
3. 8530
58
50
3. 8531
3. 8532
3. 8532
3. 8533
3. 8533
3. 8534
3. 8535
3. 8535
3. 8536
3.8536
1 59
0
3. 8537
3. 8538
3. 8538
3. 8539
3. 8539
3. 8540
3. 8541
3.8541
3. 8542
3. 8542
59
10
3. 8543
3. 8544
3. 8544
3. 8545
3. 8545
3. 8546
3. 8547
3. 8547
3. 8548
3. 8549
59
20
3. 8549
3. 8550
3. 8550
3. 8551
3. 8552
3. 8552
3. 8553
3. 8553
3. 8554
3. 8555
59
30
3. 8555
3. 8556
3. 8556
3. 8557
3. 8558
3. 8558
3. 8559
3. 8559
3. 8560
3. 8561
59
40
3. 8561
3. 8562
3. 8562
3. 8563
3. 8564
3. 8564
3. 8565
3. 8565
3. 8566
3. 8567
59
50
3. 8567
3. 8568
3. 8568
3. 8569
3. 8570
3.8570
3. 8571
3. 8572
3. 8572
3. 8573
APPENDIX
V: TABLE IX.
[Page 325
Logarithms of Small Arcs in
Space or Time.
Arc.
0"
1"
2"
3"
4"
6"
6"
7"
8"
9"
o /
2" 0™
0«
3. 8573
3. 8574
3. 8575
3.8575
3. 8576
3. 8576
3. 8577
3. 8578
3. 8578
3. 8579
0
10
3. 8579
3. 8580
3. 8581
3. 8581
3. 8582
3. 8582
3. 8583
3. 8584
3. 8584
3. 8585
0
20
3. 8585
3. 8586
3. 8587
3. 8587
3. 8588
3. 8588
3. 8589
3. 8590
3. 8590
3. 8591
0
80
3. 8591
3. 8592
3. 8593
3. 8593
3. 8594
3. 8594
3. 8595
3. 8596
3. 8596
3. 8597
0
40
3. 8597
3. 8598
3. 8599
3. 8599
3. 8600
3. 8600
3. 8601
3. 8602
3. 8602
3. 8603
0
50
3. 8603
3. 8604
3. 8605
3. 8605
3. 8606
3. 8606
3. 8607
3. 8608
3. 8608
3. 8609
2 1
0
3. 8609
3. 8610
3. 8611
3. 8611
3. 8612
3. 8612
3. 8613
3. 8614
3. 8614
3. 8615
10
3. 8615
3. 8616
3. 8617
3. 8617
3. 8618
3. 8618
3. 8619
3. 8620
3. 8620
3. 8621
20
3. 8621
3. 8622
3. 8623
3. 8623
3. 8624
3. 8624
3. 8625
3. 8625
3. 8626
3. 8627
30
3. 8627
3. 8628
3. 8628
3. 8629
3. 8630
3. 8630
3. 8631
3. 8631
3. 8632
3. 8633
40
3. 8633
3. 8634
3. 8634
3. 8635
3. 8636
3. 8636
3. 8637
3. 8637
3. 8638
3. 8639
50
3. 8639
3. 8640
3. 8640
3. 8641
3.8642
3. 8642
3. 8643
3. 8643
3. 8644
3. 8645
2 2
0
3. 8645
3. 8646
3. 8646
3. 8647
3.8647
3. 8648
3. 8649
3. 8649
3. 8650
3. 8650
2
10
3. 8651
3. 8652
3. 8652
3. 8653
3. 8653
3. 8654
3. 8655
3. 8655
3. 8656
3. 8656
2
20
3. 8657
3. 8658
3. 8658
3. 8659
3. 8659
3. 8660
3. 8661
3. 8661
3. 8662
3. 8662
2
30
3. 8663
3. 8663
3. 8664
3. 8665
3. 8665
3. 8666
3. 8666
3. 8667
3. 8668
3. 8668
2
40
3. 8669
3. 8669
3. 8670
3. 8671
3. 8671
3. 8672
3. 8672
3. 8673
3. 8673
3. 8674
2
50
3. 8675
3. 8675
3. 8676
3. 8676
3. 8677
3. 8678
3. 8678
3. 8679
3. 8679
3. 8680
3. 8686
2 3
0
3. 8681
3. 8681
3. 8682
3. 8682
3. 8683
3. 8684
3. 8684
3. 8685
3. 8685
3
10
3. 8686
3. 8687
3. 8688
3. 8688
3. 8689
3. 8689
3. 8690
3. 8691
3. 8691
3. 8692
3
20
3. 8692
3. 8693
3. 8693
3. 8694
3. 8695
3. 8695
3. 8696
3. 8696
3. 8697
3. 8698
3
30
3. 8698
3. 8699
3. 8699
3. 8700
3. 8701
3. 8701
3. 8702
3. 8702
3. 8703
3. 8703
3
40
3. 8704
3. 8705
3. 8705
3. 8706
3. 8706
3. 8707
3. 8708
3. 8708
3. 8709
3. 8709
3
50
3. 8710
3. 8710
3. 8711
3.8712
3. 8712
3.8713
3. 8713
3. 8714
3. 8715
3. 8715
2 4
0
3. 8716
3. 8716
3.8717
3.8717
3. 8718
3. 8719
3. 8719
3. 8720
3. 8720
3. 8721
4
10
3. 8722
3. 8722
3. 8723
3. 8723
3. 8724
3. 8724
3. 8725
3. 8726
3. 8726
3. 8727
4
20
3. 8727
3. 8728
3. 8729
3. 8729
3. 8730
3. 8730
3. 8731
3. 8731
3. 8732
3. 8733
4
30
3. 8733
3. 8734
3. 8734
3. 8735
3. 8736
3. 8736
3. 8737
3. 8737
3. 8738
3. 8738
4
40
3. 8739
3. 8740
3. 8740
3. 8741
3. 8741
3. 8742
3. 8742
3. 8743
3. 8744
3. 8744
4
50
3. 8745
3. 8745
3. 8746
3. 8747
3. 8747
3. 8748
3. 8748
3. 8749
3. 8749
3. 8750
2 5
0
3. 8751
3. 8751
3. 8752
3. 8752
3. 8753
3. 8754
3. 8754
3. 8755
3. 8755
3. 8756
5
10
3. 8756
3. 8757
3. 8758
3. 8758
3. 8759
3. 8759
3. 8760
3. 8760
3. 8761
3. 8762
5
20
3. 8762
3. 8763
3. 8763
3. 8764
3. 8764
3. 8765
3. 8766
3. 8766
3. 8767
3. 8767
5
30
3. 8768
3. 8769
3. 8769
3. 8770
3. 8770
3. 8771
3. 8771
3. 8772
3. 8773
3. 8773
5
.40
3. 8774
3. 8774
3. 8775
3. 8775
3. 8776
3. 8777
3. 8777
3. 8778
3. 8778
3. 8779
5
50
3. 8779
3. 8780
3. 8781
3. 8781
3. 8782
3. 8782
3. 8783
3. 8783
3. 8784
3. 8790
3. 8785
2 6
0
3. 8785
3. 8786
3. 8786
3. 8787
3. 8788
3.8788 i 3.8789
3. 8789
3. 8790
6
10
3. 8791
3. 8792
3. 8792
3. 8793
3. 8793
3. 8794
3. 8794
3. 8795
3. 8796
3. 8796
6
20
3. 8797
3. 8797
3. 8798
3. 8798
3. 8799
3. 8800
3. 8805
3.8800
3. 8801
3. 8801
3. 8802
6
30
3. 8802
3. 8803
3. 8804
3. 8804
3. 8805
3. 8806
3. 8806
3. 8807
3. 8808
6
40
3. 8808
3. 8809
3. 8809
3. 8810
3. 8810
3. 8811
3.8812
3. 8812
3. 8813
3. 8813
6
50
3. 8814
3. 8814
3. 8820
3.8815 i 3.8816
3. 8816
3. 8822
3. 8817
3. 8822
3. 8817
3. 8818
3. 8824
3. 8818
3. 8824
3. 8819
3. 8825
2 7
0
3. 8820
3. 8821
3. 8821
3. 8823
(
10
3. 8825
3. 8826
3. 8826
3. 8827
3. 8828
3. 8828
3. 8829
3. 8829
3. 8830
3. 8830
7
20
3. 8831
3. 8832
3. 8832
3. 8833
3. 8833
3. 8834
3. 8834
3. 8835
3. 8835
3. 8836
7
30
3. 8837
3. 8837
3. 8838 3. 8838
3. 8839
3. 8839
3. 8840
3. 8841
3.8841
3. 8842
7
40
3. 8842
3. 8843
3. 8843
3. 8844
3. 8845
3. 8845
3. 8846
3. 8846
3. 8847
3. 8847
7
50
3. 8848
3. 8849
3. 8849
3. 8850
3. 8850
3. 8851
3. 8851
3. 8852
3. 8852
3. 8853
2 8
0
3. 8854
3. 8854
3. 8855
3. 8855
3. 8856
3. 8856
3. 8857
3. 8858
3.8858
3. 8859
8
10
3. 8859
3. 8860
3. 8860
3. 8861
3. 8862
3. 8862
3. 8863
3. 8863
3. 8864
3. 8864
8
20
3. 8865
3. 8865
3. 8866
3. 8867
3. 8867
3. 8868
3. 8868
3. 8869
3. 8869
3. 8870
8
30
3. 8871
3. 8871
3. 8872
3. 8872
3. 8873
3. 8873
3. 8874
3. 8874
3. 8875
3. 8876
8
40
3. 8876
3. 8877
3. 8877
3. 8878
3. 8878
3.8879
3. 8880
3. 8880
3. 8881
3. 8881
8
50
3. 8882
3. 8882
3. 8883
3. 8883
3. 8884
3. 8885
3. 8885
3. 8886
3. 8886
3. 8887
2 9
0
3. 8887
3. 8888
3. 8889
3. 8889
3. 8890
3.8890
3. 8891
3. 8891
3. 8892
3. 8892
9
10
3. 8893
3. 8894
3. 8894
3. 8895
3. 8895
3. 8896
3. 8896
3. 8897
3. 8897
3. 8898
9
20
3. 8899
3. 8899
3. 8900
3. 8900
3. 8901
3. 8901
3. 8902
3. 8903
3. 8903
3. 8904
9
30
3. 8904
3. 8905
3. 8905
3. 8906
3. 8906
3. 8907
3. 8908
3. 8908
3. 8909
3. 8909
9
40
3. 8910
3. 8910
3. 8911
3. 8911
3. 8912
3. 8912
3. 8913
3. 8914
3. 8914
3. 8915
9
50
3. 8915
3. 8916
3. 8916
3. 8917
3. 8918
3. 8918
3. 8919
3. 8919
3. 8920
3. 8920
Page 326J
APPENDIX V: TABLE IX. 1
Logarithms of Small Arcs in
Space or
Time.
Arc. 1
0"
1"
2"
8"
4"
5"
6"
V
8"
9"
o /
2h 10"'
0'
3. 8921
3. 8922
3. 8922
3. 8923
3. 8923
3. 8924
3. 8924
3. 8925
3. 8925
3. 8926
10
10
5. 8927
3. 8927
3. 8928
3. 8928
3. 8929
3.8929
3. 8930
3. 8930
3. 8931
3. 8932
10
20
3. 8932
3. 8933
3. 8933
3. 8934
3. 8934
3. 8935
3. 8935
3. 8936
3. 8937
3. 8937
10
30
3. 8938
3. 8938
3. 8939
3. 8939
3. 8940
3. 8940
3. 8941
3. 8941
3. 8942
3. 8943
10
40
3. 8943
3. 8944
3. 8944
3. 8945
3. 8945
3. 8946
3. 8946
3. 8947
3. 8948
3. 8948
10
50
3. 8949 *
> 3. 8949
3. 8950
3. 8950
3. 8951
3. 8951
3. 8952
3. 8953
3. 8953
3. 8954
2 11
0
3. 8954
3. 8955
3. 8955
3. 8956
3. 8956
3. 8957
3. 8958
3. 8958
3. 8959
3. 8959
11
10
3. 8960
3. 8960
3. 8961
3. 8961
3. 8962
3. 8963
3. 8963
3.8964
3.8964
3. 8965
11
20
3. 8965
3. 8966
3. 8966
3. 8967
3. 8967
3. 8968
3. 8969
3. 8969
3. 8970
3. 8970
11
30
3. 8971
3. 8971
3. 8972
3. 8972
3. 8973
3. 8974
3. 8974
3. 8975
3. 8975
3. 8976
11
40
3. 8976
3. 8977
3. 8977
3. 8978
3. 8978
3. 8979
3. 8980
3. 8980
3. 8981
3. 8981
11
50
3. 8982
3. 8982
3. 8983
3. 8983
3. 8989
3. 8984
3. 8989
3.8985
3. 8985
3. 8991
3. 8986
3. 8991
3. 8986
3."8992
3. 8987
3. 8992
2 12
0
3. 8987
3. 8988
3. 8988
3. 8990
12
10
3. 8993
3. 8993
3. 8994
3. 8994
3. 8995
3. 8995
3. 8996
3. 8997
3. 8997
3. 8998
12
20
3. 8998
3. 8999
3. 8999
3.9000
3. 9000
3. 9001
3.9001
3. 9002
3. 9003
3. 9003
12
30
3. 9004
3. 9004
3. 9005
3. 9005
3.9006
3. 9006
3. 9007
3. 9007
3. 9008
3. 9009
12
40
3. 9009
3. 9010
3. 9010
3. 9011
3.9011
3. 9012
3. 9012
3. 9013
3. 9013
3. 9014
12
50
3. 9015
3. 9015
3. 9016
3. 9016
3.9017
3. 9017
3. 9018
3. 9018
3.9019
3. 9019
2 13
0
3. 9020
3. 9021
3. 9021
3. 9022
3. 9022
3. 9023
3. 9023
3. 9024
3. 9024
3. 9025
13
10
3. 9025
3. 9026
3. 9027
3. 9027
3. 9028
3. 9028
3. 9029
3. 9029
3. 9030
3. 9030
13
20
3. 9031
3. 9031
3. 9032
3. 9033
3. 9033
3. 9034
3. 9034
3. 9035
3. 9035
3. 9036
13
30
3. 9036
3. 9037
3. 9037
3. 9038
3. 9038
3. 9039
3. 9040
3. 9040
3. 9041
3. 9041
13
40
3. 9042
3. 9042
3.9043
3. 9043
3. 9044
3. 9044
3. 9045
3. 9046
3. 9046
3. 9047
13
50
3. 9047
3. 9048
3. 9048
3. 9049
3. 9049
3. 9050
3. 9050
3. 9051
3. 9051
3. 9052
2 14
0
3. 9053
3. 9053
3. 9054
3. 9054
3. 9055
3. 9055
3. 9056
3. 9056
3. 9057
3. 9057
14
10
3. 9058
3. 9058
3. 9059
3. 9060
3. 9060
3. 9061
3. 9061
3. 9062
3. 9062
3. 9063
14
20
3. 9063
3. 9064
3. 9064
3. 9065
3. 9066
3. 9066
3. 9067
3. 9067
3. 9068
3. 9068
14
30
3. 9069
3. 9069
3. 9070
3. 9070
3. 9071
3. 9071
3. 9072
3. 9073
3. 9073
3. 9074
14
40
3. 9074
3. 9075
3. 9075
3. 9076
3. 9076
3. 9077
3. 9077
3. 9078
3. 9078
3. 9079
14
50
3. 9079
3. 9080
3. 9081
3. 9081
3. 9082
3. 9087
3. 9082
3. 9088
3. 9083
3. 9088
3. 9083
3. 9089
3. 9084
"3. 9089
3. 9084
3. 9090
2 15
0
3. 9085
3. 9085
3. 9086
3. 9086
15
10
3. 9090
3. 9091
3. 9091
3. 9092
3. 9092
3. 9093
3. 9093
3. 9094
3. 9094
3. 9095
15
20
3. 9096
3. 9096
3. 9097
3. 9097
3. 9098
3. 9098
3. 9099
3. 9099
3. 9100
3. 9100
15
30
3. 9101
3. 9101
3. 9102
3. 9103
3. 9103
3. 9104
3.9104
3. 9105
3. 9105
3. 9106
15
40
3. 9106
3. 9107
3. 9107
3. 9108
3. 9108
3. 9109
3. 9109
3. 9110
3. 9111
3.9111
15
50
3.9112
3. 9112
3. 9113
3. 9113
3.9114
3.9114
3.9115
3. 9115
3. 9116
3. 9116
2 16
0
3.9117
3.9117
3.9118
3.9118
3.9119
3. 9120
3.9120
3. 9121
3.9121
3. 9122
16
10
3. 9122
3.9123
3. 9123
3. 9124
3. 9124
3. 9125
3. 9125
3. 9126
3. 9126
3.9127
16
20
3. 9128
3. 9128
3. 9129
3. 9129
3. 9130
3. 9130
3. 9131
3. 9131
3. 9132
3. 9132
16
30
3. 9133
3. 9133
3. 9134
3. 9134
3. 9135
3. 9135
3. 9136
3. 9137
3.9137
3. 9138
16
40
3. 9138
3. 9139
3. 9139
3. 9140
3. 9140
3. 9141
3. 9141
3. 9142
3. 9142
3. 9143
16
50
3. 9143
3. 9144
3. 9144
3. 9145
3. 9146
3.9146
3. 9147
3. 9147
3. 9148
8. 9148
2 17
0
3. 9149
3. 9149
3. 9150
3. 9150
3. 9151
3. 9151
3. 9152
3. 9152
3. 9153
3.9153
17
10
3. 9154
3.9155
3. 9155
3. 9156
3. 9156
3.9157
3. 9157
3. 9158
3. 9158
3.9159
17
20
3. 9159
3. 9160
3. 9160
3. 9161
3. 9161
3. 9162
3. 9162
3. 9163
3. 9163
3. 9164
17
30
3. 9165
3. 9165
3. 9166
3. 9166
3. 9167
3.9167
3. 9168
3.9168
3. 9169
3. 9169
17
40
3. 9170
3. 9170
3. 9171
3.9171
3. 9172
3. 9172
3. 9173
3.9173
3. 9174
3. 9175
17
50
3. 9175
3. 9176
3. 9176
3.9177
3.9177
3. 9178
3. 9178
3. 9179
3. 9179
3. 9180
2 18
0
3. 9180
3. 9181
3. 9181
3. 9182
3. 9182
3. 9183
3. 9183
3. 9184
3. 9184
3. 9185
18
10
3. 9186
3. 9186
3. 9187
3. 9187
3. 9188
3. 9188
3. 9189
3. 9189
3. 9190
3. 9190
18
20
3. 9191
3. 9191
3. 9192
3. 9192
3. 9193
3. 9193
3. 9194
3. 9194
3. 9195
3. 9195
18
30
3. 9196
3. 9197
3. 9197
3. 9198
3. 9198
3. 9199
3. 9199
3. 9200
3. 9200
3. 9201
18
40
3. 9201
3. 9202
3. 9202
3. 9203
3. 9203
3. 9204
3.9204
3. 9205
3. 9205
3.9206
18
50
3. 9206
3. 9207
3. 9207
3. 9208
3. 9209
3. 9214
3. 9209
3. 9210
3. 9210
3. 9215
3. 9211
3. 9216
3. 9211
2 19
0
3. 9212
3. 9212
3. 9213
3. 9213
3. 9214
3. 9215
3. 9216
19
10
3. 9217
3. 9217
3. 9218
3. 9218
3. 9219
3. 9219
3. 9220
3. 9221
3. 9221
3. 9222
19
20
3. 9222
3. 9223
3. 9223
3. 9224
3. 9224
3. 9225
3. 9225
3. 9226
3. 9226
3. 9227
19
30
3. 9227
3. 9228
3. 9228
3. 9229
3.9229
3. 9230
3. 9230
3. 9231
3. 9231
3. 9232
19
40
3. 9232
3. 9233
3. 9233
3. 9234
3. 9235
3. 9235
3. 9236
3. 9236
3. 9237
3. 9237
19
50
3. 9238
3. 9238
3. 9239
3. 9239
3. 9240
3. 9240
3. 9241
3. 9241
3. 9242
3. 9242
1
APPENDIX V: TABLE IX.
[Page 327
Logarithms of Small Arcs in Space or
Time.
Arc.
0"
1"
2"
8"
4"
5"
6"
7"
8"
9"
0 /
2*^ 20™
0'
3. 9243
3. 9243
3. 9244
3. 9244
3. 9245
3. 9245
3. 9246
3.9246
3. 9247
3, 9247
20
10
3. 9248
3. 9248
3. 9249
3. 9250
3. 9250
3. 9251
3. 9251
3. 9252
3. 9252
3. 9253
20
20
3. 9253
3. 9254
3. 9254
3. 9255
3. 9255
3. 9256
3. 9256
3. 9257
3. 9257
3. 9258
20
30
3. 9258
3. 9259
3. 9259
3. 9260
3. 9260
3. 9261
3. 9261
3. 9262
3. 9262
3. 9263
20
40
3. 9263
3. 9264
3. 9264
3. 9265
3. 9265
3. 9266
3. 9267
3. 9267
3. 9268
3. 9268
20
50
3. 9269
3. 9269
3. 9270
3. 9270
3. 9271
3. 9271
3. 9272
3. 9272
3. 9273
3. 9273
2 21
0
3. 9274
3. 9274
3. 9275
3. 9275
3.9276 i 3.9276
3. 9277
3. 9277
3. 9278
3. 9278
21
10
3. 9279
3. 9279
3. 9280
3. 9280
3.9281 1 3.9281
3. 9282
3. 9282
3. 9283
3. 9283
21
20
3. 9284
3. 9284 .
3. 9285
3. 9285
3.9286 1 3.9287
3. 9287
3. 9288
3. 9288
3. 9289
21
30
3. 9289
3. 9290
3. 9290
3. 9291
3. 9291 3. 9292
3. 9292
3.9293 3.9293
3. 9294
21
40
3. 9294
3. 9295
3. 9295
3. 9296
3. 9296
3. 9297
3. 9297
3.9298 3.9298
3. 9299
21
50
3. 9299
3.9300
3. 9300
3. 9301
3. 9301
3. 9302
3. 9302
3. 9303
3. 9303
3. 9304
2 22
0
3. 9304
3. 9305
3. 9305
3. 9306
3. 9306
3. 9307
3. 9307
3. 9308
3. 9308 1 3. 9309 |
22
10
3. 9309
3. 9310
3. 9311
3.9311
3. 9312
3. 9312
3. 9313
3. 9313
3. 9314
3. 9314
22
20
3. 9315
3. 9315
3. 9316
3. 9316
3.9317
3.9317
3. 9318
3. 9318
3. 9319
3. 9319
22
30
3. 9320
3. 9320
3. 9321
3. 9321
3.9322 1 3.9322
3. 9323
3. 9323
3. 9324
3. 9324
22
40
3. 9325
3. 9325
3. 9326
3. 9326
3.9327 3.9.327
3. 9328
3. 9328
3. 9329
3. 9329
22
50
3. 9330
3. 9330
3. 9331
3. 9331
379336"
3.9332 3.9332
3. 9333
3. 9333
3. 9334
3. 9334
2 23
0
3. 9335
3. 9335
3. 9336
3.9337 ; 3.9337
3. 9338
3.9338 3.9339
3. 9339
23
10
3. 9340
3. 9340
3. 9341
3. 9341
3. 9342 3.' 9342
3. 9343
3. 9343
3. 9344
3. 9344
23
20
3. 9345
3. 9345
3. 9346
3. 9346
3. 9347 3. 9348
3. 9348
3. 9349
3. 9349
3. 9350
23
30
3. 9350
3. 9351
3. 9351
3. 9352
3.9352 ! 3.9353
3. 9353
3.9354
3. 9354
3. 9355
23
40
3. 9355
3. 9356
3. 9356
3. 9357
3.9357 1 3.9358
3. 9358
3. 9359
3. 9359
3. 9360
23
50
3. 9360
3. 9361
3. 9361
3. 9362
3.9362 1 3.9363
3. 9363
3. 9364
3. 9364
3. 9365
2 24
0
3. 9365
3. 9366
3. 9366
3. 9367
3. 9367
3. 9368
3. 9368
3. 9369
3. 9369 i 3. 9370
24
10
3. 9370
3. 9371
3. 9371
3. 9372
3. 9372
3. 9373
3. 9373
3. 9374
3.9374 3.9375
24
20
3. 9375
3. 9376
3. 9376
3. 9377
3. 9377
3. 9378
3. 9378
3. 9379
3. 9379 3. 9380
24
30
3. 9380
3. 9381
3. 9381
3. 9382
3. 9382
3. 9383
3. 9383
3. 9384
3. 9384 i 3. 9385
24
40
3. 9385
3. 9386
3. 9386
3. 9387
3. 9387
3. 9388
3. 9388
3. 9389
3. 9389 i 3. 9390
24
50
3. 9390
3. 9391
3. 9391
3. 9392
3. 9392
3. 9397
3. 9393
3. 9398
3. 9393
3. 9394
3. 9394
3. 9399
3. 9395
2 25
0
3. 9395
3. 9396
3. 9396
3. 9397
3. 9398
3. 9399
3.9400
25
10
3. 9400
3. 9401
3. 9401
3. 9402
3. 9402
3. 9403
3. 9403
3. 9404
3. 9404
3. 9405
25
20
3. 9405
3. 9406
3. 9406
3. 9407
3. 9407
3. 9408
3. 9408
3. 9409
3. 9409
3. 9410
25
30
3. 9410
3.9411
3. 9411
3. 9412
3. 9412
3. 9413
3. 9413
3. 9414
3. 9414
3. 9415
25
40
3. 9415
3. 9416
3. 9416
3. 9417
3. 9417
3. 9418
3. 9418
3. 9419
3. 9419
3. 9420
25
50
3. 9420
3. 9421
3. 9421
3. 9422
3. 9422
3. 9423
3. 9423
3. 9424
3. 9424
3. 9425
2 26
0
3. 9425
3. 9426
3. 9426
3. 9427
3. 9427
3. 9428
3. 9428
3. 9429
3. 9429
3. 9430
26
10
3. 9430
3. 9430
3. 9431
3. 9431
3. 9432
3. 9432
3. 9433
3. 9433
3. 9434
3. 9434
26
20
3. 9435
3. 9435
3. 9436
3. 9436
3. 9437
3. 9437
3. 9438
3. 9438
3. 9439
3. 9439
26
30
3. 9440
3.9440
3. 9441
3. 9441
3. 9442
3. 9442
3. 9443
3. 9443
3. 9444
3. 9444
26
40
3. 9445
3.9445
3. 9446
3. 9446
3. 9447
3. 9447
3. 9448
3. 9448
3.9449
3. 9449
26
50
3. 9450
3. 9450
3. 9451
3. 9451
3. 9452
3. 9452
3. 9453
3. 9453
3. 9454
3. 9454
2 27
0
3. 9455
3. 9455
3. 9456
3. 9456
3. 9457
3. 9457
3. 9458
3. 9458
3. 9459
3. 9459
27
10
3. 9460
3. 9460
3. 9461
3. 9461
3. 9462
3. 9462
3. 9463
3. 9463
3.9464
3. 9464
27
20
3. 9465
3. 9465
3. 9466
3. 9466
3. 9466
3. 9467
3. 9467
3. 9468
3. 9468
3. 9469
2-'
30
3. 9469
3. 9470
3. 9470
3. 9471
3. 9471
3. 9472
3. 9472
3. 9473
3. 9473
3. 9474
27
40
3. 9474
3. 9475
3. 9475
3. 9476
3. 9476
3. 9477
3. 9477
3. 9478
3. 9478
3. 9479
27
50
3. 9479
3. 9480
3. 9480
3. 9481
3. 9481
3. 9482
3. 9482
3. 9483
3. 9483
3. 9484
2 28
0
3. 9484
3. 9485
3. 9485
3. 9486
3. 9486
3. 9487
3. 9487
3. 9488
3. 9488
3. 9489
28
10
3. 9489
3. 9490
3. 9490
3. 9490
3. 9491
3. 9491
3. 9492
3. 9492
3. 9493
3. 9493
28
20
3. 9494
3. 9494
3. 9495
3. 9495
3. 9496
3. 9496
3. 9497
3. 9497
3. 9498
3. 9498
28
30
3. 9499
3. 9499
3. 9500
3. 9500
3. 9501
3. 9501
3. 9502
3. 9502
3. 9503
3. 9503
28
40
3. 9504
3. 9504
3. 9505
3. 9505
3. 9506
3. 9506
3. 9507
3. 9507
3. 9508
3. 9508
28
50
3. 9509
3. 9509
3.9509
3. 9510
3. 9510
3. 9511
3. 9511
3. 9512
3. 9512
3. 9513
2 29
0
3. 9513
3. 9514
3. 9514
3. 9515
3. 9515
3. 9516
3. 9516
3. 9517
3. 9517
3. 9518
29
10
3. 9518
3. 9519
3. 9519
3. 9520
3. 9520
3. 9521
3. 9521
3. 9522
3. 9522
3. 9523
29
20
3. 9523
3. 9524
3. 9524
3. 9525
3. 9525
3. 9526
3. 9526
3. 9526
3. 9527
3. 9527
29
30
3. 9528
3. 9528
3. 9529
3. 9529
3. 9530
3. 9530
3. 9531
3. 9531
3. 9532
3. 9532
29
40
3. 9533
3. 9533
3. 9534
3. 9534
3. 9535
3. 9435
3. 9536
3. 9536
3. 9537
3. 9537
29
50
3. 9538
3. 9538
3. 9539
3. 9539
3. 9540
3. 9540
3. 9540
3. 9541
3. 9541
3.9542
Page
328]
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or Time.
Arc.
0"
1"
2"
8"
4"
5"
6"
7" 1 8" 1 9" 1
o /
2^ 30"
0'
3.9542 1 3.9543
3.9543
3.9544
3.9544
3. 9545
3. 9545
3. 9546
3.9546
3. 9547
30
10
3.9547 1 3.9548
3. 9548
3. 9549
3. 9549
3.9550
3. 9550
3. 9551
3. 9551
3. 9552
30
20
3. 9552
3. 9553
-3.9553
3. 9554
3. 9554
3. 9554
3. 9555
3. 9555
3. 9556
3. 9556
30
30
3. 9557
3. 9557
3. 9558
3. 9558
3. 9559
3. 9559
3. 9560
3. 9560
3. 9561
3. 9561
30
40
3. 9562 1 ^. 9562
3.9566 ! 3.9567
3. 9563
3. 9563
3. 9564
3. 9564
3. 9565
3. 9565
3. 9566
3. 9566
30
50
3. 9567
3. 9568
3. 9573
3. 9568
3. 9573
3. 9569
3.9574
3. 9569
3. 9570
3. 9570
3:9575'
3. 9571
3. 9576
2 31
0
3.9571 3.9572
3. 9572
3. 9574
3. 9575
31
10
3.9576 3.9577
3. 9577
3. 9578
3. 9578
3. 9578
3. 9579
3. 9579
3. 9580
3. 9580
31
20
3.9581 t 3.9581
3. 9582
3. 9582
3. 9583
3. 9583
3. 9584
3. 9584
3. 9585
3. 9585
31
30
3.9586 3.9586
3. 9587
3. 9587
3. 9588
3. 9588
3. 9589
3.9589 3.9589
3. 9590
31
40
3.9590 3.9591
3. 9591
3. 9592
3. 9592
3. 9593
3. 9593
3. 9594 3. 9594
3. 9595
31
50
3.9595 ! 3.9596
3. 9596
3. 9597
3. 9597
3. 9598
3. 9598
3. 9599 ! 3. 9599
3. 9599
2 32
0
3.9600 1 3.9600
3. 9601
3. 9601
3. 9602
3. 9602
3. 9603
3. 9603
3. 9604
3. 9604
32
10
3. 9605
3. 9605
3. 9606
3. 9606
3. 9607
3. 9607
3. 9608
3. 9608
3. 9609
3. 9609
32
20
3. 9609
3. 9610
3. 9610
3. 9611
3.9611
3. 9612
3. 9612
3. 9613
3. 9613
3. 9614
32
30
3. 9614
3. 9615
3. 9615
3. 9616
3. 9616
3. 9617
3. 9617
3. 9618
3. 9618
3. 9618
32
40
3. 9619
3. 9619
3. 9620
3. 9620
3. 9621
3. 9621
3. 9622
3. 9622
3. 9623
3. 9623
32
50
3. 9624
3. 9624
3. 9625
3. 9625
3. 9626
3. 9626
3. 9627
3. 9627
3. 9627
3. 9632
3. 9628
3. 9633
2 33
0
3. 9628
3. 9629
3. 9629
3. 9630
3. 9630
3. 9631
3. 9631
3. 9632
33
10
3. 9633
3. 9634
3. 9634
3. 9634
3. 9635
3. 9635
3. 9636
3. 9636
3. 9637
3. 9637
33
20
3. 9638
3. 96.38
3. 9639
3. 9639
3. 9640
3. 9640
3.9641
3.9641
3. 9642
3. 9642
33
30
3. 9642
3. 9643
3. 9643
3. 9644
3.9644
3.9645
3. 9645
3. 9646
3.9646
3. 9647
33
40
3. 9647
3. 9648
3. 9648
3. 9649
3. 9649
3. 9650
3. 9650
3. 9651
3. 9651
3. 9652
33
50
3. 9652
3. 9653
3. 9653
3. 9653
3. 9654
3. 9654
3. 9655
3. 9655
3. 9656
3. 9656
2 34
0
3.9657
3. 9657
3. 9658
3. 9658
3. 9658
3. 9659
3. 9659
3. 9660
3. 9660
3. 9661
34
10
3. 9661
3. 9662
3. 9662
3. 9663
3. 9663
3. 9664
3. 9664
3. 9665
3. 9665
3. 9665
34
20
3. 9666
3. 9666
3. 9667
3. 9667
3. 9668
3. 9668
3. 9669
3. 9669
3. 9670
3. 9670
34
30
3. 9671
3. 9671
3. 9672
3. 9672
3. 9672
3. 9673
3.9673
3. 9674
3. 9674
3. 9675
34
40
3. 9675
3. 9676
3. 9676
3. 9677
3. 9677
3.9678 I 3.9678
3. 9679
3. 9679
3. 9680
34
50
3. 9680
3. 9681
3. 9681
3. 9682
3. 9682
3. 9682
3. 9683
3. 9683
3. 9684 3. 9684
2 35
0
3. 9685
3. 9685
3. 9686
3. 9686
3. 9687
3. 9687
3. 9688
3. 9688
3. 9689 i 3. 9689
35
10
3. 9689
3. 9690
3. 9690
3. 9691
3. 9691
3. 9692
3. 9692
3. 9693
3. 9693
3. 9694
35
20
3. 9694
3. 9695
3. 9695
3. 9696
3. 9696
3. 9696
3. 9697
3. 9697
3. 9698
3. 9698
35
30
3. 9699
3. 9699
3. 9700
3. 9700
3. 9701
3. 9701
3. 9702
3. 9702
3. 9703
3. 9703
35
40
3. 9703
3. 9704
3. 9704
3. 9705
3. 9705
3. 9706
3. 9706
3. 9707
3. 9707 i 3. 9708 |
35
50
3. 9708
3.9713
3. 9709
3. 9709
3. 9710
3. 9710
3. 9710
3.9711
3.9711
3. 9712
3. 9712
2 36
0
3.9713
3. 9714
3. 9714
3. 9715
3. 9715
3. 9716
3. 9716
3. 9716
3. 9717
36
10
3. 9717
3.9718
3. 9718
3. 9719
3. 9719
3. 9720
3. 9720
3. 9721
3. 9721
3. 9722
36
20
3. 9722
3. 9722
3. 9723
3. 9723
3. 9724
3. 9724
3. 9725
3. 9725
3. 9726
3. 9726
36
30
3. 9727
3. 9727
3. 9728
3. 9728
3. 9729
3. 9729
3. 9729
3. 9730
3.9730 3.9731
36
40
3. 9731
3. 9732
3. 9732
3. 9733
3. 9733
3. 9734
3. 9734
3. 9735
3. 9735 1 3. 9735
36
50
3. 9736
3. 9736
3. 9737
3. 9737
3. 9738
3. 9738
3. 9739
3. 9739
3. 9740 : 3. 9740
2 37
0
3. 9741
3. 9741
3. 9741
3. 9742
3. 9742
3. 9743
3. 9743
3. 9744
3. 9744 i 3. 9745
37
10
3. 9745
3. 9746
3. 9746
3. 9746
3. 9747
3. 9747
3. 9748
3. 9748
3. 9749 i 3. 9749
37
20
3. 9750
3. 9750
3. 9751
3. 9751
3. 9752
3. 9752
3. 9752
3. 9753
3. 9753
3. 9754
37
30
3. 9754
3. 9755
3. 9755
3. 9756
3. 9756
3. 9757
3. 9757
3. 9758
3. 9758
3. 9758
37
40
3. 9759
3. 9759
3. 9760
3. 9760
3. 9761
3. 9761
3. 9762
3. 9762
3. 9763
3. 9763
37
50
3. 9763
3. 9764
3.9764
3. 9765
3. 9765
3. 9766
3. 9766
3. 9767
3. 9767
3. 9768
2 38
0
3. 9768
3. 9769
3. 9769
3. 9769
3. 9770
3. 9770
3. 9771
3. 9771
3. 9772
3. 9772
38
10
3. 9773
3. 9773
3. 9774
3. 9774
3. 9774
3. 9775
3. 9775
3. 9776
3. 9776
3. 9777
38
20
3. 9777
3. 9778
3. 9778
3. 9779
3. 9779
3. 9779
3. 9780
3. 9780
3. 9781
3. 9781
38
30
3. 9782
3. 9782
3. 9783
3. 9783
3. 9784
3. 9784
3. 9785
3. 9785
3. 9785
3. 9786
38
40
3. 9786
3. 9787
3. 9787
3. 9788
3. 9788
3. 9789
3. 9789
3. 9790
3. 9790
3. 9790
38
50
3. 9791
3. 9791
3. 9792
3. 9792
3. 9793
3. 9793
3. 9794
3. 9794
3. 9795
3. 9795
2 39
0
3. 9795
3. 9796
3. 9796
3. 9797
3. 9797
3. 9798
3. 9798
3. 9799
3. 9799
3. 9800
39
10
3. 9800
3. 9800
3. 9801
3. 9801
3. 9802
3. 9802
3. 9803
3. 9803
3. 9804
3. 9804
39
20
3. 9805
3. 9805
3. 9805
3. 9806
3. 9806
3. 9807
3. 9807
3. 9808
3. 9808
3. 9809
39
30
3. 9809
3.9810
3. 9810
3. 9810
3.9811
3. 9811
3. 9812
3. 9812
3. 9813
3. 9813
39
40
3. 9814
3.9814
3. 9815
3. 9815
3. 9815
3. 9816
3. 9816
3.9817
3.9817
3.9818
39
50
3. 9818
3.9819
.3. 9819
3.9819
3. 9820
3. 9820
3. 9821
3. 9821
3. 9822
3. 9822
APPENDIX V: TABLE IX.
[Page 329
Logarithms of Small Arcs in
Space or Time.
Arc.
0"
1"
2"
8"
4"
5"
6"
7" 1 8"
9"
o / //
2h 40m 0*
3. 9823
3. 9823
3. 9824
3. 9824
3. 9825
3. 9825
3. 9825
3. 9826
3. 9826
3. 9827
40
10
3. 9827
3. 9828
3. 9828
3. 9829
3. 9829
3. 9829
3. 9830
3. 9830
3. 9831
3. 9831
40
20
3. 9832
3. 9832
3. 9833
3. 9833
3. 9834
3. 9834
3. 9834
3. 9835
3. 9835
3. 9836
40
30
3. 9836
3. 9837
3. 9837
3. 9838
3. 9838
3. 9839
3. 9839
3. 9839
3. 9840
3. 9840
40
40
3. 9841
3. 9841
3. 9842
3. 9842
3. 9843
3. 9843
3. 9843
3. 9844
3. 9844
3. 9845
40
50
3. 9845
3. 9846
3. 9846
3. 9847
3. 9847
3. 9848
3. 9848
3. 9848
3. 9849
3. 9849
2 41
0
3. 9850
3.9850
3. 9851
3. 9851
3. 9852
3. 9852
3. 9852
3. 9853
3. 9853
3. 9854
41
10
3. 9854
3. 9855
3. 9855
3. 9856
3. 9856
3. 9857
3. 9857
3. 9857
3. 9858
3. 9858
41
20
3. 9859
3. 9859
3. 9860
3. 9860
3. 9861
3. 9861 3. 9861
3. 9862
3. 9862
3. 9863
41
30
3. 9863
3. 9864
3. 9864
3. 9865
3. 9865
3. 9865 3. 9866
3.9866
3. 9867
3. 9867
41
40
3. 9868
3. 9868
3. 9869
3. 9869
3. 9870
3.9870
3. 9870
3. 9871
3. 9871
3. 9872
41
50
3. 9872
3. 9873
3. 9873
3. 9874 3. 9874
3. 9874
3. 9875
3. 9875
3. 9876
3. 9876
2 42
0
3. 9877
3. 9877
3. 9878
3. 9878
3. 9878
3. 9879
3. 9879
3. 9880
3. 9880
3. 9881
42
10
3. 9881
3. 9882
3. 9882
3. 9882
3. 9883
3. 9883
3. 9884
3. 9884
3. 9885
3. 9885
42
20
3. 9886
3. 9886
3. 9886
3. 9887
3. 9887
3. 9888
3. 9888
3. 9889 i 3. 9889
3. 9890
42
30
3. 9890
3. 9890
3. 9891
3. 9891
3. 9892
3. 9892
3. 9893
3. 9893 i 3. 9894
3. 9894
42
40
3. 9894
3. 9895
3. 9895
3.9896 i 3.9896
3. 9897
3. 9897
3. 9898 i 3. 9898
3. 9898
42
50
3. 9899
3. 9899
3.9900
3.9900 ! 3.9901
3. 9901
3. 9902
3. 9902
3. 9903
3. 9903
2 43
0
3. 9903
3. 9904
3. 9904
3. 9905 3. 9905
3.9906
3. 9906
3. 9906
3. 9907 1 3. 9907
43
10
3. 9908
3. 9908
3. 9909
3. 9909 3. 9910
3. 9910
3. 9910
3.9911
3.9911 1 3.9912
43
20
3. 9912
3. 9913
3. 9913
3.9914 : 3.9914
3. 9914
3. 9915
3. 9915
3.9916! 3.9916
43
30
3. 9917
3. 9917
3. 9918
3.9918 I 3.9918
3. 9919
3. 9919
3. 9920
3. 9920 1 3. 9921
43
40
3. 9921
3. 9922
3. 9922
3. 9922
3. 9923
3. 9923
3. 9924
3. 9924
3. 9925 ! 3. 9925
43
50
3. 9926
3. 9926
3. 9926
3. 9927
3. 9927
3. 9928
3. 9928
3. 9929
3. 9929
3. 9930
2 44
0
3. 9930
3. 9930
3. 9931
3. 9931
3. 9932
3. 9932
3. 9933
3. 9933 1 3. 9933
3. 9934
44
10
3. 9934
3. 9935
3. 9935
3. 9936
3. 9936
3. 9937
3. 9937
3. 9937 1 3. 9938 [ 3. 9938
44
20
3. 9939
3. 9939
3. 9940 1 3. 9940
3. 9941
3. 9941
3. 9941
3. 9942 3. 9942 3. 9943
44
30
3. 9943
3. 9944
3. 9944
3. 9944
3. 9945
3. 9945
3. 9946
3. 9946 I 3. 9947 ; 3. 9947
44
40
3. 9948
3. 9948
3. 9948
3. 9949
3. 9949
3. 9950
3. 9950
3. 9951
3. 9951 i 3. 9952 |
44
50
3. 9952
3. 9952
3. 9953
3. 9953
3. 9954
3.9954 i 3.9955
3. 9955
3. 9955
3. 9956
2 45
0
3. 9956
3. 9957
3. 9957
3. 9958
3. 9958
3. 9959
3. 9959
3. 9959
3. 9960
3. 9960
45
10
3. 9961
3. 9961
3. 9962
3. 9962
3. 9962
3. 9963
3. 9963
3. 9964
3. 9964
3. 9965
45
20
3. 9965
3. 9966
3. 9966
3. 9966
3. 9967
3. 9967
3. 9968
3. 9968
3. 9969
3. 9969
45
30
3. 9969
3. 9970
3. 9970
3. 9971
3. 9971
3. 9972
3.9972
3. 9973
3. 9973
3. 9973
45.
40
3. 9974
3. 9974
3. 9975
3. 9975
3. 9976
3. 9976
3. 9976
3. 9977
3.9977
3. 9978
45
50
3. 9978
3. 9979
3. 9979
3. 9980
3. 9980
3. 9980
3. 9981
3. 9981
3. 9982
3. 9982
2 46
0
3. 9983
3. 9983
3.9983 1 3.9984
3. 9984
3. 9985
3. 9985
3. 9986
3. 9986
3. 9987
46
10
3. 9987
3. 9987
3. 9988
3. 9988
3. 9989
3. 9989
3. 9990
3. 9990
3. 9990
3. 9991
46
20
3. 9991
3. 9992
3. 9992
3. 9993
3. 9993
3. 9993
3. 9994
3. 9994
3. 9995
3. 9995
46
30
3. 9996
3. 9996
3. 9997
3. 9997
3. 9997
3. 9998
3. 9998
3.9999
3. 9999
4. 0000
46
40
4. 0000
4. 0000
4. 0001
4.0001
4. 0002
4. 0002
4. 0003
4.0003
4. 0003
4.0004
46
50
4. 0004
4. 0005
4. 0005
4.0006
4. 0006
4.0007
4. 0007
4.0007
4. 0008
4. 0008
2 47
0
4. 0009
4.0009
4. 0010
4. 0010
4. 0010
4.0011
4.0011
4. 0012
4.0012! 4.0013 1
47
10
4. 0013
4. 0013
4. 0014
4.0014
4. 0015
4. 0015
4. 0016
4. 0016
4. 0016
4.0017
47
20
4. 0017
4.0018
4. 0018
4. 0019
4. 0019
4. 0019
4. 0020
4. 0020
4. 0021
4.0021
47
30
4. 0022
4.0022
4.0023
4. 0023
4. 0023
4. 0024
4. 0024
4. 0025
4. 0025
4. 0026
47
40
4. 0026
4. 0026
4. 0027
4. 0027
4. 0028
4.0028
4. 0029
4.0029
4. 0029
4. 0030
47
50
4. 0030
4. 0031
4.0031
4. 0032
4. 0032
4. 0032
4. 0033
4. 0037
4. 0033
4. 0038
4. 0034
4.0038
4. 0034
4. 0038
2 48
0
4. 0035
4.0035
4. 0035
4. 0036
4. 0036
4. 0037
48
10
4. 0039
4.0039
4.0040
4. 0040
4. 0041
4. 0041
4. 0041
4.0042
4. 0042
4. 0043
48
20
4. 0043
4. 0044
4. 0044
4. 0045
4. 0045
4. 0045
4. 0046
4. 0046
4.0047
4. 0047
48
30
4. 0048
4. 0048
4. 0048
4. 0049
4. 0049
4. 0050
4. 0050
4. 0051
4. 0051
4.0051
48
40
4. 0052
4.0052
4. 0053
4. 0053
4. 0054
4.0054
4. 0054
4. 0055
4.0055
4. 0056
48
50
4. 0056
4. 0057
4. 0057
4.0057
4. 0058
4. 0058
4.0059
4. 0059
4.0060
4. 0060
2 49
0
4. 0060
4. 0061
4. 0061
4. 0062
4. 0062
4. 0063
4. 0063
4. 0063
4.0064
4. 0064
49
10
4. 0065
4. 0065
4. 0066
4.0066
4. 0066
4. 0067
4. 0067
4. 0068
4. 0068
4. 0069
49
20
4. 0069
4. 0069
4. 0070
4. 0070
4. 0071
4. 0071
4. 0072
4. 0072
4. 0072
4.0073
49
30
4. 0073
4.0074
4.0074
4. 0074
4. 0075
4. 0075
4. 0076
4. 0076
4. 0077
4. 0077
49
40
4.0077
4. 0078
4. 0078
4.0079
4. 0079
4. 0080
4. 0080
4. 0080
4. 0081
4. 0081
49
50
4. 0082
4.0082
4. 0083
4. 0083
4. 0083
4. 0084
4. 0084
4. 0085
4. 0085
4.0086
Page 330] APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or Time.
Arc.
0"
1"
2"
8"
4"
6"
6"
7"
8"
9"
O ' II
2" 50™ 0'
50 10
50 20
50 30
50 40
50 50
4.0086
4. 0090
4.0095
4. 0099
4. 0103
4. 0107
4.0086
4. 0091
4.0095
4. 0099
4. 0103
'4. 0108
4.0087
4.0091
4.0095
4. 0100
4. 0104
4. 0108
4.0087
4.0092
4.0096
4. 0100
4. 0104
4.0109
4.0088
4.0092
4.0096
4. 0100
4. 0105
4. 0109
4.0088
4. 0092
4.0097
4. 0101
4. 0105
4. 0109
4.0089
4. 0093
4. 0097
4. 0101
4. 0106
4.0110
4.0089
4.0093
4.0097
4. 0102
4. 0106
4.0110
4.0089
4. 0094
4. 0098
4. 0102
4. 0106
4.0111
4.0090
4. 0094
4.0098
4. 0103
4. 0107
4.0111
2 51 0
51 10
51 20
51 30
51 40
51 50
4. 0111
4.0116
4. 0120
4. 0124
4. 0128
4. 0133
4.0112
4.0116
4. 0120
4. 0125
4. 0129
4. 0133
4.0112
4.0117
4. 0121
4. 0125
4. 0129
4. 0133
4. 0113
4.0117
4. 0121
4. 0125
4. 0130
4. 0134
4.0113
4.0117
4. 0122
4.0126
4. 0130
4. 0134
4. 0114
4.0118
4.0122
4. 0126
4. 0130
4. 0135
4.0114
4.0118
4. 0122
4. 0127
4. 0131
4. 0135
4. 0114
4.0119
4. 0123
4. 0127
4. 0131
4. 0136
4.0115
4. 0119
4. 0123
4. 0128
4. 0132
4. 0136
4.0115
4. 0120
4. 0124
4. 0128
4. 0132
4. 0136
2 52 0
52 10
52 20
52 30
52 40
52 50
4. 0137
4. 0141
4. 0145
4. 0149
4. 0154
4. 0158
4. 0137
4. 0141
4. 0146
4. 0150
4. 0154
4. 0158
4. 0138
4. 0142
4. 0146
4. 0150
4. 0154
4. 0159
4. 0138
4. 0142
4. 0146
4. 0151
4. 0155
4. 0159
4. 0138
4. 0143
4. 0147
4. 0151
4. 0155
4. 0159
4. 0139
4. 0143
4. 0147
4. 0152
4. 0156
4. 0160
4. 0139
4.0144
4. 0148
4. 0152
4. 0156
4. 0160
4. 0140
4.0144
4. 0148
4. 0153
4. 0157
4. 0161
4. 0140
4. 0144
4. 0149
4. 0153
4. 0157
4. 0161
4. 0141
4. 0145
4. 0149
4. 0153
4. 0157
4. 0162
2 53 0
53 10
53 20
53 30
53 40
53 50
4. 0162
4. 0166
4.0170
4. 0175
4. 0179
4. 0183
4. 0162
4. 0167
4. 0171
4. 0175
4. 0179
4. 0183
4. 0163
4. 0167
4. 0171
4. 0175
4. 0180
4. 0184
4. 0163
4. 0167
4. 0172
4. 0176
4. 0180
4. 0184
4. 0164
4. 0168
4. 0172
4. 0176
4. 0180
4. 0185
4. 0164
4. 0168
4. 0172
4.0177
4.0181
4. 0185
4. 0164
4. 0169
4. 0173
4. 0177
4.0181
4. 0185
4. 0165
4. 0169
4. 0173
4.0177
4. 0182
4. 0186
4. 0165
4. 0169
4. 0174
4. 0178
4. 0182
4. 0186
4. 0166
4. 0170
4. 0174
4. 0178
4. 0182
4. 0187
2 54 0
54 10
54 20
54 30
54 40
54 50
4. 0187
4. 0191
4. 0195
4. 0199
4.0204
4. 0208
4. 0187
4. 0192
4. 0196
4. 0200
4. 0204
4. 0208
4. 0188
4. 0192
4. 0196
4. 0200
4. 0204
4. 0209
4.0188
4. 0192
4. 0197
4. 0201
4. 0205
4. 0209
4. 0189
4. 0193
4. 0197
4. 0201
4. 0205
4. 0209
4. 0189
4. 0193
4. 0197
4. 0202
4. 0206
4. 0210
4. 0190
4. 0194
4:0198
4. 0202
4. 0206
4. 0210
4. 0190
4. 0194
4. 0198
4. 0202
4. 0207
4.0211
4. 0190
4. 0194
4. 0199
4. 0203
4. 0207
4. 0211
4. 0191
4. 0195
4. 0199
4. 0203
4. 0207
4. 0211
2 55 0
55 10
55 20
55 30
55 40
55 50
4. 0212
4. 0216
4. 0220
4. 0224
4. 0228
4. 0233
4. 0212
4. 0216
4. 0221
4. 0225
4. 0229
4. 0233
4. 0213
4. 0217
4. 0221
4. 0225
4. 0229
4. 0233
4. 0213
4. 0217
4. 0221
4. 0225
4. 0230
4. 0234
4. 0214
4. 0218
4. 0222
4. 0226
4. 0230
4. 0234
4. 0214
4. 0218
4. 0222
4. 0226
4. 0230
4. 0235
4. 0214
4. 0219
4. 0223
4. 0227
4. 0231
4. 0235
4. 0239
4. 0243
4. 0247
4. 0251
4. 0256
4. 0260
4. 0215
4.0219
4. 0223
4. 0227
4. 0231
4. 0235
4. 0240
4. 0244
4. 0248
4. 0252
4. 0256
4. 0260
4. 0215
4. 0219
4. 0223
4. 0228
4. 0232
4. 0236
4. 0240
4. 0244
4. 0248
4. 0252
4. 0256
4. 0260
4. 0216
4. 0220
4. 0224
4. 0228
4. 0232
4. 0236
2 56 0
56 10
56 20
56 30
56 40
56 50
4. 0237
4. 0241
4.0245
4. 0249
4. 0253
4. 0257
4. 0237
4. 0241
4. 0245
4. 0249
4. 0253
4. 0258
4. 0237
4. 0242
4. 0246
4. 0250
4.0254
4. 0258
4. 0238
4. 0242
4. 0246
4. 0250
4. 0254
4. 0258
4. 0238
4. 0242
4. 0246
4. 0251
4. 0255
4. 0259
4. 0239
4. 0243
4. 0247
4. 0251
4. 0255
4. 0259
4. 0240
4. 0244
4. 0249
4. 0253
4. 0257
4. 0261
4. 0265
4. 0269
4. 0273
4. 0277
4. 0281
4. 0285
4. 0289
4. 0293
4. 0297
4. 0302
4. 0306
4. 0310
2 57 0
67 10
57 20
57 30
57 40
57 50
4. 0261
4. 0265
4. 0269
4. 0273
4. 0278
4. 0282
4. 0262
4. 0266
4. 0270
4. 0274
4. 0278
4. 0282
4. 0262
4. 0266
4. 0270
4. 0274
4. 0278
4. 0282
4. 0262
4. 0267
4. 0271
4. 0275
4. 0279
4. 0283
4. 0263
4. 0267
4. 0271
4. 0275
4. 0279
4. 0283
4. 0263
4. 0267
4. 0271
4. 0276
4. 0280
4. 0284
4. 0264
4. 0268
4. 0272
4. 0276
4. 0280
4. 0284
4. 0264
4. 0268
4. 0272
4. 0276
4. 0280
4. 0284
4. 0265
4. 0269
4. 0273
4. 0277
4. 0281
4. 0285
2 58 0
58 10
58 20
58 30
58 40
58 50
4. 0286
4. 0290
4. 0294
4. 0298
4. 0302
4. 0306
4. 0286
4.0290
4. 0294
4. 0298
4. 0302
4. 0306
4. 0287
4. 0291
4. 0295
4. 0299
4. 0303
4. 0307
4. 0287
4. 0291
4. 0295
4. 0299
4. 0303
4. 0307
4. 0287
4. 0291
4. 0295
4. 0300
4. 0304
4. 0308
4. 0288
4. 0292
4. 0296
4. 0300
4. 0304
4. 0308
4. 0288
4. 0292
4. 0296
4.0300
4. 0304
4. 0308
4. 0289
4. 0293
4. 0297
4. 0301
4. 0305
4. 0309
4. 0289
4. 0293
4. 0297
4. 0301
4. 0305
4. 0309
2 59 0
59 10
59 20
59 30
59 40
59 50
4. 0310
4. 0314
4. 0318
4. 0322
4. 0326
4. 0330
4. 0310
4. 0314
4. 0319
4. 0323
4. 0327
4. 0331
4.0311
4. 0315
4. 0319
4. 0323
4. 0327
4. 0331
4. 0311
4. 0315
4. 0319
4. 0323
4. 0327
4. 0331
4. 0312
4. 0316
4. 0320
4. 0324
4. 0328
4. 0332
4. 0312
4. 0316
4. 0320
4. 0324
4. 0328
4. 0332
4. 0312
4. 0317
4. 0321
4. 0325
4. 0329
4. 0333
4. 0313
4. 0317
4. 0321
4. 0325
4. 0329
4. 0333
4. 0313
4. 0317
4. 0321
4. 0325
4. 0329
4. 0333
4. 0314
4. 0318
4. 0322
4. 0326
4. 0330
4. 0334
APPENDIX V: TABLE X. [Page 331
Table showing the correction required, on account of Second Differences of the Moon's Motion, in
Finding the Greenwich Time corresponding to a Corrected Lunar Distance.
Approximate
interval.
Difference of the proportional logarithms in the Ephemeris. 1
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
82
34
36
h. m.
0 0
0 10
0 20
h. m.
3 0
2 50
2 40
8.
0
0
0
s.
0
0
8.
0
0
1
1
1
2
2
2
2
2
8.
0
1
1
2
2
2
2
2
3
3
8.
0
1
1
2
2
3
3
3
3
3
8.
0
1
2
2
3
3
3
4
4
4
8.
0
1
2
2
3
4
4
4
4
4
8.
0
1
2
■ 3
3
4
4
5
5
5
8.
0
1
2
3
4
5
5
5
6
6
8.
0
1
2
3
4
5
6
6
6
6
8.
0
1
3
4
5
5
6
6
7
7
8.
0
2
3
4
5
6
7
7
7
8
8.
0
2
3
8.
0
2
3
8.
0
2
4
8.
0
2
4
8.
0
2
4
8.
0
2
4
0 30
0 40
0 50
2 30
2 20
2 10
0
0
1
5
6
6
7
8
8
8
5
6
7
5
6
7
6
7
8
6
7
8
6
8
9
1 0
1 10
1 20
1 30
h. TO.
0 0
0 10
0 20
2 0
1 50
1 40
1 30
h. m.
3 0
2 50
2 40
1
1
1
1
8
8
9
9
8
9
9
9
9
9
10
10
9
10
10
11
10
11
11
11
Difference of the proportional logarithms in the Ephemeris.
38
».
0
2
5
40
8.
0
3
5
7
9
10
11
12
12
12
42
8.
0
3
5
7
9
10
12
12
13
13
44
8.
0
3
5
8
10
11
12
13
14
14
46
8.
0
3
6
8
10
12
13
14
14
14
48
8.
0
3
6
8
10
12
13
14
15
15
50
8.
0
3
6
9
11
13
62
54
56
58
60
62
64
66 68
70
8.
0
3
6
8.
0
4
7
8.
0
4
7
8.
0
4
7
8.
0
4
7
8.
0
4
8
8.
0
4
8
8. 8.
0 0
4 i 4
8 8
8.
0
5
9
0 30
0 40
0 50
2 30
2 20
2 10
7
8
9
10
11
12
12
9
11
13
9
12
14
10 10
12 13
14 15
10
13
15
11
13
16
11
14
16
12 ] 12
14 1 15
16 1 17
12
15
17
1 0
1 10
1 20
1 30
h. TO.
0 0
0 10
0 20
0 30
0 40
0 50
2 0
1 50
1 40
1 30
h. m.
3 0
•2 50
2 40
2 30
2 20
2 10
14
15
15
16
14
15
16
16
15
16
17
17
16
17
17
18
16
17
18
18
17
18
19
19
17
18
19
19
18
19
20
20
18 19
19 , 20
20 \ 21
21 ; 21
19
21
21
22
Difference of the proportional logarithms in the Ephemeris.
72
74
76
78
80
82
84
86
88
90 92
94
06
98
100
102
104
8.
0
5
9
13
16
18
20
21
22
23
8.
0
5
9
13
16
19
21
22
23
23
8.
0
5
9
13
16
19
21
22
23
24
8.
0
5
10
14
17
20
22
23
24
24
8.
0
5
10
14
17
20
22
24
25
25
8.
0
5
10
14
18
21
23
24
25
25
8.
0
6
10
14
18
21
23
25
26
26
8.
0
6
11
8.
0
6
11
8.
0
6
11
8.
0
6
11
8.
0
6
12
8.
0
6
12
8.
0
6
12
8.
0
7
12
8.
0
i
13
8.
0
7
13
15
19
22
15
19
22
16
19
22
16
20
23
16
20
23
17
21
24
17
21
24
17
22
25
18
22
26
18
22
26
1 0
1 10
1 20
1 30
h. m.
0 0
0 10
0 20
2 0
1 50
1 40
1 30
/(. m.
3 0
2 50
2 40
24
25
26
27
24
26
27
27
25
27
28
28
25
27
28
29
26
28
29
29
27
28
29
30
27
29
30
31
38
30
31
31
28
30
31
32
29
31
32
32
Difference of the proportional logarithms in the Ephemeris. . 1
106
108
110
112
114
116
118
120
122
124
126
128
180
132
134
136
138
s.
0
7
13
8.
0
7
13
8.
0
7
14
19
24
27
30
32
34
34
8.
0
7
14
19
24
28
31
33
34
35
8.
0
7
14
20
25
29
31
34
35
35
8.
0
8
14
20
25
29
8.
0
8
15
8.
0
8
15
8.
0
8
15
8.
0
8
15
8.
0
8
15
8.
0
8
16
8.
0
8
16
8.
0
9
16
8.
0
9
16
8.
0
9
17
8.
0
9
17
0 30
0 40
0 50
2 30
2 20
2 10
18
23
26
19
23
27
30
32
33
34
20
25
29
21
26
30
21
26
30
21
27
31
22
27
22
28
32
22
28
32
23
28
33
23
29
33
37
40
41
42
24
29
34
38
40
42
42
24
30
34
38
41
42
43
1 0
1 10
1 20
1 30
2 0
1 50
1 40
1 30
29
31
33
33
32
34
35
36
33
35
36
36
33
35
37
37
34
36
38
38
34
37
38
39
J5
J7
J9
J9
35
38
39
40
36
38
40
40
37
39
41
41
The correction is to be added to the approximate Greenwich time when the proportional logarithms in the Ephemeris
are decreasing, and subtracted when they are increasing.
Page 332]
APPENDIX V: TABLE XI.
1
For finding the value of N for Correcting Lunar Distances for the Compres
sion
of the Earth.
Table XI A, giving 1st part of N.
Table XI B, giving 2d part of N. 1
Moon's declination.
Other body'
3 declination.
App.
dist.
App.
dist.
1
0°
3°
6°
9°
12°
15°
18°
21°
24°
27°
80°
0°
8°
6°
9°
12°
16°
18°
21°
24°
27°
80°
II
0
„
„
„
„
„
„
„
It
„
0
/'
rt
It
//
//
„
It
II
20
-0
3
6
10
13
16
19
22
25
28
31
20
+0
3
7
10
14
17
20
24
27
30
33
22
0
3
6
9
12,
. 14
17
20
23
25
28
22
0
3
6
9
13
16
19
22
25
27
30
24
0
3
5
8
11
13
16
18
21
23
25
24
0
3
6
9
12
14
17
20
23
25
28
26
0
2
5
7
10
12
14
17
19
21
23
26
0
3
5
8
11
13
16
18
21
23
26
28
0
2
4
7
9
11
13
15
17
19
21
28
0
3
5
8
10
12
15
17
20
22
24
30
-0
2
4
6
8
10
12
14
16
18
20
30
+0
2
5
7
9
12
14
16
18
21
23
32
0
2
4
6
8
9
11
13
15
16
18
32
0
2
4
7
9
11
13
15
17
19
21
34
0
2
4
5
7
9
10
12
14
15
17
34
0
2
4
6
8
11
13
15
16
18
20
36
0
2
3
5
7
8
10
11
13
14
16
36
0
2
4
6
8
10
12
14
16
17
19
38
0
2
3
5
6
8
9
8
10
10
12
11
13
12
14
38
0
2
2
4
4
6
6
8
7
10
9
11
11
13
13
15
14
17
16
18
18
40
-0
3
4
6
7
13
40
+0
42
0
3
4
5
7
8
9
10
11
13
42
0
2
4
5
7
9
10
12
14
15
17
44
0
2
4
5
6
7
8
10
11
12
44
0
2
3
5
7
8
10
12
13
15
16
46
0
\
2
3
5
6
7
8
9
10
11
46
0
2
3
5
6
8
10
11
13
14
16
48
0
2
3
4
5
6
7
8
9
10
48
0
2
3
5
6
8
9
11
12
14
15
50
-0
2
3
4
5
6
7
8
9
10
50
+0
2
3
5
6
8
9
11
12
13
15
52
0
3
4
5
5
6
7
8
9
52
0
2
3
4
6
7
9
10
12
13
14
54
0
3
3
4
5
6
7
7
8
54
0
3
4
6
7
9
10
11
13
14
56
0
2
3
4
5
5
6
7
8
56
0
3
4
6
7
8
10
11
12
14
58
0
J
y
2
2
3
3
4
3
4
4
5
5
6
5
6
6
7
7
58
0
Y
3
3
4
4
6
5
7
7
8
8
10
9
11
11
12
12
13
13
60
-0
60
+0
m
0
2
3
3
4
4
5
5
6
62
0
3
4
5
7
8
9
10
12
13
64
0
2
2
3
3
4
4
5
6
64
0
3
4
5
7
8
9
10
11
13
66
0
2
2
3
3
4
4
5
5
66
0
3
4
5
6
8
9
10
11
12
68
0
0
0
Y
-Y
2
2
2
2
3
3
3
3
4
3
4
4
5
4
68
70
0
+0
Y
3
3
4
4
5
5
6
6
8
7
9
9
10
10
11
11
12
12
70
-0
72
0
0
2
2
2
3
3
3
4
72
0
2
4
5
6
7
9
10
11
12
74
0
0
2
2
2
3
3
3
74
0
2
4
5
6
7
8
10
11
12
76
0
0
2
2
2
3
3
76
0
2
4
5
6
7
8
9
11
12
78
0
0
0
0
0
"Y
"Y
1
1
2
1
2
2
2
2
2
78
0
Y
2
2
4
4
5
5
6
6
7
7
8
8
9
9
11
10
12
11
80
-0
2
80
+0
82
0
0
0
0
1
1
1
1
2
82
0
2
4
5
6
7
8
9
10
11
84
0
0
0
0
0
1
1
1
1
1
84
0
2
4
5
6
7
8
9
10
11
86
0
0
0
0
0
0
0
1
1
1
1
86
0
2
4
5
6
7
8
9
10
11
88
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
88
0
Y
2
2
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
90
-0
90
+0
92
+0
0
0
0
0
0
0
0
0
0
0
92
0
2
4
5
6
7
8
9
10
11
94
0
0
0
0
0
0
0
1
1
1
1
94
0
2
4
5
6
7
8
9
10
11
96
0
0
0
0
0
1
1
1
1
1
96
0
2
4
5
6
7
8
9
10
11
98
0
0
0
0
0
_o
"Y
1
1
1
1
1
2
1
2
2
2r
98
0
Y
2
2
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
100
+0
100
+0
102
0
0
0
1
2
2
2
2
102
0
2
4
5
6
7
8
9
11
12
104
0
0
2
2
2
3
3
104
0
2
4
5
6
7
8
9
11
12
106
0
0
2
2
2
3
3
3
106
0
2
4
5
6
7
8
10
11
12
108
110
0
+0
0
0
Y
-^
2
2
2
2
2
3
3
3
4
108
0
2
3
4
4
5
5
6
6
7
7
9
9
10
10
11
11
12
12
3
3
3
4
4
110
+0
112
0
0
2
2
3
3
4
4
5
112
0
3
4
5
6
8
9
10
11
12
114
0
2
2
3
3
4
4
5
5
114
0
3
4
5
6
8
9
10
11
12
116
0
2
2
3
3
4
4
5
6
116
0
3
4
5
7
8
9
10
11
13
118
0
Y
1
2
2
3
3
3
3
4
4
4
5
5
5
5
6
6
7
118
0
Y
3
3
4
4
5
5
7
7
8
8
9
9
10
11
12
12
13
13
120
+0
120
+0
122
0
2
3
4
4
5
6
6
7
122
0
3
4
6
7
8
10
11
12
13
124
0
2
2
3
4
5
5
6
7
8
124
0
3
4
6
7
8
10
11
12
14
126
0
2
3
3
4
5
6
7
7
8
126
0
3
4
6
7
9
10
11
13
14
128
0
2
3
4
5
5
6
7
8
9
128
0
2
3
4
6
7
9
10
12
13
14
130
+0
\
2
3
4
5
6
7
8
9
10
130
+0
2
3
5
6
8
9
11
12
13
15
The signs in the 0° column apply to all the numbers in the same line, and are to be used when the declination is North.
When the declination is South change the sign + to — and — to +.
INDEX TO PART I.
Subject.
Abbreviations
Account. (»S'ee Dead reckoning. )
Adjustments, horizon mirror
index mirror
plane table
sextant
permanent
theodolite or transit
Afternoon sights
Agulhas current
Airy's method for great circle sailing..
Alidade, plane table
Almanac, Nautical. {See Nautical Al-
manac. )
Altitude and azimuth
time azimuth
azimuth
circle, definition . . .'
circum-meridian
forms for . . .
definition
ex-meridian
forma for
meridian, constant
form for . .
forms for
latitude by
observation of
reduction to
forms.
observed, how corrected
of Polaris for latitude
single, for chronometer error.
latitude
longitude ashore ..
at sea...
true, definition
Altitudes, equal, forchro. error
form
longitude ashore . .
at sea...
Amplitude, definition
determination of
Anchorage, position to be plotted
Angle, danger. {See Danger angle.)
hour. {See Hour angle.)
to repeat
Angles, between three known objects .
horizon, for finding distance..
round of
sextant and theodolite in hy-
drography
vertical terrestrial, to measure.
26J°-45° on bow
Anticyclonic regions, features of
Apparent day, definition
variation in length
noon, definition
time, conversion to mean
definition
Art.
246
245
417
244
248
414
399
550
194
416
235
366
363
217
334
220
334
333
329
330
334
294
340
316
339
346
349
294
321
347
352
224
357
166
415
151
139
415
458
139
146
481
273
273
273
292
273
Page.
67
133
67
68
132
125
161
58
133
65
112
111
63
97
174
64
97
174
96
174
173
94
94
97
174
82
101
88
99
104
105
82
90
176
104
107
64
109
49
132
45
43
132
140
43
44
148
74
74
74
80
74
Subject.
Art.
Page.
Apparent time, inequality of
relation to mean
Arctic current
Aries, first point of, definition
Arming of lead
Artificial horizon, description
method of use
should be tested
Ascension, right. {See Right ascen-
sion. )
Astronomical base
bearing
time
transit instruments
work of survey
Atlantic ocean currents
storms
Attraction, local
Australia current
Axis of rotation, definition
Azimuth, altitude
and altitude
circle
definition
from Sumner line
how determined
named
of body determines use
terrestrial object
time and altitude
determination
diagram
for compass errors
in great circle sailing . .
tables
Barometer, aneroid
comparisons
definition
effect of, on tides
mercurial
sea
standard
temperature correction
to determine height
vernier
Base, astronomical
line, description
Beam compass, description
Bearing and angle, position by
distance, position by
danger
method of observing and plot-
ting
of terrestrial object
Bearings, bow and beam
cross
sun, for compass error
two, of object, with run be-
tween
Beaufort's scale for wind
273
288
536
226
19
256
257
258
446
369
277
431
450
529
494
75
546
6
363
235
33
223
380
355
354
407
369
366
359
361
88
191
361
55
56
47
501
48
50
50
54
57
51
446
438
434
142
138
157
134
369
145
134
143
67
333
334
INDEX TO PART 1.
Subject.
Bench mark, definition
Binnacles, description
Bottom, quality of, on chart
Boxing the compass
Brazil current
Buoys
C — W, definition •
Cape Horn current
Celestial coordinates
equator, definition
horizon, definition
latitude and longitude
definition
longitude and latitude
definition
meridian, definition
sphere or concave, definition .
Celo-Navigation, definition
Chart {See also Projection).
as record of piloting
employment in piloting
general features
great circle
for composite sailing.
isobaric
measures of depth on
Mercator, to construct
quality of bottom on
standard meridians on
Chilean current
Chronometer, advantage of more than
one
C — W, definition
care on shipboard
comparison
record
correction. {See Chro-
nometer error. )
description
error, by equal alts
form,
single altitude .
time sight
signals . . .
transits
definition
differs from corr .
from rate
hack, use of
max. and min. ther-
mometer
minus watch, definition.
second difference
sight. ( »S'ee Time sight. )
temperature curve
transportation of
winding
Circle, declination, definition
hour, definition
of altitude, definition
equal altitude
illumination
vertical, definition
Circum-meridian altitude
forms
Civil time
Clouds, description and symbols
Coefficients, constant
quadrantal ^ . . .
semicircular
value and relation
Collimation, line of, definition
Art.
516
34
45
27
538
162
268
547
234
215
213
238
229
238
229
216
210
4
166
165
36
189
197
465
46
40
45
44
547
265
268
260
263
264
259
321
316
316
314
315
261
312
311
268
262
268
265
266
260
262
216
216
217
373
373
217
334
Page.
277
70
112
107
103
114
414
156
17
20
16
160
47
72
161
66
63
63
65
64
65
64
63
63
11
49
48
18
57
59
143
21
19
20
20
161
72
72
71
71
72
71
90
176
88
88
87
88
71
87
87
72
71
72
72
72
71
71
63
63
63
114
114
63
97
174
74
27
38
37
36
38
132
Subject.
Page.
Comparing watch, use of
Comparison, barometer
chronometer, method ...
record
Compass, beam, description
boxing
compensation. {See Devia-
tion. )
declination
definition
deviation. (.S'fe Deviation.)
divisions on card
dry
error. (*See Error, compass.)
local attraction
Lord Kelvin
Navy service, 7 J-inch
variation
wet
Compasses (drawing)
Compensation, compass. {See Devia-
tion. )
Composite sailing, computation
definition
graphic approxima-
tion
shortest course for. .
terrestrial globe
Concave, celestial, definition
Constant deviation. {See Deviation.)
for meridian altitude
form
Conversion of time, apparent to mean.
definition
mean to apparent .
sidereal .
sidereal to mean . .
Coordinates, celestial
definition
Correction, chro. (>See Chronometer.)
index, sextant
of observed altitude
Course, definition
to lay
Culmination, definition
Current, Agulhas
allowance for
Arctic
Australia
Brazil
Cape Horn
Chilean
determined at noon
effect in piloting
equatorial, Atlantic
Indian
Pacific
Guinea
Gulf Stream
Humboldt
Japan Stream
Kamchatka
Kuro Si wo
Labrador
ocean, Atlantic
cause of
definition
determination of
drift, definition
of Atlantic
Indian
Pacific
268
56
263
264
434
27
74
25
26
30
75
32
31
74
30
198
184
199
196
200
210
333
292
286
292
290
291
234
230
250
294
6
132
271
550
206
536
546
538
547
547
398
164
529
549
541
535
532
547
542
543
542
536
529
522
521
525
523
533
548
541
72
23
71
72
136
16
29
15
16
17
29
17
17
29
17
13
59
66
59
59
59
63
96
174
80
79
80
80
80
65
64
69
82
12
42
74
161
61
160
161
160
161
161
126
48
169
161
160
160
159
161
160
161
160
160
169
168
158
158
158
160
160
161
INDEX TO PART I.
335
Subject.
Current, ocean, stream, definition
submarine !
Oya Si wo
Peruvian
Rennell's
Rossel
Southern connecting
tidal, definitions
description of
observation of
to find
Curve, temperature, chronometer
Cyclones and cyclonic circulations .
Cyclonic regions, features of
storms, description
maneuvering in
summary of rules
tropical
character
Danger angle, horizontal
vertical
bearing
Data, useful, miscellaneous
Day's work, routine
Dead reckoning, always kept
definition
form for
method of working . .
value of
Decimal fractions
Declination and hour angle
right ascension
circle, definition
definition
of compass
Declinatoire, plane table
Definitions, nautical astronomy
navigation
Departure, definition
on beginning voyage
to take
Depth, measures of, on charts
recorder, sounding machine
Deviation, causes of
classes of
compensation of
constant, coefficient
definition
definition
heeling error, compensation
definition
I^apier diagram for
quadrantal, coefficients
definition
recompensation
semicircular, coefficients
definition
table
theory of
to apply
find
Diagram, time azimuth
Difference, second. {See Second dif-
ference. )
Dip of horizon, definition
how applied
none with artificial
horizon
variation in
"when land intervenes.
Distance and bearing
by horizon angle
Art.
523
524
544
547
537
546
539
495
505
511
207
266
480
481
482
491
492
483
486
155
156
157
393
392
202
236
237
216
218
74
416
209
1
6
392
204
46
23
98
99
119
112
111
76
126
116
93
107
106
129
103
100
91
95
77
83
361
300
303
294
301
302
138
139
Page.
158
158
161
161
160
161
160
153
154
156
62
72
147
148
148
150
150
148
149
46
46
46
189
124
124
60
171
60
60
178
65
65
63
64
29
133
63
11
11
124
60
21
15
35
35
38
38
38
29
40
38
32
37
37
41
36
35
32
34
29
31
110
83
84
82
83
84
43
43
Subject.
Art.
Page.
Distance, definition
6
139
219
90
503
503
7
435.
470
144
523
533
6
248
225
214
321
12
lunar. {See Lunar distance. )
of objects of known height. .
polar, definition
43
64
zenith. (»S'i?^ Zenith distance. )
Distant object for compass error
Diurnal inequality of tide
31
154
type of tide
154
Dividers, description
13
proportional, description
Doldrums
136
144
Doubling angle on bow
44
Drift current, definition
158
currents, Atlantic
160
Earth, definitions relating to
11
Eccentricitv, sextant
68
Ecliptic, definition
64
Elevated pole
63
Ephemens. (>See Nautical Almanac.)
Equal altitudes for chro. error
form
90
176
longitude ashore . .
at sea . . .
Equation of time, definition
347
352
275
288
215
6
6
215
226
73
77
82
249
410
497
334
104
107
74
in conversion of time .
Equator, celestial, definition
79
63
earth's
11
Equatorial currents. {See Current. )
Equiangular spiral
12
Equinoctial, definition
63
Equinox, definition
64
vernal. {See First point of
Aries. )
Error, chro. (»S'ee Chronometer. )
compass, causes
29
to applv
29
find
31
heeling. ((See Deviation.)
index, sextant, description
probable, of position, how
shown
sextant. ( See Sextant. )
Establishment, tidal, definitions
Ex-meridian altitudes
68
130
153
97
forms
174
Extraordinary refraction near horizon.
Extra-tropical cyclonic storms
First point of Aries, definition
hour angle is si-
i dereal time
Flinders bar, definition
301
493
226
276
105
127
163
83
152
64
74
37
to place
40
Fogs and fog signals
48
Forms for sights, etc
171
notes on
177
use recommended .
Fractions, decimal
411
130
178
Gauges, tide, description
518
412
157
} Geodesy, definition
131
i Geometry
180
! formulae derived from
181
' Geo-Navigation, definition
4
28
259
200
193
248
189
197
6
186
11
Gimbals, compass
16
chronometer
71
i Glasses, shade. (»9('e Shade glasses.)
Globe, terrestrial, for comp. sailing. . .
gt. circle sailing.
Graduation, sextant, error -
Great circle charts
59
58
68
57
for comp. sailing. . .
course
59
12
sailing, advantages
56
336
INDEX TO PART I.
Subject.
Great circle sailing, Airy's method ...
computation
definition
graphic approx
methods
terrestrial globe.,
time azimuth
rifethods
Greenwich adopted as prime meridian.
time, to find
Guinea current
Gulf Stream, description
extraordinary dip in
Hack chronometer, use of
Heading, magnetic, determination of..
Heeling error. {See Deviation.)
Height, determination by barometer. .
Heliograph, use in surveymg
Heliotrope, use in surveying
Horizon angle, distance by
artificial, description
method of use
no dip with
should be tested . . .
celestial, definition
dip of, definition
how applied
none with artificial
horizon
variation in
when land intervenes .
mirror, adjustment
description
prismatic
visible or sea, definition
Horse latitudes
Hour angle and declination
time, conversion
definition
how measured
circle, definition
Humboldt current
Hydrographic survey, method of
surveying, definition
Hydrography in survey, description . .
to plot
Identification of unknown bodies
Index correction, sextant, to find
error, sextant, description
mirror, adjustment
description
prismatic
Induction, magnetic
Instruments, astronomical transit
nautical astronomy
navigation
surveying
Interpolation, Nautical Almanac .
Intersection, Sumner. {See Sumner. )
Intervals, lunitidal, definitions
list of
mean and sidereal time
Iron, hard and soft
Isobars, chart showing
Japan stream
Kamchatka current
Knot, length of
Kuro Si wo current
Labrador current
Lagging of tide „
Land and sea breezes
Art.
194
Page.
58
190
57
183
56
192
58
188
57
193
58
191
58
342
103
280
75
535
160
532
159
301
83
268
72
122
39
57
23
430
135
430
135
139
43
256
70
257
70
294
82
258
71
213
63
300
83
303
84
294
82 i
301
83 1
302
84
246
67
240
66
248
68
213
63
471
145
236
65
293
81
222
64
278
75
216
63
547
161
436
137
412
131
457
140
458
140
402
126
250
69
249
68
245
67
240
66
248
68 '•
96
34
431
135
239
66
7
13
413
131
283
76
497
153
190
79
289
96
34
465
143
542
160
543
160
6
12
542
160
536
160
502
154
474
145
Subject.
Latitude, by meridian altitude
forms ..
Polaris
reduction to meridian
reduction to meridian,
forms
single altitude
forms
9/ cp'^ method
forms
celestial, definition
definition
difference of, definition
horse
Lead, arming
description
line, marking of
Level of bench mark
surveying, use of
description
Lights, employment in piloting
Line, base, description of
of collimation, definition
position. ( iSt'^ Sumner line. )
sight, definition
Sumner. {See Sumner line.)
Local attraction
time, to find
Log book
chip :
ground
patent
electric registers
revolutions as substitute . .
Logarithms, explanation
Longitude, by equal altitudes ashore . .
at sea...
single altitude ashore . .
at sea . . .
time sights, forms
transit observations
celestial, definition
definition
difference of
of secondary meridians
tertiary meridians
Loxodromic Curve
Lubber's line
Lunar distance, explanation of
tables
observations, value of
Lunitidal intervals, definitions
list of
Magnetic observations in survey
Magnetism, acquired in building vessel.
features of earth's
subpermanent
transient
Main triangulation
Maneuvering, cyclonic storms
summary of rules
Marine surveying
Mean day, definition
directive force
noon, definition
sun, definition
time, conversion to apparent
sidereal
definition
intervals, relation to side-
real
Art.
329
340
334
339
339"
"229"
471
19
18
18
517
429
428
161
438
414
414
75
281
64
10
12
13
15
17
347
352
346
349
'344'
229
6
6
343
345
6
28
406
497
461
97
95
98
98
448
491
492
412
274
115
274
274
292
290
274
289
INDEX TO PART I.
337
Subject.
Mean time, relation to apparent
sidereal
Mercator projection, description
to construct
sailing
Meridian altitude, constant
forms for
latitude by
observation of
reduction to
celestial, definition
of earth, definition
passage, definition
prime, Greenwich adopted . .
secondary, definition
determination of .
standard, on charts
tertiary, definition
determination of
Meridional parts
Middle latitude sailing
correction
Mile, nautical or sea, length of
Mirror, horizon. (See Horizon mirror. )
index. (*See Index mirror.)
sextant, resilvering
Monsoon winds
Moon, correction of observed altitude .
form for latitude sights
meridian altitude
time sight
planets, and stars, use of
value of observations of
Morning sights
Nadir, definition
Napier diagram
Nautical Almanac, description
for 1879, extracts . .
gives horizontal
parallax
interpolation
reduction of ele-
ments
second differences .
Astronomy, definitions
instruments
mile, length of
Navigation, definitions
instruments and accessories
Neap tides
Noon sights
Notes on forms for sights, etc
Occupying a station
Ocean current. {See Current, ocean.)
Octant, description
Optical principle of sextant
Orient, to, a i)lane table
Oya Siwo current
Parallax, definition
horizontal, in Nautical Al-
manac
how applied
of planet or star
Parallel of latitude, definition
rulers, description
sailing, description
Passage, meriaian, definition
Pelorus, description
Peruvian current
Piloting, definition
requisites '..
Art.
288
287
38
40
179
333
329
330
334
216
6
271
342
342
343
44
342
345
39
175
178
6
254
473
294
401
406
394
212
93
282
305
283
283
285
209
239
6
1
7
499
396
415
255
242
418
544
304
305
306
294
173
271
35
547
130
131
Page.
79
79
18
19
55
96
173
94
94
97
63
11
74
103
103
103
20
103
103
18
53
54
12
69
145
82
176
174
173
126
128
124
63
32
76
163
84
76
76
78
63
66
12
11
13
153
125
177
132
70
67
1.33
161
84
84
85
82
11
13
52
74
18
161
42
42
Subject.
Art.
Plane of reference, tidal 514
sailing 169
417
416
420
418
294
table, adjustments
description
to improvise
use of
Planet, correction of observed altitude
form for latitude sights
meridian altitude . . .
time sight
identification of unknown 402
401
219
340
214
340
6
431
151
146
142
138
145
134
144
143
133
166
407
458
Planets, stars, and moon, use of
Polar distance, definition
Polaris, latitude by
Pole, elevated
star, latitude by
Poles of earth
Portable transit
Position by angles between 3 objects
26i°-45°onbow-..
bearing and angle
distance
bow and beam bearings . .
cross bearings
doubling angle on bow . . .
two bearings and run
methods of fixing
of anchorage to be plotted. . .
body determines its use...
soundings in survey
probable error of by Sumner
lines, how shown
Pressure, effect in wind
progressive areas of
seasonal variations in
variation of atmospheric
Prime meridian, Greenwich adopted ..
vertical, .definition
Priming of tide
Projection, gnomonic
Mercator
polyconic
systems in use
Proportional dividers, description
Prosection method, plane table
Protractor, ordinary
three armed, description . .
substitute
use of
Quadrantal deviation. {See Deviation.)
Quintant, description
Range of tide at various places
definitions
Ranges for finding compass error
in piloting
Rate, chronometer. (jSee Chronometer
rate. )
Reciprocal bearings for compass error.
Reckoning, dead. {See Dead reckon-
ing- )
Record of astronomical work
chronometer comparisons . .
piloting
tidal
Red sea, extraordinary dip in
Reduction to meridian
forms for
Reference, planes of, tidal
Refraction, correction for
definition
effect on dip
410
465
479
466
476
342
217
502
43
38
42
37
435
418
9
432
433
151
255
498
89
158
411
264
166
512
301
334
Page.
514
298
296
300
156
50
133
132
134
133
82
175
173
172
126
126
64
101
63
101
11
135
45
44
43
43
44
42
44
43
42
49
128
140
130
142
147
144
147
103
64
154
20
18
20
18
136
134
13
136
136
45
70
190
153
31
47
31
130
72
49
156
83
97
174
156
82
82
83
22489—03-
338
INDEX TO PART I.
Subjet't.
Refraction, extraordinary,near horizon
how applied
Relative humidity
Rennell's current
Repeat, to, an angle
Resection method, plane table
Residual deviation ---^
Rhumb line, definition
not shortest course
Right ascension and declination
definition
Roaring forties
Rossel ctirrent
Round of angles
Run, calculation of
determined at noon
Running survey, description
Sailing, composite. (See Composite. )
great circle. {See Great circle. )
Mercator
middle latitude
correction
parallel
plane
spherical
traverse
Sailings, definition
kinds of
Sargasso sea
Sea and land breezes
mile, length of
symbols for state of
water temperature
Second difference, chronometer
Nautical Almanac.
Secondary meridian, definition
determination of.
triangulation
Seconds, employment in naut. sights..
Semicircles, storm
Semicirculardeviation. (*SeeDeviation. )
Semidiameter, definition
how applied
measured
of planet or star
Semidiurnal type of tide
Sextant adjustments
permanent
angles for plotting soundings .
choice of
definition
description
eccentricity
graduation errors
index correction, to find
error, description
method of use
optical principle
prismatic mirrors
shade glasses
resilvering mirrors
surveying
vernier
Shade glasses, for artificial horizon
sextant, description
prismatic
Sidereal day, definition
noon, definition
time, conversion to mean
definition
intervals, relation to
mean
Art. 1 Page.
301
83
299
83
62
25
537
160
415
132
418
134
124
40
6
12
185
56
237
65
228
64
472
145
546
161
415
132
208
,62
398
125
462
140
179
55
175
53
178
54
173
52
169
50
168
50
172
52
167
50
168
50
534
160
474
145
6
12
72
28
63
25
265
72
285
78
342
103
343
103
449
139
409
129
490
150
307
85
308
85
251
69
294
82
503
154
244
67
248
68
458
140
253
69
239
66
240
66
248
68
248
68
250
69
249
68
252
69
242
67
248
68
248
68
254
69
427
135
241
66
256
70
240
66
248
68
276
74
276
74
291
80
276
74
289
Subject.
Sidereal time, relation to mean
Sight, chronometer. ( See Time sight. )
equal alts. {See Equal altitudes. )
latitude. (♦See Latitude. )
line of, definition
longitude. {See Longitude.)
time. ( Sec Time sight. ).
Sights, afternoon
employment of various
morning
noon
Signals, surveying, description
time, for chronometer error
Silvering sextant mirrors
Solar time. {See Apparent time. )
Solstice, definition
Sound, velocity of
Sounding machine, barometric corr
depth recorder
description
tubes
Soundings, surveying, how plotted
use in piloting
Southern connecting current
Sphere, celestial, definition
Spherical sailing
Spring tides
Stadia. {See Telemeter. )
Star, correction of observed altitude
equal altitudes for chro. error
form for latitude sights
meridian altitude
time sight
identification
observations in surveying
Starboard angle, definition
Stars, planets, and moon, use of
Station pointer. {See Protractor, three
armed. )
Storm center, motion of
rate of progress
to avoid
fix bearing
distance
semicircles
tables
Storms, along transatlantic routes
cyclonic. (»%cCyclonicstorms. )
Stream current, definition
Submarine ocean currents
Sumner line, always recommended
applications of
choice of bodies
description
' determination
287
414
399
408
394
396
447
314
254
227
314
24
i 23
! 20
I 21
458
159
539
210
168
499
294
326
79
uses
lines, intersection,computation
graphically .
when run in-
tervenes..
Sun, correction of observed altitude . . .
equal altitudes for chro. error
long, ashore . .
form for equal altitudes
latitude sights
meridian altitude
time sight
mean, definition
observations in surveying
Survey, astronomical work of
hydrographic, method of
running, description
402
454
102
401
484
485
489
487
488
490
492
494
523
524
394
400
400
372
379
377
384
382
390
294
322
347
274
454
450
436
462
INDEX TO PART I.
339
Subject.
Survey, to plot soundinga in
Surveying, hydrograpliic, definition
instruments
marine, definition
topographic, definition
transit, description
Symbols for clouds
sea ,
weather
Ta))le, plane, (See Plane table.)
tide
time azimuth
Telemeter, descrii)tion
substitute for . . ,
use of
Telescope, direct and reversed
sextant, adjustment
description
zenith
Temperature curve, chronometer
Terrestrial object, true bearing of
Tertiary meridian, definition
determination of . .
Theodolite, adjustments
angles for plotting sound -
ings
description
method of use
Thermometer, classes of
description
dry and wet bulb
max. and min., chro
Three-armed protractor. {See Pro-
tractor. )
point problem, conditions
explanation
Tidal current. {See Current, tidal.)
day, definition
establishment, definitions
observations in survey
instructions for
record
Tide, bench mark, definition
cause of
definitions relating to
diurnal inequality
type-,-
effect of, in piloting
wind and barometer on
gauges, description
observation of
planes of reference of
priming and lagging of
range of, at various places
definitions
semidiurnal type
spring and neap
tables
time of high and low
form for
tropic
types of
Time and altitude azimuth
hour angle, conversion of
apparent. {See Apparent time.)
astronomical
at different meridians
azimuth. (/Sf'e Azimuth, time.)
civil
conversion of. (/See Conversion.)
equation of. {See Equation of
time. )
458
412
413
412
412
413
70
72
69
506
361
421
426
424
415
247
240
431
266
369
342
345
414
458
413
415
58
58
61
262
153
152
502
497
460
508
512
516
496
495
503
503
164
501
518
509
514
502
498
503
499
506
506
503
503
366
293
277
279
277
Page.
140
131
131
131
131
131
27
28
27
155
110
134
135
135
132
68
66
135
72
112
103
103
132
140
131
1.32
24
24
24
71
46
45
154
153
140
156
156
156
153
153
154
154
48
154
157
156
156
154
190
153
154
153
155
155
176
154
154
112
81
74
75
74
Subject.
Time, Greenwich, to find
local, to find
mean. {See Mean time. )
of high and low water
form for . .
transit, how found
sidereal. (/SVe Sidereal time.)
signals for chrenometer error
sight for chronometer error
longitude ashore
at sea
forms for
solar. {See Apparent time.)
Topographic surveying, definition
Topography in hydrographic survey . .
Tracing paper to plot soundings
3 -point problem .
Trade wind
Transit, astronomical
definition
observations for chronometer
error
longitude
portable
surveying. (*S'ce Theodolite.)
time of, how found
Traverse sailing
tables, use of
Triangulation, main
secondary
Trigonometric functions
logarithms
Tropic tide
Tropical cyclonic storms
character
Tubes, sounding machine
Unknown bodies, identification of
Useful data, miscellaneous
Variation of compass, definition
to apply
find
Variations, atmospheric
non-periodic . .
periodic
Vernier, barometer
sextant
theodolite
Vertical angles, terrestrial, to measure .
circle, definition
prime
Visible horizon, definition
Watch, comparing, use of
Weather symbols
Wind, Beaufort's scale
causes of
definition
doldrums
effect of, on tides
land and sea breezes
monsoon
normal i)ressure
prevailing
westerly
' * Roaring forties "
storms. {See Cyclonic storms. )
Trade
true direction and force
Zenith, definition
distance, definition
how named
telescope
Page.
280
281
506
331
314
316
346
349
412
456
160
433
469
431
271
315
344
431
331
172
170
448
449
603
483
486
21
402
74
77
82
476
478
477
51
241
413
139
217
217
213
268
69
67
464
463
470
501
474
473
465
467
472
472
469
68
212
221
329
431
P^BT II.
TABLES
341
CONTENTS OF I>A.IIT II.
Page.
Explanation of the Tables 345
Table 1. Traverse Table, Quarter Points 352
2. Traverse Table, Degrees 368
3. Meridional Parts 458
4. Length of Degrees of Latitude and Longitude 466
5A. Distance of an Object by Two Bearings, Quarter Points 468
5B. Distance of an Object by Two Bearings, Degrees 471
6. Distance of Visibility of Objects of different Heights 477
7. Conversion of Arc and Time 478
8. Conversion of Sidereal into Mean Solar Time 479
9. Conversion of Mean Solar into Sidereal Time 482
10. Local mean time of Sun's visible Rising and Setting 485
11. Reduction of Moon's Meridian Passage for Longitude 509
12. Reduction of Quantities from Nautical Almanac 510
13. Change of Sun's Right Ascension 520
14. Dip of Sea Horizon 522
15. Dip at Distances short of Horizon 522
16. Parallax of Sun 522
17. Parallax of Planet 523
18. Augmentation of Moon's Semidiameter 524
19. Augmentation of Moon's Horizontal Parallax 524
20A. Mean Refraction 525
20B. Mean Refraction and Parallax of Sun 526
21. Correction of Refraction for Barometer 527
22. Correction of Refraction for Thermometer 528
23. Mean Refraction and Mean Parallax of Moon 530
24. Mean Refraction and Parallax of Moon 530
25. Variation of Altitude due to change of Declination 539
26. Variation of Altitude in one minute from Meridian 541
27. Variation of Altitude in given time from Meridian 551
28A. First Correction of Polaris •. 554
28B. Second Correction of Polaris 555
28C. Third Correction of Polaris 555
28D. Fourth Correction of Polaris 560
29. Nautical and Statute Miles 562
30. Conversion of Metric and English Linear Measure. .., 563
31. Fahrenheit, Centigrade, and Reaumur Temperatures 564
32. True Force and Direction of Wind 565
33. Distance by Vertical Angle 566
34. Distance by Horizon Angle 568
35. Speed Table for Measured Mile , 569
36. Local Mean and Standard Meridian Times 570
37. Logarithms for Equation of Equal Altitudes 571
38. Error in Longitude produced by Error in Latitude 575
39. Amplitudes 576
40. Correction for Amplitude observed in Apparent Horizon 581
41. Natural Sines and Cosines 582
42. Logarithms of Numbers 591
43. Logarithms of Trigonometric Functions, Quarter Points 607
.44. Logarithms of Trigonometric Functions, Degrees 608
343
EXPLANATION OF THE TABLES.
TABLES 1, 2: TRAVERSE TABLES.
Tables 1 and 2 were originally calculated by the natural sines taken from the fourth edition of
Sherwin's Logarithms, which were previously examined, by differences; when the proof sheets of the
first edition were examined the numbers were again calculated by the natural sines in the second edition
of Hutton's Logarithms; and if any difference was found, the numbers were calculated a third time by
Taylor's Logarithms.
The first table contains the difference of latitude and departure corresponding to distances not
exceeding 300 miles, and for courses to every quarter point of the compass. Table 2 is of the same
nature, but for courses consisting of whole degrees; it was originally of the same extent as Table 1, but
has been extended to include distances up to 600 miles. The manner of using these tables is particularly
explained imder the different problems of Plane, Middle Latitude, and Mercator Sailing in Chapter V.
The tables may be employed in the solution of any right triangle.
TABLE 3: MERIDIONAL PARTS.
This table contains the meridional parts, or increased latitudes, for every degree and minute to 80°,
calculated by the following formula:
in which
~ivr ^^^ ^^ \ '*'^° '^ 2 y ~ " (^^ *^^" I-" + 4 ^* sin' T-i + 5 <^ sin* L + . . . . ),
10800''
the Equatorial radius a = — ~ — = 3437^74677 (log 3.5362739);
M, the modulus of common logarithms = 0.4342945;
^= 2.3025^51 ( log 0.3622157) ;
C, the comprenKion or meridional eccentricity of the earth
according to Clarke ( 1880) = 293 465 = 0.003407562 (log 7.5324437) ;
^ =v/ 27 -V^ = 0.0824846 (log 8.9163666) ;
from which
^ =7915^ 7044558 ( log 3. 8984895) ;
ae^ = 23^38871 (log 1.3690072);
^ae* = 0^05.3042 (log 8. 7246192 ) ;
!«<?«= 0^000216523 (log 6.33550.38).
The results are tabulated to one decimal i)lace, which is sufficient for the ordinary problems of
navigation.
The practical application of this table is illustrated in Chapters II and V, in articles treating of the
Mercator Chart and Mercator Sailing.
TABLE 4: LENGTH OF DEGREES OF LATITTTDE AND LONGITXTDE.
This table gives the length of a degree in both latitude and longitude at each parallel of latitude on
the earth's surface, in nautical and statute miles and in meter.-!, based upon Clarke's value (1866) of the
earth's compression, 200 i-" 1" the case of latitude, the length relates to an arc of which the given
degree is the center.
TABLES 5 A, 5B: DISTANCE BY TWO BEARINGS.
These tables have been calculated to facilitate the operation of finding the distance from an object by
two bearings from a given distance run and course. In Table 5A the arguments are given in points,
in Table 5B in degrees; the first column contains the multiplier of the distance run to give the distance
of observed object at second bearing; the second, at time of passing abeam.
The method is explained in article 143, Chapter IV.
345
346
EXPLANATION OF THE TABLES.
TABLE 6: DISTANCE OF VISIBILITY OF OBJECTS.
This table contains the distances, in nautical and statute miles, at which any object is visible at sea.
It is calculated by the formulae:
rf = 1. 15 \/x^ and d' = 1.32 x/x,
in which rf is the distance in nautical miles, d^ the distance in statute miles, and x the height of the eye
or the object in feet.
To find the distance of visibility of an object, the distance given by the table corresponding to its
height should be added to that corresponding to the height of the observer's eye.
Example: Required the distance of visibility of an object 420 feet high, the observer being at an
elevation of 15 feet.
Dist. corresponding to 420 feet, 23.5 naut. miles.
Dist. corresponding to 15 feet, 4.4 naut. miles.
Dist. of visibility.
27.9 naut. miles.
TABLE 7: CONVERSION OF ABC AND TIME.
In the first column of each pair in this table arfe contained angular measures expressed in arc
(degrees, minutes, or seconds), and in the second column the corresponding angles expressed in time
(hours, minutes, or seconds). As will be seen from the headings of columns, the time corresponding
to degrees (°) is given in hours and minutes; to minutes of arc {/), in minutes and seconds of time;
and to seconds of arc ('''), in seconds and sixtieths of a second of time.
The table will be especially convenient in dealing with longitude and hour angle. The method of
its employment is best illustrated by examples.
Example I.
Required the time corresponding to 50° 31'' 21'^.
50° 00' 00''' = 3" 20"' 00^
31 00 = 2 04
21 = m
50 31 21 =3 22 05.4
Example II.
Required the arc corresponding to 6^ 33™ 26\5.
gh 32m 00^ = 98°
1 24 =
03 0
00
37.5
33 26.5 = '
21 37.5
TABLES 8 AND 9: SIDEREAL AND MEAN SOLAR TIMES.
These tables give, respectively, the reductions necessary to convert intervals of sidereal time into
those of mean solar time, and intervals of mean solar into those of sidereal time. The reduction for any
interval is found by entering with the number of hours at the top and the number of minutes at the side,
adding the reduction for seconds as given in the margin.
The relations between mean solar and sidereal time intervals, and the methods of conversion of
these times, are given in articles 289-291, Chapter IX.
TABLE 10: SUN'S RISING AND SETTING.
This table gives the local mean time of the sun's visible rising and setting — that is, of the appearance
and disappearance of the sun's upper limb in the unobstructed horizon of a person whose eye is 15 feet
above the level of the earth's surface, the atmospheric conditions being normal.
The local apparent times of rising and setting were determined from the formula for a time sight,
the altitude employed being — 0° 56' 08", made up of the following terms: Refraction, — 36'' 29'''; semi-
diameter, - 16' 00"; dip, — 3' 48"; and parallax, + 9".
To ascertain the time of rising or setting for any given date and place, enter the table with the
latitude and declination, interpolating if the degrees are not even. In the line R will be found the time
of rising; in the line S, the time of setting. Be careful to choose the page in which the latitude is of
the correct name, and in which the "approximate date" corresponds, nearly or exactly, with the
given date.
This table is computed with the intention that, if accuracy is desired, it will be entered with the
declination as an argument — not the date — as it is impossible to construct any table based upon dates
whose application shall be general to all years. But as a given degree of declination will, in the
majority of years, fall upon the date given in the table as the "approximate date," and as, when it
does not do so, it can never be more than one day removed therefrom, it will answer, where a slight
inaccuracy may be admitted, to enter the table with the date as an argument, thus avoiding the neces-
sity of ascertaining the declination.
Example: Find the local mean time of sunset at Rio de Janeiro, Brazil (lat. 22° 54' S., long.
43° 10' W.), on January 1, 1903 (dec. 23° 04' S.).
Exact method.
Lat. 22°)
Dec. 23° i
Corr. for + 54' lat +02
Corr. for -f 04' dec 00
Approximate method.
6" 48°
Lat. 22°.. )
January 2 i
Corr. for + 54' lat.
Corr. for 1 dav
L. M. T. sunset 6 50
L. M. T. sunset..
6" 48'"
+ 02
-01
6 49
EXPLANATION OB^ THE TABLES. • 347
TABIiE 11: REDUCTION FOR IffiOON'S TRANSIT.
This table was calculated by proportioning the daily variation of the time of the moon's passing the
meridian.
The numbers taken from the table are to be added to the Greenwich time of moon's transit in west
longitude, but subtracted in east longitude.
TABLE 12: REDUCTIONS FOR NAUTICAL ALMANAC.
This is a table of proportional parts for finding the variation of the sun's right ascension or declination,
or of the equation of time, in any number of minutes of time, the horary motion being given at the top of
the page in seconds, and the number of minutes of time in the side column ; also for finding the variation
of the moon's declination or right ascension in any number of seconds of time, the motion in one minute
being given at the top, and the numbers in the side column being taken for seconds.
TABLE 13: CHANGE OF SUN'S RIGHT ASCENSION.
This is a table that may \)e employed for finding the change of the sun's right ascension for any
given number of hours, the hourly change, as taken from the Nautical Almanac, being given in the
marginal columns.
TABLE 14: DIP OF SEA HORIZON.
This table contains the dip of the sea horizon, calculated by the formula:
D = 58'^8\/F,
in which F = height of the eye above the level of the sea in feet.
It is explained in article 300, Chapter X.
TABLE 16: DIP SHORT OF HORIZON.
This table ijontains the dip for various distances and heights, calculated ]jy the formula:
D = ? rf + 0.56514 X i
' a
in which D represents the dip in miles or minutes, d, the distance of the land in sea miles, and Ji, the
height of the eye of the observer in feet.
TABLE 16: PARALLAX OF SUN.
This table contains the sun's parallax in altitude calculated by the formula:
par. = sin 2 X 8'''.75,
in which z = apparent zenith distance, the sun's horizontal parallax being 8'''''.75.
It is explained in article 304, Chapter X.
TABLE 17: PARALLAX OF PLANET.
Parallax in altitude of a planet is found by entering at the top with the planet's horizontal parallax,
and at the side with the altitude.
TABLE 18: AUGMENTATION OF MOON'S SEMIDIAMETER.
V
This table gives the augmentation of the moon's semidiameter calculated by the formula:
X = c s'' sin /i + ^ c* s* sin^ h -{- ^ c'^ .v',
where /i = moon's apparent altitude;
8 = moon's horizontal semidiameter;
X = augmentation of semidiameter for altitude h; and
log c = 5.25021.
TABLE 19: AUGMENTATION OF MOON'S HORIZONTAL PARALLAX.
This table contains the augmentation of the moon's horizontal parallax, or the correction to reduce
the moon's equatorial horizontal parallax to that point of the earth's axis which lies in the vertical oi
the observer in any given latitude; it is computed by the formulae:
A7t = 7t{b-1), ^^^il-e'sw?!.)'
where * = equatorial horizontal parallax;
L= latitude;
e = eccentricity of the meridian; log ^ = 7.81602; and
A Tf = augmentation of the horizontal parallax for the latitude L.
348 . EXPLANATION OF THE TABLES.
TABLE 20A: MEAN REFRACTION.
This table gives the refraction, reduced from Bessel's tables, for a mean atmospheric condition in
which the barometer is 30.00 inches, and thermometer 50° Fahr.
TABLE 20B: MEAN REFRACTION AND PARALLAX OF SUN.
This table contains the correction to be applied to the sun's apparent altitude for mean refraction
and parallax, being a combination of the quantities for the altittides given in Tables 16 and 20A.
TABLES 21, 2t: CORRECTIONS OF REFRACTION FOR BAROMETER AND
THERMOMETER.
These are deduced from Bessel's tables. The method of their employment will be evident.
TABLE 23: MEAN REFRACTION AND MEAN PARALLAX OF MOON.
This table contains the correction of the moon's altitude for refraction and parallax corresponding
to the mean refraction (Table 20A), and a horizontal parallax of the mean value of hi' 30''^.
TABLE 24: MEAN REFRACTION AND PARALLAX OF MOON.
This table contains the correction to be applied to the moon's apparent altitude for each minute of
horizontal parallax, and for every 10'' of altitude from 5°, with height of barometer 30.00 inches, and
thermometer 50° Fahr.
For seconds of parallax, enter the table abreast the approximate correction and find the seconds of
horizontal parallax, the tens of seconds at the side and the units at the top. Under the latter and
opposite the former will be the seconds to add to the correction.
For minutes of altitude, take the seconds from the extreme right of the page, and apply them as
there directed.
TABLE 25: CHANGE OF ALTITUDE DUE TO CHANGE OF DECLINATION.
♦
This table gives the variation of the altitude of any heavenly body arising from a change of 100^'' in
the declination. It is useful for finding the equation of equal altitudes by the approximate method
explained in article 324, Chapter XI, and for other purposes.
If the change move the body toward the elevate<i pole, apply the correction to the altitude with the
signs in the table; otherwise change the signs.
TABLE 26: CHANGE OF ALTITUDE IN ONE MINUTE FROM MERIDIAN.
This table gives the variation of the altitude of any heavenly body, for one minute of time from
meridian passage, for latitudes up to 60°, declinations to 63°, and altitudes between 6° and 86°. It is
based upon the method set forth in aii;icle 334, Chapter XII, and the values may be computed by the
formula:
1^^9635 cos L cos r?
"~ sin (L-rf)
where a = variation of altitude in one minute from meridian,
L = latitude, and
d = declination — positive for same name and negative for opposite name to latitude at upper
transit, and negative for same name at lower transit.
The limits of the table take in all values of latitude, declination, and altitude which are likely to
be required. In its employment, care must be taken to enter the table at a place where the declination
is appropriately named (of the same or opposite name to the latitude) ; it should also be noted that at
the bottom of the last three pages values are given for the variation of a body at lower transit, which can
only be observed when the declination and latitude are of the same name, and in which case the reduc-
tion to the meridian is subtractive; ihe limitations in this case are stated at the Joot of the page, and
apply to all values below the heavy rules.
TABLE 27: CHANGE OF ALTITUDE IN GIVEN TIME FROM MERIDIAN.
This table gives the pro<lact of the variation in altitude in one minute of a heavenly body near the
meridian, by the square of the number of minutes. Values are given for every half minute between
0'" 30' and 26'" 0% and for all variations likely to be employed in the method of "reduction to the
meridian."
The formula for computing is:
Red. = a X f,
where a = variation in one minute (Table 26) , and
t = number of minutes (in units and tenths) from time of meridian passage.
The table is entered in the column of the nearest interval of time from meridian, and the value
taken out corrresponding to the value of a found from Table 26. The units and tenths are picked out
separately and combined, each being corrected by interpolation for intermediate intervals of time.
The result is the amount to be applied to the observed altitude to reduce it to the meridian altitude,
which is always to be added for upper transits and subtracted for lower.
EXPLANATION OF THE TABLE8. ^ 349
TABLE 28, A, B, C, D: LATITUDE BY POLARIS. '
The formula on which these tables are based is :
h = h — p (!08 t-'r^jJ^ sin V^ sin^ t tan h
— Ip^ sin'^ V^ cos t sin^ t + ^p* sin^* V^ sin* t tan* h;
in which L = the latitude of the place;
h — the true altitude;
p = the polar distance; and
t — the hour angle of the star.
Table A contains for the declination 88° 48', or/»„ = l° 12' = 4320''', the^rs^ correction,
A = —p„ cos t — ^p^g sin^ 1" cos t sin^ t;
Argument, the hour angle of the star, or 24'' — the hour angle.
Table B contains the second correction,
B = i p^o sin 1" sin^ tta.nh+ lp\ sin* 1" sin* t tan* h;
Arguments, the true altitude of the star and the hour angle, or 24'' — the hour angle. This
correction is always additive.
Table C contains the third correction,
C = \ (p* —p^o) sin 1" sin"'' t tan h;
Arguments, B and the declinaium of the star from 88° 47' 20" to 88° 49' 20".
Table D contains the fourth correction,
— {p —Pa) cos l — i {p^ — P^o) sii^* 1'''' COS <8in^/;
Arguments, J and the declination of the star from 88° 47' 20" to 88° 49' 20".
The method of employing this table is illustrated in article 341, Chapter XII.
TABLES 29, 30, 31: CONVERSION TABLES.
These are self-explanatory.
TABLE 32: TRUE FORCE AND DIRECTION OF WIND.
This table enables an observer on board of a moving vessel to determine the true force and direction
of the wind from its apparent force and direction. Enter the table with the apparent direction of the
wind (number of points on the lx)w) and force (Beaufort scale) as arguments, and pick out the direc-
tion relatively to the ship's head and the force corresponding to the known speed of the ship.
Example: A vessel steaming SE. at a speed of 15 knots appears to have a wind blowing from three
points on the starboard bow with a force of 6, Beaufort scale. What is the true direction and force?
In the column headed 3 (meaning three points on bow, apparent direction) and. in the line 6
(apparent force, Beaufort scale), we find abreast 15 (knots, speed of vessel) that the true direction is 5
points on starboard bow, i. e., S. by W., and true force 4.
TABLE 33: VERTICAL ANGLES.
This table gives the distance of an object of known height by the vertical angle that it subtends at
the position of the observer. It was computed by the formula:
/*
tan a = . , ■
where a = the vertical angle; ,
h = the height of the observed object in feet; and
d = the distance of the object, also converted into feet.
The employment of this method of finding distance is explained in article 139, chapter IV.
TABLE 34: HORIZON ANGLES.
This shows the distance in yards corresponding to any observed angle between an object and the
sea horizon beyond, the observer being at a known height.
The method of une is explained in article 139, chapter IV.
TABLE 35: SPEED TABLE.
This table shows the rate of speed, in nautical miles per hour, of a vessel which traverses a measured
mile in any given number of minutes and seconds. It is entered with the number of minutes at the top
and the number of seconds at the side; under one and abreast the other is the number of knots of speed.
350 ' EXPLANATION OF THE TABLES.
TABLE 36: LOCAL AND STANDARD TIMES.
This table contains the reduction to be applied to the local time to obtain the corresponding time
at any other meridian whose time is adopted as a standard. The results are given to the nearest minute
of time only, being intended for the reduction of such approximate quantities as the time of high water
or time of sunset. More exact reductions, when required, may be made by Table 7.
TABLE 37: LOGARITHMS FOR EQUAL ALTITUDE SIGHTS.
Logarithms of A Mid B, for computing the Equation of Equal Altitudes, are calculated by the
formulae:
■ ' 1800 sin i E' -^"ISOO tan § E '
where E in the numerator is the elapsed time in minutes, and E in the denominator the elapsed time
expressed in arc.
If we put
we have
L = latitude of the place of observation, + north, — south,
d = declination of the sun, -f north, — south,
71 = hourly change of declination, -j- north, — south,
C = correction to reduce the middle chronometer time to chronometer time of apparent
noon, algebraically additive,
C'' = the same for midnight,
C ——An tan L + B n tan d;
C = An tan L + B n tan d.
This is Chauvenet's table to aid the solution of the problem of Equal Altitudes, and is explained in
article 322 and following articles. Chapter XI.
TABLE 38: EFFECT UPON LONGITUDE OF ERROR IN LATITUDE.
Table 38 shows, approximately, the error in longitude in miles and tenths of a mile, occasioned by
an error of one mile in the latitude.
Thus, when the sun's altitude is 30°, the latitude 30°, and the polar distance 100°, the error is
eight-tenths of a mile.
The effect of an increase of latitude is as follows:
In West longitude, / East \ of meridian, the / decreased \ except where marked f increased 1
the body being \ West J longitude is \ increased / ' by *, when it is \ decreased /"
In East longitude,/ East 1 of meridian, the/ increased! except where marked / decreased 1
the body being \ West j longitude is \ decreased /' by *, when it is \ increased /*
A decrease of latitude has the contrary effect.
The direction of error may readily be seen by drawing the Sumner line in a direction at right angles
to the approximate bearing of the body.
TABLE 39: AMPLITUDES.
This table contains amplitudes of heavenly bodies, at rising and setting, for various latitudes and
declinations, computed by the formula:
sin amp. = sec Lat. X sin dec.
It is entered with the declination at the top and the latitude at the side.
Its use is explained in article 358, Chapter XIV.
TABLE 40: CORRECTION FOR AMPLITUDES.
This table gives a correction to be applied to the observed amplitude to counteract the vertical
displacement due t(j refraction, parallax, and dip, when the body is observed with its center in the
visible horizon.
The correction is to be applied for the sun, a planet, or a star, as follows:
^' SSfg r„ a ^i; } "PP'J' the correction to the right.
""^wSI ta I !il: } -PP'y 'he eerrection to the left.
For the moon, apply half the correction in the contrary manner.
EXPLANATION OF THE TABLES. 351
TABLE 41: NATURAL SINES AND COSINES.
This table contains the natural sine and cosine for every minute of the quadrant, and is to be
entered at the top or bottom with the degrees, and at the side marked M., with the minutes; the
corresponding numbers will be the natural sine and cosine, respectively, observing that if the degrees
are found at the top, the name sine, cosine, and M. must also be found at the top, and the contrary if
the degrees are found at the bottom. It should be understood that all numbers given in the table
should be divided by 100,000 — that is, ]iointed off to contain five decimal places. Thus, .43366 is the
natural sine of 25° 42^, or the cosine of 64° 18^.
In the outer columns of the margin are given tables of proportional parts, for the purpose of finding,
approximately, by inspection, the proportional part corresponding to any number of seconds in the
proposed angle, the seconds being found in the marginal column marked M., and the correction in
the adjoining column. Thus, if we suppose that it were required to find the natural sine corresponding
to 25° 42^ 19'^ the difference of the sines of 25° 42^ and 25° 43^ is 26, being the same as at the top of the
left-hand column of the table; and in this column, and opposite 19 in the column M., is the correc-
tion 8. Adding this to the above number .43366, because the numbers are increamng, we get .4c374 for
the sine of 25° 42^ 19'^. In like manner, we find the cosine of the same angle to be .90108 — 4 = .90104,
using the right-hand columns, and subtracting Ijecause the numbers are decreasing; observing, however,
that the number 14 at the top of this column varies 1 from the difference between the cosines of 25° 42''
and 25° 43', which is only 13; so that the talole may give in some cases a unit too much between the
angles 25° 42' and 25° 43'; but this is, in general, of but little importance, and when accuracy is required,
the usual method of proportional parts is to be resorted to, using the actual tabular difference.
TABLE 42: LOGARITHMS OF NUMBERS.
This table, containing the common logarithms of numbers, was compared with Sherwin's, Mutton's,
and Taylor's logarithms; its use is explained in an article on Logarithms in Appendix III.
TABLE 43: LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, QUARTER POINTS.
This table contains the logarithms of the sines, tangents, etc., corresponding to points and quarter
points of the compass. This Avas compared with Sherwin's, Hutton's, and Taylor's logarithms.
TABLE 44: LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, DEGREES.
This table contains the common logarithms of the sines, tangents, secants, etc. It was compared
with Sherwin's, Hutton's, and Taylor's tables. Two additional columns are given in this table, which
are very convenient in finding the time from an altitude of the sun; also, three columns of proportional
parts for seconds of space, and a small table at the bottom of each page for finding the proportional parts
for seconds of time. The degrees are marked to 180°, which saves the trouble of subtracting the given
angle from 180° when it exceeds 90°.
The use of this table is fully explained in Appendix III in an article on Logarithms.
Page 352
TABLE
1.
1
Difference of Latitude and
Departure for J Point. |
N. JE.
N. i W.
S.
tE.
s. i w. 1
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.0
61
60.9
3.0
121
120.9
5.9
181
180.8
8.9
241 240. 7
,11.8
2
2.0
0.1
62
61.9
3.0
22
121.9
6.0
82
181.8
8.9
42 241. 7
Ml. 9
3
3.0
0.1
63
62.9
3.1
23
122.9
6.0
83
182.8
9.0
43 242. 7
11.9
4
4.0
0.2
64
63.9
3.1
24
123.9
6.1
84
183.8
9.0
44 243.7
12.0
5
5.0
0.2
^5
64.9
3.2
25
124.8
6.1
85
184.8
9.1
45 1 244.7
12.0
6
6.0
0.3
^
65.9
3.2
26
125.8
6.2
86
185.8
9.1
46 ; 245.7
12.1
7
7.0
0.3
67
66.9
3.3
27
126.8
6.2
87
186.8
9.2
47 246. 7
12.1
8
8.0
0.4
68
67.9
3.3
28
127.8
6.3
88
187.8
9.2
48 1 247.7
12.2
9
9.0
0.4
69
68.9
3.4
29
128.8
6.3
89
188.8
9.3
49 248.7
12.2
10
10.0
0.5
70
69.9
3.4
3.5
30
129.8
6.4
90
189.8
9.3
9.4
50 1 249.7
251 1 250.7
12.3
11
11.0
0.5
71
70.9
131
130.8
6.4
191
190.8
12.3
12
12.0
0.6
72
71.9
3.5
32
131.8
6.5
92
191.8
9.4
52 ! 251. 7
12.4
13
13.0
0.6
73
72.9
3.6
33
132.8
6.5
93
192.8
9.5
53 i 252.7
12.4
14
14.0
0.7
74
73.9
3.6
34
133.8
6.6
94
193.8
9.5
54 1 253.7
12.5
15
15.0
0.7
75
74.9
3.7
35
134.8
6.6
95
194.8
9.6
55 254.7
12.5
16
16: 0
0.8
76
75.9
3.7
36
135.8
6.7
96
195.8
9.6
56 255. 7
12.6
17
17.0
0.8
77
76.9
3.8
37
136.8
6.7
97
196.8
9.7
57
256.7
12.6
18
18.0
0.9
78
77.9
3.8
38
137.8
6.8
98
197.8
9.7
58
257.7
12.7
19
19.0
0.9
79
78.9
3.9
39
138.8
6.8
99
198.8
9.8
59 i 258.7
12.7
20
20.0
1.0
80
79.9
3.9
40
139.8
6.9
200
201
199.8
9.8
60 1 259.7
12.8
21
21.0
1.0
81
80.9
4.0
141
140.8
6.9
200.8
9.9
261 I 260.7
12.8
22
22.0
1.1
82
81.9
4.0
42
141.8
7.0
02
201.8
9.9
62 I 261. 7
12.9
23
23.0
1.1
83
82.9
4.1
43
142.8
7.0
03
202.8
10.0
63 262.7
12.9
24
24.0
1.2
84
83.9
4.1
44
143.8
7.1
04
203. 8
10.0
64 263.7
13.0
25
25.0
1.2
85
84.9
4.2
45
144.8
7.1
05
204.8
10.1
65 i 264. 7
13.0
26
26.0
1.3
86
85.9
4.2
46
145.8
7.2
06
205. 8
10.1
66 265.7
13.1
27
27.0
1.3
87
86.9
4.3
47
146.8
7.2
07
206.8
10.2
67 266.7
13.1
28
28.0
1.4
88
87.9
4.3
48
147.8
7.3
08
207.7
10.2
68
267.7
13.2
29
29.0
1.4
89
88.9
4.4
49
148.8
7.3
09
208.7
10.3
69
268.7
13.2
30
30.0
1.5
90
89.9
4.4
50
149.8
7.4
10
209.7
210. 7
10.3
10.4
70
269.7
13.2
13.3
31
31.0
1.5
91
90.9
4.5
151
150.8
7.4
211
271
270.7
32
32.0
1.6
92
91.9
4.5
52
151.8
7.5
12
211.7
10.4
72
271.7
13.3
33
33.0
1.6
93
92.9
4.6
53
152.8
7.5
13
212.7
10.5
73
272.7
13.4
34
34.0
1.7
94
93.9
4.6
54
153.8
7.6
14
213.7
10.5
74
273.7
13.4
35
35.0
1.7
95
94.9
4.7
55
154.8
7.6
15
214.7
10.5
75 1 274. 7
13.5
36
36.0
1.8
96
95.9
4.7
56
155.8
7.7
16
215.7
10.6
76 275.7
13.5
37
37.0
1.8
97
96.9
4.8
57
156.8
7.7
17
216.7
10.6
77 276.7
13.6
38
38.0
1.9
98
97.9
4.8
58
157.8
7.8
18
217.7
10.7
78 ; 277.7
13.6
39
39.0
1.9
99
98.9
4.9
59
158.8
7.8
19
218.7
10.7
79 1 278.7
13.7
40
41
40.0
41.0
2.0
100
99.9
4.9
60
161
159.8
7.9
7.9
20
219.7
10.8
10.8
80 t 279. 7
13.7
2.0
101
100.9
5.0
160.8
221
220.7
281
280.7
13.8
42
41.9
2.1
02
101.9
5.0
62
161.8
7.9
22
221.7
10.9
82
281.7
13.8
43
42.9
2.1
03
102.9
5.1
63
162.8
8.0
23
222.7
10.9
83
282.7
13.9
44
43.9
2.2
04
103.9
5.1
64
163.8
8.0
24
223.7
11.0
84
283.7
13.9
45
44.9
2.2
05
104.9
5.2
65
164.8
8.1
25
224.7
11.0
85
284.7
14.0
46
45.9
2.3
06
105.9
5.2
66
165.8
8.1
26
225.7
11.1
86
285.7
14.0
47
46.9
2.3
07
106.9
5.3
67
166.8
8.2
27
226.7
11.1
87
286.7
14.1
48
47.9
2.4
08
107.9
5.3
68
167.8
8.2
28
227.7
11.2
88
287.7
14.1
49
48.9
2.4
09
108.9
5.3
69
168.8
8.3
29
228.7
11.2
89
288.7
14.2
50
51
49.9
50.9
2.5
10
109.9
5.4
70
169.8
8.3
30
229.7
11.3
90
"291
289.7
14.2
14.3
2.5
111
110.9
5.4
171
170.8
8.4
231
230. 7
11.3
290.6
52
51.9
2.6
12
111.9
5.5
72
171.8
8.4
32
231.7
11.4
92
291.6
14.3
53
52.9
2.6
13
112.9
5.5
73
172.8
8.5
33
232.7
11.4
93
292.6
14.4
54
53.9
2.6
14
113.9
5.6
74 1 173.8
8.5
34
233.7
11.5
94
293.6
14.4
55
54.9
2.7
15
114.9
5.6
75 174.8
8.6
35
234.7
11.5
95 i 294.6
14.5
56
55.9
2.7
16
115.9
5.7
76 \ 175.8
8.6
36
235.7
11.6
96 1 295.6
14.5
57
56.9
2.8
17
116.9
5.7
77
176.8
8.7
37
236. 7
11.6
97 ' 296.6
14.6
58
57.9
2.8
18
117.9
5.8
78
177.8
8.7
38
237.7
11.7
98 ; 297.6
14.6
59
58.9
2.9
19
118.9
5.8
79
178.8
8.8
39
238.7
11.7
99 ; 298.6
14.7
60
59.9
2.9
20
119.9
5.9
80
179.8
8.8
40
239.7
11.8
300 299.6
1
14.7
Dlst.
Dep.
Lat.
Dist.
Dep.
I^t.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. i Dep.
Lat.
E.
^N.
E. JS
W. iN.
A
V. i S.
[For 7J Points. 1
TABLE
1.
[Page 353
Difference of Latitude and
Depari
ure for \ Point.
N. h E.
N. J W.
S. J E. S. .
\\Y.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
1
1.0
0.1
61
60.7
6.0
121
120.4
11.9
181
180.1
17.7
241
239.8
23.6
?,
2.0
0.2
62
61.7
6.1
22
121.4
12.0
82
181.1
17.8
42
240.8
23.7
3
3.0
0.3
63
62.7
6.2
23
122.4
12.1
83
182.1
17.9
43 241. 8
23.8
4
4.0
0.4
64
63.7
6.3
24 \ 123.4
12.2
84
183. 1
18.0
44 ! 242.8
23.9
5
5.0
0.5
65
64.7
6.4
25
124.4
12.3
85
184.1
18.1
45
243.8
24.0
6
6.0
0.6
66
65.7
6.5
26
125.4
12.4
86
185.1
18.2
46
244.8
24.1
7
7.0
0.7
67
66.7
6.6
27
126.4
12.4
87
186.1
18.3
47
245.8
24.2
8
8.0
0.8
68
67.7
6.7
28
127.4
12.5
88
187.1
18.4
48
246.8
24.3
9
9.0
0.9
69
68.7
6.8
29
128.4
12.6
89
188.1
18.5
49
247.8
24.4
10
10.0
1.0
1.1
70
69.7
6.9
30
129.4
12.7
12.8
90
191
189.1
190.1
18.6
50
248.8
24.5
11
10.9
71
70.7
7.0
131
130.4
18.7
251
249.8
24.6
12
11.9
1.2
72
71.7
7.1
32
131.4
12.9
92
191.1 '• 18.8
52
250.8
24.7
13
12.9
1.3
73
72.6
7.2
33
132.4
13.0
93
192.1
18.9
53
251. 8
24.8
14
13.9
1.4
74
73.6
7.3
34
133.4
13.1
94
193.1
19.0
54
252.8
24.9
15
14.9
1.5
75
74.6
7.4
35
134.3
13.2
95
194.1
19.1
55
253.8
25.0
16
15.9
1.6
76
75.6
7.4
36
135.3
13.3
96
195.1
19.2
56
254.8
25.1
17
16.9
1.7
77
76.6
7.5
37
136.3
13.4
97
196.1
19.3
57
255.8
25.2
18
17.9
1.8
78
77.6
7.6
38
137.3
13.5
98
197.0
19.4
58
256.8
25.3
19
18.9
1.9
79
78.6
7.7
39
138. 3
13.6
99
198.0
19.5
59
257.8
25.4
20
19.9
2.0
80
79.6
7.8
7.9
40
139.3
13.7
200
199.0
19.6
60
258.7
25.5
21
20.9
2.1
81
80.6
141
140.3
13.8
201
200.0
19.7
261
259.7
25.6
22
21.9
2.2
82
81.6
8.0
42
141.3
13.9
02
201.0
19.8
62
260.7
25.7
23
22.9
2.3
83
82.6
8.1
43
142.3
14.0
03
202.0
19.9
63
261.7
25.8
24
23.9
2.4
84
83.6
8.2
44
143.3
14.1
04
203. 0
20.0
64
262.7
25.9
25
24.9
2.5
85
84.6
8.3
45
144.3
14.2
05
204.0
20.1
65
263.7
26.0
26
25.9
2.5
86
85.6
8.4
46.
145. 3
14.3
06
205. 0
20.2
66
264.7
26.1
27
26.9
2.6
87
86.6
8.5
47
146.3
14.4
07
206.0
20.3
67
265.7
26.2
28
27.9
2.7
88
87.6
8.6
48
147.3
14.5
08
207.0
20.4
68
266.7
26.3
29
28.9
2.8
89
88.6
8.7
49
148. 3
14.6
09
208.0
20.5
69
267.7
26.4
30
31
29.9
30.9
2.9
90
89.6
90.6
8.8
8.9
50
151
149.3
14.7
10
209.0
210.0
20.6
20.7
70
271
268.7
269.7
26.5
3.0
91
150.3
14.8
211
26.6
32
31.8
3.1
92
91.6
9.0
52
151. 3
14.9
12
211.0
20.8
72
270.7
26.7
33
32.8
3.2
93
92.6
9.1
53
152.3
15.0
13
212.0
20.9
73
271.7
26.8
34
33.8
3.3
94
93.5
9.2
54
153.3
15.1
14
213.0
21.0
74
272.7
26.9
35
34.8
3.4
95
94.5
9.3
55
154.3
15.2
15
214.0
21.1
75
273.7
27.0
36
•35.8
3.5
96
95.5
9.4
56
155.2
15.3
16
215.0
21.2
76
274.7
27.1
37
36.8
3.6
97
96.5
9.5
57
156.2
15.4
17
216.0
21.3
77
275. 7
27.2
38
37.8
3.7
98
97.5
9.6
58
157.2
15.5
18
217.0
21.4
78
276.7
27.2
39
38.8
3.8
99
98.5
9.7
59
158.2
15.6
19
217.9
21.5
79
277.7
27.3
40
39.8
3.9
100
99.5
9.8
60
159.2
15.7
20
218.9
21.6
80
278.7
27.4
41
40.8
4.0
101
100.5
9.9
161
160.2
15.8
221
219.9
21.7
281
279.6
27.5
42
41.8
4.1
02
101.5
10.0
62
161.2
15.9
22
220.9
21.8
82
280.6
27.6
43
42.8
4.2
03
102.5
10.1
63
162.2
16.0
23
221.9
21.9
83
281.6
27.7
44
43.8
4.3
04
103.5
10.2
64
163.2
16.1
24
222.9
22.0
84
282.6
27.8
45
44.8
4.4
05
104.5
10.3
65
164.2
16.2
25
223.9
22.1
85
283.6
27.9
46
45.8
4.5
06
105.5
10.4
66
165.2
16.3
26
224.9
22.2
86
284.6
28.0
47
46.8
4.6
07
106.5
10.5
67
166.2
16.4
27
225.9
22.2
87
285.6
28.1
48
47.8
4.7
08
107.5
10.6
68
167.2
16.5
28
226.9
22.3
88
286.6
28.2
49
48.8
4.8
09
108.5
10.7
69
168.2
16.6
29
227.9
22.4
89
287.6
28.3
50
49.8
4.9
5.0
10
109.5
10.8
70
169.2
16.7
30
228.9
22.5
22.6
90
288.6
28.4
51
50.8
111
110.5
10.9
171
170.2
16.8
231
229.9
291 289. 6
28.5
52
51.7
5.1
12
111.5
11.0
72
171.2
16.9
32
230.9
22.7
92
290.6
28.6
53
52.7
5.2
13
112.5
11.1
73
172.2
17.0
33
231.9
22.8
93
291.6
28.7
54
53.7
5.3
14
113.5
11.2
74
173.2
17.1
34
232.9
22.9
94
292.6
28.8
55
54.7
5.4
15
114.4
11.3
75
174.2
17.2
35
233.9
23.0
95
293.6
28.9
56
55.7
5.5
16
115.4
11.4
76
175.2
17.3
36
234.9
23.1
96
294.6
29.0
57
56.7
5.6
17
116.4
11.5
77
176.1
17.3
37
235.9
23.2
97
295.6
29.1
58
57.7
5.7
18
117.4
11.6
78
177.1
17.4
38
236.9
23.3
98
296.6
29.2
59
58.7
5.8
19
118.4
11.7
79
178.1
17.5
39
237.8
23.4
99
297.6
29.3
60
59.7
5.9
20
119.4
11.8
80
179.1
17.6
40
238.8
23.5
300
298.6
29.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
E. JN.
E. J S.
W. J N
W * S.
[For 7i Points. 1
22489—03-
-23
Page 354
TABLE 1.
Difference of Latitude and Depart
Lire for J Point.
N. IE.
N. 1 W
S. JE.
S. 1 AV
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.3
9.0
121
119.7
17.8
181
179.0
26.6
241
238.4
35.4
2
2.0
0.3
62
61.3
, 9.1
22
120.7
17.9
82
180.0
26.7
42
239.4
35.5
3
3.0
0.4
63
62.3
9.2
23
121.7
18.0
83
181.0
26.9
43
240.4
35.7
4
4.0
0.6
64
63.3
9.4
24
122.7
18.2
84
182.0
27.0
44
241.4
35.8
5
4.9
0.7
ei
64.3
9.5
25
123.6
18.3
85
183.0
27.1
45
242.3
35.9
6
5.9
0.9
65.3
9.7
26
124.6
18.5
86
184.0
27.3
46
243.3
36.1
7
6.9
1.0
67
66.3
9.8
27
125.6
18.6
87
185.0
27.4
47
244.3
36.2
8
7.9
1.2
68
67.3
10.0
28
126.6
18.8
88
186.0
27.6
48
245.3
36.4
9
8.9
1.3
69
68.3
10.1
29
127.6
18.9
89
187.0
27.7
49
246. 3
36.5
10
9.9
1.5
70
69.2
10.3
30
128.6
19.1
90
187.9
27.9
.50
247.3
36.7
11
10.9
1.6
71
70.2
10.4
131
129.6
19.2
191
188.9
28.0
251
248.3
36.8
12
11.9
1.8
72
71.2
10.6
32
130.6
19.4
92
189.9
28.2
52
249. 3
37.0
13
12.9
1.9
73
72.2 t 10.7
33
131.6
19.5
93
190.9
28.3
53
250.3
37.1
14
13.8
2.1
74
73.2
10.9
34
132.5
19.7
94
191.9
28.5
54
251.3
37.3
15
14.8
2.2
75
74.2
11.0
35
133.5
19.8
95
192.9
28.6
55
252.2
37.4
16
15.8
2.3
76
75.2
11.2
36
134.5
20.0
96
193.9
28.8
56
253.2
37.6
17
16.8
2.5
77
76.2
11.3
37
135.5
20.1
97
194.9
28.9
57
254.2
37.7
18
17.8
2.6
78
77.2
11.4
38
136.5
20.2
98
195.9
29.1
58
255.2
37.9
19
18.8
2.8
79
78.1
11.6
39
137.5
20.4
99
196.8
29.2
59
256.2
38.0
20
19.8
2.9
80
79.1
11.7
40
138.5
20.5
200
197.8
29.3
60
257.2
38.1
38.3
21
20.8
3.1
81
80.1
11.9
'141
139.5
20.7
201
198.8
29.5
261
258.2
22
21.8
3.2
82
81.1
12.0
42
140.5
20.8
02
199.8
29.6
62
259.2
38.4
23
22.8
3.4
83
82.1
12.2
43
141.5
21.0
03
200.8
29.8
63
260.2
38.6
24
23.7
3.5
84
83.1
12.3
44
142.4
21.1
04
201.8
29.9
64
261.1
38.7
25
24.7
3.7
85
84.1
12.5
45
143.4
21.3
05
202.8
30.1
65
262.1
38.9
26
25.7
3.8
86
85.1
12.6
46
144.4
21.4
06
203. 8
30.2
66
263.1
39.0
27
26.7
4.0
87
86.1
12.8
47
145.4
21.6
07
204.8
30.4
67
264.1
39.2
28
27.7
4.1
88
87.0
12.9
48
146.4
21.7
08
205.7
30.5
68
265.1
39.3
29
28.7
4.3
89
88.0
13.1
49
147.4
21.9
09
206.7
30.7
69
266.1
39.5
30
29.7
4.4
90
89.0
13.2
13.4
50
151
148.4
22.0
10
207.7
30.8
70
267.1
39.6
31
30.7
4.5
91
90.0
149.4
22.2
211
208.7
31.0
271
268. 1
39.8
32
31.7
4.7
92
91.0
13.5
52
150.4
22.3
12
209.7
31.1
72-
269.1
39.9
33
32.6
4.8
93
92.0
13.6
53
151.3
22.4
13
210.7
31.3
73
270.0
40.1
34
33.6
5.0
94
93.0
13.8
54
152.3
22.6
14
211.7
31.4
74
271.0
40.2
35
34.6
5.1
95
94.0
13.9
55
153.3
22.7
15
212.7
31.5
75
272.0
40.4
36
35.6
5.3
96
95.0
14.1
56
154.3
22.9
16
213.7
31.7
76
273.0
40.5
37
36.6
5.4
97
96.0
14.2
57
155.3
23.0
17
214.7
31.8
77
274.0
40.6
38
37.6
5.6
98
96.9
14.4
58
156.3
23.2
18
215.6
32.0
78
275.0
40.8
39
38.6
5.7
99
97.9
14.5
59
157.3
23.3
19
216.6
32.1
79
276.0
40.9
40
39.6
5.9
100
98.9
14.7
60
158.3
159.3
23.5
20
217.6
218.6
32.3
80
277.0
278.0
41.1
41
40.6
6.0
101
99.9
14.8
161
23.6
221
32.4
281
41.2
42
41.5
6.2
02
100.9
15.0
62
160.2
23.8
22
219.6
32.6
82
278.9
41.4
43
42.5
6.3
03
101.9
15.1
63
161.2
23.9
23
220.6
32.7
83
279.9
41.5
44
43.5
6.5
04
102.9
15.3
64
162.2
24.1
24
221.6
32.9
84
280.9
41.7
45
44.5
6.6
05
103.9
15.4
65
163.2
24.2
25
222.6
33.0
85
281.9
41.8
46
45.5
6.7
06
104.9
15.6
66
164.2
24.4
26
223.6
33.2
86
282.9
42.0
47
46.5
6.9
07
105.8
15.?
67
165.2
24.5
27
224.5
33.3
87
283.9
42.1
48
47.5
7.0
08
106.8
15.8
68
166.2
24.7
28
225.5
33.5
88
284.9
42.3
49
48.5
7.2
09
107.8
16.0
69
167.2
24.8
29
226.5
33.6
89
285.9
42.4
50
49.5
7.3
10
108.8
16.1
70
168.2
24.9
30
227.5
33.7
33.9
90
286.9
42.6
42.7
51
50.4
7.5
111
109.8
16.3
171
169.1
25.1
231
228.5
291
287.9
52
51.4
7.6
12
110.8
16.4
72
170.1
25.2
32
229.5
34.0
92
288.8
42.8
53
52.4
7.8
13
111.8
16.6
73
171.1
25.4
33
230.5
34.2
93
289.8
43.0
54
53.4
7.9
U
112.8
16.7
74
172.1
25.5
34
231. 5
34.3
94
290.8
43.1
55
54.4
8.1
15
113.8
16.9
75
173.1
25.7
35
232.5
34.5
95
291.8
43.3
56
55.4
8.2
16
114.7
17.0
76
174.1
25.8
36
233.4
34.6
96
292.8
43.4
57
56.4
8.4
17
115.7
17.2
77
175.1
26.0
37
234.4
34.8
97
293.8
43.6
58
57.4
8.5
18
116.7
17.3
78
176.1
26.1
38
235. 4
34.9
98
294.8
43.7
59
58.4
8.7
19
117.7
17.5
79
177.1
26.3
39
236. 4
35.1
99
295.8
43.9
60
59.4
8.8
20
118.7
17.6
80
178.1
26.4
40
237.4
35.2
300
296.8
44.0
Dlst,
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
E. IN
K 1 S.
W, |N
W. f S
U
For 7i P
oints.
TABLE 1.
[Page 355 |
Difference of Latitude and Departure for 1 Point.
N. by E
N. by
w.
S. by E. S. by W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.8
11.9
121
118.7
23.6
181
177.5
35.3
241
236.4
47.0
2
2.0
0.4
62
60.8
12.1
22
119.7
23.8
82
178.5
35.5
42
237.4
47.2
3
2.9
0.6
63
61.8
12.3
23
120.6
24.0
83
179.5
35.7
43
238.3
47.4
4
3.9
0.8
64
62.8
12.5
24
121.6
24.2
84
180.5
35.9
44
239.3
47.6
5
4.9
1.0
65
63.8
12.7
25
122.6
24.4
85
181.4
36.1
45
240.3
47.8
6
5.9
1.2
66
64.7
12.9
26
123.6
24.6
86
182,4
36.3
46
241.3
48.0
7
6.9
1.4
67
65.7
13.1
27
124.6
24.8
87
183.4
36.5
47
242.3
48.2
8
7.8
1.6
68
66.7
13.3
28
125.5
25.0
88
184.4
36.7
48
243.2
48.4
9
8.8
1.8
69
67.7
13.5
29
126.5
25.2
89
185.4
36.9
49
244.2
48.6
10
9.8
2.0
70
68.7
13.7
30
127.5
25.4
90
186.3
37.1
50
245.2
48.8
11
10.8
2.1
71
69.6
13.9
131
128.5
25.6
191
187.3
37.3
251
246.2
49.0
12
11.8
2.3
72
70.6
14.0
32
129.5
25.8
92 ! 188. 3
37.5
52
247.2
49.2
13
12.8
2.5
73
71.6
14.2
33
130.4
25.9
93 ' 189.3
37.7
53
248.1
49.4
14
13.7
2.7
74
72.6
14.4
34
131.4
26.1
94 190.3
37.8
54
249.1
49.6
15
14.7
2.9
75
73.6
14.6
35
132.4
26.3
95 191.3
38.0
55
250.1
49.7
16
15.7
3.1
76
74.5
14.8
36
133.4
26.5
96
192.2
38.2
56
251.1
49.9
17
16.7
3.3
77
75.5
15.0
37
134.4
26.7
97
193.2
38.4
57
252.1
50.1
18
17.7
3.5
78
76.5
15.2
38
135.3
26.9
98
194.2
38.6
58
253.0
50.3
19
18.6
3.7
79
77.5
15.4
39
136.3
27.1
99
195.2
38.8
59
254.0
50.5
20
19.6
3.9
80
78.5
15.6
40
137.3
27.3
200
196.2
39.0
60
255.0
50.7
21
20.6
4.1
81
79.4
15.8
141
138.3
^7.5
201
197.1
39.2
261
256.0
50.9
22
21.6
4.3
82
80.4
16.0
42
139.3
27.7
02 1 198. 1
39.4
62
257.0
51.1
23
22.6
4.5
83
81.4
16.2
43
140.3
27.9
03 ! 199.1
39.6
63
257.9
51.3
24
23.5
4.7
84
82.4
16.4
44
141.2
28.1
04 t 200. 1
39.8
64
258.9
51.5
25
24.5
4.9
85
83.4
16.6
45
142.2
28.3
05 ! 201. 1
40.0
65
259.9
51.7
26
25.5
5.1
86
84.3
16.8
46
143.2
28.5
06 202.0
40.2
66
260.9
51.9
27
26.5
5.3
87
85.3
17.0
47
144.2
28.7
07
203.0
40.4
67
261.9
52.1
28
27.5
5.5
88
86.3
17.2
48
145.2
28.9
08
204.0
40.6
68
262.9
52.3
29
28.4
5.7
89
87.3
17.4
49
146.1
29.1
09
205.0
40.8
69
263.8
52.5
30
29.4
5.9
90
88.3
17.6
50
147.1
29.3
10
211
206.0
206.9
41.0
41.2
70
264.8
52.7
31
30.4
6.0
91
89.3
17.8
151
148.1
29.5
271
265.8
52.9
32
31.4
6.2
92
90.2
17.9
52
149.1
29.7
12
207.9
41.4
72
266.8
53.1
33
32.4
6.4
93
91.2
18.1
53
150.1
29.8
13
208.9
41.6
73
267.8
53.3
34
33.3
6.6
94
92.2
18.3
54
151.0
30.0
14
209.9
41.7
74
268.7
53.5
35
34.3
6.8
95
93.2
18.5
55
152. 0
30.2
15
210.9
41.9
75
269.7
53.6
36
S5.3
7.0
96
94.2
18.7
56
153.0
30.4
16
211.8
42.1
76
270.7
53.8
37
36.3
7.2
97
95.1
18.9
57
154.0
30.6
17 212.8
42.3
77
271.7
54.0
38
37.3
7.4
98
96.1
19.1
58
155. 0
30.8
18
213.8
42.5
78
272.7
54.2
39
38.3
7.6
99
97.1
19.3
59
155.9
31.0
19
214.8
42.7
79
273.6
54.4
40
39.2
7.8
100
98.1
19.5
60
156.9
31.2
31.4
20
221
215.8
216.8
42.9
80
274.6
275.6
54.6
41
40.2
8.0
101
99.1
19.7
161
157. 9
43.1
281
54.8
42
41.2
8.2
02
100.0
19.9
62
158.9
31.6
22
217.7
43.3
82
276.6
55.0
43
42.2
8.4
03
101.0
20.1
63
159. 9
31.8
23
218.7
43.5
83
277.6
55.2
44
43.2
8.6
04
102.0
20.3
64
160.8
32.0
24
219.7
43.7
84
278.5
55.4
45
44.1
8.8
05
103.0
20.5
65
161.8
32.2
25
220.7
43.9
85
279.5
55.6
46
45.1
9.0
06
104.0
20.7
66
162.8
32.4
26
221.7
44.1
86
280.5
55.8
47
46.1
9.2
07
104.9
20.9
67
163.8
32.6
27
222.6
44.3
87
281.5
56.0
48
47.1
9.4
08
105.9
21.1
68
164.8
32.8
28
223.6
44.5
88
282.5
56.2
49
48.1
9.6
09
106.9
21.3
69
165.8
33.0
29
224.6
44.7
89
283.4
56.4
50
49.0
9.8
10
107.9
21.5
70
166.7
33.2
30
225.6
44.9
90
284.4
56.6
51
50.0
9.9
111
108.9
21.7
171
167.7
33.4
231
226.6
45.1
291
285.4
56.8
52
51.0
10.1
12
109.8
21.9
72
168.7
33.6
32
227.5
45.3
92
286.4
57.0
53
52.0
10.3
13
110.8
22.0
73
169.7
33.8
33
228. 5 45. 5 |
93
287.4
57.2
54
53.0
10.5
14
111.8
22.2
74
170.7
33.9
34
229.5
45.7
94
288.4
57.4
55
53.9
10.7
15
112.8
22.4
75
171.6
34.1
35
230.5
45.8
95
289.3
57.6
56
54.9
10.9
16
113.8
22.6
76
172.6
34.3
36
231.5
46.0
96
290.3
57.7
57
55.9
11.1
17
114.8
22.8
77
173. 6
34.5
37
232.4
46.2
97
291.3
57.9
58
56.9
11.3
18
115.7
23.0
78
174.6
34.7
38
233.4
46.4
98
292.3
58.1
59
57.9
11.5
19
116.7
23.2
79
175.6
34.9
39
234.4
46.6
99
293.3
58.3
60
58.8
11.7
20
117.7
23.4
80
176.5
35.1
40
235.4
46.8
300
294.2
58.5
Dist.
pep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. 1 Dep.
Lat.
Dist.
Dep.
Lat.
E.
byX.
E. I
)y S.
W. by
N. W. by S. [
For 7 p(
lints.
Page 356]
TABLE 1.
Difference of Latitude and Departure for IJ Points.
N.
by E. J E.
N. by \\
\ i w.
S. b>
' E. i E.
s.
by w. i \y.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.2
14.8
121
117.4
29.4
181
175.6
44.0
241
233.8
58.6
2
1.9
0.5
62
60.1
15.1
22
118. 3
29.6
82
176.5
44.2
42
234.7
58.8
3
2.9
0.7
63
61.1
15.3
23
119.3
29.9
83
177.5
44.5
43
235.7
59.0
4
3.9
1.0
64
62.1
15.6
24
120.3
30.1
84
178.5
44.7
44
236.7
59. 3
5
4.9
1.2
^
63.1
15.8
25
121.3
30.4
85
179.5
45.0
45
237.7
59. 5
6
5.8
1.5
66
64.0
16.0
26
122.2
30.6
86
180.4
45.2
46
238.6
59.8
7
6.8
1.7
67
65.0
16.3
27
123.2
30.9
87
181.4
45.4
47
239.6
60.0
8
7.8
1.9
68
66.0
16.5
28
124.2
31.1
88
182.4
45.7
48
240.6
60.3
9
8.7
2.2
69
66.9
16.8
29
125.1
31.3
89
183.3
45.9
49
241.5
60.5
10
9.7
2.4
70
67.9
17.0
17.3
30
126.1
31.6
90
191
184. 3
185.3
46.2
46.4
50
242.5
60.7
11
10.7
2.7
71
68.9
131
127.1
31.8
251 , 243.5
61.0
12
11.6
2.9
72
69.8
17.5
32
128.0
32.1
92
186.2
46.7
52 244.4
61.2
13
12.6
3.2
73
70.8
17.7
33
129.0
32. 3
93
187.2
46.9
53 i 245.4
61.5
14
13.6
3.4
74
71.8
18.0
34
130. 0
32.6
94
188.2
47.1
54 246.4
61.7
15
14.6
3.6
75
72.8
18.2
35
131.0
32.8
95
189.2
47.4
55 247.4
62. 0
16
15.5
3.9
76
73.7
18.5
36
131. 9
33. 0
96
190.1
47.6
56 248.3
62.2
17
16.5
4.1
77
74.7
18.7
37
132.9
33.3
97
191.1
47.9
57 249. 3
62.4
18
17.5
4.4
78
75.7
19.0
38
133.9
33. 5
98
192.1
48.1
58 250. 3
62.7
19
18.4
4.6
79
76.6
19.2
39
134.8
33.8
99
193.0
48.4
59 251.2
62.9
20
19.4
4.9
80
77.6
78.6
19.4
40
135.8
34.0
200
194.0
48.6
60 252.2
261 253.2
63.2
21
20.4
5.1
81
19.7
141
136.8
34.3
201
195. 0
48.8
63.4
22
21.3
5.3
82
79.5
19.9
42
137.7
34.5
02
195.9
49.1
62 254.1
63.7
23
22.3
5.6
83
80.5
20.2
43
138.7
34.7
03
196.9
49.3
63 ; 255.1
63.9
24
23.3
5.8
84
81.5
20.4
44
139.7
35.0
04
197.9
49.6
64 , 256. 1
64.1
25
24.3
6.1
85
82.5
20.7
45
140.7
35.2
05
198.9
49.8
65 i 257. 1
64.4
26
25.2
6.3
86
83.4
20.9
46
141.6
35.5
06
199.8
50.1
66 258. 0
64.6
27
26.2
6.6
87
84.4
21.1
47
142.6
35.7
07
200.8
50. 3
67 : 259.0
64.9
28
27.2
6.8
88
85.4
21.4
48
143.6
36.0
08
201.8
50.5
68 260.0
65.1
29
28.1
7.0
89
86.3
21.6
49
144.5
36.2
09
202.7
50.8
69 ' 260.9
65.4
30
29.1
7.3
90
87.3
21.9
50
145.5
36.4
10
203. 7
51.0
51. 3
70 1 261.9
271 ' 262.9
65.6
31
30.1
7.5
91
88.3
22.1
151
146.5
36.7
211
204.7
65.8
32
31.0
7.8
92
89.2
22.4
52
147.4
36.9
12
205. 6
51.5
72
263. 8
66.1
33
32.0
8.0
93
90.2
22.6
53
148.4
37.2
13
206.6
51.8
73
264.8
66.3
34
33.0
8.3
94
91.2
22.8
54
149.4
37.4
14
207.6
52.0
74
265. 8
66.6
35
34.0
8.5
95
92.2
23.1
55
150.4
37.7
15
208.6
52.2
75 i 266.8
66.8
36
34.9
8.7
96
93.1
23.3
56
151.3
37.9
16
209.5
52.5
76 i 267. 7
67.1
37
35.9
9.0
97
94.1
23.6
57
152.3
38.1
17
210.5
52.7
77 : 268.7
67.3
38
36.9
9.2
98
95.1
23.8
58
153. 3
38.4
18
211.5
53.0
78 i 269.7
67.5
39
37.8
9.5
99
96.0
24.1
59
154.2
38.6
19
212.4
53.2
79 270.6
67.8
40
38.8
9.7
100
97.0
24.3
60
161
155.2
156.2
38.9
39.]
20
213.4
53.5
53. 7'
80 i 271.6
281 i 272.6
68.0
68.3
41
39.8
10.0
101
98.0
24.5
221
214.4
42
40.7
10.2
02
98.9
24.8
62
157.1
39.4
22
215.3
53.9
82 273.5
68.5
43
41.7
10.4
03
99.9
25.0
63
158.1
39.6
23
216.3
54.2
83 274. 5
68.8
44
42.7
10.7
04
100.9
25.3
64
159. 1
39.8
24
217.3
54.4
84 275. 5
69.0
45
43.7
10.9
05
101.9
25.5
65
160.1
40.1
25
218. 3
54.7
85 j 277.5
69.2
46
44.6
11.2
06
102.8
25.8
66
161.0
40. 3
26
219.2
54.9
86 277.4
69.5
47
45.6
11.4
07
103.8
26.0
67
162.0
40.6
27
220.2
55. 2
87 i 278.4
69.7
48
46.6
11.7
08
104.8
26.2
68
163. 0
40.8
28
221.2
55.4
88
279.4
70.0
49
47.5
11.9
09
105.7
26.5
69
163.9
41.1
29
222. 1
55.6
89
280.3
70.2
50
48.5
12.1
12.4
10
111
106.7
107. 7"
26.7
70
164.9
41.3
41.5
30
231
223.1
224.1
55. 9
56.1
90
281.3
70.5
51
49.5
27.0
171
165.9
291
282.3
70.7
52
50.4
12.6
12
108.6
27.2
72
166.8
41.8
32
225.0
56.4
92
283.2
71.0
53
51.4
12.9
13
109.6
27.5
73
167.8
42.0
33
226.0
56.6
93
284.2
71.2
54
52.4
13.1
14
110.6
27.7
74
168.8
42.3
34
227.0
56.9
94
285. 2
71.4
55
53.4
13.4
15
111.6
27.9
75
169.8
42.5
35
228.0
57.1
95
286.2
71.7
56
54.3
13.6
16
112.5
28.2
76
170.7
42.8
36
228. 9
57.3
96
287.1
71.9
57
55.3
13.8
17
113.5
28.4
77
171.7
43.0
37
229.9
57.6
97
288.1
72.2
58
56.3
14.1
18
11-4.5
28.7
78
172.7
43. 3
38
230.9
57.8
98
289.1
72.4
59
57.2
14.3
19
115.4
28.9
79
173.6
43.5
39
231.8
58.1
99
290.9
72.7
60
58.2
14.6
20
116.4
29.2
80
174.6
43.7
40
232.8
58.3
300
291.0
72.9
Diat.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
E]
J?E. f E
Ef
?E. 1 E.
WNW. 1 V
V.
WSW. 1
VV.
[For 6| P
aints.
TABLE
1.
[Page 357
Difference of Latitud
e and Departure for 1 i Points.
N
. byE.
^E.
N. by W. ^ W.
S. by E. i E. S.
by W. i W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.4
17.7
121
115.8
35.1
181
173.2
52.5
241
230.6
70.0
2
1.9
0.6
62
59.3
18.0
22
116.7
35.4
82
174.2
52.8
42
231.6
70.2
3
2.9
0.9
63
60.3
18.3
23
117.7
35.7
83
175.1
53.1
43
232.5
70.5
4
3.8
1.2
64
61.2
18.6
24
118.7
36.0
84
176.1
53.4
44
233.5
70.8
5
4.8
1.5
65
62.2
18.9
25
119.6
36.3
85
177.0
53.7
45
234.5
71.1
6
5.7
1.7
66
63.2
19.2
26
120.6
36.6
86
178.0
54.0
46
235.4
71.4
7
6.7
2.0
67
64.1
19.4
27
121.5
36.9
87
178.9
54.3
47
236.4
71.7
8
7.7
2.3
68
65.1
19.7
28
122.5
37.2
88
179.9
54.6
48
237.3
72.0
9
8.6
2.6
69
66.0 i 20.0
29
123.4
37.4
89
180.9
54.9
49
238.3 \ 72.3
10
9.6
2.9
70
67. 0 20. 3
30
124.4
37.7
90
181.8
55.2
50
239.2 i 72.6
11
10.5
3.2
71
67.9
20.6
131
125.4
38.0
191
182.8
55.4
251
240.2
72.9
12
11.5
3.5
72
68.9
20.9
32
126.3
38.3
92
183.7
55.7
52
241.1
73.2
13
12.4
3.8
73
69.9
21.2
33
127.3
38.6
93
184.7 i 56.0
53
242.1
73.4
14
13.4
4.1
74
70.8
21.5
34
128.2
38.9
94
185.6 j 56.3
54
243.1
73.7
15
14.4
4.4
75
71.8
21.8
35
129.2
39.2
95
186.6 I 56.6
55
244.0
74.0
16
15.3
4.6
76
72.7
22.1
36
130.1
39.5
96
187.6 1 56.9
56
245.0
74.3
17
16.3
4.9
77
73.7
22.4
37
131.1
39.8
97
188. 5 57. 2
57
245. 9 74. 6
18
17.2
5.2
78
74.6
22.6
38
132.1
40.1
98
189. 5 57. 5
58
246.9 , 74.9
19
18.2
5.5
79
75.6
22.9
39
133.0
40.3
99
190.4 1 57.8
59
247.8 1 75.2
20
19.1
5.8
80
76.6
23.2
40
134.0
40.6
200
191.4 1 58.1
60
248.8 1 75.5
21
20.1
6.1
81
77.5
23.5
141
134.9
40.9
201
192. 3 58. 3
261
249.8 ! 75.8
22
21.1
6.4
82
78.5
23.8
42
135.9
41.2
02
193.3
58.6
62
250.7 ! 76.1
23
22.0
6.7
83
79.4
24.1
43
136.8
41.5
03
194.3
58.9
63
251.7 i 76.3
24
23.0
7.0
84
80.4
24.4
44
137.8
41.8
04
195. 2
59.2
64
252.6 i 76.6
25
23.9
7.3
85
81.3
24.7
45
138.8
42.1
05
196.2
59.5
65
253.6 i 76.9
26
24.9
7.5
86
82.3
25.0
46
139.7
42.4
06
197.1
59.8
66
254.5 77.2
27
25.8
7.8
87
83.3
25.3
47
140.7
42.7
07
198.1
60.1
67
255. 5 77. 5
28
26.8
8.1
88
84.2
25.5
48
141.6
43.0
08
199.0
60.4
68
256.5 77.8
29
27.8
8.4
89
85.2
25.8
49
142.6
43.3
09
200.0
60.7
69
257.4 ; 78.1
30
28.7
8.7
90
86.1
26.1
50
143.5
43.5
10
201.0
201.9
61.0
70
271
258.4 1 78.4
31
29.7
9.0
91
87.1
26.4
151
144.5
43.8
211
61.3
259. 3 i 78. 7
32
30.6
9.3
92
88.0
26.7
52
145.5
44.1
12
202.9
61.5
72
260.3 ! 79.0
33
31.6
9.6
93
89.0
27.0
53
146.4
44.4
13
203.8
61.8
73
261. 2 79. 2
34
32.5
9.9
94
90.0
27.3
54
147.4
44.7
14
204.8
62.1
74
262. 2 79. 5
35
. 33. 5
10.2
95
90.9
27.6
55
148.3
45.0
15
205.7
62.4
75
263.2 79.8
36
34.4
10.5
96
91.9
27.9
56
149.3
45.3
16
206.7
62.7
76
264.1 1 80.1
37
35.4
10.7
97
92.8
28.2
57
150.2
45.6
17
207.7
63.0
77
265.1 80.4
38
36.4
11.0
98
93.8
28.4
58
151.2
45.9
18
208.6
63.3
78
266. 0 1 80. 7
39
37.3
11.3
99
94.7
28.7
59
152.2
46.2
19 ; 209.6
63.6
79
267.0
81.0
40
38.3
11.6
11.9
100
101
95.7
96.7
29.0
60
153.1
46.4
20 210.5
63.9
80
267.9
268.9
81.3
41
39.2
29.3
161
154.1
46.7
221 i 211.5
64.2
281
81.6
42
40.2
12.2
02
97.6
29.6
62
155.0
47.0
22 212.4
64.4
82
269.9
81.9
43
41.1
12.5
03
98.6
29.9
63
156.0
47.3
23 1 213.4
64.7
83
270.8
82.2
44
42.1
12.8
04
99.5
30.2
64
156.9
47.6
24 ! 214.4
65.0
84
271.8
82.4
45
43.1
13.1
05
100.5
30.5
65
157.9
47.9
25 1 215.3
65.3
85
272.7
82.7
46
44.0
13.4
06
101.4
30.8
66
158.9
48.2
26 216.3
65.6
86
273.7
83.0
47
45.0
13.6
07
102.4
31.1
67
159.8
48.5
27 1 217.2
65.9
87
274.6
83.3
48
45.9
13.9
08
103. 3
31.4
68
160.8
48.8
28 218.2
66.2
88
275.6
83.6
49
46.9
14.2
09
104.3
31.6
69
161.7
49.1
29 219.1
66.5
89
276.6
83.9
50
47.8
14.5
10
105.3
31.9
70
162.7
49.3
30 i 220. 1
66.8
90
277.5
278.5
84.2
84.5
51
48.8
14.8
111
106.2
32.2
171
163.6
49.6
231 221. 1
67.1
291
52
49.8
15.1
12
107.2
32.5
72
164.6
49.9
32 222. 0
67.3
92
279.4
84.8
53
50.7
15.4
13
108.1 ! 32.^
73
165.6
50.2
33 ! 223.0
67.6
93
280.4
85.1
54
51.7
15.7
14
109.1 i 33.1
74
166.5
50.5
34 I 223.9
67.9
94
281.3
85.3
55
52.6
16.0
15
110.0 33.4
75
167.5
50.8
35 i 224.9
68.2
95
282.3
85.6
56
53.6
16.3
16
111.0 33.7
76
168.4
51.1
36
225.8
68.5
96
283.3
85.9
57
54.5
16.5
17
' 112.0 34.0
77
169.4
51.4
37
226.8
68.8
97
284.2
86.2
58
55.5
16.8
18
! 112.9 34.3
78
170.3
51.7
38
227.8
69.1
98
285.2
86.5
59
56.5
17.1
19
113.9 i 34.5
79
171.3
52.0
39
228.7
69.4
99
286.1
86.8
60
57.4
17.4
20
114.8 34.8
80
172.2
52.3
40
229.7
69.7
300
287.1
87.1
Dlst.
Dep.
Lat.
Dist.
1 Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
EJ
TE. h E.
ES
E. i E.
WN
\V. * W
WSW. i W.
[For 6J Point?.
Page 358J
TABLE
- 1.
Difference of Latitude and Departure for 1| Points.
N. by
E. 1 E.
N. by W. 1 AV.
S. by E. % E.
S. by W. J W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.3
61
57.4
20.6
121
113.9
40.8
181
170.4
61.0
241
226.9
81.2
2
1.9
0.7
62
58.4
20.9
22
114.9
41.1
82
171.4
61.3
42
227.9
81.5
3
2.8
1.0
63
59.3
21.2
23
115.8
41.4
83
172.3
61.7
43
228.8
81.9
4
3.8
1.3
64
60.3
21.6
24
116.8
41.8
84
173.2
62.0
44
229.7
82.2
5
4.7
1.7
6%
61.2
21.9
25
117.7
42.1
85
174.2
62.3
45
230.7
82.5
6
5.6
2.0
66
62.1
22.2
26
118.6
42.4
86
175.1
62.7
46
231.6
82.9
1
6.6
2.4
67
63.1
22.6
27
119.6
42.8
87
176.1
63.0
47
232.6
83.2
8
7.5
2.7
68
64.0
22.9
28
120.5
43.1
88
177.0
63.3
48
233.5
83.5
9
8.5
3.0
69
65.0
23.2
29
121.5
43.5
89
178.0
63.7
49
234.4
83.9
10
11
9.4
10.4
3.4
3.7
70
65.9
23.6
30
122.4
123.3
43.8
44.1
90
178.9
64.0
50
235.4
236.3
84.2
71
66.8
23.9
131
191
179.8
64.3
251
84.6
12
11.3
4.0
72
67.8
24.3
32
124.3
44.5
92
180.8
64.7
52
237.3
84.9
13
12.2
4.4
73
68.7
24.6
33
125.2
44.8
93
181. 7
65.0
53
238.2
85.2
14
13.2
4.7
74
69.7
24.9
34
126.2
45.1
94
182.7
65.4
54
239.2
85.6
15
14.1
5.1
75
70.6
25.3
35
127.1
45.5
95
183.6
65.7
55
240.1
85.9
16
15.1
5.4
76
71.6
25.6
36
128.0
45.8
96
184. 5
66.0
56
241.0
86.2
17
16.0
5.7
77
72.5
25.9
37
129.0
46.2
97
185.5
66.4
57
242.0
86.6
18
16.9
6.1
78
73.4
26.3
38
129.9
46.5
98
186.4
66.7
58
242.9
86.9
19
17.9
6.4
79
74.4
26.6
39
130.9
46.8
99
187.4
67.0
59
243.9
87.3
20
18.8
6.7
7.1
80
75.3
27.0
40
141
131.8
132.8
47.2
47.5
200
2or
188.3
189.3
67.4
67.7
60
261
244.8
245. 7
87.6
21
19.8
81
76.3
27.3
87.9
22
20.7
7.4
82
77.2
27.6
42
133.7
47.8
02
190.2
68.1
62
246.7
88.3
23
21.7
7.7
83
78.1
28.0
43
134.6
48.2
03
191.1
68.4
63
247.6
88.6
24
22.6
8.1
84
79.1
28.3
44
135.6
48.5
04
192.1
68.7
64
248.6
88.9
25
23.5
8.4
85
80.0
28.6
45
136.5
48.8
05
193.0
69.1
65
249.5
89.3
26
24.5
8.8
86
81.0
29.0
46
137.5
49.2
06
194.0
69.4
66
250.5
89.6
27
25.4
9.1
87
81.9
29.3
47
138.4
49.5
07
194.-9
69.7
67
251.4
89.9
28
26.4
9.4
88
82.9
29.6
48
139. 3
49.9
08
195.8
70.1
68
252. 3
90.3
29
27.3
9.8
89
83.8
30.0
49
140.3
50.2
09
196.8
70.4
69
253.3
90.6
30
28.2
10.1
90
84.7
85.7
30.3
50
141.2
142.2
50.5
10
197.7
198.7
70.7
70
271
254.2
255.2
91.0
91.3
31
29.2
10.4
91
30.7
151
50.9
211
71.1
32
30.1
10.8
92
86.6
31.0
52
143. 1
51.2
12
199.6
71.4
72
256.1
91.6
33
31.1
11.1
93
87.6
31.3
53
144.1
51.5
13
200.5
71.8
73
257.0
92.0
34
32.0
11.5
94
88.5
31.7
54
145.0
51.9
14
201.5
72.1
74
258.0
92.3
35
33.0
11.8
95
89.4
32.0
55
145.9
52.2
15
202.4
72.4
75
258.9
92.6
36
33.9
12.1
96
90.4
32.3
56
146.9
52.6
16
203.4
72.8
76
259.9
93.0
37
34.8
12.5
97
91.3
32.7
57
147.8
52.9
17
204.3
73.1
77
260.8
93.3
38
35.8
12.8
98
92.3
33.0
58
148.8
53.2
18
205.3
73.4
78
261.7
93.7
39
36.7
13.1
99 ; 93.2
33.4
59
149.7
53.6
19
206.2
73.8
79
262.7
94.0
40
37.7
13.5
100 1 94.2
33.7
60
150.6
53.9
54.2
20
207.1
74.1
80
263.6
94.3
41
38.6
13.8
101 95.1
34.0
161
151.6
221
208.1
74.5
281
264.6
94.7
42
39.5
14.1
02 96.0
34.4
62
152.5
54.6
22 I 209.0
74.8
82
265.5
95.0
43
40.5
14.5
03 • 97.0
34.7
63
153.5
54.9
23 i 210.0
75.1
83
266.5
95.3
44
41.4
14.8
04
97.9
35.0
64
154.4
55.2
24 210.9
75.5
84
267.4
95.7
45
42.4
15.2
05
98.9
35.4
65
155.4
55.6
25 ' 211.8
75.8
85
268.3
96.0
46
43.3
15.5
06
99.8
35.7
66
156.3
55.9
26
212.8
76.1
86
269.3
96.4
47
44.3
15.8
07
100.7
36.0
67
157.2
56.3
27
213.7
76.5
87
270.2
96.7
48
45.2
16.2
08 i 101. 7
36.4
68
158. 2
56.6
28
214.7
76.8
88
271.2
97.0
49
46.1
16.5
09
102.6
36.7
69
159.1
56.9
29 i 215.6
77.1
89
272.1
97.4
50
51
47.1
48.0
16.8
17. 2"
10
103.6
104. 5
37.1
70
171"
160.1
161.0
57.3
57.6
30
216.6
77.5
77.8
90
291
273.0
274.0
97.7
98.0
111
37.4
231
217.5
52
49.0
17.5
12
105.5
37.7
72
161.9
57.9
32
218.4
78.2
92
274.9
98.4
53
49.9
17.9
13
106.4
38.1
73
162.9
58.3
33
219.4
78.5
93
275.9
98.7
54
50.8
18.2
14
107.3
38.4
74
163.8
58.6
34
220. 3
78.8
94
276.8
99.0
55
51.8
18.5
15
108.3
.38.7
75
164.8
59.0
35
221.3
79.2
95
277.8
99.4
56
52.7
18.9
16
109.2
39.1
76
165.7
59.3
36
222.2
79.5
96
278.7
99.7
57
53.7
19.2
17
110.2
39.4
77
166.7
59.6
37
223.1
79.8
97
279.6
100. 1
58
54.6
19.5
18
111.1
39.8
78
167.6
60.0
38
224.1
80.2
98
280.6
100.4
59
55.6
19.9
19
112.0
40.1
79
168.5
60.3
39
225.0
80.5
99
281.5
100.7
60
56.5
20.2
20
113.0
40.4
80
169.5
60.6
40
226.0
80.9
300
282.5
101.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
ENE. \
E.
ESE. \ }
"^
A^
'NW. \
w. wsw. \
W.
[F
or 61 To
ints.
TABLE 1.
[Page
359
Di£ferenc3 of Latitude and Departure for
2 Points.
NNE.
NNW.
SSE.
ssw.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
56.4
23.3
121
111.8
46.3
181
167.2
69.3
241
222.7
92.2
2
1.8
0.8
62
57.3
23.7
22
112.7
46.7
82
168.1
69.6
42
223.6
92.6
3
2.8
1.1
63
58.2
24.1
23
113.6
47.1
83
169.1
70.0
43
224.5
93.0
4
3.7
1.5
64
59.1
24.5
24
114.6
47.5
84
170.0
70.4
44
225.4
93.4
5
4.6
1.9
65
60.1
24.9
25
115.5
47.8
85
170.9
70.8
45
226.4
93.8
6
5.5
2.3
66
61.0
25.3
26
116.4
48.2
86
171.8
71.2
46
227.3
94.1
7
6.5
2.7
67
61.9
25.6
27
117.3
48.6
87
172.8
71.6
47
228.2
94.5
8
7.4
3.1
68
62.8
26.0
28
118.3
49.0
88
173.7
71.9
48
229.1
94.9
9
8.3
3.4
69
63.7
26.4
29
119.2
49.4
89
174.6
72.3
49
230.0
95.3
10
9.2
10.2
3.8
4.2
70
64.7
26.8
27.2
30
120.1
49.7
50.1
90
175.5
72.7
50
231.0
231.9
95.7
11
71
65.6
131
121.0
191
176.5
73.1
251
96.1
12
11.1
4.6
72
66.5
27.6
32
122.0
50.5
92
177.4
73.5
52
232.8
96.4
13
12.0
5.0
73
67.4
27.9
33
122.9
50.9
93
178.3
73.9
53
233.7
96.8
14
12.9
5.4
74
68.4
28.3
34
123.8
51.3
94
179.2
74.2
54
234.7
97.2
15
13.9
5.7
75
69.3
28.7
35
124.7
51.7
95
180.2
74.6
55
235.6
97.6
16
14.8
6.1
76
70.2
29.1
36
125.6
52.0
96
181.1
75.0
56
236.5
98.0
17
15.7
6.5
77
71.1
29.5
37
126.6
52.4
97
182.0
75.4
57
237.4
98.3
18
16.6
6.9
78
72.1
29.8
38
127.5
52.8
98
182.9
75.8
58
238.4
98.7
19
17.6
7.3
79
73.0
30.2
39
128.4
53.2
99
183.9
76.2
59
239.3
99.1
20
18.5
19.4
7. 7
8.0
80
73.9
30.6
40
129.3
53.6
200
184.8
185.7
76.5
60
240.2
99.5
21
81
74.8
31.0
141
130.3
54.0
201
76.9
261
241.1
99.9
22
20.3
8.4
82
75.8
31.4
42
131.2
54.3
02
186.6
77.3
62
242.1
100.3
23
21.2
8.8
83
76.7
31.8
43
132.1
54.7
03
187.5
77.7
63
243.0
100.6
24
22.2
9.2
84
77.6
32.1
44
133.0
55.1
04
188.5
78.1
64
243.9
101.0
25
23.1
9.6
85
78.5
32.5
45
134.0
55.5
05
189.4
78.5
65
244.8
101.4
26
24.0
9.9
86
79.5
32.9
46
134.9
55.9
06
190.3
78.8
66
245.8
101.8
27
24.9
10.3
87
80.4
33.3
47
135.8
56.3
07
191.2
79.2
67
246.7
102.2
28
25.9
10.7
88
81.3
33.7
48
136.7
56.6
08
192.2
79.6
68
247.6
102.6
29
26.8
11.1
89
82.2
34.1
49
137.7
57.0
09
193.1
80.0
69
248.5
102.9
30
31
27.7
11.5
90
91
83.1
84.1
34.4
50
138.6
139.5
57.4
10
194.0
80.4
70
249.4
103.3
28.6
11.9
34.8
151
57.8
211
194.9
80.7
271
250.4
103.7
32
29.6
12.2
92
85.0
35.2
52
140.4
58.2
12
195.9
81.1
72
251.3
104.1
33
30.5
12.6
93
85.9
35.6
53
141.4
58.6
13
196.8
81.5
73
252.2
104.5
34
31. 4
13.0
94
86.8
36.0
54
142.3
58.9
14
197.7
81.9
74
253.1
104.9
35
32.3
13.4
95
87.8
36.4
55
143.2
59.3
15
198.6
82.3
75
254.1
105.2
36
33.3
13.8
96
88.7
36.7
56
144.1
59.7
16
199.6
82.7
76
255. 0
105.6
37
34.2
14.2
97
89.6
37.1
57
145.0
60.1
17
200.5
83.0
77
255.9
106.0
38
35.1
14.5
98
90.5
37.5
58
146.0
60.5
18
201.4
83.4
78
256.8
106.4
39
36.0
14.9
99
91.5
37.9
59
146.9
60.8
19
202.3
83.8
79
257.8
106.8
40
37.0
15.3
100
92.4
38.3
60
147.8
148.7
61.2
20
203.3
84.2
80
258.7
259.6
107.2
41
37.9
15.7
101
93.3
38.7
161
61.6
221
204.2
84.6
281
107.5
42
38.8
16.1
02
94.2
39.0
62
149.7
62.0
22
205.1
85.0
82
260. 5
107.9
43
39.7
16.5
03
95.2
39.4
63
150.6
62.4
23
206.0
85.3
83
261.5
108.3
44
40.7
16.8
04
96.1
39.8
64
151.5
62.8
24
206.9
85.7
84
262.4
108.7
45
41.6
17.2
05
97.0
40.2
65
152.4
63.1
25
207.9
86.1
85
263.3
109.1
46
42.5
17.6
06
97.9
40.6
66
153.4
63.5
26
208.8
86.5
86
264.2
109.4
47
43.4
18.0
07
98.9
40.9
67
154.3
63.9
27
209.7
86.9
87
265. 2
109.8
48
44.3
18.4
08
99.8
41.3
68
155.2
64.3
28
210.6
87.3
88
266.1
110.2
49
45.3
18.8
09
100.7
41.7
69
156.1
64.7
29
211.6
87.6
89
267.0
110.6
50
46.2
19.1
10
101.6
42.1
70
157.1
65.1
30
212.5
88.0
90
267.9
111.0
51
47.1
19.5
111
102.6
42.5
171
158.0
65.4
231
213.4
88.4
291
268.8
111.4
52
48.0
19.9
12
103.5
42.9
72
158.9
65.8
32
214.3
88.8
92
269.8
111.7
53
49.0
20.3
13
104.4
43.2
73
159. 8
66.2
33
215.3
89.2
93
270.7
112.1
54
49.9
20.7
14
105. 3
43.6
74
160.8
66.6
34
216.2
89.5
94
271.6
112.5
55
50.8
21.0
15
106.2
44.0
75
161.7
67.0
35
217.1
89.9
95
272.5
112.9
56
51.7
21.4
16
107.2
44.4
76
162.6
67.4
36
218.0
90.3
96
273.5
113.3
57
52.7
21.8
17
108.1
44.8
77
163.5
67.7
37
219.0
90.7
97
274.4
113.7
58
53.6
22.2
18
109.0
45.2
78
164.5
68.1
38
219.9
91.1
98
275.3
114.0
59
54.5
22.6
19
109.9
45.5
79
165.4
68.5
39
220.8
91.5
99
276.2
114.4
60
55.4
23.0
20
110.9
45.9
80
166.3
68.9
40
221.7
91.8
300
277.2
114.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat,
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
ENE.
ESE.
WNW
wsw
[F
or 6 Poi
nts.
Page 360
TABLE 1.
Difference of Latitude and Departure for 2J Points.
NNE
iE.
NNW
. i W. SSE.
iE.
ssw.
iW.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep..
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
55.1
26.1
121
109.4
51.7
181
163.6
77.4
241
217.9
103.0
2
1.8
0.9
62
56.0
26.5
22
110.3
52.2
82
164.5
77.8
42
218.8
103.5
3
2.7
1.3
63
57.0
26.9
23
111.2
52.6
83
165.4
78.2
43
219.7
103.9
4
3.6
1.7
64
57.9
27.4
24
112.1
53.0
84
166.3
78.7
44
220.6
104.3
5
4.5
2.1
65
58.8
27.8
25
113.0
53.4
85
167.2
79.1
45
221.5
104.8
6
5.4
2.6
6»
59.7
28.2
26
113.9
53.9
86
168.1
79.5
46
222. 4
105.2
7
6.3
3.0
67
60.6
28.6
27
114.8
54.3
87
169.0
80.0
47
223.3
105.6
8
7.2
3.4
68
61.5
29.1
28
115.7
54.7
88
169.9
80.4
48
224.2
106.0
9
8.1
3.8
69
62.4
29.5
29
116.6
55.2
89
170.9
80.8
49
225.1
106.5
10
9.0
4.3
70
63.3
29.9
30.4
30
117.5
118.4
55.6
56.0
90
171.8
172.7
81.2
81.7
50
251
226.0
226.9
106.9
11
9.9
4.7
71
64.2
131
191
107.3
12
10.8
5.1
72
65.1
30.8
32
119.3
56.4
92
173.6
82.1
52
227.8
107.7
13
11.8
5.6
73
66.0
31.2
33
120.2
56.9
93
174.5
82.5
53
228.7
108.2
14
12.7
6.0
74
66.9
31.6
34
121.1
57.3
94
175.4
82.9
54
229.6
108.6
15
13.6
6.4
75
67.8
32.1
35
122.0
57.7
95
176.3
83.4
55
230.5
109.0
16
14.5
6.8
76
68.7
32.5
36
122.9
58.1
96
177.2
83.8
56
231.4
109.5
17
15.4
7.3
77
69.6
32.9
37
123.8
58.6
97
178.1
84.2
57
232. 3
109.9
18
16.3
7.7
78
70.5
33.3
38
124.8
59.0
98
179.0
84.7
58
233.2
110.3
19
17.2
8.1
79
71.4
33.8
39 125.7
59.4
99
179.9
85.1
59
234.1
110.7
20
18.1
8.6
80
72. 3 34. 2
40 126.6
59.9
60.3
200
180.8
85.5
60
235.0
235.9
111.2
21
19.0
9.0
81
73.2
34.6
141 127.5
201
181.7
85.9
261
111.6
22
19.9
9.4
82
74.1
35.1
42 128.4
60.7
02 182. 6
86.4
62
236.8
112.0
23
20.8
9.8
83
75.0
35.5
43 i 129.3
61.1
03
183.5
86.8
63
237.7
112.4
24
21.7
10.3
84
75.9
35.9
44 130.2
61.6
04
184.4
87.2
64
238.7
112.9
25
22.6
10.7
85
76.8
36.3
45 131.1
62.0
05
185.3
87.6
65
239.6
113.3
26
23.5
11.1
86
77.7
36.8
46 132. 0
62.4
06
186.2
88.1
66
240.5
113.7
27
24.4
11.5
87
78.6
37.2
47 132. 9
62.9
07
187a
88.5
67
241.4
114.2
28
25.3
12.0
88
79.6
37.6
48 133. 8
63.3
08
188.0
88.9
68
242.3
114.6
29
26.2
12.4
89
80.5
38.1
49 134. 7
63.7
09
188.9
89.4
69
243.2
115.0
30
31
27.1
28.0
12.8
90
81.4
38.5
38.9
50 135.6
151 136. 5
64.1
10
189.8
89.8
70
244.1
245.0
115.4
13.3
91
82.3
64.6
211
190.7
90.2
271
115.9
32
28.9
13.7
92
83.2
39.3
52 137.4 i 65.0
12
191.6
90.6
72
245.9
116.3
33
29.8
14.1
93
84.1
39.8
53 i 138.3 1 65.4
13
192.5
91.1
73
246.8
116.7
34
30.7
14.5
94
85.0
40.2
54 i 139.2 1 65.8
14
193.5
91.5
74
247.7
117.2
35
31.6
15.0
95
85.9
40.6
55 140.1 66.3
15
194.4
91.9
to
248.6
117.6
36
32.5
15.4
96
86.8
41.0
56 i 141. 0 i 66. 7
16
195.3
92.4
76
249.5
118.0
37
33.4
15.8
97
87.7
41.5
57 i 141.9
67.1
17
196.2
92.8
/ 1
250.4
118.4
38
34.4
16.2
98
88.6
41.9
58
142.8
67.6
18
197.1
93.2
78
251.3
118.9
39
35.3
16.7
99
89.5
42.3
59
143.7
68.0
19
198.0
93.6
79
252.2
119.3
40
36.2
17.1
100
90.4
42.8
60
144.6
68.4
20
198.9
94.1
80
253.1
119.7
41
37.1
17.5
'lOl
91.3
43.2
161
145.5
68.8
221
199.8
94.5
281
254.0
120.1
42
38.0
18.0
02
92.2
43.6
62
146.4
69.3
22
200.7
94.9
82
254.9
120.6
43
38.9
18.4
03
93.1
44.0
63
147.4
69.7
23
201.6
95.3
83
255. 8
121.0
44
39.8
18.8
04
94.0
44.5
64
148.3
70.1
24
202.5
95.8
84
256.7
121.4
45
40.7
19.2
05
94.9
44.9
65
149.2
70.5
25
203.4
96.2
85
257.6
121.9
46
41.6
19.7
06
95.8
45.3
66
150.1
71.0
26
204.3
96.6
86
258.5
122.3
47
42.5
20.1
07
96.7
45.7
67
151.0
71.4
27
205.2
97.1
87
259.4
122.7
48
43.4
20.5
08
97.6
46.2
68
151.9
71.8
28
206.1
97.5
88
260.3
123.1
49
44.3
21.0
09
98.5
46.6
69
152.8
72.3
29
207.0
97.9
89
261.3
123.6
50
45.2
21.4
10
99.4
100.3
47.0
70
153.7
72.7
30
207.9
98.3
90
262.2
124.0
51
46.1
21.8
111
47.5
171
154.6
73.1
231
208.8
98.8
291
263.1
124.4
52
47.0
22.2
12
101.2
47.9
72
155.5
73.5
32
209.7
99.2
92
264.0
124.8
53
47.9
22.7
13
102.2
48.3
73
156.4
74.0
33
210.6
99.6
93
264.9
125.3
54
48.8
23.1
14
103.1
48.7
74
157.3
74.4
34
211.5
100.0
94
265.8
125.7
55
49.7
23.5
15
104.0
49.2
75
158.2
74.8
35
212.4
100.5
95
266.7
126.1
56
50.6
23.9
16
104.9
49.6
76
159. 1
75.2
36
213.3
100.9
96
267.6
126.6
57
51.5
24.4
17
105.8
50.0
77
160.0
75.7
37
214.2
101.3
97
268.5
127.0
58
52.4
24.8
18
106.7
50.5
78
160.9
76.1
38
215.1
101.8
98
269.4
127.4
59
53.3
25.2
19
107.6
50.9
79
161.8
76.5
39
216.1
102.2
99
270.3
127.8
60
54.2
25.7
20
108.5
51.3
80
162.7
77.0
40
217.0
102.6
300
271.2
128.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NI
:. by E.
IE.
SI
:. by E. i E.
NW. by W. 1 W.
SW. by W.
|W.
[J
For 5| P
oints.
TABLE 1.
[Page
361
Difference of Latitude and Departure for 2J Points.
NNE
^E.
NNW
. i W. SSE
iE.
SSW.
JW.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
53.8
28.8
121
106.7
57.0
181
159. 6
85.3
241
212.5
113.6
2
1.8
0.9
62
54.7
29.2
22
107.6
57.5
82
160. 5
85.8
42
213.4
114.1
3
2.6
1.4
63
55.6
29.7
23
108.5
58.0
83
161.4
86.3
43
214.3
114.5
4
3.5
1.9
64
56.4
30.2
24
109.4
58.5
84
162.3
86.7
44
215.2
115.0
5
4.4
2.4
65
57.3
30.6
25
110.2
58.9
85
163.2
87.2
45
216.1
115. 5
6
5.3
2.8
66
58.2
31.1
26
111.1
59.4
86
164.0
87.7
46
217.0
116.0
7
6.2
3.3
67
59.1
31.6
27
112.0
59.9
87
164.9
88.2
47
217.8
116.4
8
7.1
3.8
68
60.0
32.1
28
112.9
60.3
88
165.8
88.6
48
218.7
116.9
9
7.9
4.2
69
60.9
32.5
29 113.8
60.8
89
166.7
89.1
49
219.6
117.4
10
8.8
4.7
70
61.7
62. 6"
33.0
30 114. 6
61.3
90
167.6
89.6
50
220.5
117.8
11
9.7
5.2
71
33.5
131 115.5
61.8
191
168.4
90.0
251-
221.4
118.3
12
10.6
5.7
72
63.5
33.9
32 116.4
62.2
92
169.3
90.5
52
222.2
118.8
13
11.5
6.1
73
64.4
34.4
33 ! 117.3
62.7
93
170.2
91.0
53
223.1
119.3
14
12.3
6.6
74
65.3
34.9
34 { 118.2
63.2
94
171.1
91.5
54
224.0
119.7
15
13.2
7.1
75
66.1
35.4
35 ! 119.1
63.6
95
172.0
91.9
55
224.9
120.2
16
14.1
7.5
76
67.0
35.8
36
119.9
64.1
96
172.9
92.4
56
225.8
120.7
17
15.0
8.0
77
67.9
36.3
37
120.8
64.6
97
173.7
92.9
57
226.7
121.1
18
15.9
8.5
78
68.8
36.8
38
121.7
65.1
98
174.6
93.3
58
227.5
121. 6
19
16.8
9.0
79
69.7
37.2
39
122.6
65.5
99
175.5
93.8
59
228.4
122.1
20
17.6
9.4
80
70.6
37.7
40
123.5
66.0
200
201
176.4
177.3
94.3
60
229. 3
122.6
21
18.5
9.9
81
71.4
38.2
141
124.4
66.5
94.8
261
330.2
123.0
22
19.4
10.4
82
72.3
38.7
42
125.2
66.9
02
178.1
95.2
62
231.1
123. 5
23
20.3
10.8
83
73.2
39.1
43
126.1
67.4
03
179.0
95.7
63
231.9
124.0
24
21.2
11.3
84
74.1
39.6
44
127.0
67.9
04
179.9
96.2
64
232.8
124.4
25
22.0
11.8
85
75.0
40.1
45
127.9
68.4
05
180.8
96.6
65
233.7
124.9
26
22.9
12.3
86
75.8
40.5
46
128.8
68.8
06
181.7
97.1
66
234.6
125. 4
27
23.8
12.7
87
76.7
41.0
47
129.6
69.3
07
182.6
97.6
67
235.5
125.9
28
24.7
13.2
88
77.6
41.5
48
130.5
69.8
08
183.4
98.1
68
236.4
126.3
29
25.6
13.7
89
78.5
42.0
49
131.4
70.2
09
184.3
98.5
69
237. 2
126.8
30
31
26.5
27.3
14.1
90
91
79.4
42.4
50
132.3
133.2
70.7
10
185.2
99.0
70
238.1
127.3
14.6
80.3
42.9
151
71.2
211
186.1
99.5
271
239.0
127.7
32
28.2
15.1
92
81.1
43.4
52
134.1
71.7
12
187.0
99.9
72
239.9
128.2
33
29.1
15.6
93
82.0
43.8
53
134.9
72.1
13
187.8
100.4
73
240.8
128.7
34
30.0
16.0
94
82.9 1 44.3
54
135.8
72.6
14
188.7
100.9
74
241.6
129.2
35
. 30.9
16.5
95
83.8 ! 44.8
55
136.7
73.1
15
189.6
101.4
75
242.5
129.6
36
31.7
17.0
96
84.7
45.3
56
137.6
73.5
16
190.5
101.8
76
243.4
130.1
37
32.6
17.4
97
85.5
45.7
57
138.5
74.0
17
191.4
102.3
77
244.3
130.6
38
33.5
17.9
98
86.4
46.2
58
139.3
74.5
18
192.3
102.8
78
245.2
131.0
39
34.4
18.4
99
87.3
46.7
59
140.2
75.0
19
193.1
103.2
79
246.1
131.5
40
35.3
18.9
100
101
88.2
47.1
60
141.1
142.0
75.4
75.9
20
194.0
103.7
80
246.9
247.8
132.0
41
36.2
19.3
89.1
47.6
161
221
194.9
104.2
281
132.5
42
37.0
19.8
02
90.0
48.1
62
142.9
76.4
22
195.8
104.7
82
248.7
132.9
43
37.9
20.3
03
90.8
48.6
63
143. 8
76.8
23
196.7
105.1
83
249.6
133.4
44
38.8
20.7
04
91.7 49.0
64
144.6
77.3
24
197.6
105.6
84
250.5
133.9
45
39.7
21.2
05
92.6
49.5
65
145. 5
77.8
25
198.4
106.1
85
251.3
134.3
46
40.6
21.7
06
93.5
50.0
66
146.4
78.3
26
199.3
106.5
86
252.2
134.8
47
41.5
22.2
07
94.4
50.4
67
147.3
78.7
27
200.2
107.0
87
253.1
135. 3
48
42.3
22.6
08
95.2
50.9
68
148.2
79.2
28
201.1
107.5
88
254.0
135.8
49
43.2
23.1
09
96.1
51.4
69
149.0
79.7
29
202.0
107.9
89
254.9
136.2
50
44.1
23.6
10
97.0
51.9
70
149.9
80.1
30 202. 8
108.4
90
255.8
136.7
51
45.0
24.0
111
97.9
52.3
171
150.8
80.6
231
203.7
108.9
291
256.6
137.2
52
45.9
24.5
12
98.8
52.8
72
151.7
81.1
32
204.6
109.4
92
257.5
137.6
53
46.7
25.0
13
99.7
53.3
73
152.6
81.6
33
205. 5
109.8
93
258.4
138.1
54
47.6
25.5
14
100.5
53.7
74
153.5
82.0
34
206.4
110.3
94
259.3
138.6
55
48.5
25.9
15
101.4
54.2
75
154.3
82.5
35
207.3
110.8
95
260.2
139.1
56
49.4
26.4
16
102.3
54.7
76
155.2
83.0
36
208.1
111.2
96
261.0
139.5
57
50.3
26.9
17
103.2
55.2
77
156.1
83.4
37
209.0
111.7
97
261.9
140.0
58
51.2
27.3
18
104.1
55.6
78
157.0
83.9
38
209.9
112.2
98
262.8
140. 5
59
52.0
27.8
19
104.9
56.1
79
157.9
84.4
39
210.8
112.7
99
263.7
140.9
60
52.9
28.3
20
105.8
56.6
80
158.7
84.9
40
211.7
113.1
300
264.6
141.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
NE
.. by E.
^E.
SE
. by E. J E.
NW. by W. J W.
SW. by W.
* w.
[I
^or 5^ P
oints.
Page 362;
TABLE
1.
Difference of Latitude and Departure for 2| Points.
NNE. 1 E.
NNW.
JW.
SSE. 1 E
SSW. 1 W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist. : Lat.
Dep.
1
0.9
0.5
61
52.3
31.4
121
103.8
62.2
181
155. 2 93. 1
241 ' 206.7
123.9
2
1.7
1.0
62
53.2
31.9
22
104.6
62.7
82
156. 1 93. 6
42 207.6
124.4
3
2.6
1.5
63
54.0
32.4
23
105.5
63.2
83
157.0
94.1
43 208.4
124.9
4
3.4
2.1
64
54.9
32.9
24
106.4
63.7
84
157.8
94.6
44
209.3
125. 4
5
4.3
2.6
Of
55.8
33.4
25
107.2
64.3
85
158.7
95.1
45
210.1
126.0
6
5.1
3.1
66
56.6
33.9
26
108.1
64.8
86
159.5
95.6
46
211.0
126.5
7
6.0
3.6
67
57.5
34.4
27
108.9
65.3
87
160.4
96.1
47
211.9
127.0
8
6.9
4.1
68
58.3
35.0
28
109.8
65.8
'88
161.3
96.7
48
212.7
127.5
9
7.7
4.6
69
59.2
35.5
29
110.6
66.3
89
162.1
97.2
49
213.6
128.0
10
8.6
5.1
5.7
70
71
60.0
36.0
30
111.5
66.8
90
163.0
163.8
97.7
50
214.4
128.5
11
9.4
60.9
36.5
131
112.4
67.3
191
98.2
251
215.3
129.0
12
10.3
6.2
72
61.8
37.0
32
113.2
67.9
92
164.7
98.7
52
216.1
129.6
13
11.2
6.7
73
62.6
37.5
33
114.1
68.4
93
165.5
99.2
53
217.0
130. 1
14
12.0
7.2
74
63.5
38.0
34
114.9
68.9
94
166.4
99.7
54
217.9
130.6
15
12.9
7.7
75
64.3
38.6
35
115.8
69.4
95
167.3
100. 3
55
218.7
131.1
16
13.7
8.2
76
65.2
39.1
36
116.7
69,9
96
168.1
100.8
56
219.6
131.6
17
14.6
8.7
77
66.0
39.6
37
117.5
70.4
97
169.0
101.3
57 ; 220.4
132.1
18
15.4
9.3
78
66.9
40.1
38
118.4
70.9
98
169.8
101.8
58 , 221.3
132.6
19
16.3
9.8
79
67.8
40.6
39
119.2
71.5
99
170.7
102.3
59
222.2
133.2
20
17.2
10.3
80
81
68.6
69.5
41.1
40
120.1
120. 9
72.0
200
171. 5
102.8
60
223.0
133.7
134.2
21
18.0
10.8
41.6
141
72.5
201
172.4
103.3
261
223.9
22
18.9
11.3
82
70.3
42.2
42
121.8
73.0
02
173. 3
103.8
62
224.7
134.7
23
19.7
11. g
83
71.2
42.7
43
122.7
73.5
03
174.1
104.4
63
225.6
135.2
24
20.6
12.3
84
72.0
43.2
44
123.5
74.0
04
175.0
104.9
64
226.4
135.7
25
21.4
12.9
85
72.9
43.7
45
124.4
74.5
05
175.8
105.4
65
227.3
136.2
26
22.3
13.4
86
73.8
44.2
46
125.2
75.1
06
176.7
105.9
66
228.2
136.8
27
23.2
13.9
87
74.6
44.7
47
126.1
75.6
07
177.5
106.4
67
229.0
137.3
28
24.0
14.4
88
75.5
45.2
48
126.9
76.1
08
178.4
106.9
68
229.9
137.8
29
24.9
14.9
89
76.3
45.8
49
127.8
76.6
09
179.3
107.4
69
230.7
138.3
30
25.7
15.4
90
77.2
46.3
50
128.7
77.1
10
180.1
108.0
108. 5
70
231.6
138.8
139.3
31
26.6
15.9
91
78.1
46.8
151
129.5
77.6
211
181.0
271
232.4
32
27.4
16.5
92
78.9
47.3
52
130.4
78.1
12
181.8
109.0
72
233.3
139.8
33
28.3
17.0
93
79.8
47.8
53
131. 2
78.7
13
182.7
109.5
73
234.2
140.4
34
29.2
17.5
94
80.6
48.3
54
132.1
79.2
14
183.6
110.0
74
235.0
140.9
35
30.0
18.0
95
81.5
48.8
55
132.9
79.7
15
184.4
110.5
75
235.9
141.4
36
30.9
18.5
96
82.3
49.4
56
133.8
80.2
16
185.3
111.0
76
236.7
141.9
37
31.7
19.0
97
83.2
49.9
57 ! 134.7
80.7
17
186.1
111.6
77
237.6
142.4
38
32.6
19.5
98
84.1
50.4
58
135. 5
81.2
18
187.0
112.1
78
238.4
142.9
39
33.5
20.1
99
84.9
50.9
59
136.4
81.7
19
187.8
112.6
79
239.3
143.4
40
34.3
20.6
100
85.8
51.4
60
137.2
82.3
82.8
20
221
188.7
113.1
80
240.2
143.9
41
35.2
21.1
101
86.6
51.9
161
138.1
189.6
113.6
281
241.0
144.5
42
36.0
21.6
02
87.5
52.4
62
139.0
83.3
22
190.4
114.1
82
241.9
145.0
43
36.9
22.1
03
88.3
53.0
63
139.8
83.8
23
191.3
114.6
83
242.7
145.5
44
37.7
22.6
04
89.2
53.5
64
140.7
84.3
24
192.1
115.2
84
243.6
146.0
45
38.6
23.1
05
90.1
54.0
65
141.5
84.8
25
193.0
115.7
85
244.5
146.5
46
39.5
23.6
06
90.9
54.5
66
142.4
85.3
26
193.8
116.2
86
245.3
147.0
47
40.3
24.2
07
91.8
55.0
67
143.2
85.9
27
194.7
116.7
87
246.2
147.5
48
41.2
24.7
08
92.6
55.5
68
144.1
86.4
28
195. 6
117.2
88
247.0
148.1
49
42.0
25.2
09
93.5
56.0
69
145.0
86.9
29
196.4
117.7
89
247.9
148.6
50
42.9
43.7
25.7
10
111
94.4
95.2
56.6
70
145.8
146. 7"
87.4
30
197.3
198.1
118.2
118.8
90
291
248.7
149.1
149.6
51
26.2
57.1
171
87.9
231
249.6
52
44.6
26.7
12
96.1
57.6
72
147.5
88.4
32
199.0
119.3
92
250. 5
150.1
53
45.5
27.2
13
96.9
58.1
73
148.4
88.9
33
199.9
119.8
93
251.3
150.6
54
46.3
27.8
14
97.8
58.6
74
149.2
89.5
34
200.7
120.3
94
252.2
151.1
55
47.2
28.3
15
98.6
59.1
75
150.1
90.0
35
201.6
120.8
95
253.0
151.7
56
48.0
28.8
16
99.5
59. 6
76
151.0
90.5
36
202.4
121.3
96
253.9
152. 2
57
48.9
29.3
17
100.4
60.2
77
151.8
91.0
37
203. 3
121.8
97
254.7
152.7
58
49.7
29.8
18
101.2
60.7
78
152.7
91.5
38
204.1
122.4
98
255.6
153.2
59
50.6
30.3
19
102.1
61.2
79
153.5
92.0
39
205.0
122.9
99
256.5
153.7
60
51.5
30.8
20
102.9
61.7
80
154.4
92.5
40
205.9
123.4
300
257.3
154.2
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
N.
E. by E
iE.
SI
<:. by E. 1 E.
NW. by \^'
JW.
SW
. by W. \ W.
[For 5i Poi
nt«.
TABLE 1.
[Page 363
Difference of Latitude and Departure for 3 Points.
NE. by
N.
NW. by N.
SE. by S.
SW. by S.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
50.7
33.9
.121
100.6
67.2
181
150.5
100.6
241
200.4
133.9
2
1.7
1.1
62
51.6
34.4
22
101.4
67.8
82
151. 3
101.1
42
201.2
134.4
3
2.5
1.7
63
52.4
35.0
23
102.3
68.3
83
152. 2
101.7
43
202.0
135.0
4
3.3
2.2
64
53.2
35.6
24
103. 1
68.9
84
153.0
102.2
44
202.9
135. 6
5
4.2
2.8
65
54.0
36.1
25
103.9
69.4
85
153.8
102.8
45
203. 7
136.1
6
5.0
3.3
66
54.9
36.7
26
104.8
70.0
86
154. 7
103.3
46
204. 5
136.7
7
5.8
3.9
67
55.7
37.2
27
105. 6
70.6
87
155. 5
103. 9
47
205. 4
137.2
. 8
6.7
4.4
68
56.5
37.8
28
106.4
71.1
88
156.3
104.4
48
206.2
137.8
9
7.5
5.0
69
57.4
38.3
29
107.3
71.7
89
157. 1
105.0
49
207.0
138.3
10
8.3
5.6
70
58.2
38.9
30
108.1
72.2
90
158.0
105.6
50
207.9
138.9
11
9.1
6.1
71
59.0
39.4
131
108.9
72.8
191
158.8
106.1
251
"208. 7
139.4
12
10.0
6.7
72
59.9
40.0
32
109.8
73.3
92
159.6
106. 7
52
209.5
140.0
13
10.8
7.2
73
60.7
40.6
33
110.6
73.9
93
160. 5
107.2
53
210.4
140.6
14
11.6
7.8
74
61.5
41.1
34
111.4
74.4
94
161. 3
107.8
54
211.2
141.1
15
12.5
8.3
75
62.4
41.7
35
112.2
75.0
95 162. 1
108.3
55
212.0
141.7
16
13.3
8.9
76
63.2
42.2
36
113.1
75.6
96
163.0
108.9
56
212.9
142.2
17
14.1
9.4
77
64.0
42^8
37
113.9
76.1
97
163.8
109.4
57
213.7
142.8
18
15.0
10.0
78
64.9
43.3
38
114.7
76.7
98
164.6
110.0
58
214.5
143.3
19
15.8
10.6
79
65.7
43.9
39
115.6
77.2
99
165. 5
110.6
59
215. 4
143.9
20
16.6
11.1
80
66.5
67.3
44.4
45. 0
40
116.4
77.8
200
201
166. 3
167.1
111.1
60
216.2
217.0
144.4
21
17.5
11.7
81
141
117.2
78.3
111.7
261
145.0
22
18.3
12.2
82
68.2
45.6
42
118.1
78.9
02
168.0
112.2
62
217.8
145.6
23
19.1
12.8
83
69.0
46.1
43
118.9
79.4
03
168.8
112.8
63
218.7
146.1
24
20.0
13.3
84
69.8
46.7
44
119.7
80.0
04
169.6
113.3
64
219.5
146.7
25
20.8
13.9
85
70.7
47.2
45
120.6
80.6
05
170.5
113.9
65
220.3
147.2
26
21.6
14.4
86
71.5
47.8
46
121.4
81.1
06
171.3
114.4
66
221.2
147.8
27
22.4
15.0
87
72.3
48.3
47
122.2
81.7
07
172.1
115. 0
67
222.0
148.3
28
23.3
15.6
88
73.2
48.9
48
123. 1
82.2
08
172. 9 ! 115. 6
68
222.8
148.9
29
24.1
16.1
89
74.0
49.4
49
123.9
82.8
09
173.8
116.1
69
223. 7
149.4
30
24.9
16.7
90
91
74.8
75.7
50.0
50
124.7
125.6
83.3
83.9
10
174.6
116.7
70
224.5
225. 3
150.0
150.6
31
25.8
17.2
50.6
151
211
175.4
117.2
271
32
26.6
17.8
92
76.5
51.1
52
126. 4
84.4
12
176.3
117.8
72
226.2
151.1
33
27.4
18.3
93
77.3
51.7
53
127.2
85.0
13
177.1
118.3
73
227.0
151.7
34
28.3
18.9
94
78.2
52.2
54
128. 0 •
85.6
14
177.9
118.9
74
227.8
152.2
35
"29.1
19.4
95
79.0
52". 8
55
128.9
86.1
15
178.8
119.4
75
228.7
152. 8
36
29.9
20.0
96
79.8
53.3
56
129.7
86.7
16
179. 6
120.0
76
229. 5
153.3
37
30.8
20.6
97
80.7
53.9
57
130. 5
87.2
17
180.4
120.6
77
230.3
153.9
38
31.6
21.1
98
81.5
54.4
58
131.4
87.8
18
181.3
121.1
78
231.1
154.4
39
32.4
21.7
99
82.3
55.0
59
132.2
88.3
19
182.1
121.7
79
232.0
155.0
40
41
33.3
34.1
22.2
100
83.1
55. 6
60
133.0
133.9
88.9
20
182.9
122.2
80
232.8
23.3.6
155.6
22.8
101
84.0
56.1
161
89.4
221
183. 8 1 122. 8
281
156.1
42
34.9
23.3
02
84.8
56.7
62
134.7
90.0
22
184.6
123.3
82
234. 5
156.7
43
35.8
23.9
03
85.6
57.2
63
135. 5
90.6
23
185.4
123.9
83
235.3
157.2
44
36.6
24.4
04
86.5
57.8
64
136. 4
91.1
24
186.2.
124.4
84
236.1
157. 8
45
37.4
25.0
05
87.3
58.3
65
137.2
91.7
25
187.1
125.0
85
237. 0
158.3
46
38.2
25.6
06
88.1
58.9
66
138.0
92.2
26
187. 9
125.6
86
237. 8
158. 9
47
39.1
26.1
07
89.0
59.4
67
138.9
92.8
27
188.7 126. 1|
87
238. 6
159.4
48
39.9
26.7
08
89.8
60.0
68
139.7
93.3
28
189.6
126.7
88
239. 5
160.0
49
40.7
27.2
09
90.6
60.6
69
140.5
93.9
29
190.4
127.2
89
240.3
160.6
50
41.6
42.4
27.8
10
91.5
61.1
70
141.3
94.4
30
191.2
192.1
127.8
90
291
241.1
161.1
51
28.3
111
92.3
61.7
171
142.2
95.0
231
128.3
242.0
161.7
52
43.2
28.9
12
93.1
62.2
72
143.0
95.6
32
192.9
128.9
92
242.8
162.2
53
44.1
29.4
13
94.0
62.8
73
143.8
96.1
33
193.7
129.4
93
243.6
162.8
54
44.9
30.0
14
94.8
63.3
74
144.7
96.7
34
194.6
130.0
94
244. 5
163.3
55
45.7
30.6
15
95.6
63.9
75
145. 5
97.2
35
195. 4
130. 6
95
245.3
163.9
56
46.6
31.1
16
96.5
64.4
76
146.3
97.8
36
196.2
131.1
96
246.1
164.4
57
47.4
31.7
17
97.3
65.0
77
147.2
98.3
37
197.1
131.7
97
246.9
165. 0
58
48.2
32.2
18
98.1
65.6
78
148.0
98.9
38
197.9
132.2
98
247.8
165. 6
59
49.1
32.8
19
98.9
66.1
79
148.8
99.4
39
198.7
132.8
99
248.6
166.1
60
1
49.9
33.3
20
99.8
66.7
80
149.7
100.0
40
199.6
1.33. 3
300
249.4
166.7
Dist. j
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NE. by E.
(;
E. by I
:. N^
V. by W. SW. by W.
[For 5 Points. 1
Page 364
1
TABLE
1.
Difference of Latitude and Departure for S^ Points.
NE. i N.
NW.
IN.
SE. 1 S.
SW.
IS.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
1
0.8
0.6
61
49.0
36.3
121
97.2
72.1
181
145.4
107.8
241
193.6
143. 6
2
1.6
1.2
62
49.8
36.9
22
98.0
72.7
82
146.2
108.4
42
194.4
144.2
3
2.4
1.8
63
50.6
37.5
23
98.8
73.3
83
147.0
109.0
43
195.2
144.8
. 4
3.2
2.4
64
51.4
38.1
24
99.6
73.9
84
147.8
109.6
44
196.0
145. 4
5
4.0
3.0
«65
52.2
38.7
25
100.4
74.5
85
148.6
110.2
45
196.8
145. 9
6
4.8
3.6
m
53.0
39.3
26
101.2
75.1
86
149.4
110.8
46
197. 6 146. 5
7
5.6
4.2
67
53.8
39.9
27
102.0
75.7
87
150.2
111.4
47
198.4 1 147.1
8
6.4
4.8
68
54.6
40.5
28
102.8
76.2
88
151.0
112.0
48
199.2 i 147.7
9
7.2
5.4
69
55.4
41.1
29
103.6
76.8
89
151.8
112.6
49
200.0
148.3
10
8.0
6.0
70
56.2
41.7
30
104.4
105.2
77.4
90
152.6
113.2
50
200.8
201.6
148.9
149.5
11
8.8
6.6
71
57.0
42.3
131
78.0
191
153. 4
113. 8
251
12
9.6
7.1
72
57.8
42.9
32
106.0
78.6
92
154.2
114.4
52
202.4
150.1
13
10.4
7.7
73
58.6
43.5
33
106.8
79.2
93
155.0
115.0
53
203.2
150.7
14
11.2
8.3
74
59.4
44.1
34
107.6
79.8
94
155.8
115.6
54
204.0
151. 3
15
12.0
8.9
75
60.2
44.7
35
108.4
80.4
95
156.6
116. 2
55
204.8
151.9
16
12.9
9.5
76
61.0
45.3
36
109.2
81.0
96
157.4
116.8
56
205.6
152.5
17
13.7
10.1
77
61.8
45.9
37
110.0
81.6
97
158.2
117.4
57
206.4
153.1
18
14.5
10.7
78
62.7
46.5
38
110.8
82.2
98
159.0
117.9
58
207.2
153. 7
19
15.3
11.3
79
63.5
47.1
39
111.6
82.8
99
159.8
118.5
59
208.0
154.3
20
16.1
11.9
80
64.3
47.7
40
112.4
83.4
200
160.6
119.1
60
208.8
154.9
21
16.9
12.5
81
65.1
48.3
141
113.3
84.0
201
161.4
119.7
261
209.6
155.5
22
17.7
13.1
82
65.9
48.8
42
114.1
84.6
02
162.2
120.3
62
210.4
156.1
23
18.5
13.7
83
66.7
49.4
43
114.9
85.2
03
163.1
120.9
63
211.2
156.7
24
19.3
14.3
84
67.5
50.0
44
115.7
85.8
04
163.9
121.5
64
212.0
157.3
25
20.1
14.9
85
68.3
50.6
45
116.5
86.4
05
164.7
122.1
65
212.8
157.9
26
20.9
15.5
86
69.1
51.2
46
117.3
87.0
06
165.5
122.7
66
213.7
158.5
27
21.7
16.1
87
69.9
51.8
47
118.1
87.6
07
166.3
123. 3
67
214.5
159.1
28
22.5
16.7
88
70.7
52.4
48
118.9
88.2
08
167.1
123. 9
68
215.3
159.6
29
23.3
17.3
89
71.5
53.0
49
119.7
88.8
09
167.9
124. 5
69
216.1
160.2
30
24.1
17.9
90
72.3
53.6
50
120.5
89.4
10
168.7
169.5
125. 1
70
216.9
160.8
31
24.9
18.5
91
73.1
54.2
151
121.3
90.0
211
125.7
271
217.7
161.4
32
25.7
19.1
92
73.9
54.8
52
122.1
90.5
12
170.3
126.3
72
218.5
162.0
33
26.5
19.7
93
74.7
55.4
53
122.9
91.1
13
171.1
126.9
73
219.3
162.6
34
27.3
20.3
94
75. 5
56.0
54
123.7
91.7
14
171.9
127.5
74
220.1
163.2
35
28.1
20.8
95
76.3
56.6
55
124.5
92.3
15
172.7
128.1
75
220.9
163. 8
36
28.9
21.4
96
77.1
57.2
56
125.3
92.9
16
173.5
128.7
76
221.7
164.4
37
29.7
22.0
97
77.9
57.8
57
126.1
93.5
17
174.3
129.3
77
222.5
165.0
38
30.5
22.6
98
78.7
58.4
58
126.9
94.1
18
175.1
129.9
78
223.3
165.6
39
31.3
23.2
99
79.5
59.0
59
127.7
94.7
19
175.9
130.5
79
224.1
166.2
40
41
32.1
32.9
23.8
100
80.3
81.1
59.6
60.2
60
128.5
95.3
20
176.7
131.1
80
281
224.9
166.8
24.4
101
161
129.3
95.9
221
177.5
131.6
225.7
167.4
42
33.7
25.0
02
81.9
60.8
62
130.1
96.5
22
178.3
132.2
82
226.5
168.0
43
34.5
25.6
03
82.7
61.4
63
130.9
97.1
23
179.1
132.8
83
227.3
168.6
44
35.3
26.2
04
83.5
62.0
64
131.7
97.7
24
179.9
133.4
84
228.1
169.2
45
36.1
26.8
05
84.3
62.5
65
132.5
98.3
25
180.7
134.0
85
228.9
169.8
46
36.9
27.4
06
85.1
63.1
66
133. 3
98.9
26
181.5
134.6
86
229.7
170.4
47
37.8
28.0
07
85.9
63.7
67
134.1
99.5
27
182.3
135.2
87
230.5
171.0
48
38.6
28.6
08
86.7
64.3
68
134.9
100.1
28
183.1
135.8
88
231.3
171.6
49
39.4
29.2
09
87.5
64.9
69
135.7
100.7
29
183.9
136.4
89
232.1
172.2
50
40.2
29.8
10
111
88.4
89.2
65.5
70
136.5
101. 3
30
184.7
185. 5
137.0
90
232.9
233. 7
172.8
51
41.0
30.4
66.1
171
137.3
101. 9
231
137.6
291
173.3
52
41.8
31.0
12
90.0
66.7
72
138. 2
102.5
32
186.3
138.2
92
234.5
173.9
53
42.6
31.6
13
90.8
67.3
73
139.0
103. 1
33
187.1
138.8
93
235. 3
174.5
54
43.4
32.2
14
91.6
67.9
74
139.8
103.7
34
188.0
139.4
94
236.1
175.1
55
44.2
32.8
15
92.4
68.5
75
140.6
104.2
35
188.8
140.0
95
236.9
175.7
56
45.0
33.4
16
93.2
69.1
76
141.4
104.8
36
189.6
140.6
96
237.7
176.3
57
45.8
34.0
17
94.0
69.7
77
142.2
105.4
37
190.4
141. 2
97
238.6
176.9
58
46.6
34.6
18
94.8
70.3
78
143.0
106.0
38
191.2
141.8
98
239.4
177.5
59
47.4
35.1
19
95.6
70.9
79
143.8
106.6
39
192.0
142.4
99
240.2
178.1
60
48.2
35.7
20
96.4
71.5
80
144.6
107.2
40
192. 8
143.0
300
241.0
178.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. j Lat.
NE. 1
E.
SE. 1 E
X^
V. f w.
sw. i w.
[F
or 4J Points.
OF THE
UNIVERSITY
X^cyi/ °L.
:l\i- ..y
/
TABLE 1.
[Page 365
Difference of Latitude and Departure for 3i Points.
NE. i N.
NW
. JN.
SE
. ^S.
SW. i s
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
47.2
38.7
121
93.5
76.8
181
139.9
114.8
241
186.3
152.9
2
1.5
1.3
62
47.9
39.3
22
94.3
77.4
82
140.7
115.5
42
187.1
153. 5
3
2.3
1.9
63
48.7
40.0
23
95.1
78.0
83
141.5
116.1
43
187.8
154.2
4
3.1
2.5
64
49.5
40.6
24
95.9
78.7
84
142.2
116.7
44
188.6
154.8
5
3.9
3.2
65
50.2
41.2
25
96.6
79.3
85
143. 0
117.4
45
189.4
155.4
6
4.6
3.8
66
51.0
41.9
26
97.4
79.9
86
143.8
118.0
46
190.2
156.1
7
5.4
4.4
67
51.8
42.5
27
98.2
80.6
87
144.6
118.6
47
190.9
156.7
8
6.2
5.1
68
52.6
43.1
28
98.9
81.2
88
145. 3
119.3
48
191.7
157.3
9
7.0
5.7
69
53.3
43.8
29
99.7
81.8
89
146.1
119.9
49
192.5
158.0
10
11
7.7
8.5
6.3
70
71
54.1
44.4
30
100.5
82.5
90
146.9
147.6
120. 5
121. 2
50
193.3
158.6
7.0
54.9
45.0
131
101.3
83.1
191
251
194.0
159.2
12
9.3
7.6
72
55.7
45.7
32
102.0
83.7
92
148.4
121.8
52
194.8
159.9
13
10.0
8.2
73
56.4
46.3
33
102.8
84.4
93
149.2
122.4
53
195. 6
160.5
14
10.8
8.9
74
57.2
46.9
34
103.6
85.0
94
150. 0
123.1
54
196.3
161.1
15
11.6
9.5
75
58.0
47.6
35
104.4
85.6
95
150.7
123. 7
55
197.1
161.8
16
12.4
10.2-
76
58.7
48.2
36
105.1
86.3
96
151.5
124. 3
56
197.9
162.4
17
13.1
10.8
77
59.5
48.8
37
105.9
86.9
97
152.3
125.0
57
198.7
163.0
18
13.9
11.4
78
60.3
49.5
38
106.7
87.5
98
153.1
125.6
58
199.4
163.7
19
14.7
12.1
79
61.1
50.1
39
107.4
88.2
99
153. 8
126.2
59
200.2
164.3
20
15.5
12.7
80
61.8
50.8
40
108.2
88.8
200
201
154.6
155.4
126.9
60
201.0
201.8
164.9
21
16.2
13.3
81
62.6
51.4
141
109.0
89.4
127.5
261
165.6
22
17.0
14.0
82
63.4
52.0
42
109.8
90.1
02
156.1
128.1
62
202.5
166.2
23
17.8
14.6
83
64.2
52.7
43
110. 5
90.7
03
156.9
128.8
63
203.3
166.8
24
18.6
15.2
84
64.9
53.3
44
111.3
91.4
04
157.7
129.4
64
204.1
167.5
25
19.3
15.9
85
65.7
53.9
45
112.1
92.0
05
158.5
130.1
65
204.8
168.1
26
20.1
16.5
86
66.5
54.6
46
112.9
92.6
06
159.2
130.7
66
205.6
168.7
27
20.9
17.1
87
67.3
55.2
47
113.6
93.3
07
160.0
131.3
67
206.4
169.4
28
21.6
17.8
88
68.0
55.8
48
114.4
93.9
08
160.8
132.0
68
207.2
170.0
29
22.4
18.4
89
68.8
56.5
49
115. 2
94.5
09
161.6
132.6
69
207.9
170.7
30
31
23.2
24.0
19.0
90
69.6
70.3
57.1
57."7
50
151
116.0
95.2
10
211
162.3
163.1
133.2
133.9
70
208.7
171.3
19.7
91
116.7
95.8
271
209.5
171.9
32
24.7
20.3
92
71.1
58.4
52
117.5
96.4
12
163.9
134.5
72
210.3
172.6
33
25.5
20.9
93
71.9
59.0
53
118.3
97.1
13
164.7
135.1
73
211.0
173.2
34
26.3
21.6
94
72.7
59.6
54
119.0
97.7
14
165.4
135.8
74
211.8
173.8
35
.27. 1
22.2
95
73.4
60.3
55
119.8
98.3
15
166.2
136.4
75
212.6
174.5
36
27.8
22.8
96
74.2
60.9
56
120.6
99.0
16
167.0
137.0
76
213.4
175. 1
37
28.6
23.5
97
75.0
61.5
57
121.4
99.6
17
167.7
137.7
77
214.1
175.7
38
29.4
24.1
98
75.8
62.2
58
122.1
100.2
18
168.5
138.3
78
214.9
176.4
39
30.1
24.7
99
76.5
62.8
59
122.9
100.9
19
169.3
138.9
79
215. 7
177.0
40
30.9
25.4
100
101
77.3
78.1
6.3.4
60
123.7
101.5
102. 1"
20
221
170.1
170.8
139.6
140. 2
80
216.4
177.6
41
31.7
26.0
64.1
161
124.5
281
217.2
178.3
42
32.5
26.6
02
78.8
64.7
62
125. 2
102.8
22
171.6
140.8
82
218.0
178.9
43
33.2
27.3
03
79.6
65.3
63
126.0
103.4
23
172.4
141. 5
83
218.8
179.5
44
34.0
27.9
04
80.4
66.0
64
126.8
104.0
24
173.2
142.1
84
219.5
180.2
45
34.8
28.5
05
81.2
66.6
65
127.5
104.7
25
173.9
142.7
85
220.3
180.8
46
35.6
29.2
06
81.9
67.2
66
128.3
105. 3
26
174.7
143.4
86
221.1
181.4
47
36.3
29.8
07
82.7
67.9
67
' 129. 1
105. 9
27
175.5
144.0
87
221.9
182.1
48
37.1
30.5
08
83.5
68.5
68
129.9
106.6
28
176.2
144.6
88
222.6
182.7
49
37.9
31.1
09
84.3
69.1
69
130.6
107.2
29
177.0
145. 3
89
223.4
183.3
50
38.7
31.7
10
85.0
69.8
70
131.4
107.8
30
177.8
145.9
90
224.2
184. 0
51
39.4
32.4
111
85.8
70.4
171
132.2
108.5
231
178.6
146.5
291
224.9
184.6
52
40.2
33.0
12
86.6
71.1
72
133.0
109.1
32
179.3
147.2
92
225.7
185.2
53
41.0
33.6
13
87.4
71.7
73
133.7
109.8
33
180.1
147.8
93
226.5
185.9
54
41.7
34.3
14
88.1
72.3
74
134.5
110.4
34
180.9
148.4
94
227.3
186.5
55
42.5
34.9
15
88.9
73.0
75
135.3
111.0
35
181.7
149.1
95
228.0
187.1
56
43.3
35.5
16
89.7
73.6
76
136. 0
111.7
36
182.4
149.7
96
228.8
187.8
57
44.1
36.2
17
90.4
74.2
77
136.8
112.3
37
183.2
150.4
97
229.6
188.4
58
44.8
36.8
18
91.2
74.9
78
137.6
112.9
38
184.0
151.0
98
230.4
189.0
59
45.6
37.4
19
92.0
75.5
79
138.4
113.6
39
184.7
151.6
99
231.1
189.7
60
Dist.
46.4
38.1
20
92.8
76.1
80
139.1
114.2
40
185.5
152.3
300
231.9
190.3
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NE. i ]
E.
SE. JE
N
\V. J ^\
sw. i -^
V.
[F
or 4J Points. 1
Page 366]
TABLE 1.
Difference of Latitude and Departure for 3| Points.
NE. i N.
NW.
}N.
3E. J
s.
SW. J 8.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
241
Lat.
Dep.
1
0.7
0.7
61
46.2
41.0
121
89.7
81.3
181
134.1
121.6
178.6
161.8
2
1.5
1.3
62
45.9
41.6
22
90.4
81.9
82
134.9
122.2
42
179.3
162.5
3
2.2
2.0
63
46.7
42.3
23
91.1
82.6
83
135.6
122.9
43
180.1
163.2
4
3.0
2.7
64
47.4
43.0
24
91.9
83.3
84
136. 3
123.6
44
180.8
163.9
5
3.7
3.4
^
48.2
43.7
25
92.6
83.9
85
137.1
124.2
45
181.5
164.5
6
4.4
4.0
48.9
44.3
26
93.4
84.6
86
137.8
124.9
46
182.3
165.2
7
5.2
4.7
67
49.6
45.0
27
94.1
85.3
87
138.6
125. 6
47
183.0
165.9
8
5.9
5.4
68
50.4
45.7
28
94.8
86.0
88
139.3
126.3
48
183.8
166.5
9
6.7
6.0
69
51.1
46.3
29
95.6
86.6
89
140.0
126.9
49
184.5
167.2
10
7.4
6.7
70
51.9
52.6
47.0
47.7
30
96.3
97.1
87.3
88.0
90
191
140.8
141.5
127.6
128. 3
50
185.2
167.9
11
8.2
7.4
71
131
251
186.0
168.6
12
8.9
8.1
72
53.3
48.4
32
97.8
88.6
92
142.8
128.9
52
186.7
169.2
13
9.6
8.7
73
54.1
49.0
33
98.5
89.3
93
143.0
129.6
53
187.5
169.9
14
10.4
9.4
74
54.8
49.7
34
99.3
90.0
94
143.7
130.3
54
188.2
170.6
15
11.1
10.1
75
55.6
50.4
35
100.0
90.7
95
144.5
131.0
55
188.9
171.2
16
11.9
10.7
76
56.3
51.0
36
100.8
91.3
96
145.2
131.6
56
189.7
171.9
17
12.6
11.4
77
57.1
51.7
37
101.5
92.0
97
146.0
132.3
57
190.4
172.6
18
13.3
12.1
78
57.8
52.4
38
102.3
92.7
98
146.7
133.0
58
191.2
173.3
19
14.1
12.8
79
58.5
53.1
39
103.0
93.3
99
147.4
133.6
59
191.9
173.9
20
21
14.8
13.4
80
81
59.3
60.0
53.7
40
103.7
104.5
94.0
200
148.2
134.3
60
192.6
174.6
15.6
14.1
54.4
141
94.7
201
148.9
135.0
261
193.4
175.3
22
16.3
14.8
82
60.8
55. 1
42
105.2
95.4
02
149.7
135.7
62
194.1
175.9
23
17.0
15.4
83
61.5
55.7
43
106.0
96.0
03
150.4
136.3
63
194.9
176.6
24
17.8
16.1
84
62.2
56.4
44
106.7
96.7
04
151. 2
137.0
64
195.6
177.3
25
18.5
16.8
85
63.0
57.1
45
107.4
97.4
05
151.9
137. 7
65
196.4
178.0
26
19.3
17.5
86
63.7
57.8
46
108.2
98.0
06
152.6
138.3
66
197.1
178.6
27
20.0
18.1
87
64.5
58.4
47
108.9
98.7
07
153. 4
139.0
67
197.8
179.3
28
20.7
18.8
88
65.2
59.1
48
109.7
99.4
08
154.1
139.7
68
198.6
180.0
29
21.5
19.5
89
65.9
59.8
49
110.4
100.1
09
154.9
140.4
69
199.3
180.6
30
22.2
20.1
90
66.7
60.4
50
111.1
111.9
100.7
10
155.6
156.3
141. 0
70
200.1
200.8
181.3
31
23.0
20.8
91
67.4
61.1
151
101.4
211
141.7
271
182.0
32
23.7
21.5
92
68.2
61.8
52
112.6
102.1
12
157.1
142.4
72
201.5
182.7
33
24.5
22.2
93
68.9
62.5
53
113.4
102.7
13
157.8
143.0
73
202.3
183.3
34
25.2
22.8
94
69.6
63. 1
54
114.1
103.4
14
158.6
143.7
74
203. 0
184.0
35
25.9
23.5
95
70.4
63.8
55
114.8
104.1
15
159.3
144.4
75
203.8
184.7
36
26.7
24.2
96
71.1
64.5
56
115.6
104.8
16
160.0
145.1
76
204. 5
185.4
37
27.4
24.8
97
71.9
65.1
57
116.3
105.4
17
160.8
145.7
77
205.2
186.0
38
28.2
25.5
98
72.6
65.8
58
117.1
106.1
18
161.5
146.4
78
206.0
186.7
39
28.9
26.2
99
73.4
66.5
59
117.8
106.8
19
162.3
147.1
79
206.7
187.4
40
41
29.6
30.4
26.9
100
101
74.1
67.2
60
118.6
107.4
108.1
20
221
163.0
163.8
147.7
80
207.5
188.0
27.5
74.8
67.8
161
119.3
148.4
281
208.2
188.7
42
31.1
28.2
02
75.6
68.5
62
120.0
108.8
22
164.5
149.1
82
208.9
189.4
43
31.9
28.9
03
76.3
69.2
63
120.8
109.5
23
165.2
149.8
83
209.7
190.1
44
32.6
29.5
04
77.1
69.8
64
121.5
110.1
24
166.0
150.4
84
210.4
190.7
45
33. 3
30.2
05
77.8
70.5
65
122.3
110.8
25
166.7
151.1
85
211.2
191.4
46
34.1
30.9
06
78.5
71.2
66
123. 0
111.5
26
167.5
151.8
86
211.9
192.1
47
34.8
31.6
07
79.3
71.9
67
123.7
112.2
27
168.2
152.4
87
212.7
192.7
48
35.6
32.2
08
80.0
72.5
68
124.5
112.8
28
168.9
153.1
88
213.4
193.4
49
36.3
32.9
09
80.8
73.2
69
125.2
113.5
29
169.7
153.8
89
214.1
194.1
50
37.0
33.6
34.2
10
111
81.5
82.2
73.9
70
126.0
126.7
114.2
30
231
170.4
171.2
154.5
90
214.9
194.8
51
37.8
74.5
171
114.8
155.1
291
215.6
195. 4
52
38.5
34.9
12
83.0
75.2
72
127.4
115.5
32
171.9
155. 8
92
216.4
196.1
53
39.3
35.6
13
83.7
75.9
73
128.2
116.2
33
172.6
156.5
93
217.1
196.8
54
40.0
36.3
14
84.5
76.6
74
128.9
116.9
34
173.4
157.1
94
217.8
197.4
55
40.8
36.9
15
85.2
77.2
75
129.7
117.5
35
174. 1
157.8
95
218.6
198.1
56
41.5
37.6
16
86.0
77.9
76
130.4
118.2
36
174.9
158.5
96
219.3
198.8
57
42.2
38.3
17
86.7
78.6
77
131. 1
118.9
37
175.6
159.2
97
220.1
199.5
58
43.0
39.0
18
87.4
79.2
78
131.9
119.5
38
176. 3
159.8
98
220.8
200.1
59
43.7
39.6
19
88.2
79.9
79
132.6
120.2
39
177.1
160.5
99
221.5
200.8
60
44.5
40.3
20
88.9
80.6
80
133.4
120.9
40
177.8
161.2
300
222.3
201.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NE. i E.
<;
E. JE.
N)
V. i W.
S^
w. \ w.
[For 4J Points. 1
TABLE 1.
[Page 367
Difference of Latitude and
Depart
ure for 4 Points.
NE
NW.
SE.
sw.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
43.1
43.1
121
85.6
85.6
181
128.0
128.0
241
170.4
170.4
2
1.4
1.4
62
43.8
43.8
22
86.3
86.3
82
128.7
128.7
42
171.1
171.1
3
2.1
2.1
63
44.5
44.5
23
87.0
87.0
83
129.4
129.4
43
171.8
171.8
4
2.8
2.8
64
45.3
45.3
24
87.7
87.7
84
130.1
130.1
44
172.5
172.5
5
3.5
3.5
65
46.0
46.0
25
88.4
88.4
85
130.8
130.8
45
173.2
173.2
6
4.2
4.2
66
46.7
46.7
26
89.1
89.1
86
131.5
131.5
46
173.9
173.9
7
4.9
4.9
67
47.4
47.4
27
89.8
89.8
87
132.2
132.2
47
174.7
174.7
8
5.7
5.7
68
48.1
48.1
28
90.5
90.5
88
132.9
132.9
48
175.4
175.4
9
6.4
6.4
69
48.8
48.8
29
91.2
91.2
89
133.6
133.6
49
176.1
176.1
10
7.1
7.1
70
49.5
49.5
30
91.9
91.9
90
134.4
134.4
50
176.8
176.8
11
7.8
7.8
71
50.2
50.2
131
92.6
92.6
191
135.1
135.1
251
177.5
177.5
12
8.5
8.5
72
50.9
50.9
32
93.3
93.3
92
135.8
135.8
52
178.2
178.2
13
9.2
9.2
73
51.6
51.6
33
94.0
94.0
93
136.5
136.5
53
178.9
178.9
14
9.9
9.9
74
52.3
52.3
34
94.8
94.8
94
137.2
137.2
54
179.6
179.6
15
10.6
10.6
75
53.0
53.0
35
95.5
95.5
95
137.9
137.9
55
180.3
180.3
16
11.3
11.3
76
53.7
53.7
36
96.2
96.2
96
138.6
138.6
56
181.0
181.0
17
12.0
12.0
77
54.4
54.4
37
96.9
96.9
97
139. 3
139.3
57
181.7
181.7
18
12.7
12.7
78
55.2
55.2
38
97.6
97.6
98
140.0
140.0
58
182.4
182.4
19
13.4
13.4
79
55.9
55.9
39
98.3
98.3
99
140.7
140.7
59
183.1
183.1
20
14.1
14.1
80
56.6
56.6
40
99.0
99.0
200
201
141.4
142.1
141.4
60
183.8
183.8
184.6
21
14.8
14.8
81
57.3
57.3
141
99.7
99.7
142.1
261
184.6
22
15.6
15.6
82
58.0
58.0
42
100.4
100.4
02
142.8
142.8
62
185.3
185.3
23
16.3
16.3
83
58.7
58.7
43
101.1
101.]
03
143.5
143.5
63
186.0
186.0
24
17.0
17.0
84
59.4
59.4
44
101.8
101.8
04
144.2
144.2
64
186.7
186.7
25
17.7
17.7
85
60.1
60.1
45
102.5
102.5
05
145.0
145.0
65
187.4
187.4
26
18.4
18.4
86
60.8
60.8
46
103.2
103.2
06
145.7
145.7
66
188.1
188.1
27
19.1
19.1
87
61.5
61.5
47
103.9
103.9
07
146.4
146.4
67
188.8
188.8
28
19.8
19.8
88
62.2
62.2
48
104.7
104.7
08
147.1
147.1
68
189.5
189.5
29
20.5
20.5
89
62.9
62.9
49
105.4
105.4
09
147.8
147.8
69
190.2
190.2
30
31
21.2
21.2
90
63.6
63.6
50
151
106.1
106.1
10
211
148.5
149.2
148.5
149.2
70
190.9
191.6
190.9
21.9
21.9
91
64.3
64.3
106.8
106.8
271
191.6
32
22.6
22.6
92
65.1
65.1
52
107.5
107.5
12
149.9
149.9
72
192. 3
192.3
33
23.3
23.3
93
65.8
65.8
53
108.2
108.2
13
150.6
150.6
73
193.0
193.0
34
24.0
24.0
94
66.5-
66.5
54
108.9
108.9
14
151.3
151.3
74
193.7
193.7
35
24.7
24.7
95
67.2
67.2
55
109.6
109.6
15
152.0
152.0
75
194.5
194.5
36
25.5
25.5
96
67.9
67.9
56
110.3
110.3
16
152.7
152.7
76
195.2
195.2
37
26.2
26.2
97
68.6
68.6
57
111.0
111.0
17
153. 4
153.4
77
195.9
195.9
38
. 26.9
26.9
98
69.3
69.3
58
111.7
111.7
18
154.1
154.1
78
196.6
196.6
39
27.6
27.6
99
70.0
70.0
59
112.4
112.4
19
154.9
154.9
79
197.3
197.3
40
28.3
28.3
100
70.7
70.7
60
161
113.1
113.1
20
155. 6
155.6
156.3'
80
198.0
198.0
41
29.0
29.0
101
71.4
71.4
113.8
113.8
221
156.3
281
198.7
198.7
42
29.7
29.7
02
72.1
72.1
62
114.6
114.6
22
157.0
157.0
82
199.4
199.4
43
30.4
30.4
03
72.8
72.8
63
115.3
115.3
23
157.7
157.7
83
200.1
200.1
44
31.1
31.1
04
73.5
73.5
64
116.0
116.0
24
158.4
158.4
84
200.8
200.8
45
31.8
31.8
05
74.2
74.2
65
116.7
116.7
25
159.1
159.1
85
201.5
201.5
46
32.5
32.5
06
75.0
75.0
66
il7.4
117.4
26
159. 8
159.8
86
202.2
202.2
47
33.2
33.2
07
75.7
75.7
67
118.1
118.1
27
160.5
160.5
87
202.9
202.9
48
33.9
33.9
08
76.4
76.4
68
118.8
118.8
28
161.2
161.2
88
203.6
203.6
49
34.6
34.6
09
77.1
77.1
69
119.5
119.5
29
161.9
161.9
89
204.4
204.4
50
35.4
35.4
10
77.8
77.8
70
120.2
126.9
120.2
120.9
30
162.6
163.3
162.6
90
205.1
205.1
51
36.1
36.1
111
78.5
78.5
171
231
163.3
291
205.8
205.8
52
36.8
36.8
12
79.2
79.2
72
121.6
121.6
32
164.0
164.0
92
206.5
206.5
53
37.5
37.5
13
79.9
79.9
73
122.3
122.3
33
164.8
164.8
93
207.2
207.2
54
38.2
38.2
14
80.6
80.6
74
123.0
123.0
34
165. 5
165.5
94
207.9
207.9
55
38.9
38.9
15
81.3
81.3
75
123.7
123.7
35
166.2
166.2
95
208.6
208.6
56
39.6
39.6
16
82.0
82.0
76
124. 5
124.5
36
166.9
166.9
96
209.3
209.3
57
40.3
40.3
17
82.7
82.7
77
125.2
125.2
37
167.6
167.6
97
210.0
210.0
58
41.0
41.0
18
83.4
83.4
78
125.9
125.9
38
168. 3
168.3
98
210.7
210.7
59
41.7
41.7
19
84.1
84.1
79
126.6
126.6
39
169.0
169.0
99
211.4
211.4
60
42.4
42.4
20
84.9
84.9
80
127.3
127.3
40
169.7
169.7
300
212.1
212.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist
Dep.
Lat.
Dist.
Dep.
Lat.
■ NE.
NW.
?E.
SW
[1
^'or 4 Po
ints.
Page 368
TABLE
i 2.
Difference of Latitude and Departure for 1° (179", 181'
', 359°]
.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.0
61
61.0
1.1
121
121.0
2.1
181 181.0
3.2
241
241.0
4.2
2
2.0
0.0
62
62.0
1.1
22
122.0
2.1
82
182.0
3.2
42
242. 0
4.2
3
3.0
0.1
63
63.0
1.1
23
123.0
2.1
83
183.0
3.2
43
243.0
4.2
4
4.0
0.1
64
64.0
1.1
24
124.0
2.2
84
184.0
3.2
44
244.0
4.3
5
5.0
0.1
65
65.0
1.1
25
125.0
2.2
85
185.0
3.2
45
245.0
4.3
6
6.0
0.1
^6
•67
66.0
1.2
26
126.0
2.2
86
186.0
3.2
46
246.0
4.3
7
7.0
0.1
67.0
1.2
27
127.0
2.2
87
187.0
3.3
47
247.0
4.3
8
8.0
0.1
68
68.0
1.2
28
128.0
2.2
88
188.0
3.3
48
248.0
4.3
9
9.0
0.2
69
69.0
1.2
29
129.0
2.3
89 189.0
3.3
49
249.0
4.3
10
10.0
0.2
70
70.0
^1.2
30
130.0
2.3
2.3
90
191
190.0
191.0
3.3
3.3
50
251
250.0
4.4
11
11.0
0.2
71
71.0
1.2
131
131. 0
251.0
4.4
12
12.0
0.2
72
72.0
1.3
32
132.0
"2.3
92
192.0
3.4
52
252.0
4.4
13
13.0
0.2
73
73.0
1.3
33
133.0
2.3
93
193.0
3.4
53
253.0
4.4
' 14
14.0
0.2
74
74.0
1.3
34
134.0
2.3
94
194.0
3.4
54
254.0
4.4
15
15.0
0.3
75
75.0
1.3
35
135.0
2.4
95
195.0
3.4
55
255.0
4.5
16
16.0
0.3
76,
76.0
1.3
36
136.0
2.4
96
196.0
8.4
56
256.0
4.5
17
17.0
0.3
77
77.0
1.3
37
137.0
2.4
97
197.0
3.4
57
257.0
4.5
18
18.0
0.3
78
78.0
1.4
38
138.0
2.4
98
198.0
3.5
58
258.0
4.5
19
19.0
0.3
79
79.0
1.4
39
139.0
2.4
99
199.0
3.5
59
259.0
4.5
20
20.0
21.0
0.3
80
80.0
81.0
1.4
40
140.0
141.0
2.4
200
201
200.0
3.5
60
261
260.0
261.0
4.5
4.6
21
0.4
81
1.4
141
2.5
201.0
3.5
22
22.0
0.4
82
82.0
1.4
42
142.0
2.5
02
202.0
3.5
62
262.0
4.6
23
23.0
0.4
83
83.0
1.4
43
143.0
2.5
03
203.0
3.5
63
263.0
4.6
24
24.0
0.4
84
84.0
1.5
44
144.0
2.5
04
204.0
3.6
64
264.0
4.6
25
25.0
0.4
85
85.0
1.5
45
145.0
2.5
05
205.0
3.6
65
265.0
4.6
26
26.0
0.5
86
86.0
1.5
46
146.0
2.5
06
206.0
3.6
66
266.0
4.6
27
27.0
0.5
87
87.0
1.5
47
147.0
2.6
07
207.0
3.6
67
267.0
4.7
28
28.0
0.5
88
88.0
1.5
48
148.0
2.6
08
208.0
3.6
68
268.0
4.7
29
29.0
0.5
89
89.0
1.6
49
149.0
2.6
09
209.0
3.6
69
269.0
4.7
30
31
30..0
0.5
90
91
90.0
1.6
50
150.0
2.6
10
210.0
3.7
70
270.0
4.7
4.7
31.0
0.5
91.0
1.6
151
151.0
2.6
211
211.0
3.7
271
271.0
32
32.0
0.6
92
92.0
1.6
52
152.0
2.7
12
212.0
3.7
72
272.0
4.7
33
33.0
0.6
93
93.0
1.6
53
153.0
2.7
13
213.0
3.7
73
273.0
4.8
34
34.0
0.6
94
94.0
1.6
54
154.0
2.7
14
214.0
3.7
74
274.0
4.8
35
35.0
0.6
95
95.0
1.7
55
155. 0
2.7
15
215.0
3.8
75
275.0
4.8
36
36.0
0.6
96
96.0
1.7
56
156.0
2.7
16
216.0
3.8
76
276.0
4.8
37
37.0
0.6
97
97.0
1.7
57
157.0
2.7
17
217.0
3.8
/ 1
277.0
4.8
38
38.0
0.7
98
98.0
1.7
58
158.0
2.8
18
218.0
3.8
78
278.0
4.9
39
39.0
0.7
99
99.0
1.7
59
159.0
2.8
19
219.0
3.8
79
279.0
4.9
40
40.0
0.7
0.7
100
100.0
1.7
1.8
60
160.0
161.0
2.8
2.8
20
221
220.0
3.8
80
280.0
4.9
41
41.0
101
101.0
161
221.0
3.9
281
281.0
4.9
42
42.0
0.7
02
102.0
1.8
62
162.0
2.8
22
222.0
3.9
82
282.0
4.9
43
43.0
0.8
03
103.0
1.8
63
163.0
2.8
23
223.0
3.9
83
283.0
4.9
44
44.0
0.8
04
104.0
1.8
64
164.0
2.9
24
224.0
3.9
84*
284.0
5.0
45
45.0
0.8
05
105.0
1.8
65
165.0
2.9
25
225.0
3.9
85
285.0
5.0
46
46.0
0.8
06
106.0
1.8
66
166.0
2.9
26
226. 0
3.9
86
286.0
5.0
47
47.0
0.8
07
107.0
1.9
67
167.0
2.9
27
227.0
4.0
87
287.0
5.0
48
48.0
0.8
08
108.0
1.9
68
168.0
2.9
28
228.0
4.0
88
288.0
5.0
49
49.0
0.9
09
109.0
1.9
69
169.0
2.9
29
229.0
4.0
89
289.0
5.0
50
50.0
0.9
10
110.0
1.9
70
170.0
3.0
30
230.0
231. 0
4.0
90
290.0
5.1
51
51.0
0.9
111
111.0
1.9
171
171.0
3.0
231
4.0
291
291.0
5.1
52
52.0
0.9
12
112.0
2.0
72
172.0
3.0
32
232.0
4.0
92
292.0
5.1
53
53.0
0.9
13
113. 0
2.0
73
173.0
3.0
33
233.0
4.1
93
293.0
5.1
54
54.0
0.9
14
114.0
2.0
74
174.0
3.0
34
234.0
4.1
94
294.0
5.1
55
55.0
1.0
15
115. 0
2.0
75
175.0
3.1
35
235.0
4.1
95
295.0
5.1
56
56.0
1.0
16
116.0
2.0
76
176.0
3.1
36
236.0
4.1
96
296.0
5.2
57
57.0
1.0
17
117.0
2.0
77
177.0
3.1
37
237.0
4.1
97
297.0
5.2
58
58.0
1.0
18
118.0
2.1
78
178.0
3.1
38
238. 0
4.2
98
298.0
5.2
59
59.0
1.0
19
119.0
2.1
79
179.0
3.1
39
239.0
4.2
99
299.0
5.2
60
60.0
1 1-0
20
120.0
2.1
80
180.0
3.1
40
240. 0.
4.2
300
300.0
5.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
89° 0
n°, 269
^ 271°
.
TABLE 2.
[Page 369
Difference of Latitude and Departure for 1° (179°, 181
=, 359°).
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
301.0
5.3
361 ' 360.9
6.3
421
420.9
7.3
481
480.9
8.4
541
540.9
• 9. 5
02
302.0
5.3
62 361.9
6.3
22
421.9
7.4
82
481.9
8.4
42
541.9
9.5
03
303. 0
5.3
63 1 362.9
6.3
23
422.9
7.4
83
482.9
8.5
43
542.9
9.5
04
304.0
5.3
64 363.9
6.4
24
423.9
7.4
84
483.9
8.5
44
543.9
9.5
05
305.0
5.3
65 1 364.9
6.4
25
424.9
7.4
85
484.9
8.5
45
544.9
9.5
06
306.0
5.3
66
365.9
6.4
26
425.9
7.4
86
485.9
8.5
46
545.9
9.5
07
307.0
5.4
67
366.9
6.4
27
426.9
7.4
87
486.9
8.5
47
546. 9
9.6
08
308.0
5.4
68
367.9
6.4
28
427.9
7.5
88
487.9
8.6
48
547. 9
9.6
09
309.0
5.4
69
368. 9
6.4
29
428.9
7. 5
89
488.9
8.6
49
548.9
9.6
10
311
310.0
311.6
5.4
70
369.9
370.'9^
6.5
6.5
30
431
429.9
430.9
7.5
7.5
90
491
489.9
490.9
8.6
876
50
549. 9
9.6
5.4
371
551
550.9
9.6
12
312.0
5.4
72
371.9
6.5
32
-431. 9
7.5
92
491.9
8.6
52
551.9
9.6
13
313.0
5.5
73
372.9
6.5
33
432.9
7. 5
93
492.9
8.7
53
552.9
9.7
14
314.0
5.5
74
373.9
6.5
34
433.9
7.6
94
493.9
8.7
54
553.9
9.7
15
315.0
5.5
75
374.9
6.5
35
434.9
7.6
95
494.9
8.7
55
554.9
9.7
16
316.0
5.5
76-
375.9
6.6
36
435.9
7.6
96
495.9
8.7
56
555. 9
9.7
17
317.0
5.5
77
376.9
6.6
37
436.9
7.6
97
496.9
8.7
57
556.9
9.7
18
318.0
5.5
78
377.9
6.6
38
437.9
7.6
98
497.9
8.7
58
557. 9
9.7
19
319.0
5.6
79
378.9
6.6
39
438.9
7. 7
99
498.9
8.8
59
558.9
9.8
20
321
320.0
5.6
80
381
379.9
380.9
6.6
6.7
40
439.9
7. 7
500
499.9
500.9
8.8
60
559.9
"560.9
9.8
321.0
5.6
441
440.9
7. 7
501
8.8
561
9.8
22
322.0
5.6
82
381.9
6.7
42
441.9
7. 7
02
501.9
8.8
62'
561.9
9.8
23
323.0
5.6
83
382.9
6.7
43
442.9
7. 7
03
502. 9
8.8
63
562.9
9.8
24
324.0
5.6
84
383.9
6.7
44
443.9
7. 7
04
503.9
8.8
64
563.9
9.8
25
325.0
5.7
85
384.9
6.7
45
444.9
7.8
05
504.9
8.8
65
564. 9
9.9
26
326.0
5.7
86
385. 9
6.7
46
445.9
7.8
06
505.9
8.9
66
565.9
9.9
27
327.0
5.7
87
386.9
6.8
47
446.9
7.8
07
506.9
8.9
67
566.9
9.9
28
328.0
5.7
88
387.9
6.8
48
447.9
7.8
08
507.9
8.9
68
567.9
9.9
29
329.0
5.7
89
388.9
6.8
49
448.9
7.8
09
508.9
8.9
69
568.9
9.9
30
330.0
5.8
90
389. 9
390. 9
6.8
50
449. 9
7.8
10
509.9
8.9
70
571
569. 9
9.9
10.6
331
331.0
5.8
391
6.8
451
450.9
7.9
511
510.9
9.0
570. 9
32
332. 0
5.8
92
391. 9
6.8
52
451.9
7.9
12
511.9
9.0
72
571.9
10.0
33
333.0
5.8
93
392. 9
6.9
53
452.9
7.9
13
512.9
9.0
73
572. 9
10.0
34
333.9
5.8
94
393.9
6.9
54
453.9
7.9
14
513.9
9.0
74
573.9
10.0
35
334. 9
5.8
95
394.9
6.9
55
454. 9
7.9
15
514.9
9.0
75
574.9
10.0
36
335.9
5.9
96
395.9
6.9
56
455. 9
8.0
16
515.9
9.0
76
575.9
10.0
37
336.9
5.9
97
396.9
6.9
57
456. 9
8.0
17
516.9
9.1
77
576. 9
10.1
38
337.9
5.9
98
397.9
6.9
58
457.9
8.0
18
517.9
9.1
78
577. 9
10.1
39
338.9
5.9
99
398.9
7.0
59
458.9
8.0
19
518.9
9.1
79
578.9
10.1
40
341
339. 9
340.9
5.9
6.0
400
401
399.9
400.9
7.0
60
459.9
8.0
20
519.9
520.9
9.1
80
579.9
10.1
7.0
461
460.9
8.0
521
9.1
581
580.9
10.1
42
341.9
6.0
02
401.9
7.0
62
461.9
8.1
22
521.9
9.1
82
581.9
10.1
43
342.9
6.0
03
402.9
7.0
63
462. 9
8.1
23
522. 9
9.2
83
582.9
10.2
44
343.9
6.0
04
403. 9
7. 1'
64
463. 9
8.1
24
523. 9
9.2'
84
583.9
10.2
45
344.9
6.0
05
404.9
7. 1
65
464.9
8.1
25
524. 9
9.2
85
584.9
10.2
46
345.9
6.0
06
405.9
■7. 1
66
465.9
8.1
26
525. 9
9.2
86
585.9
10.2
47
346.9
6.1
07
406.9
7. 1
67
466.9
8.1
27
526.9
9.2
87
586.9
10.2
48
347.9
6.1
08
407.9
7. 1
68
467.9
8.2
28
527.9
9.2
88
587.9
10.2
49
348.9
6.1
09
408.9
7. 1
69
468.9
8.2
29
528. 9
9.3
89
588. 9
10.3
50
351
349.9
6.1
10
409.9
7.2
70
471
469.9
470.9
8.2
8.2
30
531
529.9
9.3
90
589.9
590.9
10.3
350.9
6.1
411
410.9
7.2
530.9
9.3
591
10.3
52
351.9
6.1
12
411.9
7.2
72
471.9
8.2
32
531. 9
9.3
92
591. 9
10.3
53
352.9
6.2
13
412.9 1 7.2
73
472.9
8.2
33
532.9
9.3
93
592. 9
10.3
54
353.9
6.2
14
413.9 7.2
74
473.9
8.3
34
533.9
9.3
94
593.9
10.3
55
354. 9
6.2
15
414.9
7.2
75
474.9
8.3
35
534.9
9.4
95
594. 9
10.4
56
355.9
6.2
16
415. 9
7.3
76
475.9
8.3
36
535. 9
9.4
96
595.9
10.4
57
356. 9
6.2
17
416.9
7.3
77
476. 9
8.3
37
536.9
9.4
97
596. 9
10.4
58
357.9
6.2
18
417.9
7.3
78
477.9
8.3
38
537.9
9.4
98
597. 9
10.4
59
358.9
6.3
19
418.9
7.3
79
478.9
8.4
39
538.9
9.4
99
598.9
10.4
60
359.9
6.3
20
419.9
7.3
80
479.9
8.4
40
539.9
9.4
600
599.9
10.5
Bist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
39° (91°, 269°
, 271°)
22489—03-
-24
Page 370]
TABLE 2.
Difference of Latitude and Depart
ure for 2° (178°, 182
°, 358°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.0
61
61.0
2.1
121
120.9
4.2
181
180.9
6.3
241
240.9
8.4
2
2.0
0.1
62
62.0
2.2
22
121.9
4.3
82
181.9
6.4
42
241.9
8.4
3
3.0
0.1
63
63.0
2.2
23
122.9
4.3
83
182.9
6.4
43
242.9
8.5
4
4.0
0.1
64
64.0
2.2
24
123.9
4.3
84
183.9
6.4
44
243.9
8.5
5
5.0
0.2
65
65.0
2.3
25
124.9
4.4
85
184.9
6.5
45
244.9
8.6
6
6.0
0.2
66
66.0
2.3
26
125.9
4.4
86
185.9
6.5
46
245.9
8.6
7
7.0
0.2
«7
67.0
2.3
27
126.9
4.4
87
186.9
6.5
47
246.8
8.6
8
8.0
0.3
68
68.0
2.4
28
127.9
4.5
88
187.9
6.6
48
247.8
8.7
9
9.0
0.3
69
69.0
2.4
29
128.9
4.5
89
188.9
6.6
49
248.8
8.7
10
10.0
0.3
70
70.0
2.4
30
129.9
4.5
90
189.9
6.6
50
249.8
8.7
11
11.0
0.4
71
71.0
2.5
131
130.9
4.6
191
190.9
6.7
251
250.8
8.8
12
12.0
0.4
72
72.0
2.5
32
131.9
4.6
92
191.9
6.7
52
251.8
8.8
13
13.0
0.5
73
73.0
2.5
33
132.9
4.6
93
192.9
6.7
53
252.8
8.8
14
14.0
0.5
74
74.0
2.6
34
133.9
4.7
94
193.9
6.8
54
253.8
8.9
15
15.0
0.5
75
75.0
2.6
35
134.9
4.7
95
194.9
6.8
55
254.8
8.9
16
16.0
0.6
76
76.0
2.7
36
135.9
4.7
96
195.9
6.8
56
255.8
8.9
17
17.0
0.6
77
77.0
2.7
37
136.9
4.8
97
196.9
6.9
57
256.8
9.0
18
18.0
0.6
78
78.0
2.7
38
137.9
4.8
98
197.9
6.9
58
257.8
9.0
19
19.0
0.7
79
79.0
2.8
39
138.9
4.9
99
198.9
6.9
59
258.8
9.0
20
20.0
0.7
80
80.0
2.8
40
139.9
4.9
200
199.9
7.0
60
259.8
9.1
21
21.0
0.7
81
81.0
2.8
141
140.9
4.9
201
200.9
7.0
261
260.8
9.1
22
22.0
0.8
82
82.0
2.9
42
141.9
5.0
02
201.9
7.0
62
261.8
9.1
23
23.0
0.8
83
82.9
2.9
43
142.9
5.0
03
202.9
7.1
63
262.8
9.2
24
24.0
0.8
84
83.9
2.9
44
143.9
5.0
04
203.9
7.1
64
263.8
9.2
25
25.0
0.9
85
84.9
3.0
45
144.9
5.1
05
204.9
7.2
65
264.8
9.2
26
26.0
0.9
86
85.9
3.0
46
145. 9
5.1
06
205.9
7.2
66
265.8
9.3
27
27.0
0.9
87
86.9
3.0
47
146.9
5.1
07
206.9
7.2
67
266.8
9.3
28
28.0
1.0
88
87.9
3.1
48
147.9
5.2
08
207.9
7.3
68
267.8
9.4
29
29.0
1.0
89
88.9
3.1
49
148.9
5.2
09
208.9
7.3
69
268.8
9.4
30
31
30.0
31.0
1.0
90
89.9
90.9
3.1
50
149.9
5.2
10
211
209.9
7.3
70
269.8
9.4
1.1
91
3.2
151
150.9
5.3
210.9
7.4
271
270.8
9.5
32
32.0
1.1
92
91.9
3.2
52
151.9
5.3
12
211.9
7.4
72
271. 8
9.5
33
33.0
1.2
93
92.9
3.2
53
152.9
5.3
13
212.9
7.4
73
272.8
9.5
34
34.0
1.2
94
93.9
3.3
54
153.9
5.4
14
213.9
7.5
74
273.8
9.6
35
35.0
1.2
95
94.9
3.3
55
154.9
5.4
15
214.9
7.5
75
274.8
9.6
36
36.0
1.3
96
95.9
3.4
56
155.9
5.4
16
215.9
7.5
76
275.8
9.6
37
37.0
1.3
97
96.9
3.4
57
156.9
5.5
17
216.9
7.6
77
276.8
9.7
38
38.0
1.3
98
97.9
3.4
58
157.9
5.5
18
217.9
7.6
78
277.8
9.7
39
39.0
1.4
99
98.9
3.5
59
158.9
5.5
19
218.9
7.6
79
278.8
9.7
40
40.0
1.4
100
99.9
3.5
60
159.9
5.6
20
219.9
7.7
80
279.8
280.8
9.8
9.8
41
41.0
1.4
101
100.9
3.5
161
160.9
5.6
221
220.9
7.7
281
42
42.0
1.5
02
101.9
3.6
62
161.9
5.7
22
221.9
7.7
82
281.8
9.8
43
43.0
1.5
03
102.9
3.6
63
162.9
5.7
23
222.9
7.8
83
282.8
9.9
44
44.0
1.5
04
103.9
3.6
64
163. 9
5.7
24
223.9
7.8
84
283.8
9.9
45
45.0
1.6
05
104.9
3.7
65
164.9
5.8
25
224.9
7.9
85
284.8
9.9
46
46.0
1.6
06
105.9
3.7
66
165.9
5.8
26
225.9
7.9
86
285.8
10.0
47
47.0
1.6
07
106.9
3.7
67
166.9
5.8
27
226.9
7.9
87
286.8
10.0
48
48.0
1.7
08
107.9
3.8
68
167.9
5.9
28
227.9
8.0
88
287.8
10.1
49
49.0
1.7
09
108.9
3.8
69
168.9
5.9
29
228.9
8.0
89
288.8
10.1
50
50.0
1.7
10
109.9
3.8
70
169.9
5.9
30
229.9
8.0
90
289.8
10.1
10. 2
51
51.0
1.8
111
110.9
3.9
171
170.9
6.0
231
230.9
8.1
291
290.8
52
• 52.0
1.8
12
111.9
3.9
72
171.9
6.0
32
231.9
8.1
92 i 291.8
10.2
53
53.0
1.8
13
112.9
3.9
73
172.9
6.0
33
232.9
8.1
93
292.8
10.2
54
54.0
1.9
14
113.9
4.0
74
173.9
6.1
34
233.9
8.2
94
293.8
10.3
55
55.0
1.9
15
114.9
4.0
75
174.9
6.1
35
234.9
8.2
95
294.8
10.3
56
56.0
2.0
16
115.9
4.0
76
175.9
6.1
36
235.9
8.2
96
295.8
10.3
57
57.0
2.0
17
116.9
4.1
77
176.9
6.2
37
236.9
8.3
97
296.8
10.4
58
58.0
2.0
18
117.9
4.1
78
177.9
6.2
38
237.9
8.3
98
297.8
10.4
59
59.0
2.1
. 19
118.9
4.2
79
178.9
6.2
39
238. 9
8.3
99
298.8
10.4
60
60.0
2.1
20
119.9
4.2
80
179.9
6.3
40
239.9
8.4
300
299.8
10.5
Dist.
Dep.
Lat.
Dist.
Dep.
Jj&t.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
88° (9
2°, 268°
, 272°)
TABLE 2.
[Page 371 |
Difference of Latitude and Depart
are for 2° (178°, 182
', 358°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
300.8
10.5
361
360.8
12.6
421
420.8
14.7
481
480.7
16.8
541
540.7
18.9
02
301.8
10.5
62
361.8
12.6
22
421.8
14.7
82
481.7
16.8
42
541.7
18.9
03
302.8
10.6
63
362.8
12.7
23
422.8
14.7
83
482.7
16.8
43
542.7
18.9
04
303.8
10.6
64
363.8
12.7
24
423.8
14.8
84
483.7
16.9
44
543.7
19.0
05
304.8
10.6
65
364.8
12.7
25
424.8
14.8
85
484.7
16.9
45
544.7
19.0
06
305.8
10.7
66
365.8
12.8
26
425. 7
14.9
86
485.7
16.9
46
545.7
19.0
07
306.8
10.7
67
366.8
12.8
27
426.7
14.9
87
486.7
17.0
47
546.7
19.1
08
307.8
10.7
68
367. 8
12.8
28
427.7
14.9
88
487.7
17.0
48
547.7
19.1
09
308.8
10.8
69
368.8
12.9
29
428.7
15.0
89
488.7
17.0
49
548.7
19.1
10
309.8
10.8
70
369.8
370.8
12.9
12.9
30
429.7
15.0
90
489.7
17.1
50
549.7
19.2
311
310.8
10.8
371
431
430.7
15.0
491
490.7
17.1
551
550.7
19.2
12
311.8
10.9
72
371.8
13.0
32
431.7
15.1
92
491.7
17.1
52
551.7
19.2
13
312.8
10.9
73
372.8
13.0
33
432.7
15.1
93
492.7
17.2
53
552.7
19.3
14
313.8
10.9
74
373.8
13.0
34
433.7
15.1
94
493.7
17.2
54
553.7
19.3
15
314.8
11.0
75
374.8
13.1
35
434.7
15.2
95
494.7
17.2
55
554.7
19.3
16
315.8
11.0
76
375.8
13.1
36
435.7
15.2
96
495.7
17.3
56
555.7
19.4
17
316.8
11.0
77
376.8
13.1
37
436.7
15.2
97
496.7
17.3
57
556.7
19.4
18
317.8
11.1
78
377.8
13.2
38
437.7
15.3
98
497.7
17.3
58
557.7
19.4
19
318.8
11.1
79
378.8
13.2
39
438.7
15.3
99
498.7
17.4
59
558.7
19.5
20
319.8
11.2
80
379.8
13.2
13.3
40
441
439.7
15.3
500
499.7
17.4
60
559.7
19.5
19.5
321
320.8
11.2
381
380.8
440.7
15.4
501
500.7
17.5
561
560.7
22
321.8
11.2
82
381.8
13.3
42
441.7
15.4
02
501.7
17.5
62
561.7
19.6
23
322.8
11.3
83
382.8
1.3.3
43
442.7
15.4
03
502.7
17.5
63
562.7
19.6
24
323.8
11.3
84
383.8
13.4
44
443.7
15.5
04
503.7
17.6
64
563.7
19.6
25
324.8
11.3
85
384.8
13.4
45
444.7
15.5
05
504.7
17.6
65
564.7
19.7
26
325.8
11.4
86
385.8
13.5
46
445.7
15.6
06
505.7
17.6
66
565.7
19.7
27
326.8
11.4
87
386.8
13.5
47
446.7
15.6
07
506.7
17.7
67
566.7
19.7
28
327.8
n.4
88
387.8 1 13.5
48
447.7
15.6
08
507.7
17.7
68
567.7
19.8
29
328. 8
11.5
89
388.8 ! 13.6
49
448.7
15.7
09
508.7
17.7
69
568. 7
19.8
30
329.8
11.5
90
389.8
390.8
13.6
50
449.7
450.7
15.7
10
509.7
17.8
70
569.7
19.9
331
330.8
11.5
391
13.6
451
15.7
511
510.7
17.8
571
570.7
19.9
32
331.8
11.6
92
391. 8 1 13. 7
52
451.7
15.8
12
511.7
17.8
72
571.7
19.9
33
332.8
11.6
93
392.8 ' 13.7
53
452.7
15.8
13
512.7
17.9
73
572.7
20.0
34
333.8
11.6
94
393. 8 13. 7
54
453.7
15.8
14
513.7
17.9
74
573.6
20.0
35
334.8
11.7
95
394. 8 13. 8
55
454.7
15.9
15
514.7
17.9
75
574.6
20.0
36
.335. 8
11.7
96
395.8 j 13.8
56
455.7
15.9
16
515.7
18.0
76
575. 6
20.1
37
336.8
11.7
97
396.8 I 13.8
57
456.7
15.9
17
516.7
18.0
77
576.6
20.1
38
337.8
11.8
98
397.8 i 13.9
58
457.7
16.0
18
517.7
18.1
78
577.6
20.1
39
338.8
11.8
99
398.8 1 13.9
59
458. 7
16.0
19
518.7
18.1
79
578.6
20.2
40
339.8
11.9
400
399.8 ! 13.9
60
459.7
16.0
20 1 519.7
18.1
80
579.6
20.2
341
340.8
11.9
401
400.8 1 14.0
461
460.7
16.1
521 '■ 520. 7
18.2
581
580.6
20.2
42
341.8
11.9
02
401.8 i 14.0
62
461.7
16.1
22
521.7
18.2
82
581.6
20.3
43
342.8
12.0
03
402.8 1 14.0
63
462.7
16.1
23
522.7
18.2
83
582.6
20.3
44
343.8
12.0
04
403.8 ! 14.1
64
463. 7
16.2
24
523.7
18.3
84
583.6
20.3
45
344.8
12.0
05
404. 8 14. 1
65
464.7
16.2
25
524. 7
18.3
85
584.6
20.4
46
345.8
12.1
06
405.8
14.2
66
-165.7
16.2
26 j 525. 7
18.4
86
585.6
20.4
47
346.8
12.1
07
406.8
14.2
67
466.7
16.3
27 1 526.7
18.4
87
586.6
20.4
48
347. 8
12.1
08
407.8
14.2
68
467.7
16.3
28 527. 7
18.4
88
587.6
20.5
49
348.8
12.2
09
408.8
14.3
69
468.7
16.4
29 528. 7
18.5
89
588.6
20.5
50
349.8
12.2
10 409. 8
14.3
70
469.7
16.4
30 ! 529. 7
18.5
90
589.6
20.5
351
350.8
12.2
411
410.8
14.3
471
470.7
16.4
531
530.7
18.5
591
590.6
20.6
52
351.8
12.3
12
411.8
14.4
72
471. 7
16.5
32
531.7
18.6
92
591.6
20.6
53
352.8
12.3
13
412.8
14.4
73
472.7
16.5
33
532.7
18.6
93
592.6
20.6
54
353.8
12.3
14
413.8
14.4
74
473.7
16.5
34
533.7
18.6
94
593.6
20.7
55
354.8
12.4
15 414.8
14.5
•/5
474.7
16.6
35
534.7
18.7
95
594.6
20.7
56
355.8
12.4
16 415. 8
14.5
76
475. 7
16.6
36
535.7
18.7
96
595.6
20.7
57
356.8
12.4
17 416.8
14.5
77
476.7
16.6
37
536. 7
18.7
97
596.6
•20.8
58
357.8
12.5
18 417.8
14.6
78
477.7
16.7
38
537. 7
18.8
98
597. 6
20.8
59
358.8
12.5
19 418. 8
14.6
79
478.7
16.7
39
538. 7
18.8
99
598.6
20.8
60
359.8
12.5
20 1 419.8
1
14.6
80
479.7
16.7
40
539. 7
18.8
600
599.6
20.9
Dist.
Dep.
Lat.
Dist. 1 Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
88° {{
)2°, 268'
> 979° ^
) -' -
.
Page 372]
'1
ABLP
I '2.
Difference of Latitude and Departure for 3° (177°, 183
°, 357°
).
Dist.
Lat.
Dep.
Dist.
Lat.
' Dep.
Dist.
Lat.
Dep.
Dist. i Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.9
3.2
121
120.8
6.3
181
180.8
9.5
241
240.7
12.6
2
2.0
0.1
62
61.9
3.2
22
121.8
6.4
82
181.8
9.5
42
241.7
12.7
3
3.0
0.2
63
62.9
3.3
23
122.8
6.4
83
182.7
9.6
43
242.7
12.7
4
4.0
0.2
64
63.9
3.3
24
123.8
6.5
84
183.7
9.6
44
243.7
12.8
5
5.0
0.3
65
64.9
3.4
25
124.8
6.5
85
184.7
9.7
45
244.7
12.8
6
6.0
0.3
^
65.9
3.5
26.
125.8
6.6
86
185.7
9.7
46
245.7
12.9
7
7.0
0.4
66.9
3.5
27
126.8
6.6
87
186.7
9.8
47
246.7
12.9
8
8.0
0.4
68
67.9
3.6
28
127.8
6.7
88
187.7
9.8
48
247.7
13.0
9
9.0
0.5
69
68.9
3.6
29
128.8
6.8
89
188.7
9.9
49
248.7
13.0
10
10.0
0.5
70
69.9
3.7
30
129.8
6.8
90
189.7
9.9
50
249.7
13.1
11
11.0
0.6
71
70.9
3.7
131
130.8
6.9
191
190.7
10.0
251
250.7
13.1
12
12.0
0.6
72
71.9
3.8
32
131.8
6.9
92
191.7
10.0
52
251.7
13.2
13
13.0
0.7
73
72.9
3.8
33
132.8
7.0
93
192.7
10.1
53
252. 7
13.2
14
14.0
0.7
74
73.9
3.9
34
133.8
7.0
94
193.7
10.2
54
253.7
13.3
15
15.0
0.8
75
74.9
3.9
35
134.8
7.1
95
194.7
10.2
55
254.7
13.3
16
16.0
0.8
76
75.9
4.0
36
135.8
7.1
96
195.7
10.3
56
255. 6
13.4
17
17.0
0.9
77
76.9
4.0
37
136. 8
7.2
97
196.7
10.3
57
256.6
13.5
18
18.0
0.9
78
77.9
4.1
38
137.8
7.2
98
197.7
10.4
58
257.6
13.5
19
19.0
1.0
79
78.9
4.1
39
138.8
7.3
99 198.7
10.4
59
258.6
13.6
20
20.0
1.0
80
79.9
4.2
40
139.8
7.3
200 199.7
10.5
60
259.6
13.6
21
21.0
1.1
81
80.9
4.2
141
140.8
7.4
201
200.7
10.5
261
260.6
13.7
22
22.0
1.2
82
81.9
4.3
42
141.8
7.4
02
201.7
10.6
62
261.6
13.7
23
23.0
1.2
83
82.9
4.3
43
142.8
7.5
03
202.7
10.6
63
262.6
13.8
24
24.0
1.3
84
83.9
4.4
44
143.8
7.5
04
203.7
10.7
64
263.6
13.8
25
25.0
1.3
85
84.9
4.4
45
144.8
7.6
05
204.7
10.7
65
264.6
13.9
26
26.0
1.4
86
85.9
4.5
46
145.8
7.6
06
205. 7
10.8
66
265. 6
13.9
27
27.0
1.4
87
86.9
4.6
47
146.8
7.7
07
206.7
10.8
67
266.6
14.0
28
28.0
1.5
88
87.9
4.6
48
147.8
7.7
08
207.7
10.9
68
267.6
14.0
29
29.0
1.5
89
88.9
4.7
49
148.8
7.8
09
208.7
10.9
69
268.6
14.1
30
30.0
1.6
90
89.9
90.9
4.7
4.8
50
149.8
7.9
10
209.7
11.0
70
269.6
270.6
14.1
31
31.0
1.6
91
151
150.8
7.9
211
210.7
11.0
271
14.2
32
32.0
1.7
92
91.9
4.8
52
151.8
8.0
12
211.7
11.1
72
271.6
14.2
33
33.0
1.7
93
92.9
4.9
53
152.8
8.0
13
212.7
11.1
73
272.6
14.3
34
34.0
1.8
94
93.9
4.9
54
153.8
8.1
14
213.7
11.2
74
273.6
14.3
35
35.0
1.8
95
94.9
5.0
55
154.8
8.1
15
214.7
11.3
75
274.6
14.4
36
36.0
1.9
96
95.9
5.0
56
155.8
8.2
16
215.7
11.3
76
275.6
14.4
37
36.9
1.9
97
96.9
5.1
57
156.8
8.2
17
216.7
11.4
77
276.6
14.5
38
37.9
2.0
98
97.9
5.1
58
157.8
8.3
18
217.7
11.4
78
277.6
14.5
39
38.9
2.0
99
98.9
5.2
59
158. 8
8.3
19
218.7
11.5
79
278.6
14.6
40
39.9
2.1
100
99.9
100.9
5.2
60
159.8
8.4
20
219.7
11.5
11.6
80
281
279.6
280. 6
14.7
41
40.9
2.1
101
5.3
161
160.8
8.4
221
220.7
14.7
42
41.9
2.2
02
101.9
5.3
62
161.8
8.5
22
221.7
11.6
82
281.6
14.8
43
42.9
2.3
03
102.9
5.4
63
162.8
8.5
23
222.7
11.7
83
282.6
14.8
44
43.9
2.3
04
103.9
5.4
64
163.8
8.6
24
223.7
11.7
84
283.6
14.9
45
44.9
2.4
05
104.9
5.5
65
164.8
8.6
25
224.7
11.8
85
284.6
14.9
46
45.9
2.4
06
105.9
5.5
66
165.8
8.7
26
225.7
11.8
86
285. 6
15.0
47
46.9
2.5
07
106.9
5.6
67
166.8
8.7
27
226.7
11.9
87
286.6
15.0
48
47.9
2.5
08
107.9
5.7
68
167.8
8.8
28
227.7
11.9
88
287.6
15.1
49
48.9
2.6
09
108.9
5.7
69
168.8
8.8
29
228.7
12.0
89
288.6
15.1
50
49.9
2.6
10
109.8
5.8
70
169.8
170.8
8.9
30
229.7
230.7
12.0
90
291
289.6
290.6
15.2
51
50.9
2.7
111
110.8
5.8
171
8.9
231
12.1
15.2
52
51.9
2.7
12
111.8
5.9
72
171.8
9.0
32
231.7
12.1
92
291.6
15.3
53
52.9
2.8
13
112.8
5.9
73
172.8
9.1
33
232.7
12.2
93
292.6
15.3
54
53.9
2.8
14
113.8
6.0
74
173.8
9.1
34
233. 7
12.2
94
293.6
15.4
55
54.9
2.9
15
114.8
6.0
75
174.8
9.2
35
234.7
12.3
95
294.6
15.4
56
55.9
2.9
16
115.8
6-i
76
175.8
9.2
36
235. 7
12.4
96
295. 6
15.5
57
• 56.9
3.0
17
116.8
6.i
77
176. 8
9.3
37
236.7
12.4
97
296.6
15.5
58
57.9
3.0
18
117.8
6.2
78
177.8
9.3
38
237.7
12.5
98
297.6
15.6
59
58.9
3.1
19
118.8
6.2
79
178.8
9.4
39
238.7
12.5
99
298.6
15.6
60
59.9
3.1
20
119.8
6.3
80
179.8
9.4
40
239.7
12.6
300
299.6
15.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
87° {i
)3°, 267'
', 273°]
.
TABLE 2.
[Page 373 |
Difference of Latitude and Departure for 3° (177°, 183°, 357°
).
Dist.
Lat.
Dep.
Dist.
Lat.
360. 5
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
301
300.6
15.7
361
18.9
421
420.4
22.0
481
480.3 ! 25.2
541
540.2
28.3
02
301.6
15.8
62
361.5
19.0
22
421.4
22.1
82
481.3
25.2
42
541.2
28.4
03
302.6
15.9
63
362.5
19.0
23
422. 4,
22.2
83
482.3
25.3
43
542.2
28.4
04
303.5
15.9
64
363.5
19.1
24
423.4
22.2
84
483.3
25.3
44
543.2
28.5
05
304.5
16.0
65
364.5
19.1
25
424.4
22.3
85
484.3 ; 25.4
45
544.2
28.5
06
305.5
16.0
66
365. 5
19.2
26
425.4
22.3
86
485.3 25.4
46
545.2
28.6
07
306.5
16.1
67
366.5
19.2
27
426.4
22.4
87
486. 3 25. 5
47
546.2
28.6
08
307.5
16.1
68
367.5
19.3
28
427.4
22.4
88
487. 3 25. 5
48
547.2
28.7
09
308.5
16.2
69
368.5
19.3
29 ' 428.4
22.5
89
488. 3 25. 6
49
548.2
28.7
10
311
309.5
310. 5
16.2
16.3
70
369.5
19.4
19.4
30 429. 4
431 430. 4
22.5
90
489.3
490.3
25.6
50
549. 2
28.8
371
370.5
22.6
491
25.7
551
550.2
28.8
12
311.5
16.3
72
371.5
19.5
32 431. 4
22.6
92
491.3 1 25.7
52
551.2
28.9
13
312.5
16.4
73
372.5
19.5
33 432.4
22. 7
93
492.3 1 25.8
53
552.2
28.9
14
313. 5
16.4
74
373.5
19.6
34
433. 4
22.7
94
493.3
25.9
54
553. 2
29.0
15
314.5
16.5
75
374.5
19.6
35
434.4
22.8
95
494.3
25.9
55
554.2
29.1
16
315.5
16.6
76
375.5
19.7
36
435.4
22.8
96
495.3
26.0
56
555.2
29.1
17
316.5
16.6
77
376.5
19.8
37
436.4
22.9
97
496.3 ' 26.0
57
556.2
29.2
18
317.5
16.7
78
377.4
19.8
38
437.4
22.9
98
497. 3 i 26. 1
58
557.2
29.2
19
318.5
16.7
79
378.4
19.9
39
438.4
23.0
99
498.3 26.1
59
558.2
29.3
20
319.5
16.8
16.8
80
379. 4
380.4
19.9
40
439.4
23.0
500
501
499.3 1 26.2
500.3 26.2
60
561
559.2
560.2
29.3
29.4
321
320.5
381
20.0
441
440.4
23.1
22
321.5
16.9
82
381.4
20.0
42
441.4
23.1
02
501.3 26.3
62
561.2
29.4
23
322.5
16.9
83
382.4
20.1
43
442.4
23.2
03
502.3 26.3
63
562.2
29.5
24
323.5
17.0
84
383.4
20.1
44
443.4
23. 3
04
503.3 26.4
64
563.2
29.5
25
324.5
17.0
85
384. 4
20.2
45
444.4
23.3
05
504.3 26.4
65
564.2
29.6
26
325.5
17.1
86
385.4
20.2
46
445. 4
23.4
06
505.3 1 26.5
66
565.2
29.6
27
326.5
17.1
87
386.4
20.3
47
446.4
23.4
07
506.3 26.5
67
566.2
29.7
28
327.5
17.2
88
387.4
20.3
48
447.4
23.5
08
507.3 ' 26.6
68
567.2
29.7
29
328.5
17.2
89
388.4
20.4
49
448.4
23.5
09
508.3 26.6
69
568.2
29.8
30
329.5
17.3
90
389.4
20.4
50
449.3
450.3
23.6
10
509.3 26.7
70
569.2
29.8
29.9"
331
330.5
17.3
391
390. 4
20.5
451
23.6
511 j 510. 3 i 26. 7
571
570.2
32
331.5
17.4
92
391.4
20.5
52
451.3
23. 7
12 1 511.3 ' 26.8
72
571.2
29.9
33
332.5
17.5
93
392.4
20.6
53
452.3
23.7
13
512.3
26.8
73
572.2
30.0
34
333. 5
17.5
94
393.4
20.6
54
453. 3
23.8
14
513.3
26.9
74
573.2
30.0
35
334.5
17.6
95
394.4
20.7
55
454.3
23.8
15
514.3
27.0
75
574.2
30.1
36.
335.5
17.6
96
395.4
20.7
56
455. 3
23.9
16
515.3
27.0
76
575.2
30.1
37
336. 5
17.7
97
396.4
20.8
57
456.3
23.9
17
516.3
27.1
77
576.2
30.2
38
337. 5
17.7
98
397.4
20.8
58
457. 3
24.0
18
517.3
27.1
78
577.2
30.2
39
338.5
17.8
99
398.4
20.9
59
458.3
24.0
19
518.3
27.2
79
578.2
30.3
40
339.5
17.8
400
399. 4
400.4
20.9
21.0
60
459. 3
24.1
20
521
519.3
520.3
27.2
80
579.2
30.3
341
340. 5
17.9
401
461
460. 3
24.1
27.3
581
580.2
30.4
42
341.5
17.9
02
401.4
21.1
62
461.3
24.2
22 1 521. 3
27.3
82
581.2
30.4
43
342.5
18.0
03
402.4
21.1
63
462. 3
24.2
23 522.3
27.4
83
582.2
30.5
44
343.5
18.0
04
403.4
21.2
64
463. 3
24.3
24 i 523.3
27.4
84
583.2
30.5
45
344.5
18.1
05
404.4
21.2
65
564. 3
24.4
25 i 524.3
27.5
85
584.2
30.6
46
345.5
18.1
06
405.4
21.3
66
465. 3
24.4
26 1 525.3
27.5
86
585. 2
30.6
47
346.5
18.2
07
406.4
21.3
67
466. 3
24.5
27
526.3
27.6
87
586.2
30.7
48
347.5
18.2
08
407.4
21.4
68
467.3
24.5
28
527.3
27.6
88
587.2
30.7
49
348.5
18.3
09
408.4
21.4
69
468.3
24.6
29
528.3
27.7
89
588.2
30.8
50
349.5
'350.5
18.3
18. 4
10
409.4
21.5
21.5
70
469.3
24.6
24.7
30
531
529.3
530.3
27.7
27.8
90
591
589.2
590.2
30.9
351
411
410.4
471
470.3
30.9
52
351.5
18.4
12
411.4
21.6
72
471.3
24.7
32
531.3
27.8
92
591.2
31.0
53
352.5
18.5
13
412.4
21.6
73
472.3
24.8
33
532.3
27.9
93
592.2
31.0
54
353.5
18.5
14
413.4
21.7
74
473. 3
24.8
34
533.3
27.9
94
593.2
31.1
55
354.5
18.6
15
414.4
21.7
75
474.3
24.9
35
534.3
28.0
95
594.2
31.1
56
355.5
18.6
16
415.4
21.8
76
475. 3
24.9
36
535. 3
28.1
96
595.2
31.2
57
356.5
18.7
17
416.4
21.8
77
476. 3
25.0
37
536.3
28.1
97
596.2
31.2
58
357.5
18.8
18
417.4
21.9
78
477.3
25.0
38
537.3
28.2
98
597.2
31.3
59
358. 5
18.8
19
418.4
21.9
79
478. 3
25.1
39
538.3
28.2
99
598.2
31.3
60
359.5
18.9
20
419.4
22.0
80
479.3
25.1
40
,539.3
28.3
600
599.2
31.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
87° (93°, 267=
, 273°)
Page 374J
r
rABLE 2.
Difference of Latitude and
Depart!
cirefor4° (176°, 184
°, 356°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.9
4.3
121
120.7
8.4
181
180.6
12.6
241
240.4
16.8
2
2.0
0.1
62
61.8
4.3
22
121.7
8.5
82
181.6
12.7
42
241.4
16.9
3
3.0
0.2
63
62.8
4.4
23
122.7
8.6
83
182.6
12.8
43
242.4
17.0
4
4.0
0.3
64
63.8
4.5
24
123.7
8.6
84
183.6
12.8
44
243.4
17.0
5
5.0
0.3
65
64.8
4.5
25
124.7
8.7
85
184.5
12.9
45
244.4
17.1
6
6.0
0.4
^
65.8
4.6
26
125.7
8.8
86
185.5
13.0
46
245.4
17.2
7
7.0
0.5
66.8
4.7
27
126.7
8.9
87
186.5
13.0
47
246.4
17.2
8
8.0
0.6
68
67.8
4.7
28
127.7
8.9
88
187.5
13.1
48
247.4
17.3
9
9.0
0.6
69
68.8
4.8
29
128.7
9.0
89 i 188.5
13.2
49
248.4
17.4
10
10.0
0.7
70
69.8
70.8
4.9
30
129.7
9.1
90
189.5
190. 5"
13.3
13.3
50
249.4
17.4
11
11.0
0.8
71
5.0
131
130.7
9.1
191
251
2.50. 4
17.5
12
12.0
0.8
72
71.8
5.0
32
131.7
9.2
92
191.5
13.4
52
251.4
17.6
13
13.0
0.9
73
72.8
5.1
33
132.7
9.3
93
192.5
13.5
53
252.4
17.6
14
14.0
1.0
74
73.8
5.2
34
133.7
9.3
94
193.5
13.5
54
253.4
17.7
15
15.0
1.0
75
74.8
5.2
35
134.7
9.4
95
194.5
13.6
55
254. 4
17.8
16
16.0
1.1
76
75.8
5.3
36
135.7
9.5
96
195.5
13.7
56
255.4
17.9
17
17.0
1.2
77
76.8
5.4
37
136.7
9.6
97
196.5
13.7
57
256. 4
17.9
18
18.0
1.3
78
77.8
5.4
38
137.7
9.6
98
197.5
13.8
58
257.4
18.0
19
19.0
1.3
79
78.8
5.5
39
138.7
9.7
99
198. 5
13.9
59
258.4
18.1
20
20.0
1.4
80
79.8
5.6
40
139. 7
9.8
200
199.5
200.5
14.0
60
259. 4
18.1
18.2
21
20.9
1.5
81
80.8
5.7
141
140.7
9.8
201
14.0
261
260.4
22
21.9
1.5
82
81.8
5.7
42
141.7
9.9
02
201.5
14.1
62
261.4
18.3
23
22.9
1.6
83
82.8
5.8
43
142.7
10.0
03
202. 5
14.2
63
262.4
18.3
24
23.9
1.7
84
83.8
5.9
44
143.6
10.0
04
203.5
14.2
64
263.4
18.4
25
24.9
1.7
85
84.8
5.9
45
144.6
10.1
05
204.5
14.3
65
264.4
18.5
26
25.9
1.8
86
85.8
6.0
46
145.6
10.2
06
205.5
14.4
66
265. 4
18.6
27
26.9
1.9
87
86.8
6.1
47
146.6
10.3
07 i 206.5
14.4
67
266.3
18.6
28
27.9
2.0
88
87.8
6.1
48
147.6
10.3
08
207.5
14.5
68
267.3
18.7
29
28.9
2.0
89
88.8
6.2
49
148.6
10..4
09
208.5
14.6
69
268.3
18.8
30
31
29.9
2.1
90
89.8
6.3
6.3
50
151
149.6
10.5
10
209.5
14.6
70
271
269.3
270.3
18.8
18.9
30.9
2.2
91
90.8
150.6
10.5
211
210.5
14.7
82
31.9
2.2
92
91.8
6.4
52
151.6
10.6
12
211.5
14.8
72
271.3
19.0
33
32.9
2.3
93
92.8
6.5
53
1.52. 6
10.7
13
212.5
14.9
73
272.3
19.0
34
33.9
2.4
94
93.8
6.6
54
153. 6
10.7
14
213. 5
14.9
74
273.3
19.1
35
34.9
2.4
95
94.8
6.6
55
154.6
10.8
15
214.5
15.0
75
274.3
19.2
36
35.9
2.5
96
95.8
6.7
56
155.6
10.9
16
215. 5
15.1
76
275.3
19.3
37
36.9
2.6
97
96.8
6.8
57
156.6
11.0
17
216.5
15.1
77
276.3
19.3
38
37.9
2.7
98
97.8
6.8
58
157. 6
11.0
18
217. 5
15.2
78
277.3
19.4
39
38.9
2.7
99
98.8
6.9
59
158.6
11.1
19
218.5
15.3
79
278.3
19.5
40
39.9
2.8
100
99.8
7.0
60
159.6
160.6
11.2
20
219.5
15. 3
lb. 4:
80
281
279.3
19.5
41
40.9
2.9
101
100.8
7.0
161
11.2
221
220.5
280.3
19.6
42
41.9
2.9
02
101.8
7.1
62
161.6
11.3
22
221.5
1.5.5
82
281.3
19.7
43
42.9
3.0
03
102.7
7.2
63
162.6
11.4
23
222.5
15.6
83
282.3
19.7
44
43.9
3.1
04
103.7
7.3
64
163.6
11.4
24
223. 5
15.6
84
283.3
19.8
45
44.9
3.1
05
104.7
7.3
65
164.6
11.5
25
224.5
1.5.7
85
284. 3
19.9
46
45.9
3.2
06
105.7
7.4
66
165.6
11.6
26
225.4
15.8
86
285. 3
20.0
47
46.9
3.3
07
106.7
7.5
67
166.6
11.6
27
226.4
15.8
87
286.3
20.0
48
47.9
3.3
08
107.7
7.5
68
167. 6
11.7
28
227.4
15.9
88
287.3
20.1
49
48.9
3.4
09
108.7
7.6
69
168.6
11.8
29
228.4
16.0
89
288.3
20.2
50
49.9
3.5
10
109.7
7.7
7.7
70
171
169.6
11.9
30
229.4
230.4
16.0
90
291
289. 3
20.2
51
50.9
3.6
111
110.7
170.6
11.9
231
16.1
290.3
20.3
52
51.9
3.6
12
111.7
7.8
72
171.6
12.0
32
231.4
16.2
92
291. 3
20.4
53
52.9
3.7
13
112.7
7.9
73
172.6
12.1
33
232.4
16.3
93
292.3
20.4
54
53.9
3.8
14
113.7
8.0
74
173.6
12.1
34
233.4
16.3
94-
293.3
20.5
55
54.9
3.8
15
114.7
8.0
75
174.6
12.2
35
234.4
16.4
95
294.3
20.6
56
55.9
3.9
16
115.7
8.1
76
175.6
12.3
36
235. 4
16.5
96
295. 3
20.6
57
56.9
4.0
17
116.7
8.2
77
176.6
12.3
37
236.4
16.5
97
296.3
20.7
58
57.9
4.0
18
117.7
8.2
78
177.6
12.4
38
237.4
16.6
98
297.3
20.8
59
58.9
4.1
19
118.7
8.3
79
178.6
12.5
39
238.4
16.7
99
298.3
20.9
60
59.9
4.2
20
119.7
8.4
80
179.6
12.6
40
239.4
16.7
300
299.3
20.9
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
86°; (
M°, 266
°, 274°).
tablp: 2.
[Page 375
Difference of Latitude and Departure for 4° (176°, 184
°, 356°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
300.3
21.0
361
360.1
25.2
421
420.0
29.4
481
479.8
33.5
541
539.7
37.7
02
301.3
21.1
62
361.1
25.2
22
421.0
29.4
82
480.8
33.6
42
540.7
37.8
03
302.2
21.1
63
362.1
25.3
23
422.0
29.5
83
481.8
33.7
43
541.7
37.9
04
.303. 2
21.2
64
363.1
25.4
24
423.0
29.6
84
482.8
33.7
44
542.7
37.9
05
304.2
21.3
65
364.1
25.5
25
424.0
29.6
85
483.8
33.8
45
543. 7
38. 0
06
305. 2
21.3
66
365.1
25.5
26
424.9
29.7
86
484.8
33.9
46
544. 7
38.1
07
306.2
21.4
67
366.1
25.6
27
425. 9
29.8
87
485.8
33. 9
47
545.7
.38.1
08
307.2
21.5
68
367.1
25.7
28
426.9
29.9
88
486.8
34.0
48
546.7
38.2
09
308.2
21.6
69
368.1
25.7
29
427.9
29.9
89
487.8
34.1
49
547.7
38.3
10
309.2
310. 2
21.6
70
369. 1
370.1
25.8
30
428.9
30.0
90
488.8
489.8
34.2
34.2
50
551
548.7
549.7
38.3
311
21.7
371
25.9
431
429.9
30.1
491
38.4
12
311.2
21.8
72
371.1
25.9
32
430.9
30.1
92
490.8
34.3
52
550.7
38.5
13
312.2
21.8
73
372.1
26.0
33
431.9
30.2
93
491.8
34.4
53
551.7
38.5
14
313.2
21.9
74
373.1
26.1
34
432.9
30.3
94
492.8
34.4
54
552.7
38.6
15
314.2
22.0
75
374.1
26.2
35
433.9
30.3
95
493.8
34.5
55
553.6
.38.7
16
315.2
22.1
76
375.1
26.2
36
434.9
.30.4
96
494.8
34.6
56
554.6
38.7
17
316.2
22.1
77
376.1
26.3
37
435.9
30.5
97
495. 8
34.6
57
555.6
38.8
18
317.2
22.2
78
377.1
26.4
38
436.9
30.6
98
496.8
34.7
58
556.6
38.9
19
318.2
22.3
79
378.1
26.4
39
437.9
30.6
99
497.8
34.8
59
557.6
38.9
20
319.2
320. 2
22.3
80
379. 1
380.1
26.5
40
438.9
439. 9
30.7
30.8
500
501
498.8
499.8
34.8
60
558.6
559. 6
39.0
321
22.4
381
26.6
441
34.9
561
39.1
22
321.2
22.5
82
381.1
26.6
42
440.9
30.8
02
500.8
35.0
62
560.6
39.2
23
322.2
22.5
83
382.1
26.7
43
441.9
30.9
03
501. 8
35. 0
63
561.6
39.2
24
323. 2
22.6
84
383.1
26.8
44
442.9
31.0
04
502.8
35.1
64
562.6
39.3
25
324.2
22.7
85
384. 0
26.9
45
443.9
31.0
05
503.8
35.2
65
563.6
39.4
26
325. 2
22.7
86
385.0
26.9
46
444.9
31.1
06
504.8
35.2
66
564.6
39.4
27
326.2
22.8
87
386. 0
27.0
47
445.9
31.2
07
505.8
35.3
67
565.6
39.5
28
327.2
22.9
88
387.0
27.1
48
446.9
31.2
08
506.8
35.4
68
566.6
39.6
29
328. 2
23.0
89
388.0
27.1
49
447.9
31.3
09
507.8
35.5
69
567.6
39.7
30
331
329.2
23.0
90
389.0
27.2
27.3
50
451
448.9
31.4
31.5
10
511
508.8
35.6
35.6
70
568.6
39.8
330.2
23.1
391
390. 0
449.9
509.8
571
569.6
39.8
32
331.2
23.2
92
391.0
27.3
52
450.9
31.5
12
510.8
35.7
72
570.6
39.9
33
332.2
23.2
93
392.0
27.4
53
451.9
31.6
13
511.8
35.8
73
571.6
40.0
34
333. 2
23.3
94
393.0
27.5
54
452.9
31.7
14
512.7
35.8
74
572.6
40.0
35
334.2
23.4
95
394.0
27.6
55
453.9
31.7
15
513.7
35.9
75
573.6
40.1
36
• 335. 2
23.4
96
395.0
27.6
56
454.9
31.8
16
514.7
36.0
76
574.6
40.2
37
336.2
23. 5
97
396.0
27.7
57
455.9
31.9
17
515.7
36.0
II
575.6
40.2
38
337.2
23.6
98
397.0
27.8
58
456.9
31.9
18
516.7
36.1
78
576.6
40.3
39
338.2
2.3.6
99
398.0
27.8
59
457.9
32.0
19
517.7
36.2
79
577.6
40.4
40
339.2
23.7
400
399.0
27.9
60
458.9
32.1
20
518.7
36.2
36.3
80
578.6
40.5
341
;wo.2
23.8
401
400.0
28.0
461
459. 9
32.2
521
519.7
581
579.6
40.5
42
341.2
23.9
02
401.0
28.0
62
460.9
32.2
22
520.7
36.4
82
580.6
40.6
43
342.2
23.9
03
402.0
28.1
63
461.9
32.3
23
521.7
36.4
83
581.6
40.7
44
343. 1
24.0
04
403.0
28.2
64
462.9
32.4
24
522. 7
36.5
84
582.6
40.7
45
.344. 1
24.1
05
404.0
28.2
65
463.9
32.4
25
523.7
36.6
85
583.6
40.8
46
345. 1
24.1
06
405.0
28.3
66
464.9
.32.5
26
524. 7
36.7
86
584.6
40.9
47
346. 1
24.2
07
406.0
28.4
67
465. 8
32.6
27
525.7
36.8
87
585.6
40.9
48
347.1
24.3
08
407.0
28.5
68
466.8
32.6
28
526.7
36.8
88
586.6
41.0
49
.348. 1
24.3
09
408.0
28.5
69
467.8
32.7
29
527.7
36.9
89
587.6
41.1
50
349.1
24.4
24.5
10
409.0
28.6
70
468.8
32.8
30
531
528.7
529.7
37.0
37.0
90
591
588.6
41.2
41.3
.351
350. 1
411
410.0
28.7
471
469.8
32.9
589.6
52
351.1
24.6
12
411.0
28.7
72
470.8
32.9
32
530.7
.37.1
92
590.6
41.3
53
352. 1
24.6
13
412.0
28.8
73
471.8
33.0
33
531.7
37.2
93
591.6
41.4
54
353.1
24.7
14
413.0
28.9
74
472.8
33. 1
34
532.7
37.2
94
592.6
41.5
55
354. 1
24.8
15
414.0
28.9
75
473.8
33.1
35
533. 7
37.3
95
593.6
41.5
56
355. 1
24.8
16
415. 0
29.0
76
474.8
33.2
36
534.7
.37.4
96
594.6
41.6
57
356. 1
24.9
17
416.0
29.1
77 1 475. 8
33.3
37
535.7
37.5
97
595.6
41.7
58
357.1
25.0
18
417.0
29.2
78
476.8
33.3
38
536. 7
37.5
98
596.6
41.7
59
358. 1
25.0
19
418.0
29.2
79
477.8
33.4
39
537.7
37.6
99
597. 6
41.8
60
359.1
25.1
20
419.0
29.3
80
478.8
35.5
40
538.7
37.7
600
698.6
41.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
i
36°; (94°, 266°, 274°).
1 Page 376
1
TABLE 2.
Difference of Latitude and Departure for 5° (1
75°, 185
°, 355°
).
DLst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.8
5.3
121
120.5
10.5
181
180. 3
15.8
241
240.1
21.0
2
2.0
0.2
62
61.8
5.4
22
121.5
10.6
82
181.3
15.9
42
241.1
21.1
3
3.0
0.3
63
62.8
5.5
23
122.5
10.7
83
182.3
15.9
43
242.1
21.2
4
4.0
0.3
64
63.8
5.6
24
123.5
10.8
84
183.3
16.0
44
243.1
21.3
5
5.0
0.4
65
64.8
5.7
25
124.5
10.9
85
184.3
16.1
45
244.1
21.4
6
6.0
0.5
f
65.7
5.8
26
125.5
11.0
86
185. 3
16.2
46
245.1
21.4
7
7.0
0.6
66.7
5.8
27
126.5
11.1
87
186.3
16.3
47
246.1
21.5
8
8.0
0.7
68
67.7
5.9
28
127. 5
11.2
88
187.3
16.4
48
247.1
21.6
9
9.0
0.8
69
68.7
6.0
29
128.5
11.2
89
188.3
16.5
49
248.1
21.7
10
10.0
0.9
70
69.7
6.1
30
129.5
11.3
90
189.3
16.6
50
249.0
21.8
11
11.0
1.0
71
70.7
6.2
131
130.5
11.4
191
190.3
16.6
251
250.0
21.9
12
12.0
1.0
72
71.7
6.3
32
131.5
11.5
92
191.3
16.7
52
251.0
22.0
13
13.0
1.1
73
72.7
6.4
33
132.5
11.6
93
192.3
16.8
53
252.0
22.1
14
13. 9
1.2
74
73.7
6.4
34
133.5
11.7
94
193. 3
16.9
54
253.0
22.1
15
14.9
1.3
75
74.7
6.5
35
134.5
11.8
95
194. 3
17.0
55
254.0
22.2
16
15.9
1.4
76
75.7
6.6
36
135.5
11.9
96
195. 3
17.1
56
255.0
22.3
17
16.9
1.5
77
76.7
6.7
37
136.5
11.9
97
196.3
17.2
57
256.0
22.4
18
17.9
1.6
78
77.7
6.8
38
137.5
12.0
98
197.2
17.3
58
257.0
22.5
19
18.9
1.7
79
78.7
6.9
39
138.5
12.1
99
198.2
17.3
59
258.0
22.6
20
19.9
1.7
1.8
80
79.7
7.0
40
139.5
140.5
12.2
12.3
200
201
199.2
17.4
60
259.0
22.7
21
20.9
81
80.7
7.1
141
200.2
17.5
261
260.0
22.7
22
21.9
1.9
82
81.7
7.1
42
141.5
12.4
02
201.2
17.6
62
261.0
22.8
23
22.9
2.0
83
82.7
7.2
43
142.5
12.5
03
202.2
17.7
63
262.0
22.9
24
23.9
2.1
84
83.7
7.3
44
143.5
12.6
04
203.2
17.8
64
263. 0
23.0
25
24.9
2.2
85
84.7
7.4
45
144.4
12.6
05
204.2
17.9
65
264.0
23.1
26
25.9
2.3
86
85.7
7.5
46
145.4
12.7
06
205. 2
18.0
66
265.0
23.2
27
26.9
2.4
87
86.7
7.6
47
146.4
12.8
07
206.2
18.0
67
266.0
23.3
28
27.9
2.4
88
87.7
7.7
48
147.4
12.9
08
207.2
18.1
68
267.0
23.4
29
28.9
2.5
89
88.7
7.8
49
148.4
13.0
09
208.2
18.2
69
268.0
23.4
30
29.9
2.6
90
89.7
7.8
50
149.4
150. 4
13.1
10
209.2
18.3
70
269.0
23.5
31
30.9
2.7
91
90.7
7.9
151
13.2
211
210.2
18.4
271
270.0
23.6
32
31.9
2.8
92
91.6
8.0
52
151. 4
13.2
12
211.2
18.5
72
271.0
23.7
33
32.9
2.9
93
92.6
8.1
53
152.4
13.3
13
212.2
18.6
73
272.0
23.8
34
33.9
3.0
94
93.6
8.2
54
153.4
13.4
14
213.2
18.7
74
273.0
23.9
35
34.9
3.1
95
94.6
8.3
55
154.4
13.5
15
214.2
18.7
75
274.0
24.0
36
35.9
3.1
96
95.6
8.4
56
155.4
13.6
16
215.2
18.8
76
274.9
24.1
37
36.9
3.2
97
96.6
8.5
57
156.4
13.7
17
216.2
18.9
77
275.9
24.1
38
37.9
3.3
98
97.6
8.5
58
157.4
13.8
18
217.2
19.0
78
276.9
24.2
39
38.9
3.4
99
98.6
8.6
59
158. 4
13.9
19
218.2
19.1
79
277.9
24.3
40
39.8
3.5
100
99.6
8.7
60
159.4
13.9
20
221
219.2
19.2
80
278.9
24.4
41
40.8
3.6
101
100.6
8.8
161
160.4
14.0
220.2
19.3
281
279.9
24.5
42
41.8
3.7
02
101.6
8.9
62
161.4
14.1
22*
221.2
19.3
82
280.9
24.6
43
42.8
3.7
03
102.6
9.0
63
162.4
14.2
23
222.2
19.4
83
281.9
24.7
44
43.8
3.8
04
103.6
9.1
64
163.4
14.3
24
223.1
19.5
84
282.9
24.8
45
44.8
3.9
05
104.6
9.2
65
164. 4
14.4
25
224.1
19.6
85
283.9
24.8
46
45.8
4.0
06
105.6
9.2
66
165.4
14.5
26
225.1
19.7
86
284.9
24.9
47
46.8
4.1
07
106.6
9.3
67
166.4
14.6
27
226.1
19.8
87
285.9
25.0
48
47.8
4.2
08
107.6
9.4
68
167.4
14.6
28
227.1
19.9
88
286.9
25.1
49
48.8
4.3
09
108.6
9.5
69
168.4
14.7
29
228.1
20.0
89
287.9
25.2
50
49.8
4.4
10
109.6
9.6
70
169.4
14.8
30
229.1
230. 1
20.0
90
288.9
25.3
51
50.8
4.4
111
110.6
9.7
171
170.3
14.9
231
20.1
291
289.9
25.4
52
51.8
4.5
12
111.6
9.8
72
171. 3
15.0
32
231.1
20.2
92
290.9
25.4
53
52.8
4.6
13
112.6
9.8
73
172. 3
15.1
33
232. 1
20.3
93
291.9
25.5
54
53.8
4.7
14
113.6
9.9
74
173.3
15.2
34
233.1
20.4
94
292.9
25.6
55
54.8
4.8
15
114.6
10.0
75
174.3
15.3
35
234. 1
20.5
95
293.9
25.7
56
55.8
4.9
16
115.6
10.1
76
175.3
15.3
36
235. 1
20.6
96
294.9
25.8
57
56.8
5.0
17
116.6
10.2
77
176.3
15.4
37
236.1
20.7
97
295.9
25.9
58
57.8
5.1
18
117.6
10.3
78
177.3
15.5
38
237. 1
20.7
98
296.9
26.0
59
58.8
5.1
19
118.5
10.4
79
178.3
15.6
39
238. 1
20.8
99
297.9
26.1
60
59.8
5.2
20
119.5
10.5
80
179.3
15.7
40
239.1
20.9
300
298.9
26.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
85° (S
5°, 265°, 275°).
TABLE 2.
[Page 377
Difference of Latitude and Departure for
5° (175°, 185
°, 355°
)•
Dist.
Lat.
Dep.
Dist. 1 Lat. Dep.
Dist.
Lat. 1 Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
299.9
26.2
361 359.6 31.5
421
419. 4 ' 36. 7
481
479.2
41.9
541
538.9
47.2
02
300.8
26.3
62 360.6 31.6
22
420. 4 36. 8
82
480.2
42.0
42
539. 9
47.3
03
301.8
26.4
63 361.6 i 31.6
23
421.4 36.9
83
481.2
42.1
43
540.9
47.4
04
302.8
26.5
64 i 362. 6 ! 31. 7
24
422.4 37.0
84
482.2
42.2
44
541.9
47.5
05
303.8
26.6
65 363.6 1 31.8
25
423. 4 1 37. 1
85
483.2
42.3
45
542.9
47.6
06
304.8
26.7
66 364.6
31.9
26
424. 4 37. 1
86
484.1
42.4
46
543.9
47.7
07
305.8
26.8
67 365.6
32.0
27
425. 4 37. 2
87
485.1
42.4
47
544.9
47.7
08
306.8
26.9
68 366.6
32.1
28
426.4 i 37.3
88
486. 1
42.5
48
545. 9
47.8
09
307.8
26.9
69 367. 6
32.2
29
427.4 ' 37.4
89
487.1
42.6
49
546.9
47.9
10
308.8
309.8
27.0
70
368.6 1 32.3
369.6 i 32.3
30
428.4 37.5
90
488.1
"489.1
42.7
42,8
50
551
547.9
48.0
311
27.1
371
431
429.4 37.6
491
548.9 48.1
12
310.8
27.2
72 370.6
32.4
32
430.4 37.7
92
490.1
42.9
52
549. 9 48. 2
13
311.8
27.3
73 371.6
32.5
33
431. 3 1 37. 7
93
491.1
43.0
53
550. 9 48. 3
14
312.8
27.4
74 1 372.6
32.6
34
432.3
37.8
94
492.1
43.1
54
551.9 48.4
15
313.8
27.5
75
373.6 i 32.7
35
433. 3
37.9
95
493.1
43.1
55
552.9 , 48.4
16
314.8
27.5
76
374.6
32.8
36
434.3
38.0
96
494.1
43.2
56
553. 9 ! 48. 5
17
315.8
27.6
77
375.6
32.9
37
435.3
38.1
97
495.1
43.3
57
554.9 : 48.6
18
316.8
27.7
78
376.6
33.0
38
436.3
38.2
98
496.1
43.4
58
555. 9 48. 7
19
317.8
27.8
79
377.6
33. 0
39
437.3
38.3
99
497.1
43.5
59
556.9 48.8
20
318.8
27.9
80
378.6 i 33.1
40
438.3
38.4
500
498.1
499.1
43.6
60
557.9 48.8
321
"319. 8
28.0
381
379.5 I 33.2
441
439.3 1 38.4
501
43.7
561
558.8 ; 48.9
22
320.8
28.1
82
380.5
33.3
42
440.3 ; 38.5
02 : 500. 1
43.8
62
559.8 49.0
23
321. 8
28.2
83
381. 5
33.4
43
441.3 ! 38.6
03
501.1
43. 8
63
560. 8 i 49. 1
24
322. 8
28.2
84
382.5
33.5
44
442. 3 I 38. 7
04
502.1
43.9
64
561. 8 1 49. 2
25
323.8
28.3
85
383.5
33.6
45
443.3 1 38.8
05
503.1
44.0
65
562. 8 j 49. 3
26
324.8
28.4
86
384.5
33.7
46
444.3 38.9
06
504. 1
44.1
66
563.8 , 49.4
27
325.8
28.5
87
385.5
33.7
47
445.3 { 39.0
07
505.1
44.2
67
564. 8 i 49. 5
28
326. 7
28.6
88
386.5
33.8
48
446. 3 39. 1
08
506.1
44.3
68
565.8 1 49.6
29
327. 7
28.7
89
387.5
33. 9
49
447. 3 : 39. 1
09
507.1
44.4
69
566. 8 1 49. 7
30
328.7
28.8
90
388. 5
34.0
50
448.3 1 39.2
10
508.1
44.5
70
567. 8 [ 49. 7
331
329. 7
28.9
391
389.5
34.1
451
449.3 i 39.3
511
509.0
44.5
571
568.8 1 49.8
32
330.7
28.9
92
390.5
34.2
52
450.3 39.4
12
510.0
44.6
72
569.8 1 49.9
33
331. 7
29.0
93
391.5
34.3
53
451.3 [ 39.5
13
511.0
44.7
73
570. 8 i 50. 0
34
332.7
29.1
94
392.5
34.3
54
452. 3 39. 6
14
512.0
44.8
74
571.8
50.1
35
333. 7
29.2
95
393.5
34.4
55
453. 3 39. 7
15
513.0
44.9
75
572.8
50.2
36
.334.7
29.3
96
394.5
34.5
56
454. 3 39. 8
16
514.0
45.0
76
573.8
50.3
37
335.7
29.4-
97
395. 5
34.6
57
455. 3 39. 8
17
515.0
45.1
77
574.8
50.4
38
336.7
29.5
98
396.5
34.7
58
456.3 ; 39.9
18
516.0
45.2
78
575.8
50.4
39
337.7
29.6
99
397.5
34.8
59
457.3 i 40.0
19
517.0
45.2
79
576.8 i 50.5
40
341
338.7
339.7
29.6
400
398.5
34.9
60
458.2
40.1
40.2
20
521
518.0
519.0
45.3
80
577.8 1 50.6
578.8 1 50.7
29.7
401
399.5
35.0
461
459.2
45.4
581
42
340.7
29.8
02
400.5
35.0
62
460.2 1 40.3
22
520.0
45.5
82
579.8 ! 50.8
43
341.7
29.9
03
401.5
35.1
63
46i.2
40.4
23
521.0
45.6
83
580.8
50.9
44
342.7
30.0
04
402.5
35.2
64
462.2
40.4
24
522.0
45.7
84
581.8
50.9
45
343.7
30.1
05
403.5
35.3
65
463.2
40.5
25
523.0
45.8
85
582.8
51.0
46
344.7
30.2
06
404.5
35.4
66
464.2
40.6
26
524.0
45.9
86
583. 8
51.1
47
345. 7
30.3
07
405.4
35.5
67
465.2
40.7
27
525. 0
45.9
87
584.8
51.2
48
346.7
30.3
08
406.4
35.6
68
466. 2
40.8
28
526.0
46.0
88
585.8
51.3
49
347.7
30.4
09
407.4
35.7
69
467.2
40.9
29
527.0
46.1
89
586.8
51.4
50
348.7
30.5
10
408.4
35.7
70
468.2
469.2
41.0
30
528.0
529. 0
46.2
90
587.8
51.5
351
349.7
30.6
411
409.4 j 35.8
471
41.1
531
46.3
591
588.7
51.6
52
350.7
30.7
12
410.4 1 35.9
72 470. 2
41.1
32
530. 0
46.4
92
589.7
51.6
53
351. 7
30.8
13
411.4 ' 36.0
73 471. 2
41.2
33
531.0
46.5
93
590.7
51.7
54
352.6
30.9
14
412.4 i 36.1
74 472. 2
41.3
34
532. 0
46.6
94
591.7
51.8
55
353.6
30.9
15
413.4 36.2
75
473.2
41.4
35
533. 0
46.6
95
592.7
51.9
56
354.6
31.0
16
414.4 36.3
76
474.2
41.5
36
533.9
46.7
96
593.7
52.0
57
355.6
31.1
17
415.4 1 36.4
77
475.2
41.6
37
534. 9
46.8
97
594.7
52.1
58
356.6
31.2
18
416.4 [ 36.4
78
476.2
41.7
38
535. 9
46.9
98
595. 7
52.2
59
357.6
31.3
19
417.4 [ 36.5
79
477.2
41.8
39
536.9
47.0
99
596.7
52.3
60
358.6
31.4
20
418.4 36.6
1
80
478.2
41.8
40
537.9
47.1
600
597.7
52.3
Dist.
Dep.
Lat.
Dist.
Dep. 1 Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
85° (95°, 265°, 275°)
1
Page 378]
TABLE 2.
Difference of Latitude and Departure for 6° (174°, 186
°, 354°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
25.2
1
1.0
0.1
61
60.7
6.4
121
120.3
12.6
181
180.0
18.9
241
239.7
2
2.0
0.2
62
61.7
6.5
22
121.3
12.8
82
181.0
19.0
42
240.7
25.3
3
3.0
0.3
63
62.7
6.6
23
122.3
12.9
83
182.0
19.1
43
241.7
25.4
4
4.0
0.4
64
63.6
6.7
24
123.3
13.0
84
183.0
19.2
44
242.7
25.5
5
5.0
0.5
65
64.6
6.8
25
124.3
13.1
85
184.0
19.3
45
243.7
25.6
6
6.0
0.6
1?
65.6
6.9
26
125. 3
13.2
86
185. 0
19.4
46
244.7
25.7
7
7.0
0.7
66.6
7.0
27
126.3
13.3
87
186.0
19.5
47
245. 6
25.8
8
8.0
0.8
68
67.6
7.1
28
127.3
13.4
88
187.0
19.7
48
246.6
25.9
9
9.0
0.9
69
68.6
7.2
29
128.3
13.5
89
188.0
19.8
49
247.6
26.0
10
9.9
1.0
70
69.6
7.3
30
131
129.3
130.3
13.6
90
189.0
190.0
19.9
50
251
248.6
249.6
26.1
11
10.9
1.1
71
70.6
7.4
13.7
191
20.0
26.2
12
11.9
1.3
72
71.6
7.5
32
131.3
13.8
92
190.9
20.1
52
250. 6
26.3
13
12.9
1.4
73
72.6
7.6
33
132.3
13.9
93 i 191.9
20.2
53
251.6
26.4
14
13.9
1.5
74
73.6
7.7
34
133.3
14.0
94
192.9
20.3
54
252.6
26.6
15
14.9
1.6
75
74.6
7.8
35
134.3
14.1
95
193.9
20.4
55
253.6
26.7
16
15.9
1.7
76
75.6
7.9
36
135.3
14.2
96
194.9
20.5
56
254.6
26.8
17
16.9
1.8
77
76.6
8.0
37
136.2
14.3
97
195. 9
20.6
57
255.6
26.9
18
17.9
1.9
78
77.6
8.2
38
137.2
14.4
98
196.9
20.7
58
256. 6
27.0
19
18.9
2.0
79
78.6
8.3
39
138.2
14.5
99
197.9
20.8
59
257.6
27.1
20
19.9
2.1
80
79.6
8.4
40
139. 2
14.6
200
201
198.9
20.9
60
258. 6
259.6
27.2
21
20.9
2.2
81
80.6
8.5
141
140.2
14.7
199.9
21.0
261
27.3
22
21.9
2.3
82
81.6
8.6
42
141.2
14.8
02
200.9
21.1
62
260.6
27.4
23
22.9
2.4
83
82.5
8.7
43
142.2
14.9
03
201.9
21.2
63
261.6
27.5
24
23.9
2.5
84
83.5
8.8
44
143.2
15.1
04
202.9
21.3
64
262.6
27.6
25
24.9
2.6
85
84.5
8.9
45
144.2
15.2
05
203.9
21.4
65
263.5
27.7
26
25.9
2.7
86
85.5
9.0
46
145.2
15.3
06
204.9
21.5
66
264.5
27.8
27
26.9
2.8
87
86.5
9.1
47
146.2
15.4
07
205. 9
21.6
67
265. 5
27.9
28
27.8
2.9
88
87.5
9.2
48
147.2
15.5
08
206.9
21.7
68
266.5
28.0
29
28.8
3.0
89
88.5
9.3
49
148.2
15.6
09
207.9
21.8
69
267.5
28.1
30
29.8
3.1
3.2
90
89.5
9.4
50
151
149.2
15.7
10
208.8
22.0
70
268.5
269.5
28.2
31
30.8
91
90.5
9.5
150.2
15.8
211
209.8
22.1
271
28.3
32
31.8
3.3
92
91.5
9.6
52
151.2
15.9
12
210.8
22.2
72
270. 5
28.4
33
32.8
3.4
93
92.5
9.7
53
152. 2
16.0
13
211.8
22.3
73
271.5
28.5
34
33.8
3.6
94
93.5
9.8
54
153.2
16.1
14
212.8
22.4
74
272.5
28.6
35
34.8
3.7
95
94.5
9.9
55
154.2
16.2
15
213.8
22.5
75
273.5
28.7
36
35.8
3.8
96
95.5
10.0
56
155.1
16.3
16
214.8
22.6
76
274.5
28.8
37
36.8
3.9
97
96.5
10.1
57
156.1
16.4
17
215.8
22.7
•77
275.5
29.0
38
37.8
4.0
98
97.5
10.2
58
157.1
16.5
18
216.8
22.8
78
276.5
29.1
39
38.8
4.1
99
98.5
10.3
59
158.1
16.6
19
217.8
22.9
79
277.5
29.2
40
41
39.8
4.2
100
99.5
10.5
60
159.1
160. 1
16.7
20
218.8
219.8
23.0
23.1
80
281
278.5
279.5
29.3
29.4
40.8
4.3
101
100.4
10.6
161
16.8
221
42
41.8
4.4
02
101.4
10.7
62
161.1
16.9
22
220.8
23.2
82
280.5
29.5
43
42.8
4.5
03
102.4
10.8
63
162.1
17.0
23
221.8
23.3
83
281.4
29.6
44
43.8
4.6
04
103.4
10.9
64
163.1
17.1
24
222.8
23.4
84
282.4
29.7
45
44.8
4.7
05
104.4
11.0
65
164.1
17.2
25
223.8
23.5
85
283. 4
29.8
46
45.7
4.8
06
105.4
11.1
66
165.1
17.4
26
224.8
23.6
86
284.4
29.9
47
46.7
4.9
07
106.4
11.2
67
166.1
17.5
27
225.8
23.7
87
285.4
30.0
48
47.7
5.0
08
107.4
11.3
68
167.1
17.6
28
226.8
23.8
88
286.4
30.1
49
48.7
5.1
09
108.4
11.4
69
168.1
17.7
29
227.7
2.3.9
89
287.4
30.2
50
49.7
5.2
10
109.4
11.5
70
169.1
17.8
30
228.7
24.0
24.1
90
291
288.4
30.3
51
50.7
5.3
111
110.4
11.6
171
170.1
17.9
231
229.7
289.4
30.4
52
51.7
5.4
12
111.4
11.7
72
171.1
18.0
32
230.7
24.3
92
290.4
30.5
53
52.7
5.5
13
112.4
11.8
73
172.1
18.1
33
231. 7
24.4
93
291.4
30.6
54
53.7
5.6
14
113.4
11.9
74
173.0
18.2
34
232.7
24.5
94
292.4
30.7
55
54.7
5.7
15
114.4
12.0
75
174.0
18.3
35
233. 7
24.6
95
293. 4
30.8
56
55.7
5.9
16
115.4
12.1
76
175.0
18.4
36
234. 7
24.7
96
294.4
30.9
57
56.7
6.0
17
116.4
12.2
77
176.0
18.5
37
2.35. 7
24.8
97
295.4
31.0
58
57.7
6.1
18
117.4
12.3
78
177.0
18.6
38
236. 7
24.9
98
296.4
31.1
59
58.7
6.2
19
118.3
12.4
79
178.0
18.7
39
237. 7
25.0
99
297.4
31.3
60
59.7
6.3
20
119.3
12.5
80
179.0
18.8
40
238.7
25.1
300
298.4
31.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
84° (£
►6°, 264=
, 276°)
TABLE 2.
[Page 379 |
Difference of Latitude and Departure fpr
6° (174°, 186°
, 354°)
Dlst.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
299.3
31.5
361
359.0
37.7
421
418.7
44.0
481
478.4
50.3
541
538.0
56. 5
02
300.3
31.6
62
360.0
37.8
22
419.7
44.1
82
479.4
50.4
42
539. 0
56.6
03
301.3
31.7
63
361.0
37.9
23
420.7
44.2
83
480. 4
50.5
43
540.0
56.7
04
302.3
31.8
64
362.0
38.0
24
421.7
44.3
84
481.3
50.6
44
541.0
56.8
05
303.3
31.9
65
363. 0
38.1
25
422.7
44.4
85
482.3
50.7
45
542. 0
56.9
06
304.3
32.0
66
364. 0
38.3
26
423.7
44.5
86
483. 3
50.8
46
543.0
57.0
07
305.3
32.1
67
365. 0
38.4
27
424.7
44.6
87
484.3
50.9
47
544.0
57.1
08
306.3
32.2
68
366.0
38.5
28
425. 7
44.7
88
485. 3
51.0
48
545.0
57.2
09
307.3
32.3
69
367.0
38.6
29
426.6
44.8
89
486. 3
51.1
49
546.0
57.3
10
308.3
32.4
70
368.0
369.0
38.7
38.8
30
431
427.6
428.6
44.9
45.0
90
491
487.3
51.2
50
551
547.0
548.0
57.4
57. 5
311
309.3
32.5
371
488. 3
51.3
12
310. 3
32.6
72
370. 0
38.9
32
429.6
45.2
92
489.3
51.4
52
549.0
57.6
13
311.3
32.7
73
371.0
39.0
33
430.6
45.3
93
490. 3
51.5
53
550. 0
57.7
14
312.3
32.8
74
371.9
39.1
34
431.6
45.4
94 ! 491.3
51.6
54
551.0
57.9
15
313.3
32.9
75
372.9
39.2
35
432.6
45. 5
95 i 492.3
51.7
55
552.0
58.0
16
314. 3
33.0
76
373.9
39.3
36
433.6
45.6
96
493.3
51.8
56
553. 0
58.1
17
315.3
33.1
77
374.9
39.4
37
434.6
45.7
97
494.3
51.9
57
554.0
58.2
18
316.3
33.2
78
375.9
39.5
38
435. 6
45.8
98
495.3
52.0
58
555. 0
58.3
19
317.3
33.3
79
376.9
39.6
39
436. 6
45.9
99
496.3
52.1
59
556. 0
58.4
20
318.2
33.4
80
377.9
39.7
40
437.6
46.0
46.1
500
497.3
52.3
60
556.9
58.5
58.6
321
319.2
33.6
381
378.9
39.8
441
438.6
501 1 498.3
52.4
561
557.9
22
320.2
33.7
82
379. 9
39.9
42
439.6
46.2
02
499.3
52.5
62
558.9
58.7
23
321.2
33.8
83
380.9
40.0
43
440.6
46.3
03
500.2
52.6
63
559.9
58.8
24
322.2
33.9
84
381. 9
40.1
44
441.6
46.4
04
501.2
52.7
64
560.9
59.0
25
323.2
34.0
85
382.9
40.2
45
442.6
46.5
05
502.2
52.8
65
561.9
59.1
26
324.2
34.1
86
383.9
40.3
46
443.6
46.6
06
503.2
52.9
66
562.9
59.2
27
325.2
34.2
87
384. 9
40.5
47
444.5
46.7
07
504.2
53.0
67
563.9
59.3
28
326.2
34.3
88
385.9
40.6
48
445. 5
46.8
08
505. 2
53.1
68
564.9
59.4
29
327.2
34.4
89
386.9
40.7
49
446.5
46.9
09
506.2
53.2
69
565.9
59.5
30
328.2
34.5
90
391
387.9
40.8
50
447.5
47.0
10
507.2
53.3
70
571
566.9
59.6
331
329.2
34.6
388.9
40.9
451
448.5
47.1
511
508.2
53.4
567.9
59.7
32
330.2
34.7
92
389. 9
41.0
52
449.5
47.2
12
509.2
53.5
72
568.9
59.8
33
331.2
34.8
93
390. 8
41.1
53
450.5
47.3
13
510.2
53.6
73
569.9
59.9
34
332.2
34.9
94
391.8
41.2
54
451. 5
47.5
14
511.2
53.7
74
570.9
60.0
35
333.2
35.0
95
392. 8
41.3
55
452.5
47.6
15
512.2
53.8
75
571.9
60.1
36
334.2
35.1
96
393.8
41.4
56
453. 5
47.7
16
513.2
53.9
76
572.9
60.2
37
335.2
35.2
97
394.8
41.5
57
454.6
47.8
17
514.2
54.0
77
573.9
60.3
38
336.1
35.3
98
395.8
41.6
58
455.5
47.9
18
515.2
54.1
78
574.9
60.4
39
•337. 1
35.4
99
396.8
41.7
59
456.5
48.0
19
516.2
54.2
79
575.8
60.5
40
338.1
339.1
35. 5
35.6
400
401
397.8
398.8
41.8
41.9
60
457.5
48.1
20
517.2
518.1
54.3
80
576.8
60.6
341
461
458. 5
48.2
521
54.5
581
577.8
60.7
42
340.1
35.7
02
399.8
42.0
62
459. 5
48.3
22
519.1
54.6
82
578.8
60.8
43
341.1
35.8
03
400.8
42.1
63
460*5
48.4
23
520.1
54.7
83
579.8
60.9
44
342.1
36.0
04
401.8
42.2
64
461. 5
48. 5
24
521.1
54.8
84
580.8
61.1
45
343.1
36.1
05
402.8
42.3
65
462.5
48.6
25
522.1
54.9
85
581.8
61.2
46
344.1
36.2
06
403. 8
42.4
66
463.4
48.7
26
523. 1
55.0
86
582.8
61.3
47
345.1
36.3
07
404.8
42.5
67
464.4
48.8
27
524.1
55.1
87
583.8
61.4
48
346.1
36.4
08
405.8
42.6
68
465. 4
48.9
28
525.1
55.2
88
584.8
61.5
49
347.1
36.5
09
406.8
42.7
69
466.4
49.0
29
526.1
55.3
89
585.8
61.6
50
351
348.1
349.1
36.6
36.7
10
407.8
42.9
43. 0
70
467.4
49.1
30
531
527.1
55.4
90
586.8
61.7
411
408.7
471
468.4
49.2
528.1
55.5
591
587.8
61.8
52
350.1
36.8
12
409.7
43.1
72
469.4
49.3
32
529.1
55.6
92
588.8
61.9
53
351.1
36.9
13
410.7
43.2
73
470.4
49.4
33
530. 1
55.7
93
589.8
62.0
54
352.1
37.0
14
411.7
43.3
74
471.4
49.5
34
531.1
55.8
94
590. 8
62.1
55
353.1
37.1
15
412.7
43.4
75
472.4
49.6
35
532.1
55. 9
95
591.8
62.2
56
354.0
37.2
16
413.7
43.5
76
473.4
49.8
36
533. 1
56.0
96
592.8
62.3
57
355.0
37.3
17
414.7
43.6
77
474.4
49.9
37
534. 1
56.1
97
593. 8
62.4
58
356. 0
37.4
18
. 415. 7
43.7
78
475.4
50.0
38
535. 1
56.2
98
594.7
62.5
59
357.0
37.5
19
416.7
43.8
79
476.4
50.1
39
536.1
56.3
99
595.7
62.6
60
358.0
37.6
20
417.7
43.9
80
477.4
50.2
40
537. 1
56.4
600
596.7
62.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dlst.
Dep.
Lat.
84° (
96°, 264
°, 276°
).
Page 380]
TABLE 2.
Difference of Latitude and Departure for 7° (17
•3°, 187°
, 353°)
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.5
7.4
121
120.1
14.7
181
179. 7
22.1
241
239.2
29.4
2
2.0 1
0.2
62
61.5
7.6
22
121.1
14.9
82
180.6
22.2
42
240.2
29.5
3
3.0
0.4
63
62.5
7. 7
23
122.1
15.0
83
181.6
22.3
43
241.2
29.6
4
4.0
0.5
ft4
63.5
7.8
24
123.1
15.1
84
182.6
22.4
44
242.2
29.7
5
5.0
0.6
65
64.5
7.9
25
124.1
15.2
85
183.6
22.5
45
243. 2
29.9
6
6.0
0.7
66
65.5
8.0
26
125.1
15.4
86
184.6
22.7
46
244.2
30.0
7
6.9
0.9
*7
66.5
8.2
27
126.1
15.5
87
185.6
22.8
47
245. 2
30.1
8
7.9
1.0
68
67.5
8.3
28
127.0
15.6
88
186.6
22.9
48
246.2
30.2
9
8.9
1.1
69
68.5
8.4
29
128.0
15.7
89
187.6
23.0
49
247.1
30.3
10
9.9
10.9
1.2
70
69.5
8.5
8.7
30
129.0
15.8
90
188.6
23.2
23.3
50
248.1
30.5
30.6
11
1.3
71
70.5
131
130.0
16.0
191
189.6
251
249.1
12
11.9
1.5
72
71.5
8.8
32
131. 0
16.1
92
190.6
23.4
52
250.1
30.7
13
12.9
1.6
73
72.5
8.9
33
132.0
16.2
93
191.6
23.5
53
251.1
30.8
14
13.9
1.7
74
73.4
9.0
34
133. 0
16.3
94
192.6
23.6
54
252.1
31.0
15
14.9
1.8
75
74.4
9.1
35
134. 0
16.5
95
193.5
23.8
55
253.1
31.1
16
15.9
1.9
76
75.4
9.3
36
135.0
16.6
96
194.5
23.9
56
254.1
31.2
17
16.9
2.1
77
76.4
9.4
37
136.0
16.7
97
195.5
24.0
57
255. 1
31.3
18
17.9
2.2
78
77.4
9.5
38
137.0
16.8
98
196.5
24.1
58
256.1
31.4
19
18.9
2.3
79
78.4
9.6
39
138.0
16.9
99
197.5
24.3
59
257.1
31.6
20
21
19.9
20.8
2.4
2.6
80
79.4
9.7
40
139.0
17.1
200
201
198.5
24.4
60
258.1
259.1
31.7
81
80.4
9.9
141
139.9
17.2
199. 5
24.5
261
31.8
22
21.8
2.7
82
81.4
10.0
42
140.9
17.3
02
200.5
24.6
62
260.0
31.9
23
22.8
2.8
83
82.4
10.1
43
141.9
17.4
03
201.5
24.7
63
261.0
32.1
24
23.8
2.9
84
83.4
10.2
44
142.9
17.5
04
202.5
24.9
64
262.0
32.2
25
24.8
3.0
85
84.4
10.4
45
143.9
17.7
05
203.5
25.0
65
263.0
32.3
26
25.8
3.2
86
85.4
10.5
46
144.9
17.8
06
204.5
25.1
66
264.0
32.4
27
26.8
3.3
87
86.4
10.6
47
145.9
17.9
07
205.5
25.2
67
265.0
32.5
28
27.8
3.4
88
87.3
10.7
48
146.9
18.0
08
206.4
25.3
68
266.0
32.7
29
28.8
3.5
89
88.3
10.8
49
147.9
18.2
09
207.4
25.5
69
267.0
32.8
30
29.8
3.7
3.8
90
89.3
11.0
50
148.9
18.3
10
208.4
25.6
70
268.0
32.9
31
30.8
91
90.3
11.1
151
149.9
18.4
211
209.4
25.7
271
269.0
33.0
32
31.8
3.9
92
91.3
11.2
52
150.9
18.5
12
210.4
25.8
72
270.0
33.1
33
32.8
4.0
93
92.3
11.3
53
151.9
18.6
13
211.4
26.0
73
271.0
33.3
34
33.7
4.1
94
93.3
11.5
54
152.9
18.8
14
212.4
26.1
74
272.0
3.3.4
35
34.7
4.3
95
94.3
11.6
55
153.8
18.9
15
213.4
26.2
75
273.0
33.5
36
35.7
4.4
96
95.3
11.7
56
154.8
19.0
16
214.4
26.3
76
273.9
33.6
37
36.7
4.5
97
96.3
11.8
57
155.8
19.1
17
215.4
26.4
77
274.9
33.8
38
37.7
4.6
98
97.3
11.9
58
156.8
19.3
18
216.4
26.6
78
275.9
33.9
39
38.7
4.8
99
98.3
12.1
59
157.8
19.4
19
217.4
26.7
79
276.9
34.0
40
41
39.7
4.9
100
99.3
12.2
60
158.8
19.5
20
218.4
26.8
80
277.9
34.1
40.7
5.0
101
100.2
12.3
161
159.8
19.6
221
219.4
26.9
281
278.9
34.2
42
41.7
5.1
02
101.2
12.4
62
160.8
19.7
22
220. 3
27.1
82
279.9
34.4
43
42.7
5.2
03
102.2
12.6
63
161.8
19.9
23
221.3
27.2
83
280.9
34.5
44
43.7
5.4
04
103.2
12.7
64
162.8
20.0
24
222.3
27.3
84
281.9
34.6
45
44.7
5.5
05
104.2
12.8
65
163.8
20.1
25
223.3
27.4
85
282.9
34.7
46
45.7
5.6
06
105.2
12.9
66
164.8
20.2
26
224 3
27.5
86
283.9
34.9
47
46.6
5.7
07
106.2
13.0
67
165. 8
20.4
27
225.3
27.7
87
284.9
35.0
48
47.6
5.8
08
107.2
13.2
68
166.7
20.5
28
226.3
27.8
88
285. 9
35.1
49
48.6
6.0
09
108.2
13.3
69
167.7
20.6
29
227.3
27.9
89
286.8
35.2
50
49.6
6.1
10
109.2
13.4
70
168.7
20.7
30
228.3
28.0
90
287.8
35.3
51
50.6
6.2
111
110.2
13.5
171
169.7
20.8
231
229.3
28.2
291
288.8
35.5
52
51.6
6.3
12
111.2
13.6
72
170.7
21.0
32
230. 3
28.3
92
289.8
35.6
53
52.6
6.5
13
112.2
13.8
73
171.7
21.1
33
231.3
28.4
93
290.8
35.7
54
53.6
6.6
14
113.2
13.9
74
172.7
21.2
34
232. 3
28.5
94
291.8
35.8
55
54.6
6.7
15
114.1
14.0
75
173. 7
21.3
35
233.2
28.6
95
292.8
36.0
56
55.6
6.8
16
115. 1
14.1
76
174.7
21.4
36
234. 2
28.8
96
293.8
36.1
57
56.6
6.9
17
116.1
14.3
77
175. 7
21.6
37
235. 2
28.9
97
294.8
36.2
58
57.6
7.1
18
117.1
14.4
78
176.7
21.7
38
236.2
29.0
98
295.8
36.3
59
58.6
7.2
19
IS.l
14.5
79
177.7
21.8
39
237. 2
29.1
99
296.8
36.4
60
59.6
7.3
20
ip..l
14. 6 80
178.7
21.9
40
238.2
29.2
300
297.8
36.6
Dist.
Dep.
Lat. JDist.
1 ^ep.
Lat. Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
/
83° (
97°, 263°, 277°
).
TABLE
2.
[Page
381
Difference of
Latitude and Departure for
7° (173°, 187
°, 353°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
801
298.7
36.7
361
858. 3
44.0
421
417.9
51.3
481
477.4
58.6
541
537. 0
65.9
02
299.7
36.8
62
859. 3
44.1
22
418.8
51.4
82
478.4
58.7
42
537.9
• 66.0
08
300.7
36.9
63
360. 8
44.2
28
419.8
51.5
83
479.4
58.8
48
588.9
66.2
04
301.7
37.0
64
861.3
44.4
24
420.8
51.7
84
480.4
59.0
44
589. 9
66.3
05
302.7
87.2
65
862.8
44.5
25
421.8
51. 8
85
481.4
59.1
45
540.9
66.4
06
303.7
37.3
66
363. 3
44.6
26
422.8
51.9
86
482.4
59.2
46
541. 9
66.6
07
304.7
37.4
67
364. 3
44.7
27
428. 8
52.0
87
488.4
59.4
47
542. 9
66.7
08
305. 7
37.5
68
365.2
44.8
28
424.8
52.2
88
484.3
59. 5
48
543.9
66.8
09
306.7
37.7
69
366.2
45.0
29
425.8
52.3
89
485.3
59.6
49
544.9
66.9
10
811
307.7
308.7
37.8
70
367.2
45.1
45.2
80
426.8
52.4
90
486.3
487.8
59.7
59.8
50
545. 9
67.0
37.9
371
368.2
431
427.8
52.5
491
551
546. 9
67.1
12
309.7
88.0
72
369.2
45.3
82
428.8
52.6
92
488.3
59.9
52
547.9
67.2
18
810.7
38.1
73
370. 2
45.5
33
429.8
52.8
93
489.3
60.1
53
548. 9
67.4
14
311.7
38.8
74
371.2
45.6
34
430.8
52.9
94
490.3
60.2
54
549.9
67.5
15
312.6
88.4
75
372.2
45.7
35
431.7
58.0
95
491.3
60.3
55
550. 8
67.6
16
313.6
88.5
76
373.2
45.8
36
432.7
58.1
96
492.3
60.5
56
551. 8
67.8
17
314.6
88.6
77
374.2
45.9
37
433.7
53.3
97
493.3
60.6
57
552.8
67.9
18
315.6
88.7
78
375.2
46.1
38
434.7
58.4
98
494.3
60.7
58
558.8
68.0
19
316.6
38.9
79
876.2
46.2
39 ! 435. 7
58.5
99
495.3
60.8
59
554.8
68.1
20
821
317.6
39.0
39.1
80
877.2
46.8
40
486.7
437.7
5.3.6
58.7
500
501
496.8
497.2
61.0
61.1
60
555. 8
68.3
318.6
881
878.1
46.4
441
561
556. 8
68.4
22
319.6
89.2
82
879.1
46.5
42 ! 438. 7
58.9
02
498.2
61.2
62
557. 8
68.5
28
320.6
89.4
83
880.1
46.7
43
439.7
54.0
08
499.2
61.3
63
558. 8
68.6
24
321.6
89.5
84
881.1
46.8
44
440.7
54.1
04
500. 2
61.4
64
559. 8
68.7
25
322.6
39.6
85
882.1
46.9
45
441.7
54.2
05
501.2
61. 5
65
560.8
68.9
26
823. 6
39.7
86
383.1
47.0
46
442.7
54.3
06
502.2
61.0
66
561. 8
69.0
27
324.6
89.8
87
384.1
47.2
47
44.3.7
54.5
07
503.2
61.8
67
562.8
69.1
28
325. 5
40.0
88
385. 1
47.8
48
444.7
54.6
08
504.2
61.9
68
563.8
69.2
29
326. 5
40.1
89
886.1
47.4
49
445. 6
54.7
09
505. 2
62.0
69
564.8
69.3
30
327.5
40.2
90
387.1
47.5
50
446.6
447.6
54.8
10
511
506.2
507.2
62.1
62.8"
70
571
565.8
566.7
69.4
381
828. 5
40.8
391
888.1
47.6
451
55.0
69.6
32
329. 5
40.5
92
889.1
47.8
52
448.6
55.1
12
508.2
62.4
72
567.7
69.7
33
330.5
40.6
93
390.1
47.9
53
449.6
55.2
18
509.2
62.5
73
568.7
69.8
34
881.5
40.7
94
891.1
48.0
54
450. 6
55.3
14
510.2
62.6
74
569.7
69.9
35
882.5
40.8
95
892.0
48.1
55
451.6
55.4
15
511.1
62.7
75
570. 7
70.1
36
^33.5
40.9
96
393. 0
48.3
56
452.6
55.6
16
512.1
62.9
76
571.7
70.2
37
334.5
41.1
97
894.0
48.4
57
453.6
55.7
17
518.1
68.0
77
572. 7
70.8
38
335.5
41.2
98
895.0
48.5
58
454.6
55.8
18
514.1
63.1
78
573.7
70.4
39
886. 5
41.3
99
396.0
48.6
59
455.6
55.9
19
515.1
63.2
79
574.7
70.5
40
337.5
41.4
400
397.0
398.0
48.7
48.9
60
456.6
457.6
56.1
56.2
20
516.1
63.4
63.5
80
581
575. 7
70.7
341
838. 4
41.6
401
461
521
517.1
576.7
70.8
42
839.4
41.7
02
399.0
49.0
62
458^5
56.3
22
518.1
63. 6
82
577.6
70.9
43
840.4
41.8
03
400.0
49.1
68
459. 5
56.4
23
519.1
68.7
88
578.6
71.0
44
841.4
41.9
04
401.0
49.2
64
460. 5
56.5
24
520. 1
63.8
84
579.6
71.2
45
842.4
42.0
05
402.0
49.4
65
461.5
56.7
25
521.1
64.0
85
580. 6
71.3
46
343.4
42.2
06
403.0
49.5
66
462. 5
56.8
26
522. 1
64.1
86
581.6
71.4
47
344.4
42.8
07
404.0
49.6
67
463. 5
56.9
27
523. 1
64.2
87
582. 6
71.5
48
845.4
42.4
08
405.0
49.7
68
464.5
57.0
28
524.1
64.3
88
583.6
71.6
49
846.4
42.5
09
405.9
49.8
69
465. 5
57.2
29
525.0
64. 5
89
584. 6
71.8
50
847.4
42.6
10
411
406.9
407.9
50.0
70
466. 5
467.5
57.3
57. 4
30
581
526.0
'527. 0
64.6
64.7
90
591
585. 6
71.9
351
348.4
42.8
50.1
471
586. 6
72.0
52
349.4
42.9
12
408.9
50.2
72
468. 5
57.5
32
528. 0
64.8
92
587. 6
72.1
53
850.4
48.0
13
409.9
50.3
78
469.5
57.6
38
529. 0
64.9
93
588. 6
72.2
54
851.4
43.1
14
410.9
50.4
74
470.5
57.8
84
580. 0
65.1
94
589.6
72.4
55
852. 3
48.8
15
411.9
50.6
75
471.5
57.9
85
581.0
65.2
95
590.6
72.5
56
858.3
43.4
16
412.9
50.7
76
472.4
58.0
36
582. 0
65.8
96
591. 5
72.6
57
354.3
43.5
17
413.9
50.8
77
473.4
58.1
37
533.0
65.4
97
592.5
72.7
58
355.3
43.6
18
414.9
50.9
78
474.4
58.2
38
534. 0
65.6
98
598.5
72.9
59
356.3
43.7
19
415.9
51.1
79
475.4
58.4
39
585.0
65.7
99
594. 5
7.3.0
60
357.3
43.9
20
416.9
51.2
80
476.4
58.5
40
536. d"
65.8
600
595. 5
73. 1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. "
Lat.
Dist.
Dep.
Lat.
88° (97°, 263^
, 277°)
.
Page 382]
TABLE 2.
Difference of Latitude and Departure for 8° (172", 188
°, 352°) .
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.4
8.5
121
119.8
16.8
181
179.2
25.2
241
238.7
33.5
2
2.0
0.3
62
61.4
8.6
22
120.8
17.0
82
180.2
25.3
42
239.6
33.7
3
3.0
0.4
63
62.4
8.8
23
121.8
17.1
83
181.2
25.5
43
240.6
33.8
4
4.0
0.6
64
63.4
8.9
24
122.8
17.3
84
182.2
25.6
44
241.6
34.0
5
5.0
0.7
65
64.4
9.0
25
123.8
17.4
85
183.2
25.7
45
242.6
.34.1
6
5.9
0.8
66
65.4
9.2
26
124.8
17.5
86
184.2
25.9
46
243.6
34.2
7
6.9
1.0
«7
66.3
9.3
27
125.8
17.7
87
185.2
26.0
47
244.6
34.4
8
7.9
1.1
68
67.3
9.5
28
126.8
17.8
88
186.2
26.2
48
245.6
34.5
9
8.9
1.3
69
68.3
9.6
29
127.7
18.0
89
187.2
26.3
49
246.6
34.7
10
9.9
1.4
70
69.3
9.7
30
128.7
18.1
90
188.2
26.4
50
247.6
34.8
11
10.9
1.5
71
70.3
9.9
131
129.7
18.2
191
189.1
26.6
251
248.6
34.9
12
11.9
1.7
72
71.3
10.0
32
130.7
18.4
92
190.1
26.7
52
249.5
35.1
13
12.9
1.8
73
72.3
10.2
33
131.7
18.5
93
191.1
26.9
53
250.5
35.2
14
13.9
1.9
74
73.3
10.3
34
132.7
18.6
94
192.1
27.0
54
251.5
35.3
15
14.9
2.1
75
74.3
10.4
35
133.7
18.8
95
193.1
27.1
55
252.5
35.5
16
15.8
2.2
76
75.3
10.6
36
134.7
18.9
96
194.1
27.3
56
253.5
35.6
17
16.8
2.4
77
76.3
10.7
37
135.7
19.1
97
195.1
27.4
57
254.5
35.8
18
17.8
2.5
78
77.2
10.9
38
136.7
19.2
98
196.1
27.6
58
255.5
35.9
19
18.8
2.6
79
78.2
11.0
39
137.7
19.3
99
197.1
27.7
59
256.5
36.0
20
19.8
2.8
80
79.2
11.1
40
141
138.6
139.6
19.5
200
198.1
27.8
60
257.5
36.2
21
20.8
2.9
81
80.2
11.3
19.6
201
199.0
28.0
261
258.5
36.3
22
21.8
3.1
82
81.2
11.4
42
140.6
19.8
02
200.0
28.1
62
259.5
36.5
23
22.8
3.2
83
82.2
11.6
43
141.6
19.9
03
201.0
28.3
63
260.4
36.6
24
23.8
3.3
84
83.2
11.7
44
142.6
20.0
04
202.0
28; 4
64
261.4
36.7
25
24.8
3.5
85
84.2
11.8
45
143.6
20.2
05
203.0
28.5
65
262.4
36.9
26
25.7
3.6
86
85.2
12.0
46
144.6
20.3
06
204.0
28.7
66
263.4
37.0
27
26.7
3.8
87
86.2
12.1
47
145.6
20.5
07
205.0
28.8
67
264.4
37.2
28
27.7
3.9
88
87.1
12.2
48
146.6
20.6
08
206.0
28.9
68
265.4
37.3
29
28.7
4.0
89
88.1
12.4
49
147.5
20.7
09
207. 0
29.1
69
266.4
37.4
30
31
29.7
4.2
4.3
90
89.1
12.5
50
148.5
20.9
10
211
208.0
29.2
70
271
267.4
268.4
37.6
37.7
30.7
91
90.1
12.7
151
149.5
21.0
208.9
29.4
32
31.7
4.5
92
91.1
12.8
52
150.5
21.2
12
209.9
29.5
72
269.4
37.9
33
32.7
4.6
93
92.1
12.9
53
151.5
21.3
13
210.9
29.6
73
270.3
38.0
34
33.7
4.7
94
93.1
13.1
54
152.5
21.4
14
211.9
29.8
74
271.3
38.1
35
34.7
4.9
95
94.1
13.2
55
153.5
21.6
15
212.9
29.9
75
272.3
38.3
36
35.6
5.0
96
95.1
13.4
56
154. 5
21.7
16
213.9
30.1
76
273.3
38.4
37
36.6
5.1
97
96.1
13.5
57
155.5
21.9
17
214.9
30.2
77
274.3
38.6
38
37.6
5.3
98
97.0
13.6
58
156.5
22.0
18
215.9
30.3
78
275.3
38.7
39
38.6
5.4
99
98.0
13.8
59
157.5
22.1
19
216.9
30.5
79
276.3
38.8
40
39.6
5.6
5.7
100
99.0
13.9
14.1
60
158.4
159.4
22.3
20
217.9
30.6
80
281
277. 3
278.3
39.0
41
40.6
101
100.0
161
22.4
221
218.8
30.8
39.1
42
41.6
5.8
02
101.0
14.2
62
160.4
22.5
22
219.8
30.9
82
279.3
39.2
43
42.6
6.0
03
102.0
14.3
63
161.4
22.7
23
220.8
31.0
83
280.2
39.4
44
43.6
6.1
04
103.0
14.5
64
162.4
22.8
24
221.8
31.2
84
281.2
39.5
45
44.6
6.3
05
104.0
14.6
65
163.4
23.0
25
222.8
31.3
85
282.2
39.7
46
45.6
6.4
06
105.0
14.8
66
164.4
23.1
26
223.8
31.5
86
283.2
39.8
47
46.5
6.5
07
106.0
14.9
67
165.4
23.2
27
224.8
31.6
87
284.2
39.9
48
47.5
6.7
08
106.9
15.0
68
166.4
23.4
28
225.8
31.7
88
285.2
40.1
49
48.5
6.8
09
107.9
15.2
69
167.4
23.5
29
226.8
31.9
89
286.2
40.2
50
51
49.5
7.0
7.1
10
108.9
15.3
70
168.3
23.7
30
227.8
32.0
90
287.2
40.4
50.5
111
109.9
15.4
171
169.3
23.8
231
228.8
32.1
291
288.2
40.5
52
51.5
7.2
12
110.9
15.6
72
170.3
23.9
32
229.7
32.3
92
289.2
40.6
53
52.5
7.4
13
111.9
15.7
73
171.3
24.1
33
230.7
32.4
93
290.1
40.8
54
53.5
7.5
14
112.9
15.9
74
172.3
24.2
34
231.7
32.6
94
291.1
40.9
55
54.5
7.7
15
113.9
16.0
75
173.3
24.4
35
232.7
32.7
95
292.1
41.1
56
55.5
7.8
16
114.9
16.1
76
174.3
24.5
36
233.7
32.8
96
293.1
41.2
57
56.4
7.9
17
115.9
16.3
77
175.3
24.6
37
234.7
33.0
97
294.1
41.3
58
57.4
8.1
18
116.9
16.4
78
176.3
24.8
38
235.7
33. 1
98
295.1
41.5
59
58.4
8.2
19
117.8
16.6
79
177.3
24.9
39
236.7
33.3
99
296.1
41.6
60
59.4
8.4
20
118.8
16.7
80
178.2
25.1
40
237.7
33.4
300
297.1
41.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
82° ({
)8°, 262<
', 278°
.
TABLE 2.
[Page 383 |
Difference of Latitude and Departure for 8° (172°, 188°, 352'
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. 1 Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
298.0
41.9
361
357.5
50.2
421
416.9
58.6
481
476.3
66.9
541
535.7
75.2
U2
299.0
42.0
62
358.5
50.4
22
417.9
58.7
82
477.3
67.1
42
536.7
75.4
03
300.0
42.2
63
359. 4
50.5
23
418.9
58.9
83
478.3
67.2
43
537. 7
75.5
04
301.0
42.3
64
360. 4
50.7
24
419.8
59.0
84
479.3
67.4
44
538.7
75.7
05
302.0
42.5
65
361.4
50.8
25
420.8
59.2
85
480.3
67.5
45
539.7
75.8
06
303.0
42.6
66
362.4
50.9
26
421.8
59.3
86
481.2
67.6
46
540.6
75.9
07
304.0
42.7
67
363. 4
51.1
27
422.8
59.4
87
482.2
67.8
47
541.6
76.1
08
305. 0
42.9
68
364.4
51.2
28
423.8
59.6
88
483.2
67.9
48
542.6
76.2
09
306. 0
43.0
69
365. 4
51.4
29
424.8
59.7
89
484.2
68.1
49
543.6
76.4
10
307.0
43.1
70
366.4
51.5
51.6
30
425.8
426.8
59.8
90
485.2
68.2
50
544.6
545.6
76.5
311
307.9
43.3
371
367.4
431
60.0
491
486.2
68.3
551
76.6
12
308.9
43.4
72
368.4
51.8
32
427.8
60.1
92
487.2
68.5
52
546.6
76.8
13
309.9
43.6
73
74
369.3
51.9
33
428.8
60.3
93
488.2
68.6
53
547.6
76.9
14
310.9
43.7
370.3
52.1
34
429.8
60.4
94
489.2
68.8
54
548.6
77.1
15
311.9
43.8
75
371.3
52.2
35
430. 7
60.6
95
490.2
68.9
55
549.6
77.2
16
312.9
44.0
76
372.3
52.3
36
431.7
60.7
96
491.2
69.0
56
550.6
77.4
17
313.9
44.1
77
373.3
52.5
37
432.7
60.8
97
492.1
69.2
57
551.5
77.5
18
314.9
44.3
78
374.3
52.6
38
433.7
61.0
98
493. 1
69.3
58
552.5
77.6
19
315.9
44.4
79
375.3
52.7
39
434.7
61.1
99
494.1
69.5
59
553.5
77.8
20
321
316.9
44.5
80
376.3
52.9
53.0
40
441
435.7
61.2
500
501
495.1
496.1
■69.6
60
554.5
77.9
317.9
44.7
381
377.3
436.7
61.4
69.7
561
555.5
78.1
22
318.8
44.8
82
378.3
53.2
42
437.7
61.5
02
497.1
69.9
62
556.5
78.2
23
319.8
45.0
83
379.2
53.3
43
438. 7
61.7
03
498.1
70.0
63
557.5
78.3
24
320.8
45.1
84
380.2
53.4
44
439.7
61.8
04
499.1
70.2
64
558. 5
78.5
25
321.8
45.2
85
.381. 2
53.6
45
440.6
61.9
05
500.1
70.3
65
559.5
78.6
26
322.8
45.4
86
382.2
53.7
46
441.6
62.1
06
501.0
70.4
66
560.5
78.8
27
323.8
45.5
87
383.2
53.9
47
442.6
62.2
07
502.0
70.6
67
561.5
78.9
28
324.8
45.7
88
384.2
54.0
48
443.6
62.4
08
503.0
70.7
68
562.5
79.0
29
325.8
45.8
89
385.2
54.1
49
444.6
62.5
09
504.0
70.8
69
563.5
79.1
30
331
326.8
327.8
45.9
90
386.2
387.2
54.3
50
445.6
446.6
62.6
62.8
10
505.0
70.9
70
571
564.5
79.3
46.1
391
54.4
451
511
506.0
71.1
565.4
79.4
32
328.7
46.2
92
388.2
54.6
52
447.6
62.9
12
507.0
71.2
72
566.4
79.6
33
329.7
46.3
93
389.1
54.7
53
448.6
63.0
13
508.0
71.4
73
567.4
79.7
34
330.7
46.5
94
390.1
54.8
54
449.6
63.2
14
509.0
71.5
74
568.4
79.8
35
331.7
46.6
95
391.1
55.0
55
450. 5
63.3
15
510.0
71.6
75
569.4
80.0
36
332.7
46.8
96
392.1
55.1
56
451.5
63.5
16
510.9
71.8
76
570.4
80.1
37
*333. 7
46.9
97
393.1
55.3
57
452.5
63.6
17
511.9
71.9
77
571.4
80.2
38
334.7
47.0
9$
394.1
55.4
58
453. 5
63.7
18
512.9
72.0
78
572.4
80.4
39
335.7
47.2
99
395.1
55.5
59
454.5
63.9
19
513.9
72.2
79
573.4
80.5
40
341
336. 7
47.3
400
396.1
55.7
55.8
60
455.5
456.5
64.0
20
514.9
72.3
80
574.4
80.6
337.7
47.5
401
397.1
461
64.2
521
515.9
72.4
581
575.4
80.8
42
338.6
47.6
02
398.1
56.0
62
457.5
64.3
22
516.9
72.6
82
576.4
80.9
43
339.6
47.7
03
399.1
56.1
63
45S. 5
64.4
23
517.9
72.8
83
577.4
81.1
44
340.6
47.9
04
400.0
56.2
64
459.5
64.6
24
518.9
73.0
84
578.4
81.3
45
341.6
48.0
05
401.0
56.4
65
460.4
64.7
25
519.9
73.1
85
579.4
81.4
46
342.6
48.2
06
402.0
56.5
66
461.4
64.9
26
520.9
73.2
86
580.3
81.6
47
343.6
48.3
07
403.0
56.6
67
462.4
65.0
27
521.8
73.4
87
581.3
81.7
48
344.6
48.4
08
404.0
56.8
68
463.4
65.1
28
522.8
73.5
88
582.3
81.8
49
345.6
48.6
09
405.0
56.9
69
464.4
65.3
29
523.8
73.7
89
583.3
82.0
50
351
346.6
48.7
48.9
10
411
406. 0
407. 0
57.1
70
465.4
466.4
65.4
65.6
30
531
524.8
525. 8
73.8
90
584.3
82.1
347.6
57.2
471
73.9
591
585.3
82.2
52
348.5
49.0
12
408.0
57.3
72
467.4
65.7
32
526.8
74.1
92
586.3
82.4
53
349.5
49.1
13
409.0
57.5
73
468.4
65.8
33
527.8
74.2
93
587.3
82.5
54
350. 5
49.3
14
409.9
57.6
74
469.4
66.0
34
528.8
74.3
94
588.3
82.6
55
351.5
49.4
15
410.9
57.8
75
470.4
66.1
35
529.8
74.5
95
589.3
82.8
56
352.5
49.5
16
411.9
57.9
76
471.3
66.2
36
530.8
74.6
96
590.3
83.0
57
353.5
49.7
17
412.9
58.0
77
472.3
66.4
37
531.7
74.7
97
591.2
83.1
58
354.5
49.8
18
413.9
58.2
78
473.3
66.5
38
532.7
74.9
98
592.2
83.2
59
355.5
50.0
19
414.9
58.3
79
474.3
66.7
39
533.7
75.0
99
593.2
83.3
60
356.5
50.1
20
415.9
58.5
80
475.3
66.8
40
534.7
75.1
600
594.2
83.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
82° (98°, 262°, 278°). 1
Page 384]
TABLE 2.
Difference of Latitude and Departure for 9° (171°, 189°, 351°
•
Dist.
1
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1.0
0.2
61
60.2
9.5
121
119.5
18.9
181
178.8
28.3
241
238. 0
37.7
2
2.0
0.3
62
61.2
9.7
22
120. 5
19. 1
82
179.8
28.5
42
239.0
37.9
3
3.0
0.5
63
62.2
9.9
23
121.5
19.2
83
180.7
28.6
43
240.0
38.0
4
4.0
0.6
64
63.2
10.0
24
122.5
19.4
84
181.7
28.8
44
241.0
38.2
5
4.9
0.8
65
64.2
10.2
25
123.5
19.6
85
182.7
28.9
45
242.0
38.3
6
5.9
0.9
66
65.2
10.3
26
124.4
19.7
86
183.7
29.1
46
243.0
38.5
7
6.9
1.1
«7
66.2
10.5
27
125.4
19.9
87
184.7
29.3
47
244.0
38.6
8
7.9
1.3
68
67.2
10.6
28
126.4
20.0
88
185.7
29.4
48
244.9
38.8
9
8.9
1.4
69
68.2
10.8
29
127.4
20.2
89
186.7
29.6
49
245.9
39.0
10
11
9.9
10.9
1.6
70
69.1
11.0
11.1
30
131
128.4
129.4
20.3
20. 5
90
187.7
29.7
50
246.9
247. 9
39.1
1.7
71
70.1
191
188.6
29.9
251
39.3
12
11.9
1.9
72
71.1
11.3
32
130.4
20.6
92
189.6
30.0
52
248.9
.39.4
13
12.8
2.0
73
72.1
11.4
33
131.4
20.8
93
190.6
30.2
53
249.9
39.6
14
13.8
2.2
74
73.1
11.6
34
132. 4
21.0
94
191.6
30.3
54
250.9
39.7
15
14.8
2.3
75
74.1
11.7
35
133. 3
21.1
95
192.6
30.5
55
251.9
39.9
16
15.8
2.5
76
75.1
11.9
36
134.3
21.3
96
193.6
30.7
56
252.8
40.0
17
16.8
2.7
77
76.1
12.0
37
135.3
21.4
97
194.6
30.8
57
253.8
40.2
18
17.8
2.8
78
77.0
12.2
38
136.3
21.6
98
195.6
31.0
58
254.8
40.4
19
18.8
3.0
79
78.0
12.4
39
137.3
21.7
99
196.5
31.1
59
255. 8
40.5
20
21
19.8
20.7
3.1
80
• 79.0
12.5
12.7
40
138.3
21.9
200
197.5
31.3
60
256.8
40.7
3.3
81
80.0
141
139.3
22.1
201
198.5
31.4
261
257.8
40.8
22
21.7
3.4
82
81.0
12.8
42
140.3
22.2
02
199.5
31.6
62
258.8
41.0
23
22.7
3.6
83
82.0
13.0
43
141.2
22.4
03
200.5
31.8
63
259.8
41.1
24
23.7
3.8
84
83.0
13.1
44
142.2
22.5
04
201.5
31.9
64
260.7
41.3
25
24.7
3.9
85
84.0
13.3
45
143.2
22.7
05
202.5
32.1
65
261.7
41.5
26
25.7
4.1
86
84.9
13.5
46
144.2
22.8
06
203.5
32.2
66
262.7
41.6
27
26.7
4.2
87
85.9
13.6
47
145.2
23.0
07
204.5
32.4
67
263.7
41.8
28
27.7
4.4
88
86.9
13.8
48
146.2
23.2
08
205.4
32.5
68
264.7
41.9
29
28.6
4.5
89
87.9
13.9
49
147.2
23.3
09
206.4
32.7
69
265. 7
42.1
30
29.6
4.7
90
88.9
89.9
14.1
14.2
50
151
148.2
23.5
23.6
10
207.4
32.9
70
271
266.7
42.2
42.4
31
30.6
4.8
91
149. 1
211
203. 4
33.0
267.7
32
31.6
5.0
92
90.9
14.4
52
150.1
2.3.8
12
209.4
33.2
72
268.7
42.6
33
32.6
5.2
93
91.9
14.5
53
151.1
23.9
13
210.4
33.3
73
269.6
42.7
34
33.6
5.3
94
92.8
14.7
54
•152. 1
24.1
14
211.4
33.5
74
270.6
42.9
35
34.6
5.5
95
93.8
14.9
55
153.1
24.2
15
212.4
33.6
75
271.6
43.0
36
35.6
5.6
96
94.8
15.0
56
15+. 1
24.4
16
213.3
33.8
76
272.6
43.2
37
36.5
5.8
97
95.8
15.2
57
155.1
24.6
17
214.3
33.9
77
273.6
43.3
38
37.5
5.9
98
96.8
15.3
58
156.1
24.7
18
215.3
34.1
78
274.6
43.5
39
38.5
6.1
99
97.8
15.5
59
157.0
24.9
19
216.3
34.3
79
275.6
43.6
40
41
39.5
40.5
6.3
6.4
100
101
98.8
99.8
15.6
15. 8^
60
161
158.0
159.0"
25.0
20
217.3
34.4
80
276.6
277. 5
43.8
44.0
25.2
221
218.3
34.6
281
42
41.5
6.6
02
100.7
16.0
62
160.0
25.3
22
219.3
34.7
82
278.5
44.1
43
42.5
6.7
03
101.7
16.1
63
161.0
25.5
23
220. 3
34.9
83
279.5
44.3
44
43.5
6.9
04
102.7
16.3
64
162.0
25.7
24
221.2
35.0
84
280.5
44.4
45
44.4
7.0
05
103.7
16.4
65
163.0
25.8
25
222.2
35.2
85
281.5
44.6
46
45.4
7.2
06
104.7
16.6
66
164.0
26.0
26
223. 2
35.4
86
282. 5
44.7
47
46.4
7.4
07
105.7
16.7
67
164.9
26.1
27
224.2
35.5
87
283.5
44.9
48
47.4
7.5
08
106.7
16.9
68
165.9
26.3
28
225.2
35.7
88
284.5
45.1
49
48.4
7.7
09
107.7
17.1
69
166.9
26.4
29
226.2
35.8
89
285.4
45.2
'•50
49.4
7.8
10
108.6
109.6
17.2
17.4
70
171
167.9
168.9
26.6
26.8
30
231
227.2
228.2
36.0
90
286.4
45.4
51
50.4
8.0
111
36.1
291
287.4
45.5
52
51.4
8.1
12
110.6
17.5
72
169.9
26.9
32
229.1
36.3
92
288.4
45.7
53
52. 3
8.3
13
111.6
17.7
73 j 170.9
27.1
33
230. 1
36.4
93
289.4
45.8
54
53.3
8.4
14
112.6
17.8
74 171.9
27.2
34
231.1
36.6
94
290.4
46.0
55
54.3
8.6
15
113.6
18.0
75 172.8
27.4
35
232.1
36.8
95
291.4
46.1
56
55.3
8.8
16
114.6
18.1
76 173. 8
27.5
36
233. 1
36.9
96
292.4
46.3
57
56.3
8.9
17
115.6
18. 3*
77 174.8
27.7
37
234. 1
37.1
97
293. 3
46.5
58
57.3
9.1
18
116.5
18.5
78 1 175.8
27.8
38
235. 1
37.2
98
294.3
46.6
59
58.3
9.2
19
117.5
18.6
79
176.8
28.0
39
236. 1
37.4
99
295. 3
46.8
60
59.3
9.4
20
118.5
18.8
80
177.8
28.2
40
237.0
37. 5
Lat.
300
296.3
46.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. 1 Dep.
Lat.
Dist.
Dep.
Dist.
Dep.
Lat.
81° (99°, 261°, 279°
).
TABLE S
[Page 385 |
Difference of Latitude and Departure for
9° (171°, 189
% 351°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.l
301
297.3
47.1
361
356. 6
56.5
421
415.8
65.9
481
475.1
75.2
541
534.4
84.6
02
298.3
47.2
62
357. 5
56.7
22
416.8
66.0
82
476.1
75.3
42
535.4
84.7
03
299.3
47.4
63
358. 5
56.8
23
417.8
66. 2
83
477.1
75.5
43
536. 3
84.9
04
300. 3
47.6
64
359. 5
56.9
24
418.8
66.3
84
478.0
75. 6
44
537.3
85.1
05
301.2
47.7
65
360.5
57.1
25
419.8
66.5
85
479.0
75.8
45
538.3
85.3
06
302.2
47.9
66
361.5
57.3
26
420.8
66.6
86
480.0
75.9
46
539.3
85.4
07
303.2
48.0
67
362.5
57.4
27
421.7
66.8
87
481.0
76.1
47
540.3
85.6
08
304.2
48.2
68
363. 5
57.6
28
422.7
67.0
88
482.0
76.2
48
541. 3
85.7
09
305.2
48.3
69
364.5
57.7
29
423.7
67.1
89
483.0
76.4
49
542.3
85.9
10
306.2
48.5
48.7
70
365.4
57.9
58.1
30
431
424.7
67.3
90
491
484.0
485.0
76.5
76.7
50
551
543. 3
544.3
86.0
311
307.2
371
366.4
425.7
67.4
86.2
12
308.2
48.8
72
367.4
58.2
32
426.7
67.6
92
485.9
76.8
52
545.2
86.3
13
309.1
49.0
73
368. 4
58.4
33
427.7
67.7
93
486.9
77.0
53
546. 2
86.5
14
310.1
49.1
74
369.4
58.5
34
428.7
67.9
94
487.9
77.1
54
547.2
86.6
15
311.1
49.3
75
370.4
58.7
35
429.6
68.1
95
488. 9
77.3
55
548.2
86.8
16
312.1
49.4
76
371.4
58.8
36
430.6
68.2
96
589.9
77.5
56
549.2
87.0
17
313.1
49.6
77
372.4
59.0
37
431. 6
68.4
97
490.9
77. 7
57
550.2
87.1
18
314.1
49.8
78
373.3
59. 1
38
432. 6
68.5
98
491.9
77.9
58
551. 2
87.3
19
315.1
49.9
79
374.3
59.3
39
433.6
68.7
99
492.9
78.0
59
552. 2
87.4
20
316.1
50.1
80
381
375.3
59.5
40
434.6
68.8
500
501
493.8
4914.8
78.2
78.4"
60
561
553.1
554. 1
87.6
87.7
321
317.0
50.2
376. 3
59.6
441
435.6
69.0
22
318.0
50.4
82
377. 3
59.8
42
436.6
69.1
02
495.8
78.5
62
555. 1
87.9
23
319.0
50.5
83
378.3
59.9
43
437.5
69.3
03
496.8
78.7
63
556.1
88.0
24
320.0
50.7
84
379.3
60.1
44
438.5
69.5
04
497.8
78.8
64
557.1
88.2
25
321.0
50.8
85
380.3
60.2
45
439. 5
69.6
05
498.8
79.0
65
558.1
88.3
26
322.0
51.0
86
381.2
60.4
46
440.5
69.8
06
499.8
79.1
66
559.1
88.5
27
323.0
51.2
87
382.2
60.5
47
441.5
69.9
07
500.8
79.2
67
560.1
88.6
28
324. 0
51.3
88
383.2
60.7
48
442.5
70.1
08
501.7
79.4
68
561.0
88.8
29
324.9
51.5
89
384.2
60.9
49
443.5
70.2
09
502. 7
79.5
69
562.0
88.9
30
331
325. 9
51.7
90
391
385.2
386.2
61.0
50
444.5
445. 4
70.4
10
503.7
504.7
79.7
79.8
70
571
563.0
564.0
89.1
326.9
51.8
61.2
451
70.6
511
89.2
32
327.9
51.9
92
387.2
61.3
52
446.4
70.7
12
505. 7
80.1
72
565.0
89.4
33
328.9
52.1
93
388.2
61.5
53
447.4
70.9
13
506.7
80.2
73
566. 0
89.5
34
329.9
52.3
94
389.1
61.6
54
448.4
71.0
14
507.7
80.3
74
567.0
89.7
.35
330. 9
52.4
95
390.1
61.8
55
449.4
71.2
15
508.7
80.5
75
568.0
89.9
36
331.9
52.6
96
391. 1
62.0
56
450.4
71.3
16
509.6
80.6
76
568.9
90.1
37
S32.8
52.7
97
392.1
62.1
57
451.4
71.5
17
510.6
80.8
77
569.9
90.2
38
333.8
52.9
98
393.1
62.3
58
452.4
71.7
18
511.6
80.9
78
570. 9
90.3
39
334.8
53.0
99
394.1
62.4
59
453.3
71.8
19
512.6
81.1
79
571.9
90,5
40
341
335.8
53.2
400
395. 1
62.6
60
454. 3
72.0
20
513. 6
81.3
80
572.9
90.7
336. 8
53.3
401
396.1
62.7
461
455.3
72.1
521
514.6
81.4
581
573.9
90.9
42
337.8
53.5
02
397.0
62.9
62
456.3
72.3
22
515. 6
81.6
82
574.9
91.0
43
338.8
53.7
03
398.0
63.0
63
457.3
72.4
23
516.6
81.8
83
575.9
91.2
44
339. 8
53:8
04
399.0
63.2
64
458. 3
72.6
24
517.6
81.9
84
576.9
91.3
45
340.8
54.0
05
400.0
63.4
65
459.3
72.7
25
518.6
82.1
85
577.9
91.5
46
341.7
54.1
06
401.0
63.5
66
460. 3
72.9
26
519. 5
82.3
86
578.8
91.7
47
342.7
54.3
07
402.0
63.7
67
461.2
73.1
27
520. 5
82.4
87
579.8
91.8
48
343.7
54.4
08
403.0
63.8
68
462.2
73.2
28
521.5
82.6
88
580.8
92.0
49
344.7
54.6
09
404.0
64.0
(59
463.2
73.4
29
522.5
82.7
89
581.8
92.1
50
351
345. 7
346.7
54.8
10
405.0
64.1
70
464.2
73.5
30
523.5
82.9
90
582.8
92.2
54.9
411
405.9
64.3
471
465. 2
73.7
531
524. 5
83.1
591
583.8
92.4
52
347.7
55.1
12
406.9
64.5
72
466.2
73.8
32
525. 5
83.2
92
584.8
92.5
53
348.7
55.2
13
407.9
64.6
73
467.2
74.0
33
526.5
83.4
93
585. 7
92.7
54
349.6
55.4
14
408.9
64.8
74
468.2
74.2
34
527.5
83.5
94
586.7
92.9
55
350.6
55.5
15
409.9
64.9
75
469.2
74.3
35
528.4
83.7
95
587.7
93.1
56
351.6
55.7
16
410.9
65.1
76
470.1
74.5
36
529.4
83.8
96
588.7
93.2
57
352.6
55.9
17
411.9
65.2
77
471.1
74.6
37
530. 4
84.0
97
589.7
93.4
58
353.6
56.0
18
412.9
65.4
78
472.1
74.8
38
531.4
84.1
98
590.7
93.5
59
354.6
56.2
19
413.8
65.6
79
473.1
74.9
39
532.4
84.3
99
591.7
93.7
60
355.6
56.3
20
414.8
65.7
80
474.1
Dep.
75.0
40
533.4
84.4
600
592.6
93.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
81° {{
)9°, 261'
', 279°
.
22489—03-
-25
Page 386
TABLE 2.
Difftreiue of Latitude and Departure for 10° (170°, 190°, 350°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. 1 Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
60.1
10.6
121
119.2
21.0
181
178. 3
31.4
241
237.3
41.8
2
2.0
0.3
62
61.1
10.8
22
120.1
21.2
82
179.2
31.6
42
238.3
42.0
3
3.0
0.5
63
62.0
10.9
23
121.1
21.4
83
180.2
31.8
43
239.3
42.2
4
3.9
0.7
64
63.0
11.1
24
122.1
21.5
84
181.2
32.0
44
240.3
42.4
5
4.9
0.9
65
64.0
11.3
25
123.1
21.7
85
182.2
32.1
45
241.3
42.5
6
5.9
1.0
.66
65.0
11.5
26
124.1
21.9
86
183. 2
32.3
46
242.3
42.7
7
6.9
1.2
•67
66.0
11.6
27
125.1
22.1
87
184.2
32.5
47
243.2
42.9
8
7.9
1.4
68
67.0
11.8
28
126.1
22.2
88
185.1
32.6
48
244.2
43.1
9
8.9
1.6.
69
68.0
12.0
29
127.0
22.4
fe9
186.1
32.8
49
245.2
43.2
10
11
9.8
1.7
70
71
68.9
12.2
12.3
30
131
128.0
129.0
22.6
22.7
90
191
187.1
18'8. 1
33.0
50
251
246.2
247.2
43.4
43.6
10.8
1.9
69.9
33.2
12
11 8
2.1
72
70.9
12.5
32
130.0
22.9
92
189.1
33.3
52
248.2
43.8
13
12.8
2.3
73
71.9
12.7
33
131.0
23.1
93
190.1
33.5
53
249.2
43.9
14
13.8
2.4
74
72.9
12.8
34
132.0
23.3
94
191.1
33.7
54
250.1
44.1
15
14.8
2.6
75
73.9
1.3.0
35
132.9
23.4
95
192.0
33. 9
55
251.1
44.3
16
15.8
2.8
76
74.8
1.3.2
36
133.9
23.6
96
193.0
34.0
56
252.1
44.5
17
16.7
3.0
77
75.8
13.4
37
134.9
23.8
97
194.0
34.2
57
253.1
44.6
18
17.7
3.1
78
76.8
13.5
38
135.9
24.0
98
195.0
34.4
58
254.1
44.8
19
18.7
3.3
79
77.8
13.7
39
136.9
24.1
99
196.0
34.6
59
255.1
45.0
20
21
19.7
20.7
3.5
80
78.8
13.9
40
137. 9
24.3
200
197.0
197.9
34.7
34.9
60
261
256.1
257.0
45.1
45.3
3.6
81
79. 8
14.1
141
138.9
24.5
201
22
21.7
3.8
82
80.8
14.2
42
139.8
24.7
02
198.9
35.1
62
258.0
45.5
23
22.7
4.0
83
81.7
14.4
43
140.8
24.8
03
199.9
35.3
63
259.0
45.7
24
23.6
4.2
84
82.7
14.6
44
141.8
25.0
04
200.9
.35.4
64
260.0
45.8
25
24.6
• 4.3
85
83.7
14.8
45
142.8
25.2
05
201.9
35.6
65
261.0
46.0
26
25.6
4.5
86
84.7
14.9
46
143.8
25.4
06
202.9
35.8
66
262.0
46.2
27
26.6
4.7
87
85.7
15.1
47
144.8
25.5
07
203.9
35.9
67
262. 9
46.4
28
27.6
4.9
88
86.7
15.3
48
145.8
25.7
08
204.8
36.1
68
263.9
46.5
29
28.6
5.0
89
87.6
15.5
49
146.7
25.9
09
205. 8
36.3
69
264.9
46.7
30
31
29.5
30.5
5.2
90
88.6
15.6
15.8
50
147.7
148.7
26.0
26.2
10
211
206.8
36.5
70
265.9
46.9
6.4
91
89.6
151
207.8
36.6
271
266.9
47.1
32
31.5
5.6
92
90.6
16.0
52
149.7
26.4
12
208.8
36.8
72
267.9
47.2
33
32.5
5.7
93
91.6
16.1
53
150. 7
26.6
13
209.8
37.0
73
268.9
47.4
34
33.5
5.9
94
92.6
16.3
. 54
151.7
26.7
14
210.7
37.2
74
269.8
47.6
35
34.5
6.1
95
93.6
16.5
55
152.6
26.9
15
211.7
37.3
75
270.8
47.8
36
35.5
6.3
96
94.5
16.7
56
153.6
27.1
16
212.7
37.5
76
271.8
47.9
37
36.4
6.4
97
95.5
16.8
57
154. 6
27.3
17
213.7
37.7
77
272.8
48.1
38
37.4
6.6
98
96.5
17.0
58
155. 6
27.4
18
214.7
37.9
78
273.8
48.3
39
38.4
6.8
99
97.5
17.2
59
156.6
27.6
19
215.7
38.0
79
274.8
48.4
40
39.4
6.9
7.1
100
101
98.5
17.4
17.5
60
157.6
158.6
27.8
20
216.7
38.2
80
275.7
48.6
41
40.4
99.5
161
28.0
221
217.6
38.4
281
276.7
48.8
42
41.4
7.3
02
100.5
17.7
62
159.5
28.1
22
218.6
38.5
82
277.7
49.0
43
42.3
7.5
03
101.4
17.9
63
160.5
28.3
23
219.6
38.7
83
278.7
49.1
44
43.3
7.6
04
102.4
18.1
64
161.5
28.5
24
220.6
38.9
84
279.7
49.3
45
44.3
7.8
05
103. 4
18.2
65
162. 5
28.7
25
221.6
39.1
85
280.7
49.5
46
45.3
8.0
06
104.4
18.4
66
163.5
28.8
26
222.6
39.2
86
281.7
49.7
47
46.3
8.2
07
105.4
18.6
67
164.5
29.0
27
223.6
39.4
87
282.6
49.8
48
47.3
8.3
08
106.4
18.8
68
165.4
29.2
28
224.5
39.6
88
283.6
50.0
49
48.3
8.5
09
107.3
18.9
69
166.4
29.3
29
225.5
39.8
89
284.6
50.2
50
49.2
8.7
10
108.3
109. 3~
19.1
70
167.4
29.5
30
226.5
227.5
39.9
90 .
285.6
50.4
50.5
51
50.2
8.9
ni
19.3
171
168.4
29.7
231
40.1
291
286.6
52
51.2
9.0
12
110.3
19.4
72
169.4
29.9
32
228.5
40.3
92
287.6
50.7
53
52.2
9.2
13
111.3
19.6
73
170.4
30.0
33
229.5
40.5
93
288.5
50.9
54
53.2
9.4
14
112. 3
19.8
74
171.4
30.2
34
230.4
40.6
94
289. 5
51.1
55
54.2
9.6
15
113.3
20.0
75
172.3
30.4
35
231.4
40.8
95
290. 5
51.2
56
55.1
9.7
16
114.2
20.1
76
173.3
30.6
36
232.4
41.0
96
291.5
51.4
57
56.1
9.9
17
115. 2
20.3
77
174. S
30.7
37
233. 4
41.2
97
292.5
51.6
58
57.1
10.1
18
116.2
20.5
78
175.3
30.9
38
234.4
41.3
98
293.5
51.7
59
58. 1
10.2
19
117.2
20.7
79
176.3
31.1
39
235. 4
41.5
99
294.5
51.9
60
59.1
1
10.4
20
118.2
20.8
80
177.3
31.3
40
236.4
41.7
300
295.4
52.1
Dist.
Dep.
Lat.
DLst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
80° (100°, 260°, 280°).
TABLE 27
[Page 387
Difference of Latitude and Departure for 10° (170°, 190°, 350'
')
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
296. 4
52.3
361
.355. 5
62.7
421
414.6
73.1
481
473.7
83.5
541
532.8
93.9
02
297.4
52.5
62-
356. 5
62.9
22
415.6 73.3
82
474.7
83.7
42
533.8
94.1
03
298.4
52.6
63
357. 5
63.0
23
416.6 1 73.5
83
475. 7
83.9
43
534.8
94.3
04
299.4
52.8
64
358. 5
63.2
24
417.6
73.6
84
476.6
84.1
44
535. 7
94.5
05
300.4
53. 0
65
359.5
63.4
25
418.5
73.8
85
477.6
84.2
45
536.7
94.6
06
301.4
53. 1
66
360. 4
63.6
26
419.5
74.0
86
478.6
84.4
46
537. 7
94.8
07
302. 3
53. 3
67
361.4
63.7
27
420.5
74.2
87
479.6
84.6
47
538. 7
95.0
08
303. 3
53.5
68
362.4
63.9
28
421.5
74.3
88
480.6
84.7
48
539. 7
95.1
09
304. 3
53.7
69
363. 4
64.1
29
422. 5
74.5
89
481. 6
84.9
49
540.7
95.3
10
305. 3
306. 3
53.8
70
364. 4 .
64.3
64.4
30
431
423.5
424. 5
74.7
90
482.6
483. 5
85.1
50
541. 6
542.6
95.5
311
54.0
371
365.4
74.9
491
85.2
551
95.6
12
307.3
54.2
72
366.4
64.6
32
425.4 75.0
92
484. 5
85.4
52
543. 6
95.8
13
308. 2
54.3
73
367. 3
64.8
3S
426.4 75.2
93
485. 5
85.6
53
544. 6
96.0
14
309. 2
54.5
74
368. 3
65.0
34
427.4 1 75.4
94
486.5
85.8
54
545.6
96.2
15
310.2
54.7
75
369.3
65.1
35
428.4 75.5
95
487.5
85.9
55
546.6
96.3
16
311. 2
54.9
76
370.3
65.3
36
429. 4 ; 75. 7
96
488.5
86. 1
56
547. 5
96.*
17
312.2
55.1
77
371.3
65.5
3t
430.4 i 75.9
97
489.4
86.3
57
548.5
96.7
18
313.2
55.2
78
372.3
65.6
38
431.3 76.1
98
490.4
86.5
58
549. 5
96.9
19
314.2
55. 4
79
373.2
65.8
39
432.3 76.2
99
491.4
86.6
59
550.5
97.0
20
321
315. 1
55.6
55.8
80
381
374.2
375. 2
66.0
40
433.3
76.4
76.6
500
501
492.4
493.4
86.8
87.0
60
551.5
97.2
97.4
316. 1
66.2
441
434. 3
561
552. 5
22
317.1
55.9
82
376.2
66.3
42
435.3 76.8
02
494.4
87.2
62
553.5
97.6
23
318.1
56.1
83
377.2
66.5
43
436.3 i 76.9
03
495. 3
87.3
63
554.4
97.7
24
319.1
56.3
84
378.2
66.7
44
437.3 1 77.1
04
496. 3
87.5
64
555. 4
97. 9
25
320.1
56.4
85
379. 2
66.9
45
438.2 77.3
05
497. 3
87.7
65
556.4
98.1
26
321.0
56.6
86
380. 1
67.0
46
439.2
77.5
06
498.3
87.9
66
557.4
98.3
27
322.0
56.8
87 i 381.1
67.2
47
440.2
77.6
07
499.3
88.0
67
558.4
98.4
28
323.0
57.0
88
382. 1
67.4
48
441.2
77.8
08
500.3
88.2
68
559.4
98.6
29
324.0
57.1
89
383.1
67.6
49
442.2
78.0
09
501.3
88.4
69
560.3
98.8
30
325. 0
326.0
57.3
90
384. 1
67.7
50
443.2
78.2
10
502.2
88.6
70
561.3
99.0
331
57.5
391
385.1
67.9
451
444.2
78.3
511
503.2
88.7
571
562.3
99.1
32
327.0
57.7
92
386.0
68.1
52
445.1
78.5
12
504.2
88.9
72
563.3
99.3
33
327.9
57.8
93
387.0
68.2
53
446.1
78.7
13
505.2
89.1
73
564.3
99.5
34
328.9
58.0
94
388.0
68.4
54
447.1
78.8
14
506.2
89.2
74
565.3
99.6
35
329.9
58.2
95
389. 0
68.6
55
448.1
79.0
15
507.2
89.4
75
566.3
99.8
36
530.9
58.4
96
390.0
68.8
56
449.1
79.2
16
508.2
89,6
76
567.2
100.0
37
331.9
58.5
97
391.0
68.9
57
450.1
79.4
17
509.1
89.8
77
568.2
100.2
38
332.9
58.7
98
392.0
69.1
58
451.0
79.5
18
510.1
89.9
78
569.2
100.3
39
333.9
58.9
99
392.9
69.3
59
452.0
79.7
19
511.1
90.1
79
570.2
100.5
40
334.8
59.1
59.2
400
401
393. 9
69.5
69.6
60
461
453.0
79.9
20
512.1
513. 1
90.3
90.5
80
581
571.2
572. 2"
100.7
100.9
341
335. 8
394.9
454.0
80.1
^521"
42
336.8
59.4
02
395.9
69.8
62
455. 0
80.2
22
514.1
90.6
82
573.2
101.0
43
837.8
59.6
03
396. 9
70.0
63
456.0
80.4
23
515.1
90.8
83
574.1
101.2
44
338.8
59.8
04
397.9
70.2
64
457.0
80.6
24
516.0
91.0
84
575.1
101.4
45
339.8
59.9
05
398.9
70.3
65
457.9
80.8
25
517.0
91.2
85
576.1
101.6
46
340.7
60.1
06
399.8
70.5
66
458.9
80.9
26
518.0
91.3
86
577.1
101.7
47
341.7
60.3
07
400.8
70.7
67
459.9
81.1
27
519. 0
91.5
87
578.1
101.9
48
342.7
60.4
08
401.8
70.9
68
460.9
81.3
28
520.0
91.7
88
579.1
102.1
49
343.7
60.6
09
402.8
71.0
69
461.9 81.5
29
521.0
91.9
89
580.0
102.3
50
351
344 7
60.8
10
403.8
71.2
70
471
462.9
463.8
81.6
81.8
30
521.9
92.0
90
591
581.0
102.4
345.7
61.0
411
404.8
71.4
531 522. 9
92.2
582.0
102.6
52
346.7
61.1
12
405. 7
71.6
72
464.8
82.0
32
523.9
92.4
92 .
583.0
102.8
53
347.6
61.3
13
406.7
71.7
73
465. 8
82.1
33
524.9
92.5
93
584.0
102.9
54
348.6
61.5
14
407.7
71.9
74
466.8
82.3
34
525. 9
92.7
94
585.0
103.1
55
349.6
61.7
15
408.7
72.1
75
467.8
82.5
35
526.9
92.9
95
586.0
103. 3
56
350. 6
61.8
16
409.7
72.2
76
468.8
82.7
36
527. 9
93.1
96
586.9
103.5
57
351.6
62.0
17
410.7
72.4
77
469.8
82.8
37
528.8
93.2
97
587.9
103.6
•58
352. 6
62.2
18
411.7
72. 6
78
470.7
83.0
38
529.8
93.4
98
588.9
103.8
59
353. 5
62 4
19
412.6
72.8
79
471.7
83.2
39
530.8
93.6
99
589.9
104.0
60
354.5
Dep.
62.5
20
413.6
72.9
80
472.7
83.4
40
531. 8
93.8
600
590.9
104.2
Dist.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. j Dep.
Lat.
Dist.
Dep.
Lat.'
1
^0° (100°, 260°, 280°
)•
Page 388]
TABLE '2.
Difference of Latitude and Depart
ure for 11° (169°, 191°, 349
').
Dist.
Lat.
1 Dep.
Dist.
Lat.
Dep.
Dist. Lat.
; Dep.
Dist.
Lat.
Dep.
Dist. 1 Lat.
Dep.
1
1.0
0.2
61
59.9
11.6
121
118.8
23.1
181
177.7
34.5
241
236.6
46.0
2
2.0
0.4
62
60.9
11.8
22
119.8
23.3
82
178.7
34,7
42
237.6
46.2
3
2 9
0.6
63
61.8
12.0
23
120.7
23.5
83
179.6
34.9
43
238.5
46.4
4
3.9
0.8
64
62.8
12.2
24
121.7
23.7
84
180. 6
35.1
44
239.5
46.6
5
4.9
1.0
65
63.8
12.4
25 1 122.7
23.9
85
181.6
35. 3
45
240.5
46.7
6
5.9
1.1
M
64.8
12.6
26 123. 7
24.0
86
182.6
35.5
46
241.5
46.9
7
6.9
1.3
65.8
12.8
27 1 124. 7
24.2
87
183.6
3.5.7
47
242.5
47.1
8
7.9
1.5
68
66,8
13.0
28
125.6
24.4
88
184.5
35.9
48
243.4
47.3
9
8.8
1.7
69
67.7
13.2
29
126.6
24.6
89
185.5
36.1
49
244.4
47.5
10
9.8
1.9
70
68.7
13.4
30
127.6
24.8
90
186.5
36.3
50
245.4
47.7
11
10.8
2.1
71
69.7
13.5
131
128. 6
25.0
191
187.5
36.4
251 : 246.4
47.9
12
11.8
2.3
72
70.7
13.7
32
129.6
25.2
92
188.5
36.6
52 1 247.4
48.1
13
12.8
2.5
73
71.7
13.9
33
130.6
25.4
93
189.5
36.8
53 i 248.4
48.3
14
13.7
2.7
74
72.6
14.1
34
131. 5
25.6
94
190.4
37.0
54
249.3
48.5
15
14.7
2.9
75
73.6
14.3
35
132.5
25.8
95
191.4
37.2
55
250.3
48.7
*6
15.7
3.1
76
74.6
14.5
36
133.5
26.0
96
192.4
37.4
56
251.3
48.8
17
16.7
3.2
77
75.6
14.7
37
134.5
26.1
97
193.4
37.6
57
252.3
49.0
18
17.7
3.4
78
76.6
14.9
38
135.5
26.3
98
194.4
37.8
58
253.3
49.2
19
18.7
3.6
79
77.5
15.1
39
136.4
26.5
99
195.3
.38.0
59
254.2
49.4
20
19.6
3.8
80
78.5
15.3
40
137.4
26.7
20a
196.3
38.2
60
2.55. 2
49.6
21
20.6
4.0
81
79.5
15.5
141
138.4
26.9
201
1«7.3
38.4
261
256. 2
49.8
22
21.6
4.2
82
80.5
15.6
42
139.4
27.1
02
198.3
38.5
62
257.2
50.0
23
22.6
4.4
83
81.5
15.8
43
140.4
27.3
03
199.3
38.7
63
258.2
50.2
-24
23.6
4.6
84
82.5
16.0
44
141 4
27.5
04
200.3
38.9
64
259.1
50.4
25
24.5
4.S
85
83.4
16.2
45
142.3
27.7
05
201.2
39.1
65
260.1
50.6
26
25.5
5.0
86
84.4
16.4
46
143.3
27.9
06
202.2
39.3
66
261.1
50.8
27
26.5
5.2
87
85.4
16.6
47
144.3
28.0
07
203. 2
39.5
67
262.1
50.9
28
27.5
5.3
88
86.4
16.8
48
145.3
28.2
08
204.2
39.7
68
263.1
51.1
29
28.5
5.5
89
87.4
17.0
49
146.3
28.4
09
205.2
39.9
69
264.1
51.3
30
29.4
5.7
90
88.3
17.2
50
147.2
28.6
10 ' 206. 1
40.1
40. 3
70
265.0
51.5
51.7
31
30.4
5.9
91
89.3
17.4
151
148.2
28.8
211 207. 1
271
266.0
32
31.4
6.1
92
90.3
17.6
52
149.2
29.0
12
208.1
40.5
72
267.0
51.9
33
32.4
6.3
93
91.3
17.7
53
150.2
29.2
13
209.1
40.6
73
268.0
52.1
34
33.4
6.5
94
92.3
17.9
54
151. 2
29.4
14
210.1
40.8
74
269.0
52.3
35
34.4
6.7
95
93.3
18.1
55
152.2
29.6
15 1 211.0
41.0
75
269.9
52.5
36
35.3
6.9
96
94.2
18.3
56
153.1
29.8
16
212.0
41.2
76
270.9
52.7
37
36.3
7.1
97
95.2
18.6
57
154.1
30.0
17
213.0 41.4
77
271.9
52.9
38
37.3
7.3
98
96.2
18.7
58
155.1
30.1
18
214.0 41.6
78
272.9
53.0
39
38.3
7.4
99
97.2
18.9
59
156. 1
30.3
19
215.0 1 41.8
79
273.9
53.2
40
39.3
7.6
100
98.2
19. 1
60
157.1
30.5
20
216.0 1 42.0
80
274.9
53. 4
41
40.2
7.8
101
99.1
19.3
161
158. 0
30.7
221
216.9 42.2
281
275.8
53.6
42
41.2
8.0
02
100.1
19.5
62
159.0
30.9
22
217.9 ; 42.4
82
276.8
53.8
43
42.2
8.2
03
101. 1
19.7
63
160.0
31.1
23
218.9 : 42.6
83
277.8
64.0
44
43.2
8.4
04
102.1
19.8
64
161.0
31.3
24
219. 9 42. 7
84
278.8
54.2
45
44.2
8.6
05
103. 1
20.0
65
162.0
31.5
25
220.9 \ 42.9
85
279.8
54.4
46
45.2
8.8
06
104.1
20.2
66
163.0
31.7
26
221.8 1 4.3.1
86
280.7
54.6
47
46.1
9.0
07
105.0
20.4
67
163.9
31.9
27
222.8
43. 3
87
281.7
54.8
48
47.1
9.2
08
106. X)'
20.6
68
164.9
32.1
28
223.8
43. 5
88
282.7
55.0
49
48.1
9.3
09
107.0
20.8
69
165. 9
32.2
29
224.8
43.7
89
283.7
66.1
50
49.1
9.5
10
108.0
21.0
70
166.9
32.4
30
225.8
43.9
90
291
284.7
56.3
51
50.1
9.7
111
109.0
21.2
171
167.9
32.6
231
226.8
44.1
285.7
65.5
52
51.0
9.9
12
109. 9
21.4
72
168.8
32.8
32
227.7
44.3
92
286 6
55.7
53
52.0
10.1
13
110.9
21.6
73
169.8
33.0
33
228.7
44.5
93
287.6
56.9
54
53.0
10.3
14
111.9
21.8
74
170.8
33.2
34
229. 7 1 44. 6
94
288.6
66.1
55
54.0
10.5
15
112.9
21.9
75
171.8
33.4
35
230.7 44.8
95
. 289. 6
66.3
56
55.0
10.7
16
113.9
22.1
76
172.8
33.6
36
231. 7 1 45. 0
96
290.6
56.5
57
56.0
10.9
17
114.9
22.3
77
173.7
33.8
37
232.6 i 45.2
97
291.5
56.7
58
56.9
11.1
18
115.8
22.5
78
174.7
34.0
38
233.6 i 45.4
98
292.5
56.9
59
57.9
11.3
19
116.8
22.7
79
175.7
34.2
39
234.6 45.6
99
293.5 :
57.1
60
58.9
11.4
20
117.8
22.9
80
176.7
34.3
40
235.6
45.8
300
294.5
67.2
Dlst.
Dep,
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. 1
Lat.
Dist.
Dep.
Lat.
7
9° (101°, 259'
',■281°).
TABLE 2.
[Page 389
Difference of Latitude and Departure for 11° (169°, 191
°, 349°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
295.4
57.4
361
354.3
68.9
421
413.2
80.3
481
472.1
91.8
541
531.0
103.2
02
296.4
57.6
62
355. 3
69.1
22
414.2
80.5
82
473.1
92.0
42
532.0
103.4
03
297.4
57.8
63
356. 3
69.3
23
415.2
80.7
83
474.1
92.2
43
533.0
103. 6
04
298.4
58.0
64
357. 3
69.5
24
416.2
80.9
84
475.1
92.4
44
534.0
103.8
05
299.4
58.2
65
358.3
69.6
25
417.2 81.1
85
476. 1
92.6
45
535. 0
104.0
06
300.3
58.4
66
359. 2
69.8
26
418.1 j 81.3
86
477.0
92.8
46
535.9
104.2
07
301.3
58.6
67
360.2
70.0
27
419.1 1 81.5
87
478.0
93.0
47
536.9
104.4
08
302.3
58.8
68
361.2
70.2
28
420.1 i 81.7
88
479.0
93.2
48
537.9
104.6
09
303.3
59.0
69
362.2
70.4
29
421.1 1 81.9
89
480.0
93.3
49
538. 9
104.8
10
311
304.3
305.3
59.2
70
363. 2
364.1
70.6
30
422.1 1 82.1
90
491
481.0
93.5
50
539.9
540.8
105.0
59.3
371
70.8
431
423.0 1 82.2
481.9
93.6
551
105. 1
12
306.2
59.5
72
365.1
71.0
32
424.0
82.4
92
482.9
93.8
52
541.8
105.3
13
307.2
59.7
73
366. 1
71.2
33
425. 0
82.6
93
483.9
94.0
53
542.8
105.5
14
308.2
59.9
74
367.1
71.4
34
426.0
82.8
94
484.9
94.2
54
543.8
105.7
15
309.2
,60.1
75
368.1
71.6
35
427.0
83.0
95
485.9
94.4
55
544.8
105. 9
16
310.2
60.3
76
369.1
71.7
36
428.0
83.2
96
486.9
94.6
56
545.8
106.1
17
311.1
60.5
77
370.0
71.9
37
428.9
83.4
97
487.8
94.8
57
546.7
106.3
18
312.1
60.7
78
371.0
72.1
38
429.9
83.6
98
488.8
95.0
58
547.7
106.5
19
313.1
60.9
79
372.0
72.3
39
430.9
83.8
99
489.8
95.2
59
548.7
106.7
20
321
314.1
315.1
61.1
80
381
373.0
72.5
40
431.9
432.9
84.0
84.1
500
501
490.8
491.8
95.4
60
549.7
550. T
106.9
107.1
61.3
374.0
72.7
441
95.6
561
22
316.1
61.4
82
374.9
72.9
42
433. 8
84.3
02
492.7
95.8
62
551.6
107.2
23
317.0
61.6
83
375.9
73.1
43
434.8
84.5
03
493.7
96.0
63
552.6
107.4
24
318.0
61.8
84
376.9
73.3
44
435.8
84.7
04
494.7
96.2
64
553.6
107.6
25
319.0
62.0
85
377.9
73.5
45
436.8
84.9
05
495.7
96.4
65.
554.6
107.8
26
320.0
62.2
86
378.9
73.7
46
437.8
85.1
06
496.7
96.6
66
555.6
108.0
27
321.0
62.4
87
379.9
73.8
47
438.8
85.3
07
497.7
96.8
67
556.6
108.2
28
321.9
62.6
88
380.8
74.0
48
439.7
85.5
08
498.6
97.0
68
557.6
108.4
29
322.9
62.8
89
381.8
74.2
49
440.7
85.7
09
499.6
97.2
69
558.6
108.6
30
323.9
63.0
90
382. 8
74.4
50
441.7
85.9
10
500.6
97.3
70
571
559.5
560.5
108.8
331
324.9
63.2
391
383.8
74.6
451
442.7
86.1
511
501.6
97.5
109.0
32
325. 9
63.4
92
384.8
74.8
52
443.7
86.2
12
502.6
97.6
72
561.5
109.1
33
326.8
63.5
93
385.7
75.0
53
444.6
86.4
13
503.5
97.8
73
562.5
109.3
34
327. 8
63.7
94
386.7
75.2
54
445.6
86.6
14
504.5
98.0
74
563.5
109.5
35
328.8
63.9
95
387.7
75.4
55
446.6
86.8
15
505.5
98.2
75
564.5
109.7
36
329.8
64.1
96
388.7
75.6
56
447.6
87.0
16
506.5
98.4
76
565.4
109.9
37
330.8
64.3
97
389.7
75.8
57
448.6
87.2
17
507.5
98.6
77
566.4
110.1
38
331.8
64.5
98
390.7
75.9
58
449.6
87.4
18
508.5
98.8
78
567.4
110.3
39
332.7
64.7
99
391.6
76.1
59
450.5
87.6
19
509.4
99.0
79
568.3
110.5
40
333.7
64.9
400
401
392. 6
393.6
76.3
60
451.5
87.8
20
510.4
511.4
99.2
80
569.3
570.3
110.7
341
334.7
65.1
76.5
46]
452.5
88.0
521
99.4
581
110.9
42
335.7
65.3
02
394.6
76.7
62
453.5
88.2
22
512.4
99.6
82
571.3
111.1
43
336.7
65.5
03
395. 6
76.9
63
454.5
88.3
23
513.4
99.8
83
572.3
111.3
44
337.6
65.6
04
396.5
77.1
64
455. 4
88.5
24
514.3
100.0
84
573.2
111.5
45
338.6
65.8
05
397.5
77.3
65
456.4
88.7
25
515.3
100.2
85
574.2
111.7
46
339.6
66.0
06
398.5
77.5
66
457.4
88.9
26
516.3
100.4
86
575. 2
111.8
47
340.6
66.2
07
399.5
77.7
67
458.4
89.1
27
517.3
100.6
87
576.2
112.1
48
341.6
66.4
08
400.5
77.9
68
459.4
89.3
28
518.3
100.8
88
577. 2
112.3
49
342. 6
66.6
09
401.5
78.1
69
460.4
89.5
29
519.3
101.0
89
578.2
112.4
50
351
343.5
66.8
10
402.4
403.4
78.2
78.4
70
471
461. 3
462.3
89.7
30
520.2
101.2
90
579.1
112.6
344.5
67.0
411
89.9
531
521.2
101.4
591
580. 1
112.8
52
345.5
67.2
12
404.4
78.6
72
463.3
90.1
32
522.2
101.6
92
581.1
113.0
53
346.5
67.4
13
405.4
78.8
73
464.3
90.3
33
523.2
101.7
93
582.1
113.2
54
347. 5
67.5
14
406.4
79.0
74
465.3
90.4
34
524.2
101.8
94
583.1
113.3
55
348.4
67.7
15
407.3
79.2
75
466.2
90.6
35
525.1
102.0
95
584.0
113.5
56
349.4
67.9
16
408.3
79.4
76
467.2
90.8
36
526.1
102.2
96
585.0
113.7
57
350. 4
68.1
17
409.3
79.6
77
468.2
91.0
37
527.1
102.4
97
586.0
113.9
58
351.4
68.3
18
410.3
79.8
78
469.2
91.2
38
528.1
102.6
98
587.0
114.1
59
352.4
68.5
19
411.3
80.0
79
470.2
91.4
39
529.1
102.8
99
588.0
114.3
60
353.4
68.7
20
412.3
80.1
80
471.1
91.6
40
530.1
103.0
600
589.0
114.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. 1 Dep.
Lat.
D:st.
Dep.
Lat.
79° (101°, 259°, 281°).
Page 390]
TABLE 2.
Difference of Latitude and Departure for 12°
(168°, 192°, 348°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.7
12.7
121
118.4
25.2
181
177.0
37.6
241
235.7
50.1
2
2.0
0.4
62
60.6
12.9
22
119.3
25.4
82
178.0
37.8
42
236.7
50.3
3
2.9
0.6
63
61.6
13.1
23
120.3
25.6
83
179.0
38.0
43
237.7
50.5
4
3.9
0.8
64
62.6
13.3
24
121.3
25.8
84
180.0
38.3
44
238.7
50.7
5
4.9
1.0
65
63.6
13.5
25
122.3
26.0
85
181.0
38.5
45
239.6
50.9
6
5.9
1.2
6/
64.6
13.7
26
123.2
26.2
86
181.9
38.7
46
240.6
51.1
7
6.8
1.5
65.5
13.9
27
124.2
26.4
87
182.9
38.9
47
24L6
51.4
8
7.8
1.7
68
66.5
14.1
28
125. 2
26.6
88
183.9
39.1
48
242.6
51.6
9
8.8
1.9
69
67.5
14.3
29
126.2
26.8
89
184.9
39.3
49
243.6
51.8
10
11
9.8
10.8
2.1
2.3
70
68.5 1 14.6
30
131
127.2
27.0
27.2
90
191
185.8
186.8
39.5
50
244. 5
245.5
52.0
52.2
71
69.4
14.8
128.1
39.7
251
12
11.7
2.5
72
70.4
15.0
32
129.1
27.4
92
187.8
39.9
52
246.5
52.4
13
12.7
2.7
73
71.4
15.2
33
130.1
27.7
93
188.8
40.1
53
247.5
52.6
14
13.7
2.9
74
72.4
15.4
34
131.1
27.9
94
189.8
40.3
54
248.4
52.8
15
14.7
3.1
75
73.4
15.6
35
132.0
28.1
95
190.7
40.5
55
249.4
53.0
16
15.7
3.3
76
74.3
15.8
36
133.0
28.3
96
191.7
40.8
56
250.4
53.2
17
16.6
3.5
77
75.3
16.0
37
134.0
28.5
97
192.7
41.0
57
251.4
53.4
18
17.6
3.7
78
76.3
16.2
38
135.0
28.7
98
193.7
41.2
58
252.4
53.6
19
18.6
4.0
79
77.3
16.4
39
136.0
28.9
99
194.7
41.4
59
253.3
53.8
20
21
19.6
4.2
80
78.3
16.6
40
136.9
29.1
29.3
200
201"
195.6
196.6
41.6
41.8
60
261
254.3
54.1
20.5
4.4
81
79.2
16.8
141
137.9
255. 3
54.3
22
21.5
4.6
82
80.2
17.0
42
138.9
29.5
02
197.6
42.0
62
256.3
54.5
23
22.5
4.8
83
81.2
17.3
43
139.9
29,7
03
198.6
42.2
63
257.3
54.7
24
23.5
5.0
84
82.2
17.5
44
140.9
29.9
04
199.5
42.4
64
258.2
54.9
25
24.5
5.2
85
83.1
17.7
45
141.8
30.1
05
200.5
42.6
65
259.2
55.1
26
25.4
5.4
86
84.1
17.9
46
142.8
30.4
06
201.5
42.8
66
260.2
55.3
27
26.4
5.6
87
85.1
18.1
47
143.8
30.6
07
202.5
43.0
67
261.2
55.5
28
27.4
5.8
88
86.1
18.3
48
144.8
30.8
08
203.5
43.2
68
262.1
55.7
29
28.4
6.0
89
87.1
18.5
49
145.7
31.0
09
204.4
43.5
69
263.1
55.9
30
29.3
6.2
90
88.0
18.7
50
146.7
31.2
10
205.4
206.4
43.7
43.9
70
264.1
56.1
31
30.3
6.4
91
89.0
18.9
151
147.7
31.4
211
271
265.1
56.3
32
31.3
6.7
92
90.0
19.1
52
148.7
31.6
12
207.4
44.1
72
266.1
56.6
33
32.3
6.9
93
91.0
19.3
53
149.7
31.8
13
208.3
44.3
73
267.0
56.8
34
33.3
7.1
94
91.9
19.5
54
150.6
32.0
14
209.3
44.5
74
268.0
57.0
35
34.2
7.3
95
92.9
19.8
55
151.6
32.2
15
210. 3
44.7
75
269.0
57.2
36
35.2
7.5
96
93.9
20.0
56
152.6
32.4
16
211.3
44.9
76
270.0
57.4
37
36.2
7. 7
97
94.9
20.2
57
153.6
32.6
17
212. 3
45.1
77
270.9
57.6
38
37.2
7.9
98
95.9
20.4
58
154. 5
32.9
18
213. 2
45.3
78
271.9
57.8
39
38.1
8.1
99
96.8
20.6
59
155. 5
33.1
19
214.2
45. 5
79
272.9
58.0
40
39.1
8.3
100
97.8
20.8
60
156.5
33.3
20
215.2
216.2
45.7
45.9
80
281
273.9
274. 9
58.2
58.4
41
40.1
8.5
101
98.8
21.0
161
157.5
33.5
221
42
41.1
8.7
02
99.8
21.2
62
158.5
33.7
22
217.1
46.2
82
275.8
58.6
43
42.1
8.9
03
100.7
21.4
63
159.4
33.9
23
218.1
46.4
83
276.8
58.8
44
43.0
i9.1
04
101.7
21.6
64
160.4
34.1
24
219.1
46.6
84
277.8
59.0
45
44.0
'9.4
05
102.7
21.8
65
161.4
34.3
25
220.1
46.8
85
278.8
59.3
46
45.0
9.6
oS
103.7
22.0
66
162.4
34.5
26
221.1
47.0
86
279.8
59.5
47
46.0
9.8
07
104.7
22.2
67
163.4
34.7
27
222.0
47.2
87
280.7
59.7
48
47.0
10.0
08
105.7
22.5
68
164.3
34.9
28
223.0
47.4
88
281.7
59.9
49
47.9
10.2
09
106.6
22.7
69
165.3
35.1
29
224.0
47.6
89
282.7
60.1
50
48.9
10.4
10
107.6
22.9
70
166.3
35.3
35.6
30
231
225.0
226.0
47.8
48.0
90
291
283.7
60.3
51
49.9
10.6
111
108.6
23.1
171
167.3
284.6
60.5
52
50.9
10.8
12
109.6
23.3
72
168.2
35.8
32
226.9
48.2
92
285. 6
60.7
53
51.8
11.0
13
110.5
23.5
73
169.2
36.0
33
227.9
48.4
93
286.6
60.9
54
52.8
11.2
14
111.5
23.7
74
170.2
36.2
34
228.9
48.7
94
287.6
61.1
55
53.8
11.4
15
112.5
23.9
75
171.2
36.4
35
229.9
48.9
95
288.6
61.3
56
54.8
11.6
16
113. 5
24.1
76
172.2
36.6
36
230.8
49.1
96
289.5
61.5
57
55.8
11.9
17
114.4
24.3
77
173.1
36.8
37
231.8
49.3
97
290.5
61.7
58
56.7
12.1
18
115. 4
24.5
78
174.1
37.0
38
232.8
49.5
98
291.5
62.0
59
57.7
12.3
19
116.4
24.7
79
175.1
37.2
39
233. 8
49.7
99
292.5
62.2
60
58.7
12.5
20
117.4
24.9
80
176.1
37.4
40
234.8
49.9
300
293.4
62.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lit.
Dist.
Dep.
Lat.
1
'8° (1
32°, 258
=,.282°).
TABLE 2.
[Page 391
Difference of Latitude and Departure for 12° (
168°, 192°, 348
°)-
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. j Dep.
Dist.
Lat.
Dep.
301
294.4
62.6
361
353. 1
75.0
421
411.8
87.5
481
470.5
100.0
541
529.2
112.5
02
295. 4
62.8
62
354. 1
75.2
22
412.8
87.7
82
471.5
100.2
42
530.2
112.7
03
296.4
63.0
63
355. 1
75.4
23
413.8
87.9
83
472.5
100.4
43
531.1
112.9
04
297.4
63.2
64
356.0
75.. 7
24
414.7
88.1
84
473.4
100.6
44
532. 1
113.1
05
298.3
63.4
65
357. 0
75.9
25
415. 7
88.3
85
474.4
100.8
45
533.1
113.3
0(5
299. 3
63.6
66
358. 0
76.1
26
416.7
88.6
86
475.4
101.0
46
534. 1
113.5
07
300. 3
63.8
67
359. 0
76.3
1 27
417.7
88.8
87
476.4
101. 2
47
535.1
113.7
08
301.3
64.0
68
360. 0
76.5
28
418.6
89.0
88
477.3
101.4
48
536.0
113.9
09
302. 2
64.2
69
360. 9
76.7
29
419.6
89.2
89
478.3
101.6
49
537.0
114.1
10
311
303. 2
304. 2
64.4
70
371
361.9
76.9
77.1
30
420.6
421.6
89.4
89.6
90
491
479.3
101.9
50
538. 0
538.9
114.4
114.6
64.6
362.9
1 431
480.3
102.1
551
12
305.2
64.8
72
363.9
77.3
32
422.6
89.8
92
481.2
102.3
52
539. 9
114.3
13
306. 2
65.1
73
364.8
77.5
33
423.5 ; 90.0
93
482.2
102.5
53
540.9
115.0
14
307. 1
65.3
74
365.8
77.7
34
424.5 i 90.2
94
483.2
102.7
54
541.9
115.2
15
308.1
65.5
75
366.8
77.9
35
425.5 90.4
95
484.2
102.9
55
542.9
115.4
16
309.1
65.7
76
367.8
78.2
36
426.5 90.6
96
485.2
103.1
56
543. 8
115.6
17
310. 1
65.9
77
368.8
78.4
37
427.5 . 90.8
97
486.1
103.3
57
544. 8
115.8
18
311. 1
66.1
78
369.7
78.6
38
428.4 91.0
98
487.1
103.5
58
545. 8
116.0
19
312.0
66.3
79
370.7
78.8
39
429.4 91.3
99
488.1
103.8
59
546.8
116.2
20
313. 0
66.5
80
371.7
79.0
40
430.4 91.5
500
489.1
104.0
60
547.8
116.4
321
314.0
66.7
381
372.7
79.2
441
431.4 91.7
501
490.0
104.2
561
548.7
116.6
22
315.0
66.9
82
373. 7
79.4
42
432.3 i 91.9
02
491.0
104.4
62
549.7
116.8
23
315.9
67.1
83
374.6
79.6
43
433. 3 92. 1
03
492.0
104.6
63
550.7
117.0
24
316.9
67.3
84
375.6
79.8
44
434.3 ' 92.3
04
493.0
104.8
64
551.7
117.2
25
317.9
67.6
85
376.6
80.0
45
435. 3 92. 5
05
494.0
105.0
65
552.7
117.4
26
318.9
67.8
86
377.6
80.2
46
436. 3 92. 7
06
495. 0
105.2
66
553. 7
117.6
27
319.9
68.0
87
378.5
80.4
47
437.2 ! 92.9
07
495.9
105.4
67
554.6
117.8
28
320.8
68.2
88
379. 5
80.7
48
438.2 ! 9.3.1
08
496.9
105. 6
68
555.6
118.0
29
321.8
68.4
89
380. 5
80.9
49
439.2 i 93.3
09
497.9
105. 8
69
556.6
118.2
30
331
322. 8
323.8
68.6
90
381.5
382.5
81.1
81.3
50
440.2
93.5
93.7
10
498.9
106.0
106. 2
70
571
557.5
118.5
118.7
68.8
391
451
441.1
511
499.8
558.5
32
324.7
69.0
92
383.4
81.5
52
442.1
93.9
12
500.8
106.4
72
559. 5
118.9
33
325.7
69.2
93
384.4
81.7
53
443.1
94.1
13
501.8
106.6
73
560.5
119.1
34
326.7
69.4
94
385.4
81.9
54
444.1
9'4.4
14
502.8
106.8
74
561.5
119.3
35
327.7
69.6
95
386.4
82.1
55
445. 1
94.6
15
503.7
107.0
75
562. 4
119.5
36
328.7
69.8
96
387. 3
82.3
56
446.0
94.8
16
504.7
107.2
76
563.4
119.7
37
'329. 6
70.0
97
388.3
82.5
57
447.0
95.0
17
505.7
107.4
77
564. 4
119. 9
38
330.6
70.3
98
389.3
82.7
58 1 448.0
95.2
18
506. 7
107.6
78
565.4
120.1
39
331.6
70.5
99
390.3
82.9
59 j 449.0
95.4
19
507.7
107.8
79
566,4
120.3
40
332.6
333. 5
70.7
400
391.3
392.2
83.1
60
450. 0
450. 9
95.6
95. 8
20
521
508.7
509. 6
108.1
80
567.4
120.6
120. 8
341
70.9
401
83.4
461
108.3
581
568.3
42
334. 5
71.1
02
393. 2
83.6
62
451.9
96.0
22
510.6
108.5
82
569.3
121.0
43
335.5
71.3
03
394. 2
83.8
63
452.9
96.2
23
511.6
108.7
83
570. 3
121.2
44
386.5
71.5
04
395.2
84.0
64 453.9
96.5
24
512.5
108.9
84
571.2
121.4
45
337.5
71.7
05
396.2
84.2
65
454.8
96.7
25
513.5
109.2
85
572.2
121.6
46
338. 4
71.9
06
397. 1
84.4
66
455. 8
96.9
26
514.5
109.4
86
573.2
121.8
47
339.4
72.1
07
398.1
84.6
67
456. 8
97.1
27
515. 5
109.6
87
574.2
122.0
48
340.4
72.3
08
399. 1
84.8
68 i 457.8
97.3
28
516. 5
109.8
88
575.2
122.2
49
341.4
72.5
09
400.1
85.0
69 1 458.8
97.5
29
517.5-
110.0
89
576.2
122.4
50
342.4
72.7
10
411
401.0
402.0
85.2
85. 4"
70 i 459. 7
97.7
30
518. 4
519.4
110.2
90
591
577.1
122. 6
122.8
351
343. 3
73.0
471 460. 7
97.9
531
110.4
578.1
52
344.3
73.2
12
403.0
85.6
72 ! 461. 7
98.1
32
520. 4
110.6
92
579.1
123.0
53
345. 3
73.4
13
404.0
85.8
73 . 462. 7
98.3
33
521. 3
110.8
93
580.0
123.2
54
346.3
73.6
14
405. 0
86.1
74 463.6
98.5
34
522.3
111.0
94
581.0
123.4
55
347.2
73.8
15
405. 9
86.3
75 464.6
98.7
35
523.3
111.2
95
582.0
123.6
56
.348. 2
74.0
16
406. 9
86.5
76
465.6
98.9
36
524.3
111.4
96
583.0
123.9
57
349.2
74.2
17
407.9
86.7
77
466.6
99.1
37
525.3
111.6
97
584.0
124.1
58
350. 2
74.4
18
408. 9
86.9
78
467.6
99.4
38
526.2
111.8
98
584. 9
124. 3
59
.351.2
74.6
19
409.8
87.1
79
468.5
99.6
39
527.2
112.0
99
585.9
124.5
60
352.1
74.8
20
410.8
87.3
80
469.5
99.8
40
528.2
112.3
600
586.9
124.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Di.st.
Dep.
Lat.
7
8° (102°, 258°, 282°
)•
Page 392]
TABLE
( 2.
Difference of Latitude and Departure for
13° (167°, 193
°, 347°
).
Dist.
J^t.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.4
13.7
121
117.9
27.2
181
176.4
40.7
241
234.8
54.2
2
1.9
0.4
62
60.4
13.9
22
118.9
27.4
82
177.3
40.9
42
235.8
54.4
3
2.9
0.7
63
61.4
14.2
23
119.8
27.7
83
178.3
41.2
43
236.8
54.7
4
3.9
0.9
64
62.4
14.4
24
120.8
27.9
84.
179.3
41.4
44
237.7
54.9
5
4.9
1.1
65
63.3
14.6
25
121.8
28.1
85
180.3
41.6
45
238.7
55.1
6
5.8
1.3
1?
64.3
14.8
26
122.8
28.3
86
181.2
41.8
46
239.7
55.3
7
6.8
1.6
65.3
15.1
27
123.7
28.6
87
182.2
42.1
47
240.7
55.6
8
7.8
1.8
68
66.3
15.3
28
124.7
28.8
88
183.2
42.3
48
241.6
55.8
9
8.8
2.0
69
67.2
15.5
29
125.7
29.0
89
184.2
42.5
49
242.6
56.0
10
9.7
10.7
2.2
70
68.2
15.7
30
126.7
29.2
29.5
90
185.1
42.7
50
243.6
244.6
56. 2
11
2.5
71
69.2
16.0
131
127.6
191
186.1
43.0
251
56.5
12
11.7
2.7
72
70.2
16.2
32
128.6
29.7
92
187.1
43.2
52
245.5
56.7
13
12.7
2.9
73
71.1
16.4
33
129.6
29.9
93
188.1
43.4
53
246.5
56.9
14
13.6
3.1
74
72.1
16.6
34
130.6
30.1
94
189.0
43.6
54
247.5
57.1
15
14.6
3.4
75
73.1
16.9
35
131.5
30.4
95
190.0
43.9
55
248.5
57.4
16
15.6
3.6
76
74.1
17.1
36
132.5
30.6
96
191.0
44.1
56
249.4
57.6
17
16.6
3.8
77
75.0
17.3
37
133.5
30.8
97
192.0
44.3
57
250.4
57.8
18
17.5
4.0
78
76.0
17.5
38
134.5
31.0
98
192.9
44.5
58
251.4
58.0
19
18.5
4.3
79
77.0
17.8
39
135.4
31.3
99
193.9
44.8
59
252.4
58.3
20
19.5
4.5
80
77.9
18.0
40
136.4
31.5
200
194.9
45.0
60
261
253. 3
254.3
58.5
58.7
21
20.5
4.7
81
78.9
18.2
141
137.4
31.7
201
195.8
45.2
22
21.4
4.9
82
79.9
18.4
42
138.4
31.9
02
196.8
45.4
62
255.3
58.9
23
22.4
5.2
83
80.9
18.7
43
139.3
32.2
03
197.8
45.7
63
256.3
59.2
24
23.4
5.4
84
81.8
18.9
44 140. 3
32.4
04
198.8
45.9
64
257.2
59.4
25
24.4
5.6
85
82.8
19.1
45 141. 3
32.6
05
199.7
46.1
65
258.2
59.6
26
25.3
5.8
86
83.8
19.3
46
142.3
32.8
06
200.7
46.3
66
259.2
59.8
27
26.3
6.1
87
84.8
19.6
47
143.2
33.1
07
201.7
46.6
67
260.2
60.1
28
27.3
6.3
88
85.7
19.8
48
144.2
3.3.3
08
202.7
46.8
68
261.1
60.3
29
28.3
6.5
89
86.7
20.0
49
145.2
33.5
09
203. 6
47.0
69
262.1
60.5
30
29.2
6.7
90
91
87.7
20.2
50
151
146.2
33.7
10
204.6
205.6
47.2
47.5
70
263.1
264.1
60.7
61.0
31
30.2
7.0
88.7
20.5
147.1
34.0
211
271
32
31.2
7.2
92
89.6
20.7
52
148.1
34.2
12
206.6
47.7
72
265.0
61.2
33
32.2
7.4
93
90.6
20.9
53
149.1
34.4
13
207.5
47.9
73
266.0
61.4
34
33.1
7.6
94
91.6
21.1
54
150.1
34.6
14
208.5
48.1
74
267.0
61.6
35
34.1
7.9
95
92.6
21.4
55
151.0
34.9
15
209.5
48.4
75
268.0
61.9
36
35.1
8.1
96
93.5
21.6
56
152.0
35.1
16
210.5
48.6
76 ! 268.9
62.1
37
36.1
8.3
97
94.5
21.8
57
153.0
35.3
17
211.4
48.8
77
269.9
62.3
38
37.0
8.5
98
95.5
22.0
58
154.0
35.5
18
212.4
49.0
78
270.9
62.5
39
38.0
8.8
99
96.5
22.3
59
154.9
35.8
19
213.4
49.3
79
271.8
62.8
40
39.0
9.0
100
97.4
22.5
60
155.9
36.0
20
221
214. 4
49.5
80
272.8
63.0
41
39.9
9.2
101
98.4
22.7
161
156.9
36.2
215.3
49.7
281
273.8
63.2
42
40.9
9.4
02
99.4
22.9
62
157.8
36.4
22
216.3
49.9
82
274.8
63.4
43
41.9
9.7
03,
100.4
23.2
63
158.8
36.7
23
217.3
50.2
83
275.7
63.7
44
42.9
9.9
04
101.3
23.4
64
159.8
36.9
24
218.3
50.4
84
276.7
63.9
45
43.8
10.1
05
102.3
23.6
65
160.8
37.1
25
219.2
50.6
85
277.7
64.1
46
44.8
10.3
06
103.3
23.8
66
161.7
37.3
26
220.2
50.8
86
278.7
64.3
47
45.8
10.6
07
104.3
24.1
67
162.7
37.6
27
221.2
51.1
87
279.6
64.6
48
46.8
10.8
08
105.2
24.3
68
163.7
.37.8
28
222.2
51.3
88
280.6
64.8
49
47.7
11.0
09
106.2
24.5
69
164.7
38.0
29
223.1
51.5
89
281.6
65.0
50
48.7
11.2
10
107.2
24.7
70
165. 6
166.6
38.2
38.5
30
231
224.1
51.7
90
282.6
65.2
51
49.7
11.5
111
108.2
25.0
171
225.1
52.0
291
283. 5
65.5
52
50.7
11.7
12
109.1
25.2
72
167.6
38.7
32
226.1
52.2
92
284.5
65.7
53
51.6
11.9
13
110.1
25.4
73
168.6
38.9
33
227.0
52.4
93
285. 5
65.9
54
52.6
12.1
14
111.1
25.6
74
169.5
39.1
34
228.0
52.6
94
286.5
66.1
55
53.6
12.4
15
112.1
25.9
75
170.5
39.4
35
229.0
52.9
95
287.4
66.4
56
54.6
12.6
16
113.0
26.1
76
171.5
39.6
36
230.0
53.1
96
288.4
66.6
57
55.5
12.8
17
114.0
26.3
77
172.5
39.8
37
230.9
53.3
97
289.4
66.8
58
56.5
13.0
18
115.0
26.5
78
173.4
40.0
38
231. 9
53.5
98
290.4
67.0
59
57.5
13.3
19
116.0
26.8
79
174.4
40.3
39
232.9
53.8
99
291.3
67.3
60
58.5
13.5
20
116.9
27.0
80
175.4
40.5
40
233.8
54.0
300
292.3
67.5
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
11° (103°, 257
°, 283°
)•
TABLE
2.
[Page 393 ]
Difference of Latitude and Departure for 13° (167°, 193°, 347°
)■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
301
293.3
67.7
361
351.8
81.2
421
410.2
94.7
481 468. 7 ' 108. 2
541
527.2
121.7
02
294.3
67.9
62
352.7
81.4
22
411.2
94.9
82 469. 7 108. 4
42
528.1
121.9
03
295. 2
68.1
63
353.7
81.6
23
412.2
95.1
83 ; 470. 6 108. 6
43
529.1
122.1
04
296.2
68.4
64
354. 7
81.9
24
413.1
95.3
84 1 471.6 108.8
44
530.1
122.3
05
297.2
68.6
65
355. 6
82.1
25
414.1
95.6
85 : 472.6
109.0
45
531. 1
122.5
06
298.2
68.8
66
356. 6
82.3
26
415.1
95.8
86 i 473. 6
109.3
46
532.0
122.8
07
299.1
69.0
67
357.6
82.5
27
416.1
96.0
87 474. 5
109.5
47
533.0
123.0
08
300.1
69.3
68
358.6
82.8
28
417.0
96.2
88 475. 5
109.7
48
534.0
123. 2
09
301. 1
69.5
69
359.5
83.0
29
418.0
96.5
89 476. 5
109.9
49
535.0
123.4
10
302.1
69.7
70
360.5
361.5
83.2
30
419.0
96.7
90 1 477.5 1110.1
50
535.9
123.7
311
303.0
69.9
371
83.4
431
420.0
96.9
491 478.4 110.4
551
536. 9
123.9
12
304.0
70.2
72
362.5
83.7
32
420.9
97.1
92 479.4 110.6
52
537.9
124.1
13
305.0
70.4
73
363. 4
83.9
33
421.9
97.4
93 ! 480. 4 ! 110. 9
53
538.9
124.4
14
306.0
70.6
74
364.4
84.1
34
422.9
97.6
94 ' 481.4 '111.1
54
539.8
124.6
15
306.9
70.8
75
365.4
84.3
35
423.9
97.8
95 1 482. 3 i 111. 3
55
540.8
124.9
16
307.9
71.1
76
366.4
84.6
36
424.8
98.0
96 ! 483.3 111.5
56
541.8
125. 1
17
308.9
71.3
77
367.3
84.8
37
425.8
98.3
97
484.3 111.8
57
542.8
125.3
18
309.9
71.5
78
368.3
85.0
38
426.8
98.5
98
485. 3 1 112. 0
58
543.7
125.5
19
310.8
71.7
79
369.3
85.2
39
427.8
98.7
99 486. 2 ! 112. 2
59
544.7
125.8
20
321
311. 8
72.0
72.2
80
381
370.3
85.5
40
428.7
98.9
500
487.2
488.2
112.4
60
545.7
126.0
312.8
371.2
85.7
441
429.7
99.2
501
112.6
561
546.7
126.2
22
313.8
72.4
82
372.2
85.9
42
430.7
99.4
02 489.2 112.9
62
547.6
126.4
23
314.7
72.6
83
373.2
86.1
43
431.6
99.6
03 490. 1 113. 1
63
548.6
126.7
24
315.7
72.9
84
374.2
86.4
44
432.6
99.8
04 491.1
113.3
64
549.6
126.9
25
316.7
73.1
85
375.1
86.6
45
433.6
100.1
05 492. 1
113.5
65
550.6
127.1
26
317.6
73.3
86
376.1
86.8
46
434.6
100.3
06 493. 1
113.8
66
551.5
127.3
27
318.6
73.5
87
377. 1
87.0
47
435.5
100.5
07 1 494.0
114.0
67
552.5
127.6
28
319.6
73.8
88
378.1
87.3
48
436.5
100.7
08 495.0
114.2
68
553. 5
127.8
29
320.6
74.0
89
379.0
87.5
49
437.5
101.0
09 496.0
114.5
69
554.5
128.0
30
321.5
322.5
74.2
74.4
90
391
380. 0
87.7
50
438.5
101.2
10
496.9
497. 9
114.7
70
555.4
556.4
128.3
128.5
331
381.0
87.9
451
439.4
101.4
511
114.9
571
32
323.5
74.7
92
382.0
88.2
52
440.4
101.6
12
498.9
115.1
72
557.4
128.7
33
324.5
74.9
93
382.9
88.4
53
441.4
101.9
13
499.9
115.4
73
558.4
128.9
34
325.4
75.1
94
383.9
88.6
54
442.4
102.1
14 ! 500.8
115. 6
74
559.3
129.2
35
326.4
75.3
95
384.9
88.8
55
443.3
102.3
15 i 501.8
115.8
75
560.3
129.4
36
. 327. 4
75.6
96
385.9
89.1
56
444.3
102.5
16 i 502. 8
116.0
76
561.3
129.6
37
■ 328. 4
75.8
97
386.8
89.3
57
445.3
102.8
17 503. 8
116.3
77
562.3
129.8
38
329.3
76.0
98
387.8
89.5
58
446.3
103.0
18
504.7
116.5
78
563. 2
130.0
39
330.3
76.2
99
388.8
89.7
59
447. 2
103.2
19
505.7
116.7
79
564.2
130.2
40
331.3
332.3
76.5
400
389.8
390. 7
90.0
60
448.2
449. 2
103.4
103. 7
20
506.7
116.9
80
565.2
566.2
130.4
341
76.7
401
90.2
461
521
507.7 :117.2
581
130.7
42
333.2
76.9
02
391. 7
90.4
62
450.2
103.9
22
508.6 1117.5
82
567.1
131.0
43
334.2
77.1
03
392.7
90.6
63
451.1
104.1
23
509. 6 i 117. 7
83
568.1
131. 2
44
335.2
77.4
04
393. 6
90.8
64
452. 1
104.3
24
510.6 117.9
84
569.1
131.4
45
336.2
77.6
05
394. 6
91.1
65
453. 1
104.6
25
511.6 118.1
85
570.1
131.6
46
337.1
77.8
06
395. 6
91.3
66
454.1
104.8
26
512.5 118.3
86
571.0
131.8
47
338.1
78.0
07
396.6
91.5
67
455.0
105.0
27
513.5 118.5
87
572.0
132.0
48
339. 1
78.3
08
397. 5
91.7
68
456.0
105.2
28
514.5 118.7
88
573.0
132. 3
49
340.1
78.5
09
398. 5
92.0
69
457.0
105.5
29
515.5 ,119.0
89
573.9
132.5
50
341.0
78.7
10
399.5
92.2
70
458.0
105. 7
30
516.4
119.2
90
574.9
132.8
351
342.0
78.9
411
400.5
92.4
471
458.9
105. 9
531
517.4
119.4
591
575.9
133.0
52
343.0
79.2
12
401.4
92.6
72
459. 9
106.1
32
518.4
119.6
92
576.9
133.2
53
344.0
79.4
13
402.4
92.9
73
460.9
106.4
33
519.4
119.9
93
577.8
133.4
54
344.9
79.6
14
403.4
93.1
74
461.9
106.6
34
520.3 120.1
94
578.8
133.6
55
345.9
79.8
15
404.4
93.3
75
462.8
106.8
35
521. 3 i 120. 3
95
579.8
133. 8
56
346.9
80.1
16
405.3
93.5
76
463.8
107.0
36
522. 3 ! 120. 5
96
580.8
134.0
57
347. 9
80.3
17
406.3
93.8
77
464.8
107.3
37
523.3
120.8
97
581.7
134.3
58
348.8
80.5
18
407.3
94.0
78
465.8
107.5
38
524.2
121.0
98
582.7
134.5
59
349.8
80.7
19
408.3
94.2
79
466.7
107.7
39
525.2
121.2
99
583.7
134.8
60
350.8
81.0
20
409.2
94.4
80
467.7
107.9
40
526.2
121.5
600
584.6
135.0
Dist.
Dep.
Lat.
Dist
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. 1 Lat.
Dist.
Dep.
Lat.
77° (1
03°, 257
°, 283°
)•
Page 394]
TABLE 2.
Difference of Latitude and Departure for 14° (166°, 194
°, 346°
)•
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1 0
0.2
61
59.2
14.8
121
117.4
29.3
181
175.6
43.8
241
233.8
58.3
2
1.9
0.5
62
60.2
15.0
22
118.4
29.5
82
176.6
44.0
42
234.8
58.5
3
2.9
0.7
63
61.1
15.2
23
119.3
29.8
83
177.6
44.3
43
235.8
58.8
4
3.9
1.0
64
62.1
15.5
24
120.3
30.0
84
178.5
44.5
44
236.8
59.0
5
4.9
1.2
65
63.1
15.7
25
121.3
30.2
85
179.5
44.8
45
237.7
59.3
6
5.8
1.5
66
(54.0 16.0
26
122.3
30.5
86
180.5
45.0
46
238.7
59.5
7
6.8
1.7
t7
65.0 1 16.2
27
123.2
30.7
87
181.4
45.2
47
239. 7
59.8
8
7.8
1.9
68
66.0 16.5
28
124.2
31.0
88
182.4
45.5
48
240.6
60.0
9
8.7
2.2
69
67. 0 ! 16. 7
29
125.2
31.2
89
183.4
45.7
49
241.6
60.2
10
11
9.7
10.7
2.4
70
67.9 1 16.9
30
126.1
31.4
31.7
90
191
184.4
46.0
46.2
50
251
242. 6
243.5
60.5
2.7
71
68.9
17.2
131
127.1
185. 3
60.7
12
11.6
2.9
72
69.9
17.4
32
128.1
31.9
92
186.3
46.4
52
244.5
61.0
13
12.6
3.1
73
70.8
17.7
33
129.0
32.2
93
187.3
46.7
53
245. 5
61.2
14
13.6
3.4
74
71.8
17.9
34
130.0
32.4
94
188.2
46.9
54
246.5
61.4
15
14.6
3.6
75
72.8
18.1
35
131. 0
32.7
95
189. 2
47.2
55
247.4
61.7
16
15.5
3.9
76
73.7
18.4
36
132.0
32.9
96
190.2
47.4
56
248.4
61.9
17
16.5
4.1
77
74.7
18.6
37
132.9
33.1
97
191.1
47.7
57
249.4
62.2
18
17.5
4.4
78
75.7
18.9
38
133.9
33.4
98
192.1
47.9
58
250.3
62.4
19
18.4
4.6
79
76.7
19.1
39
134.9
33.6
99
193.1
48.1
59
251.3
62.7
20
19.4
4.8
80
77.6
19.4
40
135.8
33.9
200
194.1
48.4
60
252.3
62.9
21
20.4
5.1
81
78.6
19.6
141
136.8
34.1
201
195.0"
48.6
261
253.2
63.1
22
21.3
5.3
82
79.6
19.8
42
137.8
34.4
02
196.0
48.9
62
254.2
63.4
23
22.3
5.6
83
80.5
20.1
43
138.8
34.6
03
197.0
49.1
63
255. 2
63.6
24
23.3
5.8
84
81.5
20.3
44
139. 7
34.8
04
197.9
49.4
64
256.2
63.9
25
24.3
6.0
85
82.5
20.6
45
140.7
35.1
05
198.9
49.6
65
257.1
64.1
26
25.2
6.3
86
83.4
20.8
46
141.7
35.3
06
199.9
49.8
66
258. 1
64.4
27
26.2
6.5
87
84,4
21.0
47
142.6
35.6
07
200.9
50.1
67
259.1
64.6
28
27.2
6.8
88
85.4
21.3
48
143.6
35.8
08
201.8
50.3
68
260.0
64.8
29
28.1
7.0
89
86.4
21.5
49
144.6
36.0
09
202.8
50.6
69
261.0
65.1
30
29.1
7.3
90
87.3
21.8
50
145.5
36.3
10
203.8
204.7
50.8
70
262.0
65.3
31
30.1
7.5
91
88.3
22.0
151
146.5
36.5
211
51.0
271
'263. 0
65.6
32
31.0
7.7
92
89.3
22.3
52
147.5
36.8
12
205.7
51.3
72
263.9
65.8
33
32.0
8.0
93
90.2
22.5
53
148. 5
37.0
13
206.7
51.5
73
264.9
66.0
34
33.0
8.2
94
91.2
22.7
54
149.4
37.3
14
207.6
51.8
74
265.9
66.3
35
34.0
8.5
95
92.2
23.0
55
150.4
37.5
15
208.6
52.0
75
266.8
66.5
36-
34.9
8.7
96
93.1 1 23.2
56
151. 4
37.7
16
209.6
52.3
76
267.8
66.8
37
35.9
9.0
97
94.1 ! 23.5
57
152.3
38.0
17
210.6
52.5
77
268.8
67.0
38
36.9
9.2
98
95.1 i 23.7
58
153. 3
38.2
18
211.5
52.7
78
269.7
67.3
39
37.8
9.4
99
96.1 24.0
59
154.3
. .38. 5
19
212. 5
53.0
79
270.7
67.5
40
38.8
9.7
100
97.0 24.2
60
155.2
38.7
20
213. 5
53.2
80
271.7
67.7
68.0
41
39.8
9.9
101
98.0 j 24.4
161
156. 2
38.9
221
214.4
53.5
281
272.7
42
40.8
10.2
02
99. 0 ' 24. 7
62
157. 2
39.2
22
215.4
53.7
82
273.6
68.2
43
41.7
10.4
03
99.9 1 24.9
63
158.2
39.4
23
216.4
53. 9
83
274.6
68.5
44
42.7
10.6
04
100.9 ! 25.2
64
159.1
39.7
24
217.3
54.2
84
275. 6
68.7
45
43.7
10.9
05
101.9 25.4
65
160.1
39.9
25
218.3
54.4
85
276.5
68.9
46
44.6
11.1
06
102. 9 25. 6
66
161.1
40.2
26
219.3
54.7
86
277.5
69.2
47
45.6
11.4
07
103.8 25.9
67
162.0
40.4
27
220.3
54.9
87
278.5
69.4
48
46.6
11.6
08
104. 8 26. 1
68
163.0
40.6
28
221.2
55.2
88
279.4
69.7
49
47.5
11.9
09
105. 8 26. 4
69
164.0
40.9
29
222.2
55.4
89
280.4
69.9
50
48.5
12.1
10
106.7 1 26.6
70
165.0
165.9
41.1
30
223.2
55.6
90
281.4
282.4
70.2
70. 4
51
49.5
12.3
111
107. 7 26. 9
171
41.4
231
224.1
55. 9
291
52
50.5
12.6
12
108. 7 27. 1
72
166.9
41.6
32
225. 1
56.1
92
283.3
70.6
53
51.4
12.8
13
109. 6 27. 3
73
167.9
41.9
33
226.1
56.4
93
284. 3
70.9
54
52.4
13.1
14
110.6 1 27.6
74
168.8
42.1
34
227.0
56.6
94
285. 3
71.1
55
53.4
13.3
15
111.6
27.8
75
169.8
42.3
35
228.0
56.9
95
286.2
71.4
56
54.3
13.5
16
112,6
28.1
76
170.8
42.6
36
229.0
57.1
96
287.2
71.6
57
55.3
13.8
17
113.5
28.3
77
171.7
42.8
37
230. 0
57.3
97
288.2
71.9
58
56.3
14.0
18
114. 5
28.5
78
172.7
43.1
38
230. 9
57.6
98
289.1
72.1
59
57.2
14.3
19
115.5
28.8
79
173.7
43.3
39
231.9
57.8
99
290.1
72.3
60
58.2
14.5
20
116.4
29.0
80
174.7
43.5
40
232.9
58.1
300
291.1
72.6
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
■6° (1
04°, 256°,. 284°
).
TABLE
J 2.
[Page 395
Difference of Latitude and Departure for 14° (166°, 194
°, 346°
)•
Dist.
301
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
292.0
72.8
361
350. 2
87.3
421
408.5
101.8
481
466.7
116.3
541
525. 0
130.9
02
293.0
73.0
62
351. 2
87.6
22
409.4
102.1
82
467.7
116.6
42
525. 9
131.2
03
294.0
73.3
63
352. 2
87.8
23
410.4
102.3
83
468.6
116.8
43
526. 9
131.4
04
294.9
73.5
64
353. 2
88.0
24
411.4
102.6
84
469.6
117.1
44
527. 9
131.6
05
295.9
73.8
65
354.1
88.3
25
412.3
102.8
85
470.6
117.3
45
528. 8
131.9
06
296.9
74.0
66
355. 1
88.5
26
413.3
103.0
86
471.5 117.6
46
52a. 8
132. 1
07
297.8
74.2
67
356. 1
88.8
27
414.3
103.3
87
472.5
117.8
47
530.8
132. 3
08
298.8
74.5
68
357.0
89.0
28
415.3
103.5
88
473.5
118.0
48
531. 7
132.6
09
299.8
74.7
69
358.0
89.2
29
416.2
103.8
89
474.5
118.3
49
532. 7
132.8
10
311
300.8
75.0
70
359.0
359.9
89.5
30
431
417.2
104.0
90
475.4
118.5
50
551
533. 7
534.6
133.0
133.3
301. 7
75.2
371
89.7
418.2
104.2
491
476.4
118.8
12
302.7
75.5
72
360.9
90.0
32
419.1
104. 5
92
477.4
119.0
52
535. 6
133.6
13
303.7
75.7
73
361.9
90.2
33
420.1
104.7
93
478.3
119.2
53
536.6
133.8
14
304.6
7S.9
74
362.9
90.5
34
421.1
105.0
94
479.3
119.5
54
537.5
134.0
15
305.6
76.2
75
363.8
90.7
35
422.0
105. 2
95
480.3
119.7
55
538.5
134. 3
16
306.6
76.4
76
364.8
90.9
36
423.0
105.5
96
481.3
120.0
56
539.5
134. 5
17
307.6
76.7
77
365.8
91.2
37
424.0
105.7
97
482.2
120.2
57
540. 5
134.8
18
308.5
76.9
78
366.7
91.4
38
425.0
105. 9
98
483.2
120.4
58
541.4
135. 0
19
309.5
77.2
79
367. 7 *
91.7
39 425. 9
106.2
99
484.2
120.7
59
542.4
135. 2
20
321
310.5
77.4
80
368.7
91.9
40
426.9
106.4
500
501
485.1
486.1
121.0
60
543.4
544. 3
135. 5
135. 7
311.4
77.6
381
369. 6
92.2
441
427.9
106.7
121.2
561
22
312.4
77.9
82
370.6
92.4
42
428.8
106.9
02
487.1
121.4
62
545. 3
135.9
23
313. 4
78.1
83
371.6
92.6
43
429.8
107.1
03
488.0
121.7
63
546.3
136.2
24
314.3
78.4
84
372. 6
92.9
44
430.8
107.4
04
489.0
122.0
64
547.2
136. 5
25
315. 3
78.6
85
373.5
93.1
45
431.7
107.6
05
490.0
122.1
65
548.2
136.6
26
316. 3
78.8
86
374. 5
93.4
46 432. 7
107.9
06
491.0
122.4
66
549.2
136.9
27
317. 3
79.1
87
375. 5
93.6
47
433. 7
108.1
07
491.9
122.6
67
550.1
137.1
28
318.2
79.3
88
376. 4
93.8
48
434.7
108.4
08
492.9
122.9
68
551.1
137.4
29
319.2
79.6
89
377.4
94.1
49
435.6
108.6
09
493.9
123.1
69
552.1
137.6
30
331
320.2
79.8
90
378.4
94.3
94.6
50
451
436.6
437.6
108.8
109.1
10
511
494. 9
495. 8
123. 4
70
553.1
554.0
137.9
138.1
321.1
80.1
391
379.4
123.6
571
32
322. 1
80.3
92
380.3
94.8
52 ! 438.5
109.3
12
496.8
123. 8
72
555. 0
138. 3
33
323. 1
80.5
93
381. 3
95.1
53 1 439.5
109.6
13
497.8
124.1
73
556.0
138.6
34
324. 0
80.8
94
382. 3
95. 3
54 440.5
109.8
14
498.7
124.3
74
557.0
138. 8
35
325. 0
81.0
95
383. 2
95. 5
55
441.5
110.1
15
499. 7
124.6
75
557.9
139.1
36
■ 326. 0
81.3
96
384. 2
95.8
56
442.4
110.3
16
500.7
124.8
76
558.9
139.3
37
327. 0
81.5
97
385.2
96.0
57
443.4
110.5
17
501.7
125.0
77
559.9
139.5
38
327. 9
81.7
98
386. 1
96.3
58
444.4
110.8
18
502.6
125.3
78
560.9 I 139.8
39
328.9
82.0
99
387. 1
96.5
59
445. 3
111.0
19
503.6
125.6
79
561.8 140.0
40
341
329.9
82.2
400
388.1
96.7
97.0
60 1 446. 3
461 i 447. 3
111.3
20
521
504. 6
505.5
12.5. 8
126. 0
80
581
562.8 i 140.3
330.8
82.5
401
389.1
111.5
563.8
140.5
42
331.8
82.7
02
390. 0
97.2
62
448.2
111.7
22
506. 5
126.2
82
564.7
140.8
43
332.8
83.0
03
391.0
97.5
63
449.2
112.0
23
507.5
126.5
83
565.7
141.0
44
333.7
83.2
04
392.0
97.7
64
450.2
112.2
24
508. 4
126.8
84
566.7
141.3
45
334.7
83.4
05
392.9
98.0
65
451. 2
112.5
25
509. 4
127.0
85
567.6
141.5
46
335. 7
83.7
06
393.9
98.2
66
452. 1
112.7
26
510.4
127.2
86
568. 6
141.8
47
336. 7
83.9
07
394.9
98.4
67
453.1
113.0
27
511.4
127.5
87
569. 6
142.0
48
337.6
84.2
08
395.8
98.7
68
454.1
113.2
28
512. 3
127.8
88
570. 6
142.3
49
338. 6
84.4
09
396.8
98.9
69
455. 0
113.4
29
513.3
128.0
89
571. 5
142.5
50
351
339.6
340.5
84.7
84.9
10
411
397. 8
99.2
70
456.0
457.0
113.7
113.9
30
531
514.3
515.3
128.2
128.5
90
591
572.5
142.8
398.8
99.4
471
573.5 1 143.0
52
341.5
85.1
12
399.7
99.7
72
457.9
114.2
32
516.2
128.8
92
574.4 1 143.3
53
342.5
85.4
13
400. 7
99.9
73
458. 9
114.4
33
517.2
129.0
93
575.4 j 143.5
54
343. 5
85.6
14
401.7
100.1
74
459. 9
114.6
34
518. 2
129.2
94
576.4 ' 143.8
55
344.4
85.9
15
402.6
100.4
75
460.9
114.9
35
519. 1
129.4
95
577.3 i 144.0
56
345.4
86.1
16
403. 6
100.6
76
461.8
115.1
36
520.1
129.7
96
578.3 ; 144.2
57
346. 4
86.3
17
404.6
100.9
77 i 462.8
115.4
37
521.1
129.9
97
579.3 144.5
58
347.3
86.6
18
405. 5
101.1
78
463.8
115.6
38
522. 1
130. 2
98
580.3 144.7
59
348. 3
86.8
19
406. 5
101.3
79
464.7
115. 9
39
523. 0
130. 4
99
581.2 144.9
60
349.3
87.1
20
407. 5
101.6
80
465.7
116.1
40
524. 0
130.6
600
582.2 145.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. 1 Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
76° (104°, 256
°, 284°
)•
1 Page 396]
TABLE
2.
Difference of Latitude and Departure for 15° (165°, 195°
, 345°)
Dist.
Lat.
Dep.
Dist
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.9
15.8
121
116.9
31.3
181
174.8
46.8
241
232.8
62.4
2
1.9
0.5
62
59.9
16.0
22
117.8
31.6
82
175.8
47.1
42
233. 8
62.6
3
2.9
0.8
63
60.9
16.3
23
118.8
31.8
83
176. 8
47.4
43
234.7
62.9
4
3.9
1.0
64
61.8
16.6
24
119.8
32.1
84
177.7
47.6
44
235.7
63.2
5
4.8
1.3
65
62.8
16.8
25
120.7
32.4
85
178.7
47.9
45
236.7
63.4
6
5.8
1.6
66
63.8
17.1
26
121.7
32.6
86
179.7
48.1
46
237.6
63.7
7
6.8
1.8
•67
64.7
17.3
27
122.7
32.9
87
180.6
48.4
47
238.6
63.9
8
7.7
2,1
68
65.7
17.6
28
123.6
33.1
88
181.6
48.7
48
239.5
64.2
9
8.7
2.3
69
66.6
17.9
29
124.6
33.4
89
182.6
48.9
49
240.5
64.4
10
9.7
2.6
2.8
70
71
67.6
18.1
30
125.6
33.6
90
191
183.5
184.5
49.2
50
241.5
242.4
64.7
65.0
11
10.6
68.6
18.4
131
126.5
33.9
49.4
251
12
11.6
3.1
72
69.5
18.6
32
127.5
34.2
92
185.5
49.7
52
243.4
65.2
13
12.6
3.4
73
70.5
18.9
33
128.5
34.4
93
186.4
50.0
53
244.4
65.5
14
13.5
3.6
74
71.5
19.2
34
129.4
34.7
94
187.4
50.2
54
245.3
65.7
15
14.5
3.9
75
72.4
19.4
35
130.4
34.9
95
188.4
50.5
55
246.3
66.0
16
15.5
4.1
76
73.4
19.7
36
131.4
35.2
96
189.3
50.7
56
247.3
66.3
17
16.4
4.4
77
74.4
19.9
37
132.3
35.5
97
190.3
51.0
57
248.2
66.5
18
17.4
4.7
78
75.3
20.2
38
133.3
35.7
98
191.3
51.2
58
249.2
66.8
19
18.4
4.9
79
76.3
20.4
39
134.3
36.0
99
T92.2
51.5
59
250.2
67.0
20
19.3
5.2
80
77.3
20.7
40
135.2
36.2
200
193.2
51.8
60
251.1
252.1
67.3
67.6
21
20.3
5.4
81
78.2
21.0
141
136.2
36.5
201
194.2
52.0
261
22
21.3
5.7
82
79.2
21.2
42
137.2
36.8
02
195.1
52.3
62
253.1
67.8
23
22.2
6.0
83
80.2
21.5
43
138. 1
37.0
03
196.1
52.5
63
254.0
68.1
24
23.2
6.2
84
81.1
21.7
44
139. 1
37.3
04
197.0
52.8
64
255.0
68.3
25
24.1
6.5
85
82.1
22.0
45
140.1
37.5
05
198.0
53.1
65
256.0
68.6
26
25.1
6.7
86
83.1
22.3
46
141.0
37.8
06
199.0
53.3
66
256.9
68.8
27
26.1
7.0
87
84.0
22.5
47
142.0
38.0
07
199.9
53.6
67
257. 9
69.1
28
27.0
7.2
88
85.0
22.8
48
143.0
38.3
08
200.9
53.8
68
258.9
69.4
29
28.0
7.5
89*
86.0
23.0
49
143.9
38.6
09
201. 9
54.1
69
259.8
69.6
30
29.0
7.8
90
86.9
23.3
50
144.9
38.8
10
202.8
54.4
70
260.8
69.9
31
29.9
8.0
91
87.9
23.6
151
145.9
39.1
211
203.8
54.6
271
261.8
70.1
32
30.9
8.3
92
88.9
23.8
52
146.8
39.3
12
204.8
54.9
72
262.7
70.4
33
31.9
8.5
93
89.8
24.1
53
147.8
39.6
13
205.7
55.1
73
263.7
70.7
34
32.8
8.8
94
90.8
24.3
54
148.8
39.9
14
206.7
55.4
74
264.7
70.9
35
33.8
9.1
95
91.8
24.6
55
149.7
40.1
15
207.7
55.6
75
265.6
71.2
36
34.8
9.3
96
92.7
24.8
56
150.7
40.4
16
208.6
55.9
76
266.6
71.4
37
35.7
9.6
97
93.7
25.1
57
151.7
40.6
17
209.6
56.2
77
267.6
71.7
38
36.7
9.8
98
94.7
25.4
58
152.6
40.9
18
210.6
56.4
78
268.5
72.0
39
37.7
10.1
99
95.6
25.6
59
153.6
41.2
19
211.5
56.7
79
269.5
72.2
40
38.6
10.4
100
96.6
25.9
60
154.5
41.4
20
212.5
56.9
80
281
270.5
72.5
41
39.6
10.6
101
97.6
26.1
161
155. 5
41.7
221
213.5
57.2
271.4
72.7
42
40.6
10.9
02
98.5
26.4
62
156.5
41.9
22
214.4
57.5
82
272.4
73.0
43
41.5
11.1
03
99.5
26.7
63
157.4
42.2
23
215.4
57.7
83
273.4
73.2
44
42.5
11.4
04
100.5
26.9
64
158.4
42.4
)J^
216.4
58.0
84
274.3
73.5
45
43.5
11.6
05
101.4
27.2
65
159.4
42.7
'-^5
217.3
58.2
85
275. 3
73.8
46
44.4
11.9
06
102.4
27.4
66
160.3
43.0
26
218.3
58.5
86
276.3
74.0
47
45.4
12.2
07
103.4
27.7
67
161.3
43.2
27
219.3
58.8
87
277.2
74.3
48
46.4
12.4.
08
104.3
28.0
68
162.3
43.5
28
220.2
59.0
88
278.2
74.5
49
47.3
12.7
09
105.3
28.2
69
163.2
43.7
29
221.2
59.3
89
279.2
74.8
50
51
48.3
12.9
10
106.3
28.5
70
171
164.2
44.0
30
222.2
59.5
90
280.1
75.1
49.3
13.2
111
107.2
28.7
165.2
44.3
231
223.1
59.8
291
281.1
75.3
52
50.2
13.5
12
108.2
29.0
72
166.1
44.5
32
224.1
60.0
92
282.1
75.6
53
51.2
13.7
13
109.1
29.2
73
167.1
44.8
33
225.1
60.3
93
283.0
75.8
54
52.2
14.0
14
110.1
29.5
74
168.1
45.0
34
226.0
60.6
94
284.0
76.1
55
53.1
14.2
15
111.1
29.8
75
169.0
45.3
35
227.0
60.8
95
284.9
76.4
56
54.1
14.5
16
112.0
30.0
76
170.0
45.6
36
228.0
61.1
96
285. 9
76.6
57
55.1
14.8
17
113.0
30.3
77
171.0
45.8
37
228.9
61.3
97
286.9
76.9
58
56.0
15.0
18
114.0
30.5
78
171.9
46.1
38
229.9
61.6
98
287.8
77.1
59
57.0
15.3
19
114.9
30.8
79
172.9
46.3
39
230. 9
61.9
99
288.8
77.4
60
58.0
15.5
20
115.9
31.1
80
173.9
46.6
40
231.8
62.1
300
289.8
77.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
75° (105°, 25,
>°, 285<
')•
TABLE 2.
[Page 397
Difference of Latitude and Departure for
15° (165°, 195
°, 345°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
290. 7
77.9
361
348.7
93.4
421
406.6
109.0
481
464.6
124.5
541
522.6
140.0
02
291.7
78.2
62
349. 6
93.7
22
407.6
109.2
82
465.6
124.8
42
523.5
140.3
03
292.7
78.4
63
350. 6
94.0
23
408.6
109. 5
83
466.5
125. 0
43
524.5
140.5
04
293.6
78.7
64
351.6
94.2
24
409. 5
109.7
84
467.5
125. 3
44
525.5
140.8
05
294.6
78.9
65
352. 5
94.5
25
410. 5
110.0
85
468.5
125. 6
45
526.4
141.1
06
295.6
79.2
66
353.5
94.7
26
411.5
110.3
86
469. 4
125. 8
46
527. 4
141.4
07
296.5
79.5
67
354. 5
95.0
27
412.4
110.5
87
470.4
126.1
47
528. 4
141.6
08
297.5
79.7
68
355. 4
95.3
28
413.4
110.8
88
471.4
126.4
48
529.3
141.9
09
298.4
80.0
69
356.4
95.5
29
414.4
111.0
89
472.3
126.6
49
530. 3
142.1
10
311
299.4
300.4
80.2
70
357. 4
358.3
95.8
96.0
30
431
415.3
416.3
111.3
90
473.3
126.9
50
551
531. 3
532. 2
142.4
80.5
371
111.6
491
474. 3
127.1
142.6
12
301.3
80.8
72
359.3
96.3
32
417.3
111.8
92
475.2
127.4
52
533. 2
142.9
13
302. 3
81.0
73
360.3
96.5
33
418.2
112.1
93
476.2
127.6
53
534.2
143.1
14
303.3
81.3
74
361.2
96.8
34
419.2
112.3
94
477.2
127.9
54
535.1
143.4
15
304.2
81.5
75
362.2
97.1
35
420. 2 i 112. 6
95
478.1
128.1
55
536.1
143.7
16
305.2
81.8
76
363.2
97.3
36
421.1 [112.9
96
479.1
128.4
56
537. 1
143.9
17
306.2
82.1
77
364.1
97.6
37
422.1 113.1
97
480.1
128.6
57
538. 0
144.2
18
307. 1
82.3
78 1 365. 1
97.8
38
423.1 113.4
98
481.0
128.9
58
539. 0
144.4
19
308.1
82.6
79 i 366. 1
98.1
39
424.0 113.6
99
482.0
129.1
59
540. 0
144.7
20
309. 1
82.8
80
367.0
98.4
40
425.0 113.9
500
483.0
483.9
129.4
129.7
60
540. 9
144.9
321
310. 0
83.1
381
368.0
98.6
441
426.0 114.1
501
561
541.9
145.2
22
311.0
83.3
82
369.0
98.9
42
426.9
114.4
02
484.9
129.9
62
542.9
145.4
23
312.0
83.6
83
369. 9
99.1
43
427.9
114.7
03
485.9
130. 2
63
.543.8
145.7
24
312.9
83.9
84
370.9
99.4
44
428.8
114.9
04
486.8
130.4
64
544.8
146.0
25
313.9
84.1
85
371.9
99.6
45
429.8
115. 2
05
487.8
130.7
65
545.8
146.2
26
314.9
84.4
86 1 372. 8
99.9
46
4.30. 8
115.4
06
488.8
131.0
66
546.7
146.5
27
315.8
84.6
87
373.8
100.2
47
431.7
115. 7
07
489.7
131.2
67
547.7
146.7
28
316.8
84.9
88
374.8
100.4
48
432.7
116.0
08
490.7
131.5
68
548. 7
147.0
29
317.8
85.1
89
375.7
100.7
49
433. 7
116.2
09
491.7
131.7
69
549.6
147.2
30
318.7
85.4
90
376.7
100.9
50
434.6
116. 5
10
492.6
493.6
132. 0
70
550.6
147.5
331
319.7
85.7
391
377.7
101.2
451
435. 6
116. 7
511
132.3
571
551.6
147.8
32
320. 7
85.9
92
378.6
101.5
52
436.6
117.0
12
494.5
132. 5
72
552.5
148.0
33
321.6
86.2
93
379.6
101.7
53
437.5
117.3
13
495.5
132.8
73
553.5
148.3
34
322.6
86.5
94
380.6
102.0
54
438. 5
117.5
14
496.5
133. 0
74
554.4
148.5
35
323.6
86.7
95
381.5
102.2
55
439.5
117.8
15
497.4
133.3
75
555.4
148.8
36
324. 5
87.0
96
382. 5
102.5
56
440.4
118.0
16
498.4
133.5
76
556.4
149.0
37
325. 5
87.2
97
383. 4
102.8
57
441.4
118.3
17
499.4
133.8
77
557.3
149.3
38
326.5
87.5
98
384.4
103.0
58
442.4
118.5
18
500.3
134.0
78
558.3
149. 5
39
327. 4
87.7
99
385.4
103:3
59
443.3
118.8
19
501.3
134.3
79
559. 3
149.8
40
328.4
88.0
400
386.3
103.5
T03.8
60
444.3
119.1
20
502. 3
134.6
80
560.2
150.1
341
329. 4
88.3
401
387.3
461
445.3
119.3
521
503.2
134.8
581
561.2
150.3
42
330. 3
88.5
02
388.3
104.1
62
446.2
119.6
22
504.2
135.1
82
562.2
150.6
43
331. 3
88.8
03
389.2
104.3
63
447.2
119.8
23
505. 2
135. 3
83
563. 1
150.8
44
332. 3
89.0
04
390. 2
104.6
64
448.2
120.1
24
506. 1
135. 6
84
564. 1
151.1
45
333. 2
89.3
05
391.2
104.8
65
449.1
120.4
25
507. 1
135. 9
85
565. 1
151.4
46
334. 2
89.6
06
392. 1
105. 1
66
450. 1
120.6
26
508. 1
136.1
86
566. 0
151.6
47
335.2
89.8
07
393.1
105. 3
67
451. 1
120.9
27
509.0
136. 4
87
567.0
151.9
48
336.1
90.1
08
394. 1
105. 6
68
452. 0
121.1
28
510.0
136. 6
88
568.0
152.2
49
337.1
t)0.3
09
395. 0
105.9
69
453.0
121. 4
29
511.0
136.9
89
568.9
152.4
50
351
338.1
90.6
10
396.0
106.1
70
454.0
121.7
30
511.9
137.2
137.4
90
569.9
152.7
339. 0
90.9
411
397. 0
106.4
471
454. 9
121.9
531
512.9
591
570.9
153. 0
52
340.0
91.1
12
397.9
106.6
72
455. 9
122.2
32
513. 9
137. 7
92
571.8
153.2
53
340.9
91.4
13
398.9
106.9
73
456.9
122.4
33
514.8
137. 9
93
572.8
153.5
54
341. 9
91.6
14
399.9
107.2
74
457.8
122.7
34
515. 8
138.2
94
573.8
153.7
55
342.9
91.9
15
400.8
107.4
75
458.8
122.9
35
516. 8
138.4
95
574.7
154.0
56
343.8
92.1
16
401.8
107.7
76
459. 8
123.2
36
517. 7
138. 7
96
575. 7
154. 2
57
344.8
92.4
17
402. 8
107.9
77
460.7
123.5
37
518. 7
139.0
97
576.7
154.5
58
345.8
92.7
18
403.7
108.2
78
461.7
123.7
38
519.7
139.2
98
577.6
154.8
59
346.7
92.9
19
404.7
108.5
79
462.7
124.0
39
520.6
139. 5
99
578.6
155.0
60
347.7
93.2
20
405.7
108.7
80
463.6
124.2
40
521.6
139.7
600
579.5
155.3
Dist.
Dep.
Lav.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
"i
'5° (1
[)5°, 255°, 285°;
.
Page 398]
TABLE 2.
difference of Latitude and Departure for 16° (
L64°, 196°, 344=
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. 1 Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
66.4
1
1.0
0.3
61
58. 6 16. 8
121 116.3
33.4
181
174.0
49.9
241
231.7
2
1.9
0.6
62
59.6 17.1
22 1 117.3
33.6
82
174.9
50.2
42
232. 6
66.7
3
2.9
0.8
63
60.6 17.4
23
118.2
33.9
83
175. 9
50.4
43
233. 6
67.0
4
3.8
1.1
64
61.5
17.6
24
119.2
34.2
84
176.9
50.7
44
234.5
67.3
6
4.8
1.4
65
62.5
17.9
25
120.2
34.5
85
177.8
51.0
45
235.5
67.5
6
5.8
1.7
^6
63.4
18.2
26
121.1
34.7
86
178.8
51.3
46
236.5
67.8
7
6.7
1.9
67
64.4
18.5
27
122.1
35.0
87
179.8
51.5
47
237. 4
68.1
• 8
7.7
2.2
68
65.4
18.7
28
123.0
35.3
88
180.7
51.8
48
238. 4
68.4
9
8.7
2.5
69
66.3
19.0
29
124.0
35.6
89
181. 7
52.1
49
239.4
68.6
10
11
9.6
2.8
70
67.3
19.3
30
125.0
125.9
35.8
90
182.6
52.4
50
251
240. 3
241.3
68.9
69. 2
10.6
3.0
71
68.2
19.6
131
36.1
191
183.6
52.6
12
11.5
3.3
72
69.2
19.8
32
126.9 36.4
92
184.6
52.9
52
242.2
69.5
13
12.5
3.6
73
70.2
20.1
33
127.8 1 .36.7
93
185.5
53.2
53
243. 2
69.7
14
13.5
3.9
74
71.1
20.4
34
128.8 36.9
94
186. 5
53.5
54
244.2
70.0
15
14.4
4.1
75
72.1
20.7
35
129.8 37.2
95
187.4
53.7
55
245. 1
70.3
16
15.4
4.4
76
73.1
20.9
36
130.7 1 37.5
96
188.4
54.0
56
246.1
70.6
17
16.3
4.7
77
74.0
21.2
37
131.7 37.8
97
189.4
54.3
57
247.0
70.8
18
17.3
5.0
78
75.0
21.5
38
132.7 38.0
98
190.3
54.6
58
248.0
71.1
19
18.3
5.2
79
75.9
21.8
39
133.6 1 38.3
99
191.3
54.9
59
249.0
71.4
20
19.2
5.5
80
81
76.9
22.1
40
134.6
38.6
200
201
192.3
193.2
55.1
55.4
60
261
249.9
250.9
71.7
21
20.2
5.8
77.9
22.3
141
135.5
38.9
71.9
22
21.1
6.1
82
78.8
22.6
42
136.5
39.1
02
194.2
55.7
62
251.9
72.2
23
22.1
6.3
83
79.8
22.9
43
137.5
39.4
03
195.1
56.0
63
252.8
72.5
24
23.1
6.6
84
80.7
23.2
44
138.4
39.7
04
196.1
56.2
64
253.8
72.8
25
24.0
6.9
85
81.7
23.4
45
139.4
40.0
05
197.1
56.5
65
254.7
73.0
26
25.0
7.2
86
82.7
23.7
46
140.3
40.2
06
198.0
56.8
66
255.7
73.3
27
26.0
7.4
87
83.6
24.0
47
141.3
40.5
07
199.0
57.1
67
256. 7
73.6
28
26.9
7.7
88
84.6
24.3
48
142.3
40.8
08
199.9
57.3
68
257.6
73.9
29
27.9
8.0
89
85.6
24.5
49
143.2
41.1
09
200.9
57.6
69
258.6
74.1
30
28.8
8.3
90
86.5
87.5
24.8
50
144.2
145. 2
41.3
41.6
10
201.9
57.9
70
259.5
260.5
74.4
31
29.8
8.5
91
25.1
151
211
202.8
58.2
271
74.7
32
30.8
8.8
92
88.4
25.4
52
146.1
41.9
12
203.8
58.4
72
261.5
75.0
33
31.7
9.1
93
89.4
25.6
53
147.1
42.2
13
204.7
58.7
73
262.4
75.2
34
32.7
9.4
94
90.4
25.9
54
148. 0
42.4
14
205.7
59.0
74
263.4
75.5
35
33.6
9.6
95
91.3
26.2
55
149.0
42.7
15
206.7
59.3
75
264.3
75.8
36
34.6
9.9
96
92.3
26.5
56
150.0
43.0
16
207.6
59.5
76
265.3
76.1
37
35.6
10.2
97
93.2
26.7
57
150.9
43.3
17
208.6
59.8
77
266.3
76.4
38
36.5
10.5
98
94.2
27.0
58
151.9
43.6
18
209.6
60.1
78
267.2
76.6
39
37.5
10.7
99
95.2
27.3
59
152.8
43.8
19
210. 5
60.4
79
268.2
76.9
40
38.5
11.0
100
96.1
27.6
60
153. 8
154.8
44.1
44.4'
20
221
211.5
60.6
80
269.2
77.2
41
39.4
11.3
101
97.1
27.8
161
212.4
60.9
281
270.1
77.5
42
40.4
11.6
02
98.0
28.1
62
155. 7
44.7
22
213.4
61.2
82
271.1
77.7
43
41.3
11.9
03
99.0
28.4
63
156. 7 44. 9
23
214. 4
61.5
83
272.0
78.0
44
42.3
12.1
04
100.0
28.7
64
157.6 1 45.2
24
215. 3
61.7
84
273.0
78.3
45
43.3
12.4
05
100.9
28.9
65 ! 158.6 ! 45.5
25
216.3
62.0
85
274.0
78.6
46
44.2
12.7
06
101.9
29.2
66 1 159.6
45.8
26
217.2
62.3
86
274.9
78.8
47
45.2
13.0
07
102.9
29.5
67
160.5
46.0
27
218.2
62.6
87
275.9
79.1
48
46.1
13.2
08
103. 8
29.8
68
161.5
46.3
28
219.2
62.8
88
276. 8
79.4
49
47.1
13.5
09
104.8
30.0
69
162.5
46.6
29
220.1
63.1
89
277.8
79.7
50
48.1
13.8
14.1
10
111
105. 7 1 30. 3 1
70
163.4
164.4
46.9
30
221.1
222.1
63.4
63.7
90
291
278.8
279.7
79.9
80. 2
51
49.0
106.7
30.6
171
47-1
231
52
50.0
14.3
12
107.7
30.9
72
165.3
47.4
32
223.0
63.9
92
280.7
80.5
53
50.9
14.6
13
108.6
31.1
73
166. 3
47.7
33
224.0
64.2
93
281.6
80.8
54
51.9
14.9
14
109.6
31.4
74
167.3
48.0
34
224.9
64.5
94
282.6
81.0
55
52.9
15.2
15
110.5
31.7
75
168.2
48.2
35
225.9
64.8
95
283. 6
81.3
56
53.8
15.4
16
111.5
32.0
76
169.2
48.5
36
226.9
65.1
96
284.5
81.6
57
54.8
15.7
17
112.5
32.2
77
170.1
48.8
37
227.8
65.3
97
285. 5
81.9
58
55.8
16.0
18
113.4
32.5
78
171.1
49.1
38
228.8
65.6
98
286.5
82.1
59
56.7
16.3
19
114.4
32.8
79
172.1
49.3
39
229.7
65.9
99
287.4
82.4
60
57.7
16.5
20
115.4
33.1
80
173.0
49.6
40
230.7
66.2
300
288.4
82.7
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
ri° (106°, 254°, 286°
).
TABLE 2.
[Page
399
Difference of Latitude and Departure for 16° (164°, 196°, 344'
)■
Dist.
Lat.
Dep.
Dist.
1 Lat.
Dep.
Dist.
1 Lat.
Dep.
116.0
1 Dist.
481
Lat.
Dep.
132.5
Dist.
Lat.
Dep.
301
289.3
82.9
361
347.0
99.5
421
404.7
462.4
541
520.1
149.1
02
290.3
83.2
62
348.0
99.7
22
405.6
116.3
82 1 463.3
132.8
42
521.0
149.4
03
291.2
83.5
68
348. 9
100.0
23
406.6
116. 6
83 1 464.3
133.1
43
522.0
149.7
04
292.2
83.8
64
349.9
100. 3
24
407.6
116.8
84 i 465.2
133.4
44
523.0
150. 0
05
293.2
84.0
65
350.8
100.6
25
408.5
117.1
85 i 466.2
133. 6
45
523.9
150.2
06
294.1
84.3
66
351.8
100.8
26
409.5
117.4
86 ( 467.2
133. 9
46
524.9
150.4
07
295. 1
84.6
67
352.8
101.1
27
410.4
117.7
87 1 468. 1
134.2
47
525.9
150.7
08
296.0
84.9
68
353.7
101.4
28
411.4
117.9
88 469.1
134.5
48
526. 8
151.0
09
297.0
85.1
69
354.7
101.7
29
412.4
118.2
89 j 470. 1
134. 8
49
527.8
151.3
10
298.0
85.4
70
355. 6
356. 6
101. 9
102.2
30
431
413. 3
414.3
118. 5
90 1 471.0
135.0
135.3
50
551
528.7
529.7
151.6
151.9
311
298.9
85.7
371
118.8
491
472.0
12
299.9
86.0
72
357.6
102.5
32
415.2
119. 0
92
472.9
135. 6
52
530.6
152.2
13
300.9
86.2
73
358.5
102.8
33 1 416.2
119. 3
93
473. 9
135. 9
53
531.6
152. 5
14
301.8
86.5
74
359.5
103. 1
34 417.2
119.6
94
474.9
136. 2
54
532.6
152.8
15
302.8
86.8
75
360.4
103.3
35 i 418. 1
119.9
95
475. 8
136.4
55
533. 5
153.0
16
303.7
87.1
76
361.4
103.6
36 419. 1
120.1
96
476.8
136. 7
56
534.5
153.2
17
304.7
87.3
77
362.4
103.9
37 1 420.0
120.4
97
477.7
137.0
57
535. 4
153. 5
18
305.7
87.6
78
363.3
104.2
38 1 421.0
120.7
98
478.7
137.3
58
536.4
153.8
19
306. 6
87.9
79
364.3
104.4
39 i 422.0
121.0
99
479.7
137. 5
59
537.4
154. 1
20
321
307.6
308.5
88.2
88.4
80
381
365.3
366.2
104.7
105. 0
40
441
422.9
121.2
121. 5
500
501
480. 6 ' 137. 8
481.6 138.1
60
538.3
154.4
154. 7
423. 9
561
539.3
22
309.5
88.7
82
367.2
105.3
42 i 424.9
121.8
02
482. 6 138. 3
62
540.3
154.9
23
310.5
89.0
83
368.1
105. 5
43
425.8
122.1
03
483. 5 138. 6
63
541.2
155.2
24
311.4
89.3
84
369.1
105.8
44
426.8
122.3
04 , 484.5 138.9
64
542.2
155.4
25
312. 4
89.5
85
370.1
106.1
45
427.7
122.6
05 [ 485. 4 139. 2
65
543.1
155.7
26
313.3
89.8
86
371.0
106.4
46
428.7
122.9
06 4^6. 4 139. 4
66
544.1
156.0
27
314.3
90.1
87
372.0
106.6
47
429.7
123. 2
07 487. 3 i 139. 7
67
545.1
156.3
28
315. 3
90.4
88
372.9
106.9
48
430.6
123.4
08
488. 3 140. 0
68
546.0
156.6
29
316.2
90.6
89
373.9
107.2
49
431.6
123. 7
09
489.3 !l40.3
69
547.0
156.9
30
331
317.2
318.2
90.9
91.2
90
391
374. 9
375.8
107.5
107.7
50
451
432.6
433.5
124.0
124.3
10
511
490.2
140.6
70
547.9
548. 9"
157.1
491.2
140.8
571
157.3
32
319.1
91.5
92
376.8
108.0
52
434.5
124.6
12
492.1
141.1
72
549.8
157.6
33
320.1
91.8
93
377.8
108.3
53
435.4
124.8
13
493.1
141.4
73
550.8
157.9
34
321.0
92.0
94
378. 7 1 108. 6
54
436. 4
125. 1
14
494.1 jl41.7
74
551.8
158.2
35
322.0
92.3
95
379.7
108.8
55
437. 4
125.4
15
495.0 !l41.9
75
552.7
158.4
36
323.0
92.6
96
380.6
109.1
56
438.3
125.7
16
496.0
142.2
76
553.7
158.7
37
323.9
92.9
97
381.6
109.4
57
439. 3
125. 9
17
496.9
142.5
77
554.6
159.0
38
324.9
93.1
98
382.6
109.7
58
440.2
126.2
18
497.9
142.8
78
555.6
159.3
39
325. 8
93.4
99
383.5
109.9
59
441.2
126.5
19
498.9
143.0
79
556.5
159.5
40
341
326. 8
93.7
400
384.5
110.2
60
442.2
443.1
126.8
127.0
20
521"
499.8
143.3
80
557.5
159. 8
327.8
94.0
401
385.4
110.5
461
500.8
143.6
581
558.4
160.1
42
328.7
94.2
02
386. 4
110.8
62
444.1
127. 3
22
501.7
143.9
82
559.4
160.4
43
329.7
94.5
03
387.4
111.0
63
445.0
127.6
23
502.7
144.1
83
560.4
160.6
44
330.7
94.8
04
388.3 111.3
64
446. 0
127.9
24
503.7
144.4
84
561.3
161.0
45
331.6
95.1
05
389.3 111.6
65
447.0
128.1
25
504.6
144.7
85
562.3
161.3
46
332. 6
95.3
06
390.2 1111.9
66
447.9
128.4
26
505.6
145. 0
86
563.2
161.6
47
333. 5
95.6
07
391.2
112.1
67
448.9
128.7
27
506. 6
145.3
87
564.2
161.8
48
334.5
95.9
08
392.2
112.4
68
449.8
129.0
28
507.5
145.6
88
565.2
162.1
49
335. 5
96.2
09
393.1
112.7
69
450. 8
129.2
29
508. 5
145. 8
89
566.1
162.4
50
351
336.4
96.4
96.7
10
411
394.1
395.1"
113.0
70
471"
451.8
452.7
129.5
129.8
30
531
509.4
146.1
146.4
90
591
567.1
568.1
162.7
337. 4
113.3
510.4
162.9
52
338.3
97.0
12
396.0
113.5
72
453. 7
130. 1
32
511.4
146.7
92
569.0
163. 2
53
339. 3
97.3
13
397.0
113. 8
73
454. 7
130.3
33
512. 3
146.9
93
570.0
163. 5
54
340. 3
97.5
14
397. 9
114.1
74
455.6
130.6
34
513. 3
147.2
94
571.0
163.8
55
341.2
97.8
15
398.9
114.4
75
456.6
130.9
35
514.3
147.5
95
571.9
164.0
56
342. 2
98.1
16
399. 9
114.6
76
457.5
131.2
36
515. 2
147.8
96
572.9
164.3
57
343. 1
98.4
17
400.8
114.9
77
458.5
131.4
37
516.2
148.0
97
573.9
164.6
58
344.1
98.6
18
401.8
115. 2
78
459.5
131.7
38
517.2
148.2
98
574.8
164.9
59
345. 1
98.9
19
402.7
115.5
79
460.4
132.0
39
518.1
148.5
99
575.8
165.1
60
346.0
99.2
20
403.7
115.8
80
461.4
132.3
40
519.1
148.8
600
576.8
165.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Di.st.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
•4° (106°, 254
=, 286°
).
Page 400
TABLE 2.
Difference of Latitude and Departure for 1
7° (163°, 197
=, 343°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.3
17.8
121
115.7
35.4
181
173.1
52.9
241
230.5
70.5
2
1.9
0.6
62
59.3
18.1
22
116.7
35.7
82
174.0
53.2
42
231.4
70.8
3
2.9
0.9
63
60.2
18.4
23
117.6
36.0
83
175.0
53.5
43
232.4
71.0
4
3.8
1.2
64
61.2
18.7
24
118.6
36.3
84
176.0
53.8
44
2.33. 3
71.3
5
4.8
1.5
65
62.2
19.0
25
119.5
36.5
85
176.9
54.1
45
234.3
71.6
6
5.7
1.8
^6
63.1
19.3
26
120.5
36.8
86
177.9
54.4
46
235.3
71.9
7
6.7
2.0
64.1
19.6
27
121.5
37.1
87
178. 8
54.7
47
236. 2
72.2
8
7.7
2.3
68
65.0
19.9
28
122.4
37.4
88
179.8
55.0
48
237.2
72.5
9
8.6
2.6
69
66.0
20.2
29
123.4
37.7
89
180.7
55.3
49
238.1
72.8
10
11
9.6
10.5
2.9
70
66.9
20.5
30
124.3
38.0
38.3
90
181.7
55.6
55. 8
50
251
239.1
240.0
73.1
3.2
71
67.9
20.8
131
125.3
191
182.7
73.4
12
11.5
3.5
72
68.9
21.1
32
126.2 : 38.6
92
183. 6
56.1
52
241.0
73.7
13
12.4
3.8
73
69.8
21.3
33
127.2 i 38.9
93
184.6
56.4
53
241.9
74.0
14
13.4
4.1
74
70.8
21.6
34
128.1
39.2
94
185.5
56.7
54
242.9
74.3
15
14.3
4.4
75
71.7
21.9
35
129.1
39.5
95
186.5
57.0
55
243.9
74.6
16
15.3
4.7
76
72.7
22.2
36
130.1
39.8
96
187.4
57.3
56
244.8
74.8
17
16.3
6.0
77
73.6
22.5
37
131.0
40.1
97
188.4
57.6
57
245. 8
75.1
18
17.2
5.3
78
74.6
22.8
38
132.0
40.3
98
189.3
57.9
58
246. 7
75.4
19
18.2
5.6
79
75.5
23.1
39
132.9
40.6
99
190.3
58.2
59
247.7
75.7
20
19.1
5.8
6.1
80
76.5
23.4
40
133.9
40.9
200
191.3
58.5
60
248.6
76.0
76.3
21
20.1
81
77.5
23.7
141
]34.8
41.2
201
192.2
58.8
261
249.6
22
21.0
6,4
82
78.4
24.0
42
135.8
41.5
02
193.2
59.1
62
250.6
76.6
23
22.0
6.7
83
79.4
24.3
43
136.8
41.8
03
194.1
59.4
63
251.5
76.9
24
23.0
7.0
84
80.3
24.6
44
137. 7
42.1
04
195.1
59.6
64
252. 5
77.2
25
23.9
7.3
85
81.3
24.9
45
138.7
42.4
05
196.0
59.9
65
253.4
77.5
26
24.9
7.6
86
82.2
25.1
46
139.6
42.7
06
197.0
60.2
66
254.4
77.8
27
25.8
7.9
87
83.2
25.4
47
140.6
43.0
07
198.0
60.5
67
255. 3
78.1
28
26.8
8.2
88
84.2
25.7
48
141.5
43.3
08
198.9
60.8
68
256.3
78.4
29
27.7
8.5
89
85.1
26.0
49
142.5
43.6
09
199.9
61.1
69
257. 2
78.6
30
28.7
8.8
90
86.1
26.3
50
143.4
144.4
43.9
10
200.8
61.4
61. 7'
70
271
258.2
78.9
31
29.6
9.1
91
87.0
26.6
151
44.1
211
201.8
259.2
79.2
32
30.6
9.4
92
88.0
26.9
52
145.4
44.4
12
202.7
62.0
72
260.1
79.5
33
31.6
9.6
93
88.9
27.2
53
146.3
44.7
13
203.7
62.3
73
261.1
79.8
34
32.5
9.9
94
89.9
27.5
54
147.3
45.0
14
204.6
62.6
74
262.0
80.1
35
33.5
10.2
95
90.8
27.8
55
148.2
45.3
15
205.6
62.9
75
263.0
80.4
36
34.4
10.5
96
91.8
28.1
56
149.2
45.6
16
206.6
63.2
76
263.9
80.7
37
35.4
10.8
97
92.8
28.4
57
150.1
45.9
17
207.5
63.4
77
264.9
81.0
38
36.3
11.1
98
93.7
28.7
58
151.1
46.2
18
208.5
63.7
78
265.9
81.3
39
37.3
11.4
99
94.7
28.9
59
152.1
46.5
19
209.4
64.0
79
266.8
81.6
.4a
38.3
11.7
100
101
95.6
96.6
29.2
29.5
60
161
153.0
154.0
46.8
20
210.4
211.3
64.3
80
267.8
81.9.
41
39.2
12.0
47.1
221
64.6
281
268.7
82.2
42
40.2
12.3
02
97.5
29.8
62
154.9
47.4
22
212.3
64.9
82
269.7
82.4
43
41.1
12.6
03
98.5
30.1
63
155. 9
47.7
23
213.3
65.2
83
270.6
82.7
44
42.1
12.9
04
99.5
30.4
64
156.8
47.9
24
214.2
65.5
84
271.6
83.0
45
43.0
13.2
05
100.4
30.7
65
157.8
48.2
25
215.2
65.8
85
272.5
83.3
46
44.0
13.4
06
101.4
31.0
66
158.7
48.5
26
216.1
66.1
86
273. 5
83.6
47
44.9
13.7
07
102.3
31.3
67
159.7
48.8
27
217.1
66.4
87
274.5
83.9
48
45.9
14.0
08
103.3
31.6
68
160.7
49.1
28
218.0
66.7
88
275.4
84.2
49
46.9
14.3
09
104.2
31.9
69
161.6
49.4
29
219.0
67.0
89
276.4
84.5
50
47.8
14.6
10
105.2
32.2
70
162.6
49.7
30
220.0
67.2
90
277.3
278.3
84.8
85.1
51
48.8
14.9
111
106.1
32.5
171
163.5
50.0
231
220.9
67.5
291
52
49.7
15.2
12
107.1
32.7
72
164.5
50.3
32
221.9
67.8
92
279.2
85.4
53
50.7
15.5
13
108.1
33.0
73
165.4
50.6
33
222.8
68.1
93
280.2
85.7
54
51.6
15.8
14
109.0
33.3
74
166.4
50.9
34
223.8
68.4
94
281.2
86.0
55
52.6
16.1
15
110.0
33.6
75
167.4
51.2
35
224.7
68.7
95
282.1
86.2
56
53.6
16.4
16
110.9
33.9
76
168.3
51.5
36
225.7
69.0
96
283.1
86.5
57
54.5
16.7
17
111.9
34.2
77
169.3
51.7
37
226.6
69.3
97
284.0
86.8
58
55.5
17.0
18
112.8
34.5
78
170.2
52.0
38
227.6
69.6
98
285.0
87.1
59
56.4
17.2
19
113.8
34.8
79
171.2
52.3
39
228.6
69.9
99
285.9
87.4
60
57.4
17.5
20
114.8
35.1
80
172.1
52.6
40
229.5
70.2
300
286.9
87.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
73° (1
07°, 253°, 287°
)•
TABLE 2.
[Page 401
Difference of Latitude and Departure for 17° (163°, 197°, 343°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
301
287.8
88.0
361
345. 2
105.5
421
402. 6 123. 1
481 460.0
140.6
541
517.3
158.2
02
288.8
88.3
62
346.1
105.8
22
403.5
123.4
82 ' 460.9
140.9
42
518.3
158.5
03
289.7
88.6
63
347. 1
106.1
23
404.5
123. 7
83 1 461.9
141.2
43
519.2
158.8
04
290.7
88.9
64
348.1
106.4
24
405. 4
124.0
84
462.8
141.5
44
520.2
159.1
05
291.6
89.2
65
349. 0
106.7
25
406.4
124.3
85
463.8
141.8
45
521.2
159. 3
06
292.6
89.5
66
350. 0
107.0
26
407. 3
124.6
86
464.7
142.1
46
522.1
159.6
07
293.5
89.8
67
350. 9
107.3
27
408.3
124.8
87
465. 7
142. 3
47-
523. 1
159. 9
08
294.5
90.1
68
351. 9
107.6
28
409.3
125.1
88
466.7
142.6
48
524.0
160.2
09
295. 5
90.3
69
352. 8
107.9
29
410.2
125. 4
89
467.6
142.9
49
1 525.0
160.5
10
311
296.4
297.4
90.6
70
353. 8
108.2
30
411.2
412.1
125.7
90
468.6
143. 2
50
1 526.0
160.8
161.1
90.9
371 i 354.8
108.5
431
126.0
491
469.5
143. 5
551
526. 9
12
298.3
91.2
72 355.7
108.8
32
413.1
126.3
92
470.5
143.8
52
527.9
161.4
13
299.3
91.5
73 ! 356. 7
109.1
33
414.0
126.6
93
471.4
144.1
53 i 528.8
161.7
14
300.2
91.8
74
357. 6
109.4
34 ' 415.0
126.9
94
472.4
144.4
54 i 529.8
162.0
]5
301.2
92.1
75
358.6
109.6
35 416.0
127.2
95
473.4
144.7
55
530.8
162.3
16
302.2
92.4
76
359. 5
109.9
36 416.9
127.5
96
474.3
145. 0
56
531.7
162.6
17
303. 1
92.7
77
360. 5
110.2
37 i 417.9 1127.8
97
475. 3
145.3
57
532.7
162.9
18
304.1
93.0
78
361.4
110.5
.38 ; 418.8 1128.1
98
476.2
145. 6
58 533.6
163.2
19
305.0
93.3
79
362.4
110.8
39 419. 8 128. 4
99
477.2
145. 9
59 i 534.6
163. 5
20
306. 0
306.9
93.6
80
381
363.4
111.1
40 1 420. 7 128. 6
500
478.1
479. 1
146.2
60 1 535.5
561 536.5
163.8
321
93.9
364.3
111.4
441 i 421. 7 : 128. 9
501
146.5
164.1
22
307.9
94.1
82
365.3
111.7
42
422. 7 ! 129. 2
02
480.1
146.8
62 537.5
164.4
23
308.8
94.4
83
366.2
112.0
43
423. 6 1 129. 5
03
481.0
147.1
63 i 538.4
164.6
24
309.8
94.7
84
367.2
112.3
44
424.6 129.8
04
482.0
147.4
64 : 5,39.4
164.8
25
310.8
95.0
85
368. 1
112. 6
45
425.5 130.1
05
482.9
147.7
65 540.3
165.1
26
311.7
95.3
86
369.1
112.9
46
426.5
130.4
06
483. 9
148.0
66 541.3
165.4
27
312.7
95.6
87
370.1
113.2
47
427.4
130.7
07
484.8
148.3
67 542.2
165.7
28
313.6
95.9
88
371.0
113.4
48
428.4
131.0
08
485. 8
148.6
68 543.2
166. 0
29
314.6
96.2
89
372.0
113.7
49
429.3
131. 3
09
486.7
148.9
69 544.1
166.4
30
315. 5
316. 5
96.5
90
372.9
373.9
114.0
50
430.3
431. 3
131.6
10
487.7
149.1
70
545. 1
546.1
166.7
331
96.8
391
114.3
451
131.9
511
488.7
149.4
571
167.0
32
317.5
97.1
92
374.8
114.6
52
432.2
132.2
12
489.6
149.7
72 ! 547.0
167.2
33
318.4
97.4
93
375. 8
114.9
53
433.2
132.4
13
490.6
150.0
73 ! 548.0
167.5
34
319.4
97.7
94
376. 7
115.2
54
434.1
132.7
14
491.5
150. 2
74
548. 9
167.8
35
320.3
97.9
95
377.7
115.5
55
435.1
133. 0
15
492.5
150. 5
75
549.9
168.1
36
321. 3
98.2
96
378. 7
115.8
56
436.0
133.3
16
493.4
150. 8
76
550. 8
168.4
37
322.2
98.5
97
379.6
116.1
57
437.0
133.6
17
494.4
151.1
77
551. 8
168.7
38
323. 2
98.8
98
380.6
116.4
58
4.38. 0
133. 9
18
495. 3
151.4
78
552.7
169.0
39
324.2
99.1
99
.381.5
116.7
59
438. 9
134.2
19
496.3
151.7
79
553.7
169.3
40
325. 1
326.1
99.4
99. 7
400
382. 5
383.4
117.0
117. 2
60 i 439.9
461 440. 8
f34.5
134.8
20
521
497.2
152.0
80
554.6
169.6
341
401
498.2
152.3
581
555.6
169.9
42
327.0
100.0
02
384.4
117.5
62 441. 8
135.1
22
499.2
152.6
82
556. 5
170.2
43
328.0
100.3
03
385. 4
117.8
63 i 442. 7
135. 4
23
500.1
152. 9
83
557.5
170.5
44
328.9
100.6
04
386.3
118.1
64 ! 443. 7
135.7
24
501.1
153.2
84
558.4
170.8
45 i
329.9
100.9
05 387. 3
118.4
65 444.6
136.0
25
502.0
153.5
85
559.4
171.1
46 '
330.8
101.2
06 1 388. 2
118.7
66 445.6
136.2
26
503.0
153. 8
86
560.4
171.3
47
331.8
101.5
07 ! 389.2
119.0
67 1 446.6
136.5
27
503. 9
154.1
87
561.3
171.6
48
332.8
101.8
08 390. 1
119.3
68 i 447.5
136. 8
28
504. 9
154. 4
88
562.3
171.9
49
333.7
102.0
09 391. 1
119.6
69 448. 5
137.1
29
505. 9
154. 7
89
563.2
172.2
50
351
334.7
335. 6
102. 3
10 !
392.0
393.0
119.9
70
449.4
450.4
137.4
30
531
506. 8
155. 0
90
591
564.2
172.5
172.8
102. 6
411 i
120.2
471
137. 7
507.8
155. 3
565. 1
52
336.6
102.9
12 1 394. 0
120.5
72
451. 3
138.0
32
508.7
155.6
92
566.1
173. 1
53
337.5
103. 2
13 394.9
120.8
73
452. 3
138.3
33
509. 7
155. 9
93
567.1
173. 4
54
338. 5
103.5
14
395. 9
121.0
74
453. 3
138.6
34
510.6
156. 2
94
568.0
173.7
55
339.5
103.8
15
396. 8
121.3
75
454. 2
138.9
35
511.6
156. 5
95
569. 0
174.0
56
340.4
104.1
16
397.8
121.6
76
455. 2
139.2
36
512.6
156. 8
96
569.9
174. 3
57
341.4
104.4
17
398. 7
121.9
77
456. 1
139.5
37
513. 5
157. 1
97
570.9
174.6
58
342.3
104.7
18
399. 7
122.2
78
457. 1
139.8
38
514. 5
157.3
98
571.8
174.9
59
343. 3
105. 0
19 400.7 1
122.5
79
458. 0
140.0
39
515. 4
157. 6
99
572.8
175. 2
60
344.2
105.3
20 401. 6
122.8
80
459.0
140.3
40
516.4
157.9
600
573.8
175. 4
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat. |
Dist.
Dep.
Lat.
^3° (107°, 253°, 287°
)•
22489—03-
-26
Page 402]
TABLE 2.
Difference of Latitude and Departure for 18° (162°, 198
°, 342°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.0
18.9
121
115.1
37.4
181
172.1
55.9
241
229.2
74.5
2
1.9
0.6
62
59.0
19.2
22
116.0
37.7
82
173.1
56.2
42
230.2
74.8
3
2.9
0.9
63
59.9
19.5
23
117.0
38.0
83
174.0
56.6
43
231.1
75.1
4
3.8
1.2
64
60.9
19.8
24
117.9
38. 3
84
175. 0
56.9
44
232.1
75.4
5
4.8
1.5
«5
61.8
20.1
25
118.9
38.6
85
175.9
57.2
45
233.0
75.7
6
5.7
1.9
66
62.8
20.4
26
119.8
38.9
86
176.9
57.5
46
234. 0
76.0
7
6.7
2.2
67
63.7
20.7
27
120.8
39.2
87
177.8
57.8
47
234.9
76.3
8
7.6
2.5
68
64.7
21.0
28 i 121.7
.39.6
88
178.8
58.1
48
2.35. 9
76.6
9
8.6
2.8
69
65.6
21.3
29 1 122. 7
39.9
89
179.7
58.4
49
236.8
76.9
10
11
9.5
10.5
3.1
3.4
70
71
66.6
21.6
21.9
30
123.6
124.6
40.2
40.5
90
191
180.7
181.7
58.7
50
237. 8
238. 7
77.3
67.5
131
59.0
251
77.6
12
11.4
3.7
72
68.5
22.2
32
125.5
40.8
92
182.6
59.3
52
239.7
77.9
13
12.4
4.0
73
69.4
22.6
33
126. 5
41.1
93
183.6
59.6
53
240.6
78.2
14
13.3
4.3
74
70.4
22.9
34
127.4
41.4
94
184.5
59.9
54
241.6
78.5
15
14.3
4.6
75
71.3
23.2
35
128.4
41.7
95
185. 5
60.3
55
242.5
78.8
16
15.2
4.9
76
72.3
23.5
36
129. 3
42.0
96
186.4
60.6
56
243. 5
79.1
17
16.2
5.3
77
73.2
23.8
37
130. 3
42.3
97
187.4
60.9
57
244.4
79.4
18
17.1
5.6
78
74.2
24.1
38
131.2
42.6
98
188. 3
61.2
58
245.4
79.7
19
18.1
5.9
79
75.1
24.4
39
132.2
43.0
99
189.3
61.5
59
246. 3
80.0
20
19.0
20.0
6.2
6. 5
80
81
76.1
24.7
40
133.1
43.3
200
190.2
61.8
60
247. 3
248.2
80.3
80.7
21
77.0
25.0
141
134.1
43: 6
201
191.2
62.1
261
22
20.9
6.8
82
78.0
25.3
42
135.1
43.9
02
192.1
62.4
62
249.2
81.0
23
21.9
7.1
83
78.9
25.6
43
136.0
44.2
03
193.1
62.7
63
250.1
81.3
24
22.8
7.4
84
79.9
26.0
44
137.0
44.5
04
194. 0
63.0
64
251.1
81.6
25
23.8
7.7
85
80.8
26.3
45
137.9
44.8
05
195. 0
63.3
65
252.0
81.9 .
26
24.7
8.0
86
81.8
26.6
46
138.9
45.1
06
195.9
63.7
66
253.0
82.2
27
25.7
8.3
87
82.7
26.9
47
139. 8
45.4
07
196. 9
64.0
67
253. 9
82.5
28
26.6
8.7
88
83.7
27.2
48
140.8
45.7
08
197.8
64.3
68
254. 9
82.8
29
27.6
9.0
89
84.6
27.5
49
141.7
46.0
09
198.8
64.6
69
255. 8
83.1
30
28.5
9.3
90
91
85.6
27.8
50
142.7
46.4
10
199.7
^200.7
64.9
70
256.8
83.4
83.7
31
29.5
9.6
86.5
28.1
151
143.6
46.7
211
65.2
271
257. 7
32
30.4
9.9
92
87.5
28.4
52
144.6
47.0
12
201.6
65.5
72
258.7
84.1
33
31.4
10.2
93
88.4
28.7
53
145. 5
47.3
13
202.6
65.8
73
259.6
84.4
34
32.3
10.5
94
89.4
29.0
54
146.5
47.6
14
203. 5
66.1
74
260.6
84.7
35
33.3
10.8
95
90.4
29.4
55
147.4
47.9
15
204.5
66.4
75
261.5
85.0
36
34.2
11.1
96
91.3
29.7
56
148.4
48.2
16
205. 4
66.7
76
262. 5
85.3
37
35.2
11.4
97
92.3
30.0
57
149. 3
48.5
17
206.4
67.1
77
263.4
85.6
38
36.1
11.7
98
93.2
30.3
58
150. 3
48.8
18
207. 3
67.4
78
264.4
85.9
39
37.1
12.1
99
94.2
30.6
59
551.2
49.1
19
208. 3
67.7
79
265.3
86.2
40
38.0
12.4
12.7
100
95.1
30.9
31.2
60
152.2
153. 1
49.4
20
209.2
210.2
68.0
80
266.3
86.5
41
39.0
101
96.1
161
49.8
221
68.3
281
267.2
86.8
42
39.9
13.0
02
97.0
31.5
62
154. 1
50.1
22
211.1
68.6
82
268.2
87.1
43
40.9
13.3
03
98.0
31.8
63
155. 0
50.4
23
212.1
68.9
83
269.1
87.5
44
41.8
13.6
04
98.9
32.1
64
156.0
50.7
24
213. 0
69.2
84
270.1
87.8
45
42.8
13.9
05
99.9
.32.4
65
156.9
51.0
25
214.0
69.5
85
271.1
88.1
46
43.7
14.2
06
100.8
32.8
66
157. 9
51.3
26
214.9
69.8
86
272.0
88.4
47
44.7
14.5
07
101.8
33.1
67
158. 8
51.6
27
215. 9
70.1
87
273.0
88.7
48
45.7
14.8
08
102.7
33.4
68
159. 8
51.9
28
216.8
70.5
88
273.9
89.0
49
46.6
15.1
09
103. 7
33. 7
69
160.7
52.2
29
217.8
70.8
89
274.9
89.3
50
51
47.6
15.5
10
104.6
34.0
70
161. 7
52.5
52.8
30
231
218.7
71.1
90
275.8
89.6
48.5
15.8
111
105.6
34.3
171
162.6
219.7
71.4
291
276.8
89.9
52
49.5
16.1
12
106.5
34.6
72
163.6
53.2
32
220.6
71.7
92
277.7
90.2
53
50.4
16.4
13
107.5
34.9
73
164. 5
53.5
33
221.6
72.0
93
278.7
90.5
54
51.4
16.7
14
108.4
35.2
74
165. 5
53.8
34
222. 5
72.3
94
279. 6
90.9
55
52.3
17.0
15
109.4
35.5
75
166.4
54.1
35
223. 5
72.6
95
280.6
91.2
56
53.3
17.3
16
110.3
35.8
76
167.4
54.4
36
224.4
72.9
96
281.5
91.5
57
54.2
17.6
17
111.3
36.2
77
168.3
54.7
37
225. 4
73.2
97
282. 5
91.8
58
55.2
17.9
18
112.2
36.5
78
169.3
55.0
38
226.4
73.5
98
283.4
92.1
59
56.1
18.2
19
113. 2 36. 8
79
170.2
55.3
39
227.3
73.9
99
284.4
92.4
60
57.1
18.5
20
114.1
37.1
80
171.2
55.6
40
228.3
74.2
300
285.3
92.7
Dist.
Dep.'
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
^2° (1
}8°, 252°, 288°
)•
TABLE 2.
Difference of Latitude and Departure for 18° (162°, 198°, 342°).
[Page 403
341
42
43
44
45
46
Lat.
286.3
287.2
288.2
289.1
290.1
291.0
292. 0
292.9
293.9
294.8
295.8
296.7
297.7
298.6
299.6
300.5
301. 5
302. 4
303. 4
304.3
305. 3
306. 2
307. 2
308.2
309.1
310. 1
311.0
312. 0
312.9
313.9
Dep.
314. 8
315. 8
316.7
317.7
318.6
319.6
320.5
321.5
322.4
323.4
324.3
325. 3
326.2
327.2
328. 1
329.1
93.0
93.3
93.7
94.0
94.3
94.6
94.9
95.2
95.5
96.1
96.4
96.7
97.0
97.4
97.7
98.0
98. 3
98.6
98^
99.2
99.5
99.8
100.1
100.4
100.7
101. 1
101.4
101.7
102.0
102.3
102.6
102.9
103.2
103.5
103.8
104.1
104.5
104.8
105.1
Dist.
361
62
63
64
65
66
67
68
69
70
47
330.0
48
331.0
49
331.9
50
332.9
351
333.8
52
334.8
53
335.7
54
336.7
55
337.6
56
338.6
57
339.5
58
340.5
59
341.4
60
342.4
Dist.
Dep.
105.4
105. 7
106.0
106. 3
106.6
106.9
107.2
107.5
107.9
108.2
108. 5
108.8
109.1
109.4
109.7
110.0
110. 3
110.6
110.9
111.3
Lat. Dist.
371
72
73
74
75
76
77
78
79
80
381
82
83
84
85
86
87
88
89
90
391
92
93
94
95
96
97
98
99
400
401
02
03
04
05
06
07
08
09
10
411
12
13
14
15
16
17
18
19
20
Lat.
343. 3
344.3
345. 2
346.2
347.1
348.1
349. 0
350. 0
350. 9
^1.9
352. 9'
353. 8
354. 8
355.7
356.7
357.6
358.6
359.5
360.5
361.4
362.4
363. 3
364.3
365.2
366.2
367. 1
368.1
369.0
370.0
370.9
371.9
372.8
373. 8
374.7
375. 7
376.6
377.6
378. 5
379. 5
380.4
Dep.
111.6
111.9
112.2
112.5
112.8
113.1
113.4
113.7
114.0
114.3
114.7
115.0
115.3
115.6
115.9
116.2
116.5
116.8
117.1
117.Jl^
117.7
118.1
118.4
118.7
119.0
119. 3
119.6
119.9
120.2
120.5
Dist.
381.4
382.3
383. 3
384.2
385.2
386.1
387. 1
388.0
389.0
389.9
390. 9
391.8
392.8
393. 7
394.7
395. 6
396.6
397.5
398. 5
399.5
Dep.
120.8
121.1
121.5
121.8
122.1
122.4
122.7
123.0
123. 3
123. 6
123.9
124.2
124.5
124.9
125.2
125. 5
125. 8
126.1
126.4
126^
127.0
127.3
127.6
127.9
128. 3
128.6
128.9
129.2
129.5
129.8
Lat. Dist
421
22
23
24
25
26
27
28
29
30
431
32
33
34
35
36
37
38
39
40
441
42
43
44
45
46
47
48
49
50
451
52
53
54
55
56
57
58
59
60^
461
62
63
64
65
66
67
68
69
JO
471
72
73
74
75
76
77
78
79
80
lAt.
400.4
401.4
402.3
403. 3
404.2
405.2
406.1
407.1
408.0
409^0
"409. 9
410.9
411.8
412.8
413.7
414.7
415.6
416.6
417.5
418.5
Dep.
130.1
130.4
130. 7
131.0
131.3
131.7
132.0
132.3
132.6
132.9
133.2
133.5
133.8
134.1
134.4
134.7
135.1
135.4
135.7
136.0
419.4
420.4
421.3
422.3
423.2
424.2
425. 1
426. 1
427.0
428.0
428. 9
429.9
430.8
431.8
432.7
433.7
434.6
435.6
436. 5
437. 5
448.0
448.9
449. 9
450. 8
451.8
452.7
453.7
454.6
455. 6
456.5
Dep.
136.3
136.6
136.9
137.2
137. 5
137. 8
138.1
138.4
138.8
139. 1
139.4
139.7
140.0
140. 3
140.6
140.9
141.2
141.5
141.8
142.2
142.5
142.8
143.1
143. 4
143.7
144.0
144. 3
144.6
144.9
145. 2
145.6
145. 9
146.2
146.5
146.8
147.1
147.4
147.7
148.0
148.3
Lat. Dist,
Dist.
481
82
83
84
85
86
87
88
89
90
491
92
93
94
95
96
97
98
99
500
501
02
03
04
05
06
07
08
09
10
Lat.
457.5
458.5
459.4
460.4
461. 3
462.3
463.2
464.2
465. 1
466.1
Dep. Dist
467.0
468.0
468.9
469.8
470.8
471.7
472.7
473. 6
474.6
475.5
476
477,
478,
479
480,
481,
482.2
483.2
484.1
485.1
511
12
13
14
15
16
17
18
19
20
521
22
23
24
25
26
27
28
29
30
486.0
487.0
487.9
488.9
489.8
490.8
491.7
492.7
493.6
494.6
531
32
33
34
35
36
37
38
39
40
495.5
496. 5
4^^7.4
498.4
499. 3
500.3
501.2
502.2
503. 1
504.1
505. 0'
506. 0
506. 9
507. 9
508. 8
509.8
510.7
511.7
512. 6
513. 6
Dep.
148.6
148.9
149. 3
149.6
149.9
150.2
150. 5
150.8
151. 1
15L4
151. 7
152.0
152.3
152. 6
153. 0
153.3
153. 6
153.9
154.2
154.5
154.8
155.1
155. 4
155. 7
156.1
156. 4
156. 7
157. 0
157. 3
157^
157. 9
158. 2
158. 5
158. 8
159. 1
159. 4
159.7
160.0
160.3
160.^
161. 0
161.3
161.6
161.9
162.2
162.5
162.9
163.2
163.5
163. 8
164.1
164.4
164.7
165. 0
165.3
165. 6
165. 9
166.2
166.5
166.9
541
42
43
44
45
46
47
48
49
50
551
52
53
54
55
56
57
58
59
60
561
62
63
64
65
66
67
68
69
70
571
72
73
74
75
76
77
78
79
80
581
82
83
84
85
86
87
88
89
90
591
92
93
94
95
96
97
98
99
600
Lat. Dist.
Lat.
514.5
515. 5
516. 4
517.4
518. 3
519. 3
520.2
521.2
522.1
523. 1
524. 0
525. 0
525. 9
526.9
527.8
528.8
529.7
530.7
531. 6
^2^6_
533.5
534.5
535. 4
536.4
537. 3
538.3
539. 2
540. 2
541.1
542.1
543.0
544. 0
544. 9
545. 9
546. 8
.547.8
548. 7
549. 7
550. 6
551.6
552. 5
553. 5
554. 4
555.4
556.3
557. 3
558. 2
559.2
560.1
561.1
562. 0
563. 0
563. 9
564.9
565. 8
566.8
567. 7
568. 7
569. 6
570.6
Dep.
Dep.
167.2
167. 5
167.9
168.2
168. 5
168.8
169.1
169.4
169.7
170^0^
170. 3
170.6
170.9
171.2
171.5
171.8
172.1
172.4
172.7
173.0
173.3
173. 6
173.9
174.2
174.6
174.9
175.2
175.5
175.8
176.1
176. 4"
176.7
177.0
177.3
177.6
178.0
178.3
178.6
178.9
179^
179. 5
179.8
180.1
180.4
180.7
181.1
181.4
181.7
182.0
182.^
182. 7
183.0
183.3
183. 6
183.9
184.2
184.5
184.8
185. 1
185. 4
Lat.
72° (108, 252°, 288°).
Page 404]
TABLE 2.
Difference of Latitude and
Departure for 19° (161°, 199
°, 341°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.3
61
57.7
19.9
121
114.4
39.4
181
171.1
58.9
241
227.9
78.5
2
1.9
0.7
62
58.6
20.2
22
115.4
39.7
82
172.1
59.3
42
228.8
78.8
3
2.8
1.0
63
59.6
20.5
23
116. 3
40.0
83
173.0
59.6
43
229.8
79.1
4
3.8
1.3
64
60.5
20.8
24
117.2
40.4
84
174.0
59.9
44
230. 7
79.4
5
4.7
1.6
65
61.5
21.2
25
118.2
40.7
85
174.9
60.2
45
231. 7
79.8
6
5.7
2.0
«6
62.4
21.5
26
119.1
41.0
86
175.9
60.6
46
232.6
80.1
7
6.6
2.3
67
63.3
21.8
27
120.1
41.3
87
176.8
60.9
47
233.5
80.4
8
7.6
2.6
68
64.3
22.1
28
121.0
41.7
88
177.8
61.2
48
234.5
80.7
9
8.5
2.9
69'
65.2
22.5
29
122.0
42.0
89
178.7
61.5
49
235.4
81.1
10
9.5
3.3
70
66.2
22.8
30
122.9
123.9
42.3
90
179.6
61.9
50
251
236.4
237.3
81.4
81.7
11
10.4
3.6
71
67.1
23.1
131
42.6
191
180.6
62.2
12
11.3
3.9
72
68.1
23.4
32
124.8
43.0
92
181.5
62.5
52
238.3
8gi0
13
12.3
4,2
73
69.0
23.8
33
125.8
43.3
93
182.5
62.8
53
239.2
8^.4
14
13.2
.4.6
74
70.0
24.1
34
126.7
43.6
94
183.4
63.2
54
240.2
82.7
15
14.2
4.9
75
70.9
24.4
35
127.6
44.0
95
184.4
63.5
55
241.1
83.0
16
15.1
5.2
76
71.9
24.7
36
128.6
44.3
96
185. 3
63.8
56
242.1
83.3
17
16.1
5.5
77
72.8
25.1
37
129.5
44.6
97
186.3
64.1
57
243.0
83.7
18
17.0
5.9
78
73.8
2.5.4
38
130. 5
44.9
98
187.2
64.5
58
243.9
84.0
19
18.0
6.2
79
74.7
25.7
39
131.4
45.3
99
188.2
64.8
59
244.9
84.3
20
18.9
6.5
80
75.6
26.0
40
132.4
45.6
45.9
200
189.1
190.0
65.1
60
245.8
246.8
84.6
21
19.9
6.8
81
76.6
26.4
141
133. 3
201
65.4
261
85.0
22
20.8
7.2
82
77.5
26.7
42
134.3
46.2
02
191.0
65.8
62
247.7
85.3
23
21.7
7.5
83
78.5
27.0
43
135.2
46.6
03
191.9
66.1
63
248.7
85.6
24
22.7
7.8
84
79.4
27.3
44
136.2
46.9
04
192.9
66.4
64
249. 6
86.0
25
23.6
8.1
85
80.4
27.7
45
137.1
47.2
05
193.8
66.7
65
250.6
86.3
26
24.6
8.5
86
81.3
28.0
46
138.0
47.5
06
194.8
67.1
66
251.5
86.6
27
25.5
8.8
87
82.3
28.3
47
139.0
47.9
07
195.7
67.4
67
252.5
86.9
28
26.5
9.1
88
83.2
28.7
48
139.9
48.2
08
196.7
67.7
68
253. 4
87.3
29
27.4
9.4
89
84.2
29.0
49
140.9
48.5
09
197.6
68.0
69
254.3
87.6
30
28.4
9.8
90
85.1
29.3
50
141.8
48.8
10
211
198.6
199. 5
68.4
68. 7
70
271
255.3
256.2
87.9
31
29.3
10.1
91
86.0
29.6
151
142.8
49.2
88.2
32
30.3
10.4
92
87.0
30.0
52
143.7
49.5
12
200.4
69.0
72
257.2
88.6
33
31.2
10.7
93
87.9
30.3
53
144.7
49.8
13
201.4
69.3
73
258.1
88.9
34
32.1
11.1
94
88.9
30.6
54
145.6
50.1
14
202.3
69.7
74
259.1
89.2
35
33.1
11.4
95
89.8
30.9
55
146.6
50.5
15
203.3
70.0
75
260.0
89.5
36
34.0
11.7
96
90.8
31.3
56
147.5
50.8
16
204.2
70.3
76
261.0
89.9
37
35.0
12.0
97
91.7
31.6
57
148.4
51.1
17
205. 2
70.6
77
261.9
90.2
38
35.9
12.4
98
92.7
31.9
58
149.4
51.4
18
206.1
71.0
78
262.9
90.5
39
36.9
12.7
99
93.6
32.2
59
150. 3
51.8
19
207.1
71.3
79
263.8
90.8
40
37.8
13.0
100
94.6
32.6
60
151.3
52.1
20
208.0
71.6
72.0
80
264.7
91.2
41
38.8
13.3
101
95.5
32.9
161
152.2
52.4
221
209.0
281
265.7
91.5
42
39.7
13.7
02
96.4
33.2
62
153.2
52.7
22
209.9
72.3
82
266. 6
91.8
43
40.7
14.0
03
97.4
33.5
63
154. 1
53.1
23
210.9
72.6
83
267.6
92.1
44
41.6
14.3
04
98.3
33.9
64
155. 1
53.4
24
211.8
72.9
84
268. 5
92.5
45
42.5
14.7
05
99.3
34.2
65
156.0
53.7
25
212.7
73.3
85
269.5
92.8
46
43.5
15.0
06
100.2
34.5
66
157. 0
54.0
26
213.7
73.6
86
270.4
93.1
47
44.4
15.3
07
101.2
34.8
67
157.9
54.4
27
214.6
73.9
87
271.4
93.4
48
45.4
15.6
08
102.1
35.2
68
158.8
54.7
28
215.6
74.2
88
272.3
93.8
49
46.3
16.0
09
103.1
35.5
69
159.8
55.0
29
216.5
74.6
89
273. 3
94.1
50
47.3
16.3
10
104.0
35.8
70
160.7
55.3
30
217.5
218.4
74.9
75.2
90
291
274.2
275.1
94.4
94.7
51
48.2
16.6
111
105. 0
36.1
171
161.7
55.7
231
52
49.2
16.9
12
105. 9
36. 5
72
162.6
56.0
32
219.4
75.5
92
276.1
95.1
53
50.1
17.3
13
106.8
36.8
73
163.6
56.3
33
220. 3
75.9
93
277.0
95.4
54
51.1
17.6
14
107.8
37.1
74
164.5
56.6
34
221.3
76.2
94
278.0
95.7
55
52.0
17.9
15
108.7
37.4
75
165. 5
57.0
35
222.2
76.5
95
278.9
96.0
56
52.9
18.2
16
109.7
37.8
76
166.4
57.3
36
223. 1
76.8
96
279.9
96.4
57
53.9
18.6
17
110.6
38.1
77
167.4
57.6
37
224.1
77.2
97
280.8
96.7
58
54.8
18.9
18
111.6
38.4
78
168.3
58.0
38
225. 0
77.5
98
281.8
97.0
59
55.8
19.2
19
112.5
38.7
79
169.2
58.3
39
226.0
77.8
99
282.7
97.3
60
56.7
19.5
20
113.5
39.1
80
170.2
58.6
40
226.9
78.1
300
283.7
97.7
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
■1° (1
09°, 251
°, 289°
)•
TABLE '2.
[Page 405
Difference of Latitude and
Departure for 19° (161°, 199
°, 341°
)•
Dlst.
Lat.
Dep.
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
284.6
98.0
361
341.3
117. 5
421
398.1
137.0
481
454. 8
156.6
541
511.5
176.1
02
285.5
98.3
62
342.3
117.8
22
399.0
137.4
82
455. 7
156.9
42
512.4
176.4
03
286.5
98.6
63
343.2
118.2
23
400.0
137. 7
83
456.7
157. 2
43
513. 4
176.8
04
287.4
99.0
64
344.2
118.5
24
400.9
138.0
84
457.6
157. 6
44
514.3
177.1
05
288. 4
99.3
65
345.1
118.8
25
401.8
138.4
85
458.6
157.9
45
515. 3
177.4
06
289.3
99.6
66
346.1
119.1
26
402.8
138.7
86
459. 5
158. 2
46
516. 2
177.7
07
290.3
99.9
67
347. 0
119.5
27
403. 7
139.0
87
460.5
158. 5
47
517.2
178.1
08
291.2
100. 3
68
348.0
119.8
28
404.7
139. 3
88
461.4
158. 9
48
518.1
178.4
09
292.2
100.6
69
348.9
120.1
29
405. 6
139.7
89
462.4
159.2
49
519.1
178.7
10
311
293.1
294. 1
100.9
101.2
70
371
349.8
120.4
30
431
406.6
407.5
140.0
90
491
463.3
464.3
159.5
50
551
520.0
521.0
179.0
179.4
350.8
120.8
140.3
159.8
12
295. 0
101.6
72
351.7
121.1
32
408. 5
140.6
92
465.2
160.^2
52
521.9
179. 7
13
295.9
101.9
73
352.7
121.4
33
409.4
141.0
93
466.1
160. 5
53
522.8
180.0
14
296.9
102.2
74
353.6
121.7
34
410.4
141. 3
94
467.1
160.8
54
523. 8
180.3
15
297.8
102.5
75
354.6
122.1
35
411.3
141.6
95
468.0
161.1
55
524.7
180.7
16
298.8
102.9
76
355.5
122.4
36
412.2
141.9
96
469.0
161.5
56
525.7
181.0
17
299.7
103.2
77
356.5
122.7
37
413.2
142.3
97
469.9
161. 8
57
526.6
181.3
18
300.7
103.5
78
357. 4
123. 0
38
414.1
142.6
98
470.9
162.1
58
527.6
181.6
19
301.6
103. 8
79
358.4
123.4
39
415.1
142.9
99
471.8
162.4
59
528. 5
182.0
20
321
302.6
303. 5
104.2
104. 5"
80
359.3
123.7
124. 0'
40
441
416.0
143.2
143. 6'
500
472.8
473.7
162.8
60
529. 5
530. 4"
182.3
182.6
381
360. 2
417.0
501
163.1
561
22
304.5
104.8
82
361.2
124.4
42
417.9
143.9
02
474.7
163.4
62
531.4
182.9
23
305.4
105.1
83
362. 1
124.7
43
418.9
144.2
03
475. 6
163.7
63
532.3
183.3
24
306.3
105.5
84
363.1
125.0
44
41§.8
144.5
04
476. 5
164.1
64
533.2
183. 6
25
307.3
105.8
85
364. 0
125. 3
45
420.8
144.9
05
477. 5
164.4
65
534.2
183. 9
26
308.2
106.1
86
365. 0
125. 7
46
421.7
145.2
06
478.4
164.7
66
535. 1
184.2
27
309.2
106. 4
87
365. 9
126.0
47
422.6
145.5
07
479.4
165.0
67
536. 1
184.6
28
310.1
106.8
88
366. 9
126.3
48
423. 6
145.8
08
480.3
165.4
68
537. 0
184. 9
29
311.1
107.1
89
367.8
126.6
49
424. 5
146.2
09
481.2
165.7
69
538. 0
185.2
30
331
312.0
107.4
90
368.8
369. 7
127.0
50
425. 5
426.4
146.5
10
482.2
483.1
166.1
70
538.9
185. 6
185. 9
313.0
107.7
391
127.3
451
146.8
511
166.4
571
539.9
32
313.9
108.1
.92
370.6
127.6
52
427.4
147.1
12
484.1
166.7
72
540.8
186.2
33
314.9
108.4
93
371.6
127.9
53
428. 3
147.5
13
485. 0
167.0
73
541.7
186. 5
34
315. 8
108.7
94
372. 5
128.3
54
429.3
147.8
14
486.0
167.4
74
542. 7
186. 9
35
316.7
109.1
95
373.5
128. 6
55
430. 2
148.1
15
486.9
167.7
75
543. 6
187.2
36
317.7
109.4
96
374.4
128.9
56
431.2
148.4
16
487.9
168. 0
76
.544. 6
187. 5
37
318.6
109.7
97
375.4
129.2
57
432. 1
148.8
17
488.8
168.3
77
545. 5
187. 8
38
319.6
110.0
98
376. 3
129.6
58
433. 0
149.1
18
489.7
168.7
78
546. 5
188.2
39
320.5
110.4
99
377.3
129.9
59
434.0
149.4
19
490.7
169. 0
79
547.4
188. 5
40
341
321. 5
110.7
400
378.2
130.2
60
434.9
149.7
150.1
20
521
491.6
492.6
169. 3
169. 6
80
581
548.4
549. 3
188.8
189.1
322.4
111.0
401
379.2
130.5
461
435.9
42
323.4
111.3
02
380. 1
130.9
62
436.8
150.4
22
493.5
170.0
82
550. 3
189. 5
43
324.3
111.7
03
381.0
131.2
63
437.8
150.7
23
494.5
170. 3
83
551. 2
189.8
44
325.3
112.0
04
382.0
131.5
64
438.7
151.0
24
495.4
170.6
84
552.2
190.1
45
326. 2
112.3
05
382.9
131.8
65
439.7
151.4
25
496.4
170.9
85
553.1
190.4
46
327.1
112. 6
06
383.9
132. 2
66
440.6
151.7
26
497.3
171.2
86
554. 1
190. 8
47
328.1
113.0
07
384.8
132.5
67
441.6
152.0
27
498. 3
171.6
87
555. 0
191.1
48
329.0
113.3
08
385. 8
132.8
68
442.5
152.4
28
499.2
171.9
88
555. 9
191.4
49
330. 0
113.6
09
386. 7
133.1
69
443.4
152.7
29
500.1
172.2
89
556. 9
191.7
50
330.9
331.9
113.9
114. 3
10
411
387.7
388.6
133.5
70
444.4
445.3
153. 0
30
531
501.1
502. 0
172.5
90
557.8
558.8
192.1
192. 4
351
133.8
471
153.3
172.9
591
52
332.8
114.6
12
389.6
134.1
72
446.3
153.7
32
503. 0
173.2
92
559.7
192.7
53
333.8
114.9
13
390.5
134.4
73
447.2
154.0
33
503. 9
173.5
93
560.7
193. 0
54
334.7
115.2
14
391.4
134.8
74
448.2
154.3
34
504.9
173.8
94
561.6
193.4
55
335. 7
115.6
15
392.4
135.1
75
449.1
154.6
35
505. 8
174.2
95
562.6
193.7
56
336. 6
115.9
16
393. 3
135. 4
76
450.1
155.0
36
506. 8
174. 5
96
563. 5
194.0
57
337. 5
116.2
17
394. 3
135. 7
77
451.0
155.3
37
507. 7
174.8
97
564.5
194. 3
58
338.5
116.5
18
395.2
136.1
78
452.0
155.6
38
508. 7
175. 1
98
565. 4
194.7
59
339.4
116.9
19
396.2
136.4
79
452.9
155.9
39
509. 6
175. 5
99
566.4
195. 0
60
340.4
117.2
20
397.1
136.7
80
Dist.
453. 8
156.3
40
510.6
175. 8
600
567.3
195. 3
Dist.
Dep.
Lat'.
Dist.
Dep.
Lat.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
71° (1
09°, 251
°, 289°).
Page 406]
TABLE 2.
Difference of Latitude and Departure for 20° (160°, 20C
°, 340°
).
DIst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep. 1
1
0.9
0.3
61
57.3
20.9
121
113.7
41.4
181
170.1
61.9
241
226.5 82.4
2
1.9
0.7
62
58.3
21.2
22
114.6
41.7
82
171.0
62.2
42
227.4 j 82.8
3
2.8
1.0
63
59.2
21.5
23
115.6
42.1
83
172.0
62.6
43
228. 3 1 83. 1
4
3.8
1.4
64
60.1
21.9
24
116.5
42.4
84
172.9
62.9
44
229.3 i 83.5
5
4.7
1.7
65
61.1
22.2
25
117.5
42.8
85
173.8
63.3
45
230. 2
83.8
6
5.6
2.1
66
62.0
22.6
26
118.4
43.1
86
174.8
63.6
46
231.2
84.1
7
6.6
2.4
• 67
63.0
22.9
27
119.3
43.4
87
175.7
64.0
47
232.1
84.5
8
7.5
2.7
68
63.9
23.3
28
120. 3
43.8
88
176.7
64.3
48
233. 0
84.8
9
8.5
3.1
69
64.8
23.6
29
,121.2
44.1
89
177.6
64.6
49
234.0 ! 85.2
10
11
9.4
10.3
3.4
70
65.8
23.9
30
131
122.2
123.1
44.5
90
178. 5
65.0
50
251
234.9 1 85.5
235.9 j 85.8
3.8
71
66.7
24.3
44.8
191
179.5
65.3
12
11.3
4.1
72
67.7
24.6
32
124.0
45.1
92
180.4
65.7
52
236.8 ! 86.2
13
12.2
4.4
73
68.6
25.0
33
125. 0
45.5
93
181.4
66.0
53
237.7
86.5
14
13.2
4.8
74
69.5
25. 3
34
125.9
45.8
94
182.3
66.4
54
238.7
86.9
15
14.1
5.1
75
70.5
25.7
35
126.9
46.2
95
183. 2
66.7
55
239.6
87.2
16
15.0
5.5
76
71.4
26.0
36
127.8
46.5
96
184.2
67.0
56
240.6
87.6
17
16.0
5.8
77
72.4
26.3
37
128.7
46.9
97
185.1
67.4
57
241.5
87.9
18
16.9
6.2
78
73.3
26.7
38
129.7
47.2
98
186.1
67.7
58
242.4
88.2
. 19
17.9
6.5
79
74.2
27.0
39
130.6
47.5
99
187.0
68.1
59
243.4
88.6
' 20
18.8
19.7
6.8
7.2
80
75.2
76.1
27.4
27.7
40
141
131.6
132. 5
47.9
48.2
200
187.9
188. 9
68.4
60
244.3
88.9
21
81
201
68.7
261
245. 3
89.3
22
20.7
. 7.5
82
77.1
28.0
42
133.4
48.6
02
189.8
69.1
62
246. 2
89.6
23
21.6
7.9
83
78.0
28.4
43
134.4
48.9
03
190.8
69.4
63
247.1
90.0
24
22.6
8.2
84
78.9
28.7
44
135. 3
49.3
04
191.7
69.8
64
248.1
90.3
25
23.5
8.6
85
79.9
29.1
45
136.3
49.6
05
192.6
70.1
65
249.0
90.6
26
24.4
8.9
86
80.8
29.4
46
137.2
49.9
06
193.6
70.5
66
250. 0
91.0
27
25.4
9.2
87
81.8
29.8
47
138.1
50.3
07
194.5
70.8
67
250.9
91. 3
28
26.3
9.6
88
82.7
30.1
48
139.1
50.6
08
195. 5
71.1
68
251.8
91.7
29
27.3
9.9
89
83.6
30.4
49
140.0
51.0
09
■196. 4
71.5
69
252.8
92.0
30
28.2
10.3
90
84.6
85.5
30.8
31.1
50
140.9
51.3
10
197.3
198.3
71.8
72.2
70
271
253.7
254.7
92.3
92.7
31
29.1
10.6
91
151
141.9
51.6
211
32
30.1
10.9
92
86.5
31.5
52
142.8
52.0
12
199.2
72.5
72
255.6
93.0
33
31.0
11.3
93
87.4
31.8
53
143.8
52.3
13
200.2
72..9
73
256.5
93.4
34
31.9
11.6
94
88.3
32.1
54
144.7
52.7
14
201.1
73.2
74
257.5
93.7
35
32.9
12.0
95
89.3
32.5
55
145.7
53.0
15
202.0
73.5
75
258.4
94.1
36
33.8
12.3
96
90.2
32.8
56
146.6
53.4
16
203.0
73.9
76
259.4
94.4
37
34.8
12.7
97
91.2
33.2
57
147.5
53.7
17
203.9
74.2
77
260.3
94.7
38
35.7
13.0
98
92.1
33.5
58
148.6
54.0
18
204.9
74.6
78
261.2
95.1
39
36.6
13.3
99
93.0
33.9
59
149.4
54.4
19
205.8
74.9
79
262.2
95.4
40
37.6
13.7
100
94.0
34.2
60
161
150.4
151.3
54.7
20
221
206.7
207.7
75.2
75.6
80
28 r
263.1
264.1
95.8
41
38.5
14.0
101
94.9
34.5
55.1
96.1
42
39.5
14.4
02
95.8
34.9
62
152.2
55.4
22
208.6
75.9
82
265. 0
96.4
43
40.4
14.7
03
96.8
35.2
63
153.2
55.7
23
209.6
76.3
83
265. 9 96. 8 1
44
41.3
15.0
04
97.7
35.6
64
154. 1
56.1
24
210. 5
76.6
84
266.9
97.1
45
42.3
15.4
05
98.7
35.9
65
155. 0
56.4
25
211.4
77.0
85
267.8
97.5
46
43.2
15.7
06
99.6
36.3
66
156.0
56.8
26
212.4
77.3
86
268.8
97.8
47
44.2
16.1
07
100.5
36.6
67
156.9
57.1
27
213. 3
77.6
87
269.7
98.2
48
45.1
16.4
08
101.5
36.9
68
157.9
57.5
28
214.2
78.0
88
270.6
98.5
49
46.0
16.8
09
102.4
37.3
69
158.8
57.8
29
215.2
78.3
89
271.6
98.8
50
47.0
17.1
10
103.4
37.6
38.0
70
159.7
58.1
30
216.1
217.1
78.7
90
272.5
99.2
99.5
51
47.9
17.4
111
104.3
171
160.7
58.5
231
79.0
291
273.5
52
48.9
17.8
12
105. 2
38.3
72
161.6
58.8
32
218.0
79.3
92
274.4
99.9
53
49.8
18.1
13
106.2
38.6
73
162. 6
59.2
33
218.9
79.7
93
275. 3
100.2
54
50.7
18.5
14
107.1
39.0
74
163.5
59.5
34
219. 9
80.0
94
276. 3
100. 6
55
51.7
18.8
15
108.1
39.3
75
164.4
59.9
35
220.8
80.4
95
277.2
100.9
56
52.6
19.2
16
109.0
39.7
76
165.4
60.2
36
221.8
80.7
96
278.1
101.2
57
53.6
19.5
17
109.9
40.0
77
166.3
60.5
37
222.7
81.1
97
279.1
101.6
58
54.5
19.8
18
110.9
40.4
78
167.3
60.9
38
223.6
81.4
98
280.0
101.9
59
55.4
20.2
19
111.8
40.7
79
168.2
61.2
39
224.6
81.7
99
281.0
102. 3
60
56.4
20.5
20
112.8
41.0
80
169.1
61.6
40
225.5
82.1
300
281.9
102.6
Dlst.
Dep.
Lat.
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
70° (110°, 250
% 290°
)■
1
TABLE 2.
[Page
407
Difference of Latitude and Departure for 20° (160°, 20C
)°, 340=
)•
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist. Lat.
Dep.
Dist.
481
Lat. i
j
Dep.
Dist.
Lat. j
Dep.
301
282,9
103. 0
361
339.2
123.5
421 395. 6
144.0
452.0
164.5
541
508.4
185.0
02
283.8
103.3
62
340.2
123.8
22 396. 6
144.3
82
453.0
164.8
42
509.3
185.4
03
284.7
103.6
63
341.1
124.2
23
397. 5
144.7
83
453.9
165.2
43
510.3
185.7
04
285. 7
104.0
64
342.1
124.5
24
398. 4
145. 0
84
454.8
165.5
44
511.2
186.0
05
286.6
104.3
65
343.0
124.8
25
399.4
145. 4
85
455.8
165.9
45
512.1
186.4
06
287.6
104.7
66
343.9
125.2
26
400.3
145.7
86
456.7
166.3
46
513.1
186.8
07
288.5
105. 0
67
344.9
125.5
27
401.3
146.1
87
457.7
166.6
47
514.0
187.1
08
289.4
105.4
68
345.8
125. 9
28
402.2
146.4
88
458.6
166.9
48
515.0
187.4
09
290.4
105. 7
69
346.8
126.2
29
403. 1
146.7
89
459.5
167.3
49
515.9
187.8
10
291.3
106.0
106.4
70
371
347.7
348.6
126.6
126.9
30
431
404.1
405.0
147.1
147.4
90
191^
460.5
167.7
50
516.8
188.2
311
292.3
461.4
168.0
551
517.8
188.5
12
293.2
106.7
72
349.6
127.2
32
406.0
147.8
92
462.4
168.3
52
518.7
188.8
13
294.1
107.1
73
350.5
127.6
33
406.9
148.1
93
463.3
168.6
53
519.7
189.1
14
395.1
107.4
74
351.5
127.9
34
407.8
148.4
94
464.2
168.9
54
520. 6
189.4
15
296.0
107.7
75
352.4
128.3
35
408.8
148.8
95
465.2
169.3
55
521.5
189.8
16
297.0
108.1
76
353. 3 i 128. 6
36
409.7
149.1
96
466.1
169.6
56
522.5
190.2
17
297.9
108.4
77
354. 3
129.0
37
410.7
149.5
97
467.0
170.0
57
523. 4
190. 5
18
298.8
108.8
78
355. 2
129.3
38
411.6
149.8
98
468.0
170. 3
58
524. 4
190.8
19
299.8
109.1
79
356. 2
129.6
39
412.5
150.2
99
468.9
170.7
59
525.3
191.2
20
300. 7
301.6
109. 5
80
357. 1
130.0
130. 3
40
441
413.5
414.4
150.5
500
501
469.9
470.8
171.0
60
561
526.2
191.6
321
109.8
381
358. 0
150.8
171.3
527.2
191.9
22
302.6
110.1
82
359. 0
130.7
42
415.4
151.2
02
471.7
171.7
62
528. 1
192.2
23
303.5
110.5
83
359.9
131.0
43
416.3
151. 5
03
472.7
172.0
63
.529.0
192. 5
24
304.5
110.8
84
360.8
131.3
44
417.2
151.9
04
473.6
172.4
64
530.0
192.9
25
305. 4
111.2
85
361. 8
131.7
45
418.2
152.2
05
474.5
172.7
65
530.9
193.2
26
306.3
111.5
86
362. 7
132.0
46
419.1
152.5
06
475.4
173.0
66
531.8
193.6
27
307.3
111.8
87
363. 7
132.4
47
420.0
152.9
07
476.4
173. 4
67
532.8
193.9
28
308.2
112.2
88
364. 6
132.7
48
421.0
153.2
08
477.3
173.7
68
533. 7
194.2
29
309.2
112.5
89
365. 5
133. 1
49
421.9
153. 6
09
478.3
174.1
69
534. 7
194.6
30
310. 1
112.9
90
366. 5
133.4
50
451
422.9
153.9
10
511
479.2
174.4
70
535. 6
195.0
331 i 311.0
113. 2
391
367.4
133.7
423.8
154. 3
480.2
174.8
571
536. 6
195.3
32 312.0
113.6
92
368.4
134.1
52
424.7
154. 6
12
481.1
175.1
72
537. 5
195.6
33
312.9
113.9
93
369.3
134.4
53
425.7
154.9
13
482.1
175.4
73
538.5
195.9
34
313.9
114.2
94
370.2
134.8
54
426.6
155.3
14
483. 0
175.8
74
539.4
196.3
35
314.8
114.6
95
371.2
135. 1
55
427. 6 i 155. 6
15
484.0
176.1
75
540. 3
196.6
36 t 315. 7
114.9
96
372.1
135. 4
56
428.5 156.0
16
484.9
176.5
76
541. 3
197.0
37
316.7
115.3
97
373.1
135. 8
57
429.4 156.3
17
485.8
176.8
77
542.2
197.3
38
317.6
115.6
98
374.0
136.1
58
430.4 156.7
18
486.8
177.2
78
543. 2
197.7
39
318.6
116.0
99
374.9
136.5
59
431.3 ,157.0
19
487.7
177.5
79
544.1
198.0
40
319.5
116.3
400
401
375.9
136.8
60
432.3
433.2
157.4
20
488.7
489. 6
177.9
80
545.0
198.4
341 320.4
116.6
376.8
137.2
461
157.7
521
178.2
581
546.0
198.7
42 ! 321.4
117.0
02
377.8
137.5
62
434. 1 158. 0
22
490.5
178.5
82
546.9
199.0
43
322.3
117.3
03
378.7
137.8
63
435.1
158. 4
23
491.5
178.9
83
547.9
199.4
44
323. 3
117.7
04
379.6
138.2
64
436.0
158.7
24
492.4
179.2
84
548. 8
199. 8
45
324.2
118.0
05
380.6
138.5
65
437.0
159.0
25
493.4
179.6
85
549.8
200.1
46
325.1
118.4
06
381.5
138.9
66
437.9
159.4
26
494.3
179.9
86
550. 7
200.4
47
326.1
118.7
07
382.5
139.2
67
438. 8
159.7
27
495.3
180.2
87
551.7
200.8
48
327. 0
119.0
08
383.4
139.6
68
439.8
160.1
28
496.2
180.6
88
552. 6
201.2
49
328.0
119.4
09
384.3
139.9
69
440.7
160.4
29
497.1
181.0
89
553. 5
201.5
50
328.9
329.8
119.7
120.1
10
411
385.3
386.2
140.2
70
471
441.7
442.6
160.8
161.1
30
531
498.1
181.3
90
554. 4
201.8
351
140.6
499.0
181.6
591
555.4
202.1
52
330.8
120.4
12
387.2
1 40. 9
72
443.5
161.4
32
499.9
181.9
92
556.3
202.4
53
331.7
120.7
13
388.1
141.3
73
444.5
161.8
33
500.9
182.3
93
557.3
202.8
54
332.7
121.1
14
389.0
141.6
74
445.4
162.1
34
501.8
182.6
94
558. 2
203.2
55
333.6
121.4
15
390.0
141.9
75 1 446.4
162.5
35
502.7
183.0
95
559. 1
203. 5
56
334.5
121.8
16
390.9
142.3
76 447.3
162.8
36
503.7
183. 3
96
560.0
203. 8
57
335.5
122.1
17
391.9
142.6
77 448.2
163.2
37
504.6
183.7
97
561. 0
204.2
58
336. 4
122.5
18
392.8
143.0
78 ' 449.2
163. 5
38
505. 5
184.0
98
561. 9
204.6
59
337.4
122.8
19
393. 7
143.3
79 450. 1
163. 8
39
506. 5
184.3
99
562.9
204.9
60
338.3
123.1
20
394.7
143.7
80 451. 1
164.2
40 507.4
184.7
600
563.8
205.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Di.st. Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
70° (110°, 250°, 290°).
Page 408]
TABLE 2.
Difference of Latitude and Departure for 21° (159°, 201
°, 339°
).
Dist
1
Lat.
Dep.
Dist.
Lat.
Dep. iDlst. Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
0.9
0.4
61
56.9
21.9 1 121 1 113.0 43.4
181
169.0
64.9
241
225.0
86.4
2
1.9
0.7
62
57.9
22.2
22 1 113.9 j 43.7
82
169.9
65.2
42
225.9
86.7
3
2.8
1.1
63
58.8
22.6
23 114.8 1 44.1
83
170.8
65.6
43
226.9
87.1
4
3.7
1.4
64
59.7
22.9
24 115.8 1 44.4
84
171.8
65.9
44
227.8
87.4
5
4.7
1.8
65
60.7
23.3
25 116.7 j 44.8
85
172. 7
66.3
45
228.7
87.8
6
5.6
2.2
i?
61.6
23.7
26 117.6 45.2
86
173.6
66.7
46
229.7
88.2
7
6.5
2.5
62.5
24.0
27 118.6 i 45.5
87
174.6
67.0
47
230.6
88.5
8
7.5
2.9
68
63.5
24.4
28 119.'5 1 45.9
88
475.5
67.4
48
231.5
88.9
9
8.4
3.2
69
64.4
24.7
29 120. 4 46. 2
89
176.4
67.7
49
232.5
89.2
10
9.3
3.6
70
65.4
25.1
30 i 121.4 1 46.6
90
177.4
178. 3
68.1
68.4
50
251
233.4
234.3
89.6
90.0
11
10.3
3.9
71
66.3
25.4
131 122.3 1 46.9
191
12
11.2
4.3
72
67.2
25.8
32 123.2 47.3
92
179.2
68.8
52
235. 3
90.3
13
12.1
4.7
73
68.2
26.2
33 1 124.2 47.7
93
180.2
69.2
53
236. 2
90.7
14
13.1
5.0
74
69.1
26.5
34 125. 1 I 48. 0
94
181.1
69.5
54
237.1
91.0
15
14.0
5.4
75
70.0
26.9
35 126.0 48.4
95
182.0
69.9
55
238.1
91.4
16
14.9
5. 7
76
71.0
27.2
36 127.0 48.7
96
183.0
70.2
56
239.0
91.7
17
15.9
6.1
77
71.9
27.6
37 127. 9 49. 1
97
183.9
70.6
57
239.9
92.1
18
16.8
6.5
78
72.8
28.0
38 1 128.8 49.5
98
184.8
71.0
58
240.9
92.5
19
17.7
6.8
79
73.8
28.3
39 1 129.8 49.8
99
185.8
71.3
59
241.8
92.8
20
18.7
7.2
80
74.7
28.7
40 130.7 50.2
200
186.7
71.7
60
242.7
243.7
93.2
93.5
21
19.6
7.5
81
75.6
29.0
141 131.6 1 50.5
201
187.6
72.0
261
22
20.5
. 7.9
82
76.6
29.4
42 132.6 i 50.9
02
188.6
72.4
62
244.6
93.9
23
21.5
8.2
83
77.5
29.7
43 133.5 51.2
03
189.5
72.7
63
245.5
94.3
24
22.4
8.6
84
78.4
30.1
44 134.4 51.6
04
190. 5
73.1
64
246.5
94.6
25
23.3
9.0
85
79.4
30.5
45 135.4 1 52.0
05
191.4
73.5
65
247.4
95.0
26
24.3
9.3
86
80.3
30.8
46 136.3 \ 52.3
06
192. 3
73.8
66
248.3
95.3
27
25.2
9.7
87
81.2
31.2
47 137.2 i 52.7
07
193. 3
74.2
67
249. 3
95. 7
28
26.1
10.0
88
82.2
31.5
48 , 138.2 53.0
08
194.2
74.5
68
250.2
96.0
29
27.1
10.4
89
83.1
31.9
49 139.1 53.4
09
195.1
74.9
69
251.1
96.4
30
28.0
10.8
90
84.0
85.0
32.3
32.6
50
151
140.0 ! 53.8
10
196.1
197.0
75.3
75.6
70
252.1
253.0
96.8
97.1
31
28.9
11.1
91
141.0 54.1
211
271
32
29.9
11.5
92
85.9
33.0
52 141.9 54.5
12
197.9
76.0
72
253. 9
97.5
33
30.8
11.8
93
86.8
33. 3
53 142.8 54.8
13
198.9
76.3
73
254.9
97.8
34
31.7
12.2
94
87.8
33.7
54 143.8 . 55.2
14
199.8
76.7
74
255. 8
98.2
35
32.7
12.5
95
88.7
34.0
55 ! 144.7 i 55.5
15
200.7
77.0
75
256. 7
98.6
36
33.6
12.9
96
89.6
34.4
56 145.6 55.9
16
201.7
77.4
76
257. 7
98.9
37
34.5
13.3
97
90.6
34.8
57 146.6 56.3
17
202.6
77.8
77
258. 6
99.3
38
35.5
13.6
98
91.5
35.1
58 147.5 56.6
18
203. 5
78.1
78
259. 5
99.6
39
36.4
14.0
99
92.4
35.5
59 1 148.4 57.0
19
204.5
78.5
79
260.5
100.0
40
37.3
14.3
100
93.4
35.8
36.2
60 149.4 57.3
20
221
205.4
78.8
80
281
261.4
262. 3
100.3
41
38.3
14.7
101
94.3
161 150.3 57.7
206.3
79.2
100.7
42
39.2
15.1
02
95.2
36.6
62 : 151.2 58.1
22
207.3
79.6
82
263. 3
101.1
43
40.1
15.4
03
96.2
86.9
63 152.2 58.4
23
208.2
79.9
83
264.2
101.4
44
41.1
15.8
04
97.1
37.3
64 I 153.1 58.8
24
209.1
80.3
84
265. 1
101.8
45
42.0
16.1
05
98.0
37.6
65 154. 0 59. 1
25
210.1
80.6
85
266. 1
102.1
46
42.9
16.5
06
99.0
38.0
66 155. 0 59. 5
26
211.0
81.0
86
267.0
102. 5
47
43.9
16.8
07
99.9
38.3
67
155.9 59.8
27
211.9
81.3
87
267.9
102.9
48
44.8
17.2
08
100.8
38.7
68
156.8 60.2
28
212.9
81.7
88
268. 9
103. 2
■ 49
45.7
17.6
09
101.8
39.1
69
157.8 60.6
29
213. 8
82.1
89
269.8
103.6
50
51
46.7
17.9
18.3
10
111
102.7
103. 6~
39.4
39.8
70
171
158.7 60.9
30
231
214.7
215.7
82.4
90
270.7
103.9
104. 3
47.6
159.6 61.3
82.8
291
271.7
52
48.5
18.6
12
104.6
40.1
72 1 160.6 61.6
32
216.6
83.1
92
272.6
104.6
53
49.5
19.0
13
105.5
40.5
73 ; 161.5, 62.0
33
217.5
83.5
93
273. 5
105. 0
54
50.4
19.4
14
106.4
40.9
74 j 162.4 62.4
34
318.5
83.9
94
274. 5
105. 4
55
51.3
19.7
15
107.4
41.2
75 ' 163.4 62.7
35
219.4
84.2
95
275. 4
105.7
56
52.3
20.1
16
108.3
41.6
76 ; 164.3 63.1
36
220. 3
84.6
96
276.3
106.1
57
53.2
20.4
17
109.2
41.9
77 165. 2 63. 4
37
221.3
84.9
97
277.3
106.4
58
54.1
20.8
18
110.2
42.3
78 166.2 63.8
38
222.2
85.3
98
278.2
106.8
59
55.1
21.1
19
111.1
42.6
79 1 167. 1 64. 1
39
233.1
85.6
99
279.1
107.2
60
56.0
21.5
20
112.0
43.0
80 168.0 j 64.5
40
224.1
86.0
300
280.1
107.5
Dist.
Dep.
Lat.
Di.st.
Dep.
Lat.
Dist. 1 Dep. j Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
69° (111°, 249°., 291°).
TABLE 2.
[Page 409
Difference of Latitude and Departure for
21° (159°, 201°, 339
")■
Dist.
Lat. 1 Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
281.0 107.9
361
337.0
129.4
421 393.0
150. 9
481
449.0
172.4
541
505. 1
193.9
02
281.9 108.2
62
337. 9
129.7
22 394.0
151.2
82
450.0
172.7
42
506.0
194.2
08
282. 9 108. 6
63
338.9
130.1
23 394.9
151. 6
83
450. 9
173.1
43
507.0
194.6
04
283. 8 1 108. 9
64
339. 8
130.4
24 1 395.8
152.0
84
451.8
173.5
44
507. 9
195.0
05
284. 7 109. 3
65
340.7
130. 8
25 1 396.8
152.3
85
452. 8
173.8
45
508.8
195.3
06
285. 7 ! 109. 7
66
341.7
131.2
26 ! 397. 7
152.7
86
453. 7
174.2
46
509.8
195.7
07
286.6
110.0
67
342.6
131.5
27
398. 6
153. 0
87
454. 6
174.5
47
510.7
196.0
08
287.5
110. 4
68
343. 5
131.9
28
399. 6
153. 4
88
455.6
174.9
48
511.6
196.4
09
288.5
110.7
79
344.5
132.2
29
400.5
153.7
89
456. 5
175.2
49
512.6
196.8
10
289.4
111.1
Til. 5
70
371
345.4
346.3
132.6
30
401.4
154.1
90
457.4
175.6
176.0
50
551
513.5
514.4
197.1
197.5
311
290.3
133. 0
431
402.4
154.5
491
458. 4
12
291.3
111.8
72
347.3
133.3
32
403.3
154.8
92
459. 3
176.3
52
515.4
197.8
13
292.2
112.2
73
348.2
133. 7
33
404.2
155. 2
93
460.2
176.7
53
516. 3
198.2
14
293.1 1112.5
74
349.1
134.0
34
405. 2
155. 5
94
461.2
177.0
54
517.2
198.6
15
294.1 112.9
75
350. 1
134.4
35
406.1
155.9
95
462. 1
177.4
55
518.2
198.9
16
295. 0 113. 2
76
351.0
134.7
36
407.0
156. 3
96
463.0
177.8
56
519.1
199.3
17
295. 9 113. 6
77
351.9
135.1
37
408. 0
156.6
97
464.0
178.1
57
520.0
199.6
18
296.9 114.0
78
352.9
135.5
38
408.9
157. 0
98
464.9
178.5
58
521.0
200.0
19
297.8 114.3
79
353.8
135.8
39
409.8
157.3
99
465.8
178.8
59
521.9
200.3
20
298.7
114.7
115.0
80
354. 7
136.2
40
410.8
157. 7
158. 0
500
566.8
179.2
60
522. 8
523.8
200.7
201. 0
321
299.7
381
355. 7
136. 5
441
411.7
501
467.7
179.5
561
22
300. 6 115. 4
82
356. 6
136.9
42
412.6
158. 4
02
468.6
179.9
62
524.7
201.4
23
301. 5 1 115. 8
83
357. 5
137.3
43
413.6
158.8
03
469.6
180.3
63
525. 6
201.8
24
302.5 116.1
84
358. 5
137.6
44
414.5
159.1
04
470. 5
180.6
64
526.6
202.1
25
303.4
116.5
85
359.4
138.0
45
415.4
159.5
05
471.5
181.0
65
527. 5
202.5
26
304. 3
116.8
86
360. 3
138. 3
46
416.4
159. 8
06
472.4
181.3
66
528. 4
202.8
27
305. 3 117. 2
87
361. 3
138.7
47
417.3
160.2
07
473.3
181.7
67
529.4
203.2
28
306. 2 1 117. 5
88
362.2
139. 1
48
418.2
160. 5
08
474.3
182.0
68
530. 3
203.5
29
307.1 '117.9
89
363.1
139.4
49
419.2
160. 9
09
475.2
182.4
69
531.2
203.9
30
308.1 1118.3
90
364.1
365. 0
139. 8
140. 1
50
420.1
161.3
10
476.1
477.1
182.8
70
532.2
533.1
204.3
204.6
331
309.0 118.6
391
451
421.0
161.6
511
183.1
571
32
309.9
119.0
92
365.9
140.5
52
422.0 162.0
12
478.0
183.5
72
534. 0
205.0
33
310.9
119.3
93
366.9
140.8
53
422. 9 162. 3
13
478.9
183. 8
73
535. 0
205. 4
34
311.8
119.7
94
367.8
141.2
54-
423. 8 162. 7
14
479.9
184.2
74
535. 9
205. 7
35
312. 7
120.1
95
368.7
141.6
55
424. 8 163. 1
15
480.8
184.6
to
536.8
206.1
36
313.7
120.4
96
369.7
141.9
56
425. 7 163. 4
16
481.7
184.9
76
537.8
206.4
37
314.6
120.8
• 97
370. 6
142.3
57
426. 6 163. 8
17
482.7
185.3
77
538.7
206. 8
38
315.5
121.1
98
371.5
142.6
58
427.6 164.1
18
483.6
185. 6
78
539. 6
207.1
39
316.5
121.5
99
372.5
143.0
59
428.5 164.5
19
484.5
186.0
79
540. 6
207.5
40
341
317.4
121.8
400
373. 4
143.4
143. 7
60
429.4 164.9
20
485. 5
486.4
186.4
186.7
80
581
541.5
'542. 4
207.9
318.3
122: 2
401
374.3
461
430. 4 , 165. 2
521
208.2
42
319.3
122.6
02
375.3
144. 1
62
431. 3 165. 6
22
487.3
187.1
82
•543.4
208.6
43
320.2
122.9
03
376.2
144.4
63
432. 2 165. 9
23
488. 3
187.4
83
544. 3
208.9
44
321.1
123.2
04
377.1
144.8
64
433. 2 ' 166. 3
24
489.2
187.8
U
545. 2
209.3
45
322.1
123.6
05
378.1
145.1
65 434.1 166.6
25
490.1
188.1
85
546.2
209.6
46
323.0
124.0
06
379. 0
145. 5
66
435. 0 167. 0
26
491.1
188.5
86
547. 1
210.0
47
323. 9 124. 4
07
379.9
145.9
67
436. 0 ; 167. 4
27
492.0
188.9
87
548. 0
210.4
48
324. 9 124. 7
08
380. 9
146.2
68 436. 9 167. 7
28
492.9
189.2
88
549.0
210.7
49
325. 8 i 125. 1
09
381.8
146.6
69 437. 8 168. 1
29
493. 9
189.6
89
549.9
211.1
50
326. 7 1 125. 4
10
382. 7
146.9
70 438. 8 1 168. 4
30
494.8
189.9
90
550.8
551.8
211.4
351
327.7
125.8
411
383.7
147.3
471
439. 7 ! 168. 8
531
495. 7
190.3
591
211.8
52
328.6
126.1
12
384.6
147.7
72
440. 6 169. 2
32
496.7
190.7
92
552. 7
212.2
53
329.5
126.5
13
385.5
148.0
73
441.6 169.5
33
497.6
191. 0
93
553.6
212.5
54
330.5
126.9
14
386. 5
148.4
74
442. 5 169. 9
34
498.5
191.4
94
554.6
212. 9
55
331.4 127.2
15
387.4
148.7
75
443.4 1170.2
35
499.5
191.7
95
555. 5
213.2
56
332. 3 127. 6
16
388.4
149.1
76
444.4
170.6
36
500.4
192.1
96
556.4
213. 6
57
333.3 127.9
17
389. 3
149.4
77 445.3
170.9
37
501.3
192.4
97
557. 4
213.9
58
334.2
128.3
18
390.2
149.8
78 446.2
171.3
38
502. 3
192.8
98
558. 2
214. 3
59
335.1
128.7
19
391.2
150.2
79 1 447.2
171.7
39
503. 2
193. 2
99
559. 2
214.7
60
336.1
129.0
20
392.1
150.5
80 448. 1
t
172.0
40
504.1
193.5
600
560.1
215. 0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. j Dep. 1 Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
6
)9° (111°, 249°, 291°
)•
Page 410]
TABLE 2.
Difference of Latitude and Departure for 22° (158°, 202, 338°)
.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
22.9
Dist.
Lat.
Dep. Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
56.6
121
112.2
45. 3 181
167.8
67.8
241
223.5
90.3
2
1.9
0.7
62
57. 5
23.2
22
113.1
45.7
82
168.7
68.2
42
224.4
90.7
3
2.8
1.1
63
58.4
23.6
23
114.0
46.1
83
169.7
68.6
43
225.3
91.0
4
3.7
1.5
64
59.3
24.0
24
115.0
46.5
84
170.6
68.9
44
226.2
91.4
5
4.6
1.9
65
60.3
24.3
25
115.9
46.8
85
171.5
69.3
45
227.2
91.8
6
5.6
2.2
66
61.2
24.7
26
116.8
47.2
86
172.5
69.7
46
228.1
92.2
/
6.5
2.6
• 67
62.1
25.1
27
117.8
47.6
87
173.4
70.1
47
229.0
92.5
8
7.4
3.0
68
63.0
25.5
28
118.7
47.9
88
174.3
70.4
48
229.9
92.9
9
8.3
3.4
69
64.0
25.8
29
119.6
48.3
89
175.2
70.8
49
230.9
93.3
10
9.3
3.7
70
64.9
26.2
30
120.5
48.7
90
191
176.2
71.2
50
231.8
232.7
93.7
11
10.2
4.1
71
65.8
26.6
131
121.5
49.1
177.1
71.5
251
94.0
12
11.1
4.5
72
66.8
27.0
32
122.4
49.4
92
178.0
71.9
52
233.7
94.4
13
12.1
4.9
73
67.7
27.3
33
123.3
49.8
93
178.9
72.3
53
234. 6
94.8
14
13.0
5.2
74
68.6
27.7
34
124.2
50.2
94
179.9
72.7
54
235.5
95.2
15
13.9
5.6
75
69.5
28.1
35
125.2
50.6
95
180.8
73.0
55
236.4
95.5
16
14.8
6.0
76
70.5
28.5
36
126.1
50.9
96
181.7
73.4
56
237.4
95.9
17
15.8
6.4
77
71.4
28.8
37
127.0
51.3
97
182.7
73.8
57
238.3
96.3
18
16.7
6.7
78
72.3
29.2
38
128.0
51.7
98
183.6
74.2
58
239.2
96.6
19
17.6
7.1
79
73.2
29.6
39
128.9
52.1
99
184. 5
74.5
59
240.1
97.0
20
18.5
7.5
80
74.2
30.0
40
129.8
52.4
200
185.4
74.9
60
241.1
242.0
97.4
21
19.5
7.9
81
75.1
30.3
141
130.7
52.8
201
186. 4
75.3
261
97.8
22
20.4
8.2
82
76.0
30.7
42
131. 7
53.2
02
187.3
75.7
62
242.9
98.1
23
21.3
8.6
83
77.0
31.1
43
132.6
53. 6
03
188.2
76.0
63
243.8
98.5
24
22.3
9.0
84
77.9
31.5
44
133.5
53.9
04
189.1
76.4
64
244.8
98.9
25
23.2
9.4
85
78.8
31.8
45
134.4
54.3
05
190.1
76.8
65
245.7
99.3
26
24.1
9.7
86
79.7
32.2
46
135.4
54.7
06
191.0
77.2
66
246.6
99.6
27
25.0
10.1
87
80.7
32.6
47
136.3
55.1
07
191.9
77.5
67
247.6
100.0
28
26.0
10.5
88
81.6
33.0
48
137.2
55.4
08
192.9
77.9
68
248.5
100.4
29
26.9
10.9
89
82.5
33.3
49
138. 2
55.8
09
■ 193. 8
78.3
69
249.4
100.8
30
27.8
28.7
11.2
90
83.4
84.4
33.7
34.1
50
151
139. 1 1 56. 2
10
194.7
78.7
70
250.3
101.1
31
11.6
91
140. 0
56.6
211
195.6
79.0
271
251.3
101.5
32
29.7
12.0
92
85.3
34.5
52
140.9
56.9
12
196.6
79.4
72
252.2
101. 9'
33
30.6
12.4
93
86.2
34.8
53
141.9
57.3
13
197.5
79.8
73
253.1
102.3
34
31.5
12.7
94
87.2
35.2
54
142. 8
57.7
14
198.4
80.2
74
254.0
102.6
35
32.5
13.1
95
88.1
35.6
55
143.7
58.1
15
199.3
80.5
75
255.0
103.0
36
33.4
13.5
96
89.0
36.0
56
144.6
58.4
16
200.3
80.9
76
255.9
103.4
37
34.3
13.9
97
89.9
36.3
57
145.6
58.8
17
201.2
81.3
77
256. 8
103.8
38
35.2
14.2
98
90.9
36.7
58
146.5
59.2
18
202.1
81.7
78
257.8
104.1
39
36.2
14.6
99
91.8
37.1
59
147.4
59.6
19
203.1
82.0
79
258.7
104.5
40
41
37.1
38.0
15.0
100
92.7
93.6
37.5
37.8
60
148.3
59.9
60.3
20
204.0
82.4
82.8
80
281
259.6
260.5
104.9
15.4
101
161
149.3
221
204.9
105.3
42
38.9
15.7
02
94.6
38.2
62
150.2
60.7
22
205.8
83.2
82
261.5
105. 6
43
39.9
16.1
03
95.5
38.6
63
151.1
61.1
23
206.8
83.5
83
262.4
106.0
44
40.8
16.5
04
96.4
39.0
64
152.1
61.4
24
2or.7
83.9
84
263.3
106.4
45
41.7
16.9
05
97.4
39.3
65
153.0
61.8
25
208.6
84.3
85
264.2
106.8
46
42.7
17.2
06
98.3
39.7
66
153.9
62.2
26
209.5
84.7
86
265.2
107.1
47
43.6
17.6
07
99.2
40.1
67
154.8
62.6
27
210.5
85.0
87
266.1
107.5
48
44.5
18.0
08
100.1
40.5
68
155.8
62.9
28
211.4
85.4
88
267.0
107.9
49
45.4
18.4
09
101.1
40.8
69
156.7
63.3
29
212.3
85.8
89
268.0
108.3
50
51
46.4
47.3
18.7
10
102.0
41.2
70
157.6
63.7
30
213.3
86.2
90
268.9
108.6
19.1
111
102.9
41.6
271
158.5
64.1
231
214.2
86.5
291
269.8
109.0
52
48.2
19.5
12
103.8
42.0
72
159.5
64.4
32
215.1
86.9
92
270.7
109.4
53
49.1
19.9
13
104.8
42.3
73
160.4
64.8
33
216.0
87.3
93
271.7
109.8
54
50.1
20.2
14
105.7
42.7
74
161.3
65.2
34
217.0
87.7
94
272.6
110.1
55
51.0
20.6
15
106.6
43.1
75
162.3
65.6
35
217.9
88.0
95
273.5
110.5
56
51.9
21.0
16
107.6
43.5
76 1 163.2
65.9
36
218.8
88.4
96
274.4
110.9
57
52.8
21.4
17
108.5
43.8
77
164.1
66.3
37
219.7
88.8
97
275. 4
111.3
58
53.8
21.7
18
109.4
44.2
78
165.0
66.7
38
220.7
89.2
98
276.3
111.6
59
54.7
22.1
19
110.3
44.6
79
166.0
67.1
39
221.6
89.5
99
277.2
112.0
60
55.6
22.5
20
111.3
45.0
80
166.9
67.4
40
222.5
89.9
300
278.2
112,4
Dist.
Dep.
Lat,
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
68° (112°, 248°, 292°).
TABLE 2.
[Page 411
Difference of Latitude and Departure for 22° (158°, 202
°, 338°
).
Dist.
. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
301
279.1
112.7
361
334.7
135.2
421
390.3
157.7
481
446.0
180.2
541
501.6
202.7
02
280. 0
113.1
62
335. 6
135. 6
22
391.3
158.1
82
446.9
180.6
42
502.5
203.1
03
280.9
113.5
63
336.6
136.0
23
392.2
158.4
83
447.8
180.9
43
503.4
203.5
04
281.9
113.9
64
337.5
136. 3
24
393.1
158.8
84
448.8
181.3
44
504.4
203.8
05
282.8
114.2
65
338. 4
136.7
25
394.1
159. 2
85
449.7
181.7
45
505.3
204.2
06
283. 7
114.6
66
339.3
1.37. 1
26
395. 0
159.6
86
450.6
182.1
46
506. 2
204.6
07
284.6
115.0
67
340. 3
137.5
27
395.9
159. 9
87
451.6
182.4
47
507.2
205. 0
08
285.6
115. 4
68
341.2
137.8
28
396.8
160.3
88
452. 5
182.8
48
508. 1
205.3
09
286. 5
115.7
69
342.1
138.2
29
397.8
160.7
89 ! 453.4
183. 2
49
509.0
205. 7
10
287.4
116.1
70
343.1
138.6
30
398.7
161.1
90 454.3
183.6
50
551
510.0
206.1
206.5
311
288.4
116. 5
371
344.0
139.0
431
399.6
161.4
491 \ 455.3
184. 0'
510.9
12
289.3
116.8
72
344.9
139.3
32
400.5
161.8
92
456.2
184.3
52
511.8
206.8
13
290.2
117.2
73
345.8
139.7
33
401.5
162.2
93
457.1
184.7
53
512.7
207.2
14
291.1
117.6
74
346.8
140.1
34
402.4
162.6
94
458.0
185.1
54
513.6
207.6
15
292.1
118.0
75
347.7
140.5
35
403. 3
162.9
95
459.0
185.4
55
514.6
208.0
16
293.0
118.3
76
348.6
140.8
36
404.3
163. 3
96
459.9
185.8
56
515.5
208.3
17
293.9
118.7
77
349.5
141.2
37
405.2
163.7
97
460.8
186.2
57
516.4
208.7
18
294.8
119.1
78
350.5
141.6
38
406.1
164.1
98
461.8
186.6
58
517.4
209.1
19
295. 8
119.5
79
351. 4
141.9
39
407.0
164.4
99
462.7
186.9
59
518.3
209.4
20
296.7
119.8
80
352. 3
142.3
40
408.0
164.8
500
463.6
187.3
60
519.2
209.8
321
297.6
120.2
381
353.3
142.7
441
408.9
165.2
501
464.5
187.7
561
520.1
210.2
22
298.6
120.6
82
354.2
143.1
42
409.8
165.5
02
4a5.4
188.0
62
521.0
210.5
23
299.5
121.0
83
355. 1
143.4
43
410.7
165.9
03
466.4
188.4
63
522.0
210.9
24
300.4
121.3
84
356.0
143.8
44
411.7
166. 3
04
467.3
188.8
64
522.9
211.3
25
301.3
121.7
85
357.0
144.2
45
412.6
166.7
05
468.2
189.2
65
523.8
211.7
26
302.3
122.1
86
357. 9
144.6
46
413.6
167.0
06
469.2
189. 5
66
524.8
212.0
27
303.2
122.5
87
358.8
144.9
47
414. 5
167.4
07
470.1
189.9
67
525.7
212.4
28
304.1
122.8
88
359.7
145.3
48
415. 4
167.8
08
471.0
190. 3
68
526.6
212.8
29
305. 0
123.2
89
360.7
145. 7
49
■ 416. 3
168.2
09
471.9
190.7
69
527.5
213.2
30
306. 0
123. 6
90
361.6
146.1
50
417.2
418.2
168.5
10
472.9
191.1
191. 4
70
571
528.5
213.5
331
306.9
124.0
391
362.5
146.4
451
168.9
511
473.8
529.4
213.9
32
307.8
124.3
92
363.5
146.8
52
419.1
169.3
12
474.7
191.8
72
530.3
214.3
33
308.8
124.7
93
364.4
147.2
53
420.0
169.7
. 13
475.6
192.2
73
531.2
214.7
34
309.7
125. 1
94
365. 3
147.6
54
420.9
170.0
14
476.6
192.5
74
532.2
215. 0
35
310.6
125.5
95
366.2
147.9
55
421.9
170.4
15
477.5
192.9
75
533.1
215. 4
36
311.5
125.8
96
367.2
148.3
56
422.8
170.8
16
478.4
193. 3
76
534.0
215.8
37
312. 5
126.2
97
368.1
148.7
57
423.7
171.2
17
479.3
193. 7
77
534. 9
216.2
38
313.4
126.6
98
369.0
149.1
58
424.6
171.5
18
480.3
194.0
78
535. 9
216. 5
39
314.3
127.0
99
369.9
149.4
59
425. 6
171.9
19
481.2
194.4
79
536. 8
216.9
40
341
315. 2
127.3
400
370.9
149.8
60
426.5
427.4
172.3
20
482.1
194.8
195.2
80
581
537. 7
538.6
217.3
316.2
127.7
401
371.8
150.2
461
172.7
521
483.0
217.7
42
317.1
128.1
02
372. 7
150. 6
62
428.4
173.0
22
484.0
195.5
82
539.6
218.0
43
318.0
128.5
03
373.7
150.9
63
429.3
173.4
23
484.9
195.9
83
540.5
218.4
44
319.0
128.8
04
374.6
151.3
64
430.2
173.8
24
485.8
196.3
84
541.4
218.8
45
319.9
129.2
05
375.5
151.7
65
431.1
174.2
25
486.7
196.7
85
542.4
219.2
46
320. 8
129.6
06
376. 4
152.1
66-
432.1
174. 5
26
487.7
197.0
86
543.3
219. 5
47
321. 7
130.0
07
377.4
152. 4
67
433.0
174.9
27
488.6
197.4
87
544. 2
219.9
48
322.7
130.3
08
378. 3
152.8
68
433. 9
175. 3
28
489.5
197.8
88
545.1
220. 3
49
323.6
130.7
09
379.2
153.2
69
434.8
175.7
29
490.4
198.2
89
546.1
220.7
50
324.5
131. 1
10
380.1
381. i
153.6
153.9
70
471
435.8
436.7
176.0
176. 4
30
531
491.4
492.3
198.5
90
547.0
221.0
351
325. 4
131.5
411
198.9
591
547.9
221.4
52
326.4
131.8
12
382.0
154.3
72
437.6
176.8
32
493.2
199.3
92
548. 9
221.8
53
327.3
132.2
13
382.9
154.7
73
438.6
177.2
33
494.2
199.7
93
549.8
222.2
54
328.2
132.6
14
383. 9
155. 1
74
439.5
177.5
34
495.1
200.0
94
550.7
222. 5
55
329.2
133.0
15
384.8
155.4
75
440.4
177.9
35
496.0
200.4
95
551. 7
222.9
56
330.1
133.3
16
385.7
155.8
76
441.3
178.3
36
496.9
200.8
96
552.6
223.3
57
331.0
133.7
17
386.6
156.2
77
442.3
178.7
37
497.9
201.2
97
553.5
223.7
58
332.0
134.1
18
387. 6
156.6
78
443.2
179. 0
38
498.8
201.5
98
554.4
224.0
59
332.9
134.5
19
388.5
156.9
79
444.1
179.4
39
499.7
201.9
99
555. 4
224.4
60
333.8
134.8
20
389.4
157.3
80
445.0
179.8
40
500.7
202. 3
600
556.3
224.8
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
€
8° (112°, 248°, 292°
).
Page 412]
TABLE L>.
Difference of I-atitude and Departure for 23° (157°, 203°, 337°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
56.2
2S.8
121
111.4
47.3
181
166.6
70.7
241
221.8
94.2
2
1.8
0.8
62
57.1
24.2
22
112.3
47.7
82
167. 5
71.1
42
222.8
94.6
3
2.8
1.2
63
58.0 24.6
23
113. 2
48.1
83
168.5
71.5
43
223.7
94.9
4
3.7
1.6
64
58.9 25.0
24
114.1
48.5
84
169.4
71.9
44
224.6
95.3
5
4.6
2.0
65
59. 8 25. 4
25
115.1
48.8
85
170.3
72.3
45
225.5
95.7
6
5.5
2.3
1?
60. 8 25. 8
26
116.0
49.2
86
171.2
72.7
46
226.4
96.1
7
6.4
2.7
61. 7 26. 2
27
116.9
49.6
•87
172.1
73.1
47
227.4
96.5
8
7.4
3.1
68
62.6 : 26.6
28 ! 117.8
50.0
88
173.1
73.5
48
228.3
96.9
9
8.3
3.5
69
63.5
27.0
29 118. 7
50.4
89
174.0
73.8
49
229.2
97.3
10
11
9.2
3.9
70
64.4
65.4
27.4
27.7
30 119. 7
50.8
51.2
90
191
174.9
175.8
74.2
50
251
230.1
231.0
97.7
98.1
10.1
4.3
71
131 120.6
74.6
12
11.0
4.7
72
66. 3 i 28. 1
32 , 121.5
51.6
92
176.7
75.0
52
232.0
98.5
13
12.0
5.1
73
67.2 1 28.5
33
122.4
52.0
93
177.7
75.4
53
232. 9
98.9
14
12.9
5.5
74
68.1
28.9
34
123.3 ! 52.4
94
178.6
75.8
54
233. 8
99.2
15
13.8
5.9
75
69.0
29.3
35
124. 3 i 52. 7
95
179,5
76.2
55
234.7
99.6
16
14.7
6.3
76
70.0
29.7
36
125. 2 53. 1
96
180.4
76.6
56
235.6
100.0
17
15.6
6.6
77
70.9
30.1
37
126. 1 i 53. 5
97
181.3
77.0
57
236.6
100.4
18
16.6
7.0
78
71.8
30.5
38
127.0
53.9
98
182.3
77.4
58
237.5
100.8
19
17.5
7.4
79
72.7 30.9
39
128.0
54.3
99
183.2 1 77.8
59
238.4
101.2
20
21
18.4
7.8
80
81
73.6
31.3
31.6
40
141
128.9
129.8
54.7
55.1
200
201
184.1
78.1
60
239.3
240.3
101.6
19.3
8.2
74.6
185.0
78.5
261
102.0
22
20.3
8.6
■ 82
75.5 1 32.0
42
130.7
55.5
02
185.9
78.9
62
241.2
102.4
23
21.2
9.0
83
76.4 \ 32.4
43
131.6
55.9
03
186.9
79.3
63
242.1
102.8
24
22.1
9.4
84
77.3 1 32.8
44
132.6
56.3
04
187. 8 1 79.7
64
243.0
103. 2
25
23.0
9.8
85
78.2 1 33.2
45
133.5
56.7
05
188.7
80.1
65
243.9
103.5
26
23.9
10.2
86
79.2 33.6
46
134. 4
57.0
06
189.6
80.5
66
244.9
103.9
27
24.9
10.5
87
80. 1 34. 0
47
135.3
57.4
07
190.5
80.9
67
245. 8
104.3
28
25.8
10.9
88
81.0 i 34.4
48
136.2
57.8
08
191.5
81.3
68
246.7
104.7
29
26.7
11.3
89
81.9 ; 34.8
49
137. 2
58.2
09
192.4
81.7
69
247.6
105. 1
30
31
27.6
28.5
11.7
90
82.8 1 35.2
50
138.1
139.0
58.6
59.0
10
211
193.3
194.2
82.1
82.4
70
271
248.0
249. 5
105. 5
f05. 9
12.1
91
83.8 ' 35.6
151
32
29.5
12.5
92
84. 7 1 35. 9
52 139. 9
59.4
12
195.1
82.8
72
250.4
106.3
33
30.4
12.9
93
85.6 i 36.3
53
140.8
59.8
13
196.1
83.2
73
251.3
106.7
34
31.3
13.3
94
86. 5 1 36. 7
54
141.8
60.2
14
197.0
83.6
74
252.2
107.1
35
32.2
13.7
95
87. 4 j 37. 1
55
142.7
60.6
15
197.9
84.0
75
253. 1
107.5
36
33.1
14.1
96
88.4 1 37.5
56
143.6
61.0
16
198.8
84.4
76
254.1
107.8
37
34.1
14.5
97
89.3 37.9
57
144.5
61.3
17
199.7
84.8
77
255. 0
108.2
38
35.0
14.8
98
90. 2 38. 3
58
145.4
61.7
18
200.7
85.2
78
255.9
108.6
39
35.9
15.2
99
91. 1 38. 7
59
146.4
62.1
19
201.6
85.6
79
256. 8
109.0
40
36.8
15.6
100
92. 1 39. 1
93.0 39.5
60
147.3
62.5
20
221
202.5
86.0
80
257.7
258.7
109.4
41
37.7
16.0
101
161 j 148.2 62.9
203.4
86.4
281
109.8
42
38.7
16.4
02
93.9 1 39.9
62 149. 1 : 63. 3
22
204.4
86.7
82
259. 6
110.2
43
39.6
16.8
03
94.8 ; 40.2
63 150.0 63.7
23
205.3
87.1
83
260. 5
110.6
44
40.5
17.2
04
95. 7 ! 40. 6
64 151.0 ' 64.1
24
206.2
87.5
84
261.4
111.0
45
41.4
17.6
05
96. 7 : 41. 0
65 151.9 64.5
25
207.1
87.9
85
262. 3
111.4
46
42.3
18.0
06
97.6 41.4
66
152.8 &4.9
26
208.0
88.3
86
263. 3
111.7
47
43.3
18.4
07
98. 5 41. 8
67
153.7 65.3
27
209.0
.88.7
87
264.2
112.1
48
44.2
18.8
08
99. 4 42. 2
68
154.6
65.6
28
209.9
89.1
88
2a5. 1
112.5
49
45.1
19.1
09
100. 3 42. 6
69
155. 6
66.0
29
210. 8
89.5
89
266.0
112.9
50
51
46.0 I
46.9 1
19.5
19.9
10
111
101. 3 43. 0
70
156.5
66.4
30
211.7
212.6
89.9
90.3
90
291
266. 9
267. 9
113.3
113. 7
102.2
43.4
171
157. 4
66.8
231
52
47.9 1
:20.3
12
103.1
43.8
72
158.3
67.2
32
213.6
90.6
92
268.8
114.1
53
48.8
20.7
13
104.0
44.2
73
159.2
67.6
33
214.5
91.0
93
269.7
114.5
54
49.7
21.1
14
104.9
44.5
74
160.2
68.0
34
215.4
91.4
94
270.6
114.9
55
50.6
21.5
15
105. 9
44.9
75
161.1
68.4
35
216.3
91.8
95
271. 5
115.3
56
51.5
21.9
16
106.8
4o.3
76 162.0
68.8
36
217.2
92.2
96
272. 5
115.7
57
52.5
22.3
17
107.7
45.7
77 1 162.9
69.2
37
218.2
92.6
97
273.4
116.0
58
53.4
22.7
18
108.6
46.1
78 i 163.8
69.6
38
219.1
93.0
98
274. 3
116.4
59
54.3
23.1
19
109. 5
46.5
79
164.8
69.9
39
220.0
93.4
99
275. 2
116.8
60
55.2
23.4
20
110.5
46.9
80
165.7
70.3
40
220.9
93.8
300
276.2
117.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat. Dist.
Dep.
Lat.
67° (113°, 247^, 293°).
TABLE 2.
[Page 413
Difference of Latitude and Departure for 23° (157°, 203°, 337'
')•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
277.1
117.6
361
332.3
141.1
421
387.5
164.5
481
442.7
188.0
541
498.0
211.4
02
278.0
118.0
62
333.2
141.5
22
388.5
164.9
82
443.7
188.4
42
498.9
211. 8
03
278.9
118.4
63
334.1
141.8
23
389.4
165. 3
83
444.6
188.8
43
499.8
212.2
04
279.8
118.8
64
335. 1
142.2
24
390.3
165.7
84
445. 5
189.2
44
500.7
212.6
05
280.8
119.2
65
336.0
142.6
25
391.2
166.1
85
446.4
189.5
45
501.7
213.0
06
281.7
119. 6
66
336. 9
143.0
26
392.1
166.5
86
447.3
189.9
46
502. 6
213. 4
07
282.6
120.0
67
337.8
143.4
27
393.1
166.8
87
448. 3
190.2
47
503. 5
213. 8
08
283. 5
120.4
68
338.7
143.8
28
394.0
167.2
88
449. 2 : 190. 6
48
504.4
214.2
09
284.4
120.8
69
339. 7
144.2
29
.394. 9
167.6
89
450. 1 191. 0
49
505. 3
214.6
10
311
285. 4
121.2
70
371
340.6
341. 5
144.6
14.5. 0
30
431
395.8
396.7
168.0
90
451.0
191.4
191.8
50
506.3
507.2
215.0
215.3
286.3
121.6
168.4
491
451. 9
551
12
287.2
121.9
72
342.4
145. 4
32
397.7
168.8
92
452. 9 192. 2
52
508.1
215.6
13
288.1
122.3
73
343. 4
145. 7
33
398.6
169.2
93
453. 8 192. 6
53
509.0
216. 0
14
289.0
122.7
74
344. 3
146.1
34
399.5
169.6
94
454.7 193.0
54
509.9
216.4
15
290.0
123.1
75
345.2
146.5
35
400.4
170.0
95
455. 6
193.4
55
510. 9
216. S
16
290.9
123.5
76
346.1
146.9
36
401.3
170.4
96
456. 6
193. 8
56
511. 8
217.2
17
291.8
123.9
77
347. 0
147.3
37
402.3
170.8
■ 97
457. 5
194.2
Oi
512. 7
217.6
18
292.7
124.3
78
348.0
147.7
38
403. 2
171.1
98
458.4
194.6
58
513. 6
218.0
19
293.6
124.6
79
348. 9
148.1
39
404.1
171. 5
99
459. 3
195. 0
59
514. 5
218.4
20
294.6
295.5
125. 0
80
349. 8
148. 5
40
405. 0
171.9
500
460.2
461.2
195.4
60
515. 5
516.4
218. 8
219.2"
321
125.4
381
350.7
148.9
441
405.9
172.3
501
195.8
561
22
296.4
125.8
82
351.6
149.3
42
406.9
172.7
02
462.1
196.2
62
517.3
219.6
23
297.3
126.2
83
352.6
149.7
43
407.8
173.1
03
463.0
196.6
63
518. 2
220.0
24
298.2
126.6
84
353.5
150.0
44
408.7
173.5
04
463.9
197.0
64
519.2
220.4
25
299.2
127.0
85
354. 4
150. 4
45
409.6
173.9
05
464.9
197.4
65
520.1
220.8
26
300.1
127.4
86
355. 3
150.8
46
410.5
174.3
06
465. 8
197.8
66
521.0
221.2
27
301.0
127.8
87 1 356.2
151.2
47
411.5
174.7
07
466.7
198.1
67
521.9
221.6
28
301.9
128.2
88 1 357.2
151.6
48
412.4
175.1
08
467.6
198.5
68
522.8
222.0
29
302.8
128.6
89 358.1
152.0
49
413.3
175.4
09
468. 5
198.8
69
523. 8
222.3
30
303. 8
128.9
90 359.0
1.52. 4
50
414.2
415.2
175.8
10
469.5
199.3
70
524. 7
222.7
223. 1
331
304.7
129.3
391 359. 9
152.8
451
176.2
511 1 470.4
199.7
571
525. 6
32
305.6
129.7
92 360. 8
153.2
52
416.1
176.6
12 471.3
200.0
72
526.5
223. 4
33
306. 5
130.1
93 361. 8
153. 6
53
417.0
177.0
13 ! 472.2
200.4
73
527.4
223. 8
34
307.5
130.5
94 362.7
154.0
54
417.9
177.4
14 ; 473. 1
200.8
74
528. 4
224.2
35
308.4
130.9
95 363. 6
154.3
55
418.8
177.8
15 ! 474.0
201.2
75
529. 3
224. 6
36
309.3
131.3
96
364. 5
154.7
56
419.8
178.2
16 \ 475.0
201.6
76
530. 2
225. 0
37
310.2
131.7
97
365.4
155. 1
57
420.7
178.6
17 i 475.9
202. 0
77
531.1
225. 4
38
311.1
132.1
98
366.4
155. 5
58
421.6
179.0
18 476.8
202.4
78
532.0
225. 8
39
312.1
132.5
99
367.3
155. 9
59
422. 5
179.4
19 477. 7
202.8
79
533. 0
226.2
40
341
313.0
132.9
400 j 368.2
156. 3
60
423.4
424.4
179.7
20 ' 478.6
521 , 479.6
203.2
203.6
80
533.9
226.6
313.9
133.2
401
369.1
156. 7
461
180.1
581
534.8
227.0
42
314.8
133.6
02
370.0
157. 1
62
425. 3
180.5
22 1 480. 5
204.0
82
535. 7
227.4
43
315. 7
134.0
03
371.0
157.5
63
426.2
180.9
23 i 481.4
204.4
83
536.6
227.8
44
316.7
134.4
04
371.9
157.9
64
427.1
181.3
24 1 482.3
204.8
84
537.6
228.2
45
317.6
134.8
05
372.8
158. 3
65
428.0
181.7
25 1 483.2
205. 2
85
538. 5
228.6
46
318.5
135.2
06
373.7
158. 6
66
429.0
182.1
26 ' 484. 2
205. 5
86
539. 4
229.0
47
319.4
135. 6
07
374.6
159. 0
67
429. 9
182.5
27 i 485. 1
205. 9
87
540.3
229.4
48
320.3
136.0
08
375. 6
159. 4
68
430.8
182.9
28 ! 486.0
206. 3
88
.541. 2
229.8
49
321.3
136.4
09
376.5
159. 8
69
431.7
183.3
29
486.9
206.7
89
542. 2
230. 2
50
322.2
136.8
137.2
10
377.4
378.3
160. 2
160.6
70
471
432.6
433. 6
183.7
184.0
30
531
487.8
488.8
207.1
207. 4
90
591
543. 1
.544. 0
230. 6
231.0
351
323.1
411
52
324.0
137.5
12
379. 3
161.0
72
434. 5
184.4
32
489.7
207.8
92
544. 9
231.3
53
324.9
137.9
13
380.2
161.4
73
435. 4
184.8
33
490.6
208. 2
93
545. 8
231.7
54
325. 9
138.3
14
381.1
161. 8
74
436. 3
185. 2
34
491.5
208.6
94
.546. 8
232. 0
55
326.8
138.7
15
382.0
162.2
75
437.2
185. 6
35
492. 5
209.0
95
547. 7
232.4
56
327.7
139.1
16
382.9
162.5
76
438.2
186.0
36
493. 4
209. 4
96
548.6
232.8
57
328.6
139.5
17
383.9
162. 9
77
4.39. 1
186.4
37
494.3
209.8
97
549. 5
233.2
58
329.5
139.9
18
384.8
163. 3
78
440.0
186.8
38
495. 2
210.2
98
550. 4
233. 6
59
330.5
140.3
19
385.7
163. 7
79
440. 9
187.2
39
496.1
210.6
99
.551.3
234. 0
60
331.4
140.7
20
386.6
164.1
80
441.8
187.6
40
497.1
211.0
600
552.3
234.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
(
)7°(11
3°, 247°, 293°).
Page 414]
TABLE 2.
Difference of Latitude and Departure for 24'
(156
=,204°, 336°).
Dlst.
1
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
49.2
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
0.9
0.4
61
55.7
24.8
121
110.5
181
165.4
73.6
241
220.2
98.0
2
1.8
0.8
62
56.6
25.2
22
111.5
49.6
82
166. 3
74.0
42
221. 1
98.4
3
2.7
1.2
63
57.6
25.6
23
112.4
50.0
83
167.2
74.4
43
222.0
98.8
4
3.7
1.6
64
58.5
26.0
24
113.3
50.4
84
168.1
74.8
44
222.9
99.2
5
4.6
2.0
65
59.4
26.4
25
114.2
50.8
85
169.0
76.2
45
223.8
99.7
6
5.5
2.4
i6
60.3
26.8
26
115.1
51.2
86
169.9
76.7
46
224.7
100.1
7
6.4
2.8
67
61.2
27.3
27
116.0
51.7
87
170.8
76.1
47
226. 6
100.5
8
7.3
3.3
68
62.1
27.7
28
116.9
52.1
88
171.7
76.6
48
226. 6
1(X).9
9
8.2
3.7
69
63.0
28.1
29
117.8
52.5
89
172.7
76.9
49
227. 6
101.3
10
11
9.1
4.1
4.5'
70
71
63.9
64.9
28.5
28. 9
30
131
118.8
119.7
52.9
53.3
90
173.6
174.5
77.3
"77.7
60
228.4
101.7
102.1
10.0
191
251
229. 3
12
11.0
4.9
72
65.8
29.3
32
120.6
53.7
92
175.4
78.1
62
230.2
102.6
13
11.9
5.3
73
66.7
29.7
33
121.5
54.1
93
176.3
78.5
63
231.1
102.9
14
12.8
5.7
74
67.6
30.1
34
122.4
54.5
94
177.2
78.9
64
232.0
103. 3
15
13.7
6.1
75
68.5
30.5
35
123.3
54.9
95
178.1
79.3
56
233. 0
103. 7
16
14.6
6.5
76
69.4
30.9
36
124.2
55.3
96
179.1
79.7
66
233.9
104.1
17
15.5
6.9
77
70.3
31.3
37
125.2
55. 7
97
180.0
80.1
67
234.8
104.5
. 18
16.4
7.3
78
71.3
31.7
38
126.1
56.1
98
180.9
80.5
68
235. 7
104. 9
19
17.4
7.7
79
72.2
32.1
39
127.0
56.5
99
181.8
80.9
69
236. 6
105. 3
20
21
18.3
19.2
8.1
8.5'
80
81
73.1
74.0
32.5
32.9
40
141
127.9
56.9
57.3
200
201
182.7
183.6
81.3
60
261
237.6
105.8
106. 2
128.8
81.8
238.4
22
20.1
8.9
82
74.9
33.4
42
129.7
57.8
02
184.5
82.2
62
239.3
106.6
23
21.0
9.4
83
75.8
33.8
43
130.6
58.2
03
185.4
82.6
63
240.3
107.0
24
21.9
9.8
84
76.7
34.2
44
131.6
58.6
04
186.4
83.0
64
241.2
107.4
25
22.8
10.2
85
77.7
34.6
45
132.5
69.0
05
187.3
83.4
66
212.1
107.8
26
23.8
10.6
86
78.6
35.0
46
133.4
59.4
06
188.2
83.8
66
243.0
108.2
27
24.7
11.0
87
79.5
35.4
47
134.3
59.8
07
189.1
84.2
67
243.9
108. 6
28
25.6
11.4
88
80.4
35.8
48
135. 2
60.2
08
190.0
84.6
68
244.8
109.0
29
26.5
11.8
89
81.3
36.2
49
136.1
60.6
09
190. 9
85.0
69
246.7
109.4
30
27.4
28.3
12.2
12.6
90
82.2
36.6
37.0
50
137.0
61.0
10
191.8
192.8
86.4
85.8
70
246.7
109.8
110.2
31
91
83.1
151
137.9
61.4
211
271
247.6
32
29.2
13.0
92
84.0
37.4
52
138.9 1 61.8
12
193.7
86.2
72
248.5
110.6
33
30.1
13.4
93
85.0
37.8
53
139.8 ! 62.2
13
194.6
86.6
73
249.4
111.0
34
31.1
13.8
94
85.9
38.2
54
140.7 i 62.6
14
195.6
87.0
74
260.3
111.4
35
32.0
14.2
95
86.8
38.6
55
141.6 , 63.0
15
196.4
87.4
76
261.2
111.9
36
32.9
14.6
96
87.7
39.0
56
142.5 ' 63.5
16
197.3
87.9
76
252.1
112.3
37
33.8
15.0
97
88.6
39.5
57
143.4
63.9
17
198.2
88.3
77
253.1
112.7
38
34.7
15.5
98
89.5
39.9
58
144.3
64.3
18
199.2
88.7
78
264.0
113.1
39
35.6
15.9
99
90.4
40.3
59
145. 3 I 64. 7
19
200.1
89.1
79
254.9
113.6
40
36.5
37.5
16.3
100
91.4
92.3
40.7
60
146.2
147.1
65.1
20
201.0
201.9
89.5
80
281
265.8
256.7
113.9
"114. 3
41
16.7
101
41.1
161
65.5
221
89.9
42
38.4
17.1
02
93.2
41.5
62
148.0 ! 65.9
22
202.8
90.3
82
267.6
114.7
43
39.3
17.5
03
94.1
41.9
63
148.9
66.3
23
203.7
90.7
83
258.5
115.1
44
40.2
17.9
04
95.0
42.3
64
149.8
66.7
24
204.6
91.1
84
259.4
115.5
45
41.1
18.3
05
95.9
42.7
65
150.7
67.1
25
206.5
91.5
85
260.4
116.9
46
42.0
18.7
06
96.8
43.1
66
151.6
67.5
26
206.5
91.9
86
261.3
116. 3
47
42.9
19.1
07
97.7
43.5
67
152.6
67.9
27
207.4
92.3
87
262.2
116.7
48
43.9
19.5
08
98.7
43.9
68
153.5
68.3
28
208.3
92.7
88
263.1
117.1
49
44.8
19.9
09
99.6
44.3
69
154.4
68.7
29
209.2
93.1
89
264.0
117.5
50
45.7
20.3
10
111
100. 5
101.4
44.7
45. 1'
70
155.3
69.1
69. 6
30
210.1
211.0
93.6
90
291
264.9
118.0
51
46.6
20.7
171
156.2
231
94.0
265.8
118.4
52
47.5
21.2
12
102.3
45.6
72
157.1
70.0
32
211.9
94.4
92
266.8
118.8
53
48.4
21.6
13
103.2
46.0
73
158.0
70.4
33
212.9
94.8
93
267.7
119.2
64
49.3
22.0
14
104.1
46.4
74
159.0
70.8
34
213.8
96.2
94
268.6
119.6
55
50.2
22.4
15
105. 1
46.8
75
159.9
71.2
35
214.7
95.6
96
269.6
120.0
56
51.2
22.8
16
106.0
47.2
76
160.8
71.6
36
215.6
96.0
96
270. 4
120.4
57
52.1
23.2
17
106.9
47.6
77
161.7
72.0
37
216.6
96.4
97
271.3
120.8
58
53.0
23.6
18
107.8
48.0
78
162.6
72.4
38
217.4
96.8
98
272.2
121.2
59
53.9
24.0
19
108.7
48.4
79
163.5
72.8
38
218.3
97.2
99
273.2
121.6
60
54.8
24.4
20
109.6
48.8
80
164.4
73.2
40
219.3
97.6
300
274.1
122.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
(
)6° (1
14°, 246°, 294°
)•
TABLE 2.
[Page 415 |
Difference of Latitude and Departure for 24° (156°, 204
°, 336°
)•
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
275.0
122.4
361
329.8
146.8
421
384. 6
171.2
481
439.4
195.6
541
494.2
220.0
02
275.9
122.8
62
330. 7 I 147. 2
22
385.5
171.6
82
440.3
196.0
42
495.1
220.4
03
276.8
123.2
63
331.6 147.6
23
386.4
172.1
83
441.2
196.5
43
496.0
220.9
04
277.7
123.7
64
332.5
148.1
24
387.3
172.5
84
442.1
196.9
44
496.9
. 221.3
05
278.6
124.1
65
333.4
148.5
25
388.2
172.9
85
443.0
197.3
45
497.8
221.7
06
279.5
124.5
66
334.3
148.9
26
389. 2
173.3
86
444.0
197.7
46
498.8
222.1
07
280.4
124.9
67
335. 3
149.3
27
390.1
173.7
87
444.9
198.1
47
499.7
222.5
08
281.4
125.3
68
336.2
149.7
28
391.0
174.1
88
445.8
198.5
48
500.6
222.9
09
282.3
125.7
69
337.1
150.1
29
391.9
174.5
89
446.7
198.9
49
501.5
223.3
10
283.2
126.1
70
338.0
150.5
30
392.8
174.9
90
447.6
199.3
50
502.4
223.7
311
284.1
126.5
371
338.9
m).9
431
393.7
175.3
491
448.6
199.7
551
503. 4
224.1
12
285.0
126.9
72
339.8
32
394.6
175.7
92
449.5
200.1
52
504. 3
224.5
13
285.9
127.3
73
340. 7,
151.7
33
395.6
176.1
93
450.4
200.5
53
505. 2
224.9
14
286.8
127.7
74
341. 7^
152.1
34
396.5
176.5
94
451.3
200.9
54
506.1
225. 3
15
287.8
128.1
75
342.6
152.5
35
397.4
176.9
95
452.2
201.3
55
507.0
225.7
16
288.7
128.5
76
343.5
152.9
36
398.3
177.3
96
453.1
201.7
56
507.9
226.1
17
289.6
128.9
77
344.4
153.3
37
399.2
177.7
97
454.0
202.2
57
508.8
226.6
18
290.5
129.3
78
345. 3
153.7
38
400.1
178.2
98
454. 9
202.6
58
509. 7
227.0
19
291.4
129.8
79
346.2
154.2
39
401.0
178.6
99
455. 8
203. 0
59
510.6
227.4
20
292.3
293.2
130.2
130.6
80
381
347.1
348. i
154.6
155.0
40
441
402.0
179.0
500
456.8
203.4
60
511.6
512. 5
227.8
321
402.9
179.4
501
457.7
203.8
561
228.2
22
294.2
131.0
82
349.0
155.4
42
403.8
179.8
02
458.6
204.2
62
513.4
228.6
23
295.1
131.4
83
349. 9
155.8
43
404.7
180.2
03
459.5
204.6
63
514.3
229.0
24
296.0
131.8
84
350. 8
156. 2
44 405.6
180.6
04
460.4
205.0
64
515.2
229.4
25
296.9
132. 2
85
351.7
156:6
45 406.5
181.0
05
461.3
205.4
65
516.1
229.8
26
297.8
132.6
86
352.6
157.0
46
407.4
181.4
06
462.2
205. 8
66
517.0
230.2
27
298.7
133.0
87
353.5
157. 4
47
408.3
181.8
07
463.2
206.2
67
518. 0
230.6
28
299.6
133.4
88
354.4
157.8
48
409.3
182.2
08
464.1
206.6
.68
518.9
231.0
29
300.5
133.8
89
355.4
158.2
49
410.2
182.6
09
465.0
207.0
69
519.8
231.4
30
301.5
302.4
134.2
90 356. 3
158.6
50
411.1
183.0
10
465.9
207.4
70
"571
520.7
521.6
231.8
232.2
331
134.6
391 357.2
159.0
451
412.0
183. 4
511
466.8
207.8
32
303.3
135.0
92 358.1
159.4
52
412.9
183.8
12
467.7
208.2
72
522.5
232.7
33
304.2
135.4
93
359.0
159.8
53
413.8
184.3
13
468.6
208.7
73
523.4
233. 1
34
305.1
135.9
94
359.9
160.3
54
414.7
184.7
14
469.5
209.1
74
524.3
233.5
35
306.0
136.3
95
360.8
160.7
55
415.7
185.1
15
470. 5
209.5
75
525.3
233.9
36
306. 9
136.7
96
361.8
161.1
56
416.6
185.5
16
471.4
209.9
76
526.2
234. 3
37
307.9
137.1
97
362.7
161.5
57
417.5
185.9
17
472.3
210.3
77
527.1
234. 7
38
308.8
137.5
98
363.6
161.9
58
418.4
186.3
18
473.2
210.7
78
528. 0
235. 1
39
309.7
137.9
99
364.5
162.3
59
419. 3
186.7
19
474.1
211.1
79
528. 9
235. 5
40
341
310.6
138.3
400
365.4
366.3
162.7
60
420.2
187.1
20
475.0
475.9
211.5
80
529.8
235.9
236.3
311.5
138.7
401
163.1
461
421.1
187.5
521
211.9
581
530.8
42
312.4
139.1
02
367.2
163.5
62
422.0
187.9
22
476.8
212.3
82
531.7
236.7
43
313.3
139.5
03 i 368.2
163.9
63
423.0
188.3
23
477.8
212.7
83
532. 6
237. 1
44
314. 3
139.9
04 1 369. 1
164.3
64
423.9
188.7
24
478.7
213.1
84
533. 5
237.5
45
315.2
140.3
05 370.0
164.7
65
424.8
189.1
25
479.6
213.5
85
534.4
237.9
46
316. 1
140.7
06 370.9
165.1
66
425.7
189.5
26
480.5
213.9
86
535. 3
238.3
47
317.0
141.1
07 i 371.8
165.5
67
426.6
189.9
27
481.4
214.4
87
536. 2
238.8
48
317.9
141.5
08 ! 372.7
165.9
68
427.5
190.4
28
482.3
214.8
88
537.1
239.2
49
318.8
142.0
09 i 373.6
166.4
69
428.4
190.8
29
483.2
215. 2
89
538.0
239.6
50
319.7
142.4
10 ! 374. 5
166.8
167.2
70
429.4
191.2
30
484.2
485. 1
215. 6
90
539.0
539. 9
240.0
351
320.6
142.8
411 ! 375.5
471
430. 3
191.6
531
216.0
591
240.4
52
321.6
143. 2
12
376.4
167.6
72
431.2
192.0
32
486.0
216.4
92
540.8
240.8
53
322.5
143.6
13
377.3
168.0
73
432.1
192.4
33
486.9
216.8
93
541.7
241.2
54
323.4
144.0
14
378.2
168.4
74
433.0
192.8
34
487.8
217.2
94
542.6
241.6
55
324.3
144.4
15
379.1
168.8
75
433.9
193.2
35
488.7
217.6
95
543.5
242.0
56
325.2
144.8
16
380. 0
169.2
76
434.8
193. 6
36
489.6
218.0
96
544.4
242.4
57
326.1
145.2
17
380.9
169.6
77
435.8
194.0
37
490.6
218.4
97
545.4
242.8
58
327.0
145.6
18
381.9
170.0
78
436.7
194.4
38
491.5
218.8
98
546.3
243.2
59
328. 0
146.0
19
382. 8
170.4
79
437.6
194.8
39
492.4
219.2
99
547.2
243.6
60
328.9
146.4
20
383.7
170.8
80
438.5
195.2
40
493.3
219.6
600
548.1
244.0
Dist.
Dep.
Lat.
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
(
56° (114°, 246
°, 294°
).
Page 416]
TABLE 2.
Difference of Latitude and
Departure for 25° (155°, 205
°, 335°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
55.3
25.8
121
109.7
51.1
181
164.0
76.5
241
218.4
101.9
2
1.8
0.8
62
56.2
26.2
22
110.6
51.6
82
164.9
76.9
42
219. 3
102. 3
3
2.7
1.3
63
57.1
26.6
23
111.5
52.0
83
165. 9
77.3
43
220.2
102.7
4
3.6
1.7
64
58.0
27.0
24
112.4
52.4
84
166.8
77.8
44
221.1
103. 1
5
4.5
2.1
65
58.9
27.5
25
113.3
52.8
85
167.7
78.2
45
222.0
103.5
6
5.4
2.5
«6
59.8
27.9
26
114.2
53.2
86
168.6
78.6
46
223. 0
104.0
7
6.3
3.0
67
60.7
28.3
27
115.1
53.7
87
169. 5
79.0
47
223.9
104.4
8
7.3
3.4
68
61.6
28.7
28
116.0
54.1
88
170.4
79.5
48
224.8
104.8
9
8.2
3.8
69
62.5
29.2
29
116.9
54.5
89
171.3
79.9
49
225.7
105.2
10
9.1
10.0
4.2
70
63.4
29.6
30.0
30
131
117.8
54.9
90
172.2
80.3
50
226.6
105.7
106.1
11
4.6
71
64.3
118.7
55.4
191
173.1
80.7
251
227.5
12
10.9
5.1
72
65.3
30.4
32
119.6
55.8
92
^74.0
81.1
52
228.4
106.5
13
11.8
5.5
73
66.2
30.9
33
120.5.
56.2
93
174.9
81.6
53
229.3
106.9
14
12.7
5.9
74
67.1
31.3
34
121.4
56.6
94
17^.8
82.0
54
230.2
107. 3
15
13.6
6.3
75
68.0
31.7
35
122.4
57.1
95
176.7
82.4
55
231.1
107.8
16
14.5
6.8
76
68.9
32.1
36
123.3
57.5
96
177.6
82.8
56
232.0
108.2
17
15.4
7.2
77
69.8
32.5
37
124.2
57.9
97
178.5
83.3
57
232.9
108.6
18
16.3
7.6
78
70.7
33.0
38
125.1
58.3
98
179.4
83.7
58
233.8
109.0
19
17.2
8.0
79
71.6
33.4
39
126.0
58.7
99
180.4
84.1
59
234.7
109.5
20
18.1
19.0
8.5
80
72.5
73.4
33.8
34.2
40
126.9
59.2
59.6
200
201
181.3
182. 2"
84.5
84.9
60
261
235.6
236.5
109.9
110.3
21
8.9
81
141
127.8
22
19.9
9.3
82
74.3
34.7
42
128.7
60.0
02
183.1
85.4
62
237.5
110.7
23
20.8
9.7
83
75.2
35.1
43
129.6
60.4
03
184.0
85.8
63
238.4
111.1
24
21.8
10.1
84
76.1
35.5
44
130.5
60.9
04
184.9
86.2
64
239.3
111.6
25
22.7
10.6
85
77.0
35.9
45
131.4
61.3
05
185.8
86.6
65
240.2
112.0
26-
23.6
11.0
86
77.9
36.3
46
132.3
61.7
06
186.7
87.1
66
241.1
112.4
27
24.5
11.4
87
78.8
36.8
47
133.2
62.1
07
187.6
87.5
67
242.0
112.8
28
25.4
11.8
88
79.8
37.2
48
134.1
62.5
08
188.5
87.9
68
242.9
113. 3
29
26.3
12.3
89
80.7
37.6
49
135.0
63.0
09
189.4
88.3
69
243.8
113.7
30
27.2
12.7
90
81.6
38.0
^38. 5
50
135.9
136.9
63.4
10
190. 3
88.7
70
271
244.7
114.1
31
28.1
13.1
91
82.5
151
63.8
211
191.2
89.2
245.6
114.5
32
29.0
13.5
92
83.4
38.9
52
137.8
64.2
12
192. 1
89.6
72
246.5
115.0
33
29.9
13.9
93
84.3
39.3
53
138.7
64.7
13
193.0
90.0
73
247.4
115. 4
34
30.8
14.4
94
85.2
39.7
54
139.6
65.1
14
193.9
90.4
74
248.3
115.8
35
31.7
14.8
95
86.1
40.1
55
140.5
65.5
15
194.9
90.9
75
249.2
116.2
36
32.6
15.2
96
87.0
40.6
56
141.4
65.9
16
195.8
91.3
76
250.1
116.6
37
33.5
15.6
97
87.9
41.0
57
142. 3
66.4
17
196.7
91.7
77
251.0
117.1
38
34.4
16.1
98
88.8
41.4
58
143.2
66.8
18
197.6
92.1
78
252.0
117.5
39
35.3
16.5
99
89.7
41.8
59
144.1
67.2
19
198.5
92.6
79
252.9
117.9
40
36.3
16.9
17.3
100
101
90.6
91.5
42.3
42.7
60
161
145.0
67.6
20
221
199.4
200.3^
93.0
80
253.8
118.3
118.8
41
37.2
145.9
6870
93.4
281
254.7
42
38.1
17.7
02
92.4
43.1
62
146.8
68.5
22
201.2
93.8
82
255.6
119.2
43
39.0
18.2
03
93.3
43.5
63
147.7
68.9
23
202.1
94.2
83
256. 5
119.6
44
39.9
18.6
04
94.3
44.0
64
148.6
69.3
24
203.0
94.7
84
257.4
120.0
45
40.8
19.0
05
95.2
44.4
65
149.5
69.7
25
203. 9
95.1
85
258.3
120.4
46
41.7
19.4
06
96.1
44.8
66
150.4
70.2
26 i 204.8
95.5
86
259.2
120.9
47
42.6
19.9
07
97.0
45.2
67
151.4
70.6
27 1 205.7
95.9
87
260.1
121.3
48
43.5
20.3
08
97.9
45.6
68
152.3
71.0
28 '• 206.6
96.4
88
261.0
121.7
49
44.4
20.7
09
98.8
46.1
69
153.2
71.4
29
207. 5
96.8
89
261.9
122.1
50
45.3
21.1
10
111
99.7
100.6
46.5
46. 9
70
171
154.1
155.0
71.8
30
208.5
209.4
97.2
97.6"
90
262.8
263.7
122.6
123.0
51
46.2
21.6
72.3
231
291
52
47.1
22.0
12
101.5
47.3
72
155.9
72.7
32
210.3
98.0
92
264. 6
123.4
53
48.0
22.4
13
102.4
47.8
73
156. 8
73.1
33
211.2
98.5
93
265.5
123. 8
54
48.9
22.8
14
103.3
48.2
74
157. 7
73.5
34
212.1
98.9
94
266.5
124.2
55
49.8
23.2
15
104.2
48.6
75
158.6
74.0
35
213.0
99.3
95
267.4
124.7
56
50.8
23. 7
16
105.1
49.0
76
159.5
74.4
36
213.9
99.7
96
268.3
125.1
57
51.7
24.1
17
106.0
49.4
77
160.4
74.8
37
214. 8
100. 2
97
269.2
125. 5
58
52.6
24.5
18
106.9
49.9
78
161.3
75.2
38
215. 7
100.6
98
270.1
125. 9
59
53.5
24.9
19
107.9
50.3
79
162.2
75.6
39
216.6
101.0
99
271.0
126.4
60
54.4
25.4
20
108.8
50.7
80
163.1
76.1
40
217.5
101.4
300
271.9
126.8
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
65° (1
15°, 245°, 295°).
TABLE 2.
[Page
417
Difference of Latitude and Departure for 25° (155°, 205
^ 335°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
272.8
127.2
361
327. 1
152.5
421
381.5
177.9
481
435.9
203.3
541
490.3
228.6
02
273.7
127.6
62
328.0
153. 0
22
382.4
178.3
82
436.8
203.7
42
491.2
229.0
03
274.6
128.0
63
329. 0
153. 4
23
383. 3
178.7
83
437.7
204.1
43
492.1
229.4
04
275. 5
128.4
64
329. 9
153. 8
24
384.2
179.2
84
438.6
204. 5
44
493.0
229.9
05
276. 4
128.9
65
330. 8
1.54.2
25
385. 1
179.6
85
439. 5
204.9
45
493.9
230.3
06
277.3
129. 3
66
331. 7
154.6
26
386.0
180.0
86
440.4
205. 4
46
494.8
230. 7
07
278.2
129. 7
67
332. 6
155. 1
27
387.0
180.4
87
441.3
205. 8
47
495. 7
231. 1
08
279.1
130. 1
68
333. 5
155.5
28
387.9
180.9
88
442.2
206.2
48
496.6
231.6
09
280.0
130. 6
69
334. 4
155.9
29
388.8
181.3
89
443.1
206.6
49
497.5
232.0
10
280.9
131.0
131.4
70
335. 3
156.3
30
389.7
181.7
90
491
444.0
207.1
50
551
498.4
232.4
311
281.8
371
336. 2
156. 8
431
390.6
182.1
444.9
207. 5
499.3
232.8
12
282.7
131.8
72
337. 1
157.2
32
391.5
182.5
92
445.9
207.9
52
500.2
233. 2
13
283.6
132. 2
73
338. 0
157. 6
33
392.4
183.0
93
446.8
208.3
53
501.1
233.7
14
284.5
132.7
74
338. 9
158.0
34
393. 3
183.4
94
447.7
208.7
54
502.0
234.1
15
285.4
133. 1
75
339.8
158.5
35
394.2
183.8
95
448.6
209.1
55
503.0
234.5
16
286.4
133. 5
76
340. 7
158.9
36
395.1 184.2
96
449.5
209.6
56
503. 9
235.0
17
287.3
133.9
77
341. 6
159. 3
37
396.0
184.7
97
450.4
210.0
57
504.8
235.4
18
288.2
134.4
78
342. 5
159.7
38
396. 9
185. 1
98
451.3
210.4
58
505.7
235.8
19
289.1
134.8
79
343. 5
160. 1
39
397. 8
185.5
99
452.2
210.9
59
506. 6
236.2
20
290.0
135.2
80
344. 4
160.6
40
398. 7 ! 185. 9
500
453.1
211.3
60
507. 5
236.6
321
290.9
135. 6
381
34573
161.0
441
399.6 186.3
501
454.0
211.7
561
508.4
237.1
22
291.8
136.1
82
346. 2
161.4
42
400.6
186.8
02
454.9
212.1
62
509.3
237. 5
23
292.7
136.5
83
347.1
161.8
43
401.5
187.2
03
455.8
212.5
63
510.2
237.9
24
293.6
136.9
84
348. 0
162. 3
44
402.4
187.6
04
456.7
213.0
64
511.1
238.3
25
294.5
137.3
85
348. 9
162.7
45
403.3
188.0
05
457.7
213.4
65
512.0
238.7
26
295.4
137.7
86
349. 8
163. 1
46
404. 2 i 188. 5
06
458.6
213.8
66
512.9
239.2
27
296.3
138.2
87
350. 7
163.5
47
405.1 '188.9
07
459.5
214.2
67
513.8
239.6
28
297.2
138.6
88
351.6
163.9
48
406. 0 i 189. 3
08
460.4
214.7
68
514.8
240.1
29
298.1
139.0
89
352. 5
164.4
49
406. 9 i 189. 7
09
461.3
215.1
69
515. 7 >
240.5
30
331
299.0
300. 0
139.4
139. 9
90
391
353.4
354. 3
164.8
50
407.8
190.1
10
462.2
215.5
215. 9
70
571
516.6
517.5
240.9
165.2
451^
408.7
190.6
511
463.1
241.3
32
300.9
140. 3
92
355. 2
165. 6
52
409.6
191.0
12
464.0
216.4
72
518.4
241.7
33
301.8
140.7
93
356.1
166.1
53
410.5
191.4
13
464.9
216.8
73
519.3
242.1
34
302.7
141.1
94
357. 0
166.5
54
411.4
191.8
14
465.8
217.2
74
520. 2
242.6
35
303.6
141.5
95
358.0
166.9
55
412.3
192.3
15
466.7
217.7
75
521. 1
243.0
36
304.5
142. 0
96
358.9
167.3
56
413. 2
192.7
16
467.6
218.1
76
522.0
243.4
37
305.4
142.4
97
359. 8
167.7
57
414.1
193.1
17
468.5
218.5
77
522. 9
243. 8
38
306. 3
142.8
98
360.7
168.2
58
415.1
193.5
18
469.4
218.9
78
523. 8
244.3
39
307. 2
143.2
99
361.6
168.6
59
416.0
194.0
19
470.3
219.3
79
524.7
244.7
40
341
308.1
309.0
143.7
144. 1
400
362.5
169.0
169.4
60 I 416.9
194.4
20
471.2
219.8
220.2
80
581
525. 6
526. 5
245.1
245. 5
401
363.4
461
417.8
194.8
521
472.2
42
309.9
144.5
02
364.3
169.9
62
418.7
195. 2
22
473.1
220.6
82
527.4
246.0
43
310.8
144.9
03
365.2
170.3
63
419.6
195.6
23
474.0
221.0
83
528. 3
246.4
44
311.7
145.4
04
366.1
170.7
64
420.5
196.1
24
474.9
221.4
84
529. 3
246.8
45
312.6
145.8
05
367. 0
171.1
65
421.4
196.5
25
475. 8
221.9
85
530. 2
247.2
46
313.5
146.2
06
367.9
171.6
66
422. 3
196.9
26
476.7
222.3
86
531.1
247.7
47
314.5
146.6
07
368.8
172.0
67
423.2
197.3
27
477.6
222.7
87
532.0
248.1
48
315.4
147.0
08
369.7
172.4
68
424. 1
197.8
28
478.5
223.2
88
532. 9
248.5
49
316.3
147.5
09
370.6
172.8
69
425.0
198.2
29
479.4
223.6
89
5.33. 8
248.9
50
317.2
318.1
147.9
148.3
10
411
371.5
372.5
173.2
173.7
70
471
425.9
426.8
198.6
199.0
30
531
480.3
481.2
224.0
224. 4
90
534.7
249.4
249.8
351
591
535. 6
52
319.0
148.7
12
373. 4
174.1
72
427.7
199.4
32
482.1
224.8
92
536. 5
250. 2
53
319.9
149.2
13
374.3
174.5
73
428.6
199.9
33
483.0
225. 3
93
537. 4
250. 6
54
320.8
149.6
14
375.2
174.9
74
429.6
200. 3
34
483.9
225.7
94
538.3
251. 1
55
321.7
150.0
15
376.1
175.4
75
430.5
200.7
35
484.8
226.1
95
539.2
251. 5
56
322.6
150.4
16
.377. 0
175.8
76
431.4
201.1
36
485.7
226.5
96
540.1
251. 9
57
323.5
150.8
17
377.9
176.2
77
432.3
201.6
37
486.7
226.9
97
541.0
252.3
58
324.4
151.3
18
378. 8
176. 6
78
433.2
202.0
38
487. 6
227.4
98
541.9
252.7
59 1 325.3
151. 7
19
379. 7
177.0
79
434. 1
202.4
39
488. 5
227.8
99
542.8
253. 1
60 326.2
152.1
20
380.6
177.5
80
435.0
202.8
40
489.4
228.2
600
543.8
253.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
(
55° (115°, 245°, 295°
)•
22489—03-
-2V
Page 418]
TABLE 2.
Difference of Latitude and Departure for 26° (154°, 206°, 334
').
Dist.
Lat.
Dep.
Di.st.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
181
Lat.
Dep.
Dist.
241
Lat.
Dep.
1
0.9
0.4
61
54.8
26.7
121
108.8
53.0
162.7
79.3
216.6
105.6
2
1.8
0.9
62
55. 7
27.2
22
109.7
53.5
82
163.6
79.8
42
217.5
106.1
3
2.7
1.3
63
56.6
27.6
23
110.6
53.9
83
164.5
80.2
43
218.4
106.5
4
3.6
1.8
64
57.5
28.1
24
111.5
54.4
84
165.4
80.7
44
219.3
107.0
5
4.5
2.2
%5
58.4
28.5
25
112.3
54.8
85
166.3
81.1
45
220.2
107.4
6
5.4
2.6
66
59. 3
28.9
26
113.2
55.2
86
167.2
81.5
46
221.1
107.8
7
6.3
3.1
67
60.2
29.4
27
114.1
55.7
87
168.1
82.0
47
222.0
108.3
8
7.2
3.5
68
61.1
29.8
28
115.0
56.1
88
169.0
82.4
48
222.9
108.7
9
8.1
3.9
69
62.0
30.2
29
115.9
56. 5
89
169.9
82.9
49
223.8
109.2
10
11'
9.0
4.4
70
62.9
30.7
30
116.8
57.0
90
170.8
83.3
50
224.7
109. 6
9.9
4.8
71
63.8
31.1
131 , 117.7
57.4
191
171.7'
83.7
251
225. 6
110.0
12
10.8
5.3
72
64.7
31.6
32
118.6
57.9
92
172.6
84.2
52
226.5
110.5
13
11.7
5. 7
73
65.6
32.0
33
119.5
58.3
93
173.5
84.6
53
227.4
110.9
14
12.6
6.1
74
66.5
32.4
34
120.4
58.7
94
174.4
85.0
54
228. 3
111.3
15
13.5
6.6
75
67.4
32.9
35
121.3
59.2
95
175.3
85.5
55
229.2
111.8
16
14.4
7.0
76
68.3
33.3
36
122.2
59.6
96
176.2
85.9
56
230.1
112.2
17
15.3
7.5
77
69.2
33. 8
37
123.1
60.1
97
177.1
86.4
57
231.0
112.7
18
16.2
7.9
78
70.1
34.2
38
124.0
60.5
98
178.0
86.8
58
231.9
113.1
19
17.1
8.3
79
71.0
34.6
39
124.9
60.9
99
178.9
87.2
59
232.8
113.5
20
21
18.0
18.y~
8.8
9.2
_80
81
71.9
35.1
40
125.8
126. 7
61.4
200
179.8
87.7
60
233.7
114.0
72.8
35.5
141
61.8
201
180.7
88.1
261
234.6
114.4
22
19.8
9.6
82
73.7
35.9
42
127.6
62.2
02
181.6
88.6
62
235. 5
114.9
23
20.7
10.1
83
74.6
36.4
43
128.5
62.7
03
182. 5
89.0
63
236.4
115.3
24
21.6
10.5
84
75.5
36.8
44
129.4
63.1
04
183.4
89.4
64 i 237.3
115.7
25
22.5
11.0
85
76.4
37.3
45
130.3
63.6
05
184.3
89.9
65 i 238.2
116.2
26
23.4
11.4
86
77.3
37.7
46
131.2
64.0
06
185.2
90.3
66 I 239. 1
116.6
27
24.3
11.8
87
78.2
38.1
47
132.1
64.4
07
186.1
90.7
67 240.0
117.0
28
2p.2
12.3
88
79.1
38.6
48
133.0
64.9
08 186. 9
91.2
68 i 240.9
117.5
29
26.1
12.7
89
80.0
39.0
49
133.9
65.3
09 i 187.8
91.6
69
241.8
117.9
30
27.0
27.9
13.2
90
80.9
39.5
50
134.8
65.8
10 1 188.7
92.1
70
242.7
243.6
118.4
118.8
31
13.6
91
81.8
39.9
151
135.7
66.2
211
189.6
92.5
271
32
28.8
14.0
92
82.7
40.3
52
136.6
66.6
12
190.5
92.9
72
244.5
119.2
33
29.7
14.5
93
83.6
40.8
53
137.5
67.1
13
191.4
93.4
73
245.4
119.7
34
30.6
14.9
94
84.5
41.2
54
138.4
67.5
14
192.3
93.8
74
246.3
120. 1
35
31.5
15.3
95
85.4
41.6
55
139.3
67.9
15
193.2
94.2
75
247.2
120.6
36
32.4
15.8
96
86.3
42.1
56
140.2
68.4
16
194.1
94.7
76
248.1
121.0
37
33.3
16.2
97
87.2
42.5
57
141.1
68.8
17
195.0
95.1
77
249.0
121.4
38
34.2
16.7
98
88.1
43.0
58
142.0
69.3
18
195.9
95.6
78
249.9
121.9
39
35.1
17.1
99
89.0
43.4
59
142.9
69.7
19
196.8
96.0
79
250.8
122.3
40
41
36.0
36.9
17.5
100
101
89.9
90.8^
43.8
60
143.8
144. 7
70.1
20
197.7
96.4
80
251.7
252. 6
122.7
123.2
18.0
44.3
161
70.6
221
198.6
96.9
281
42
37.7
18.4
02
91.7
44.7
62
145.6
71.0
22
199. 5
97.3
82
253. 5
123.6
43
38.6
18.8
03
92.6
45.2
63
146.5
71.5
23
200.4
97.8
83
254. 4
124.1
44
39.5
19.3
04
93.5
45.6
64
147.4
71.9
24
201.3
98.2
84
255. 3
124.5
45
40.4
19.7
05
94.4
46.0
65
148.3
72.3
25
202.2
98.6
85
256.2
124.9
46
41.3
20.2
06
95.3
46.5
66
149.2
72.8
26
203.1
99.1
86
257.1
125.4
47
42.2
20.6
07
96.2
46.9
67
150.1
73.2
27 204. 0
99.5
87
258.0
125. 8
48
43. 1
21.0
08
97.1
47.3
68
151.0
73.6
28 204. 9
99.9
88
258.9
126.3
49
44.0
21.5
09
98.0
47.8
69
151.9
74.1
29 205. 8
100.4
89
259.8
126.7
50
51
44.9
45.8
21.9
22.4'
10
98.9
48.2
70
152.8
74.5
30 206. 7
100.8
90
260.7
127.1
111
99.8
48.7
171
153.7
75.0
231 207.6
101.3
291
261.5
127.6
52
46.7
22.8
12
100.7
49.1
72
154. 6
75.4
32 208.5
101.7
92
262.4
128.0
53
47.6
23.2
13
101.6
49.5
73
155.5
75.8
33 ! 209.4
102.1
93
263.3 128.4 1
54
48.5
23.7
14
102.5
50.0
74
156.4
76.3
34 210. 3
102.6
94
264.2
128.9
55
49.4
24.1
15
103.4
50.4
75 157. 3
76.7
35
211.2
103.0
95
265.1
129.3
56
50.3
24.5
16
104. 3
50. 9
76 158. 2
77.2
36
212.1
103. 5
96
266.0
129. 8
57
51.2
25.0
17
105. 2
51.3
77
159.1
77.6
37
213.0
103. 9
97
266. 9 130. 2
58
52.1
25.4
18
106.1
51.7
78
160.0
78.0
38
213. 9
104. 3
98
267. 8 130. 6
59
53.0
25.9
19
107.0
52.2
79
160.9
78.5
39
214.8
104.8
99
268.7 131.1
60
53.9
26.3
20
107.9
52.6
80
161.8
78.9
40
215.7
105.2
300
269.6
131.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. 1
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
(
34° (116°, 244°, 296°
)•
TABLE ±
[Page 419 |
Difference of Latitude and Departure for 26° (154°, 206°, 334).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
270.5
132.0
361
324. 5
158. 3
421
378.4
184.6
481
432. 3
210.9
541
486.2
237.2
02
271.4
132.4
62
325.4
158. 7
22
379. 3
185.0
■ 82
433. 2
211.3
42
487.1
237. 6
03
272.3
132. 8
63
326. 3
159. 1
23
380.2
185.4
83
434.1
211.7
43
488. 0
238. 0
04
273.2
133. 3
64
327. 2
1.59. 6
24
381.1
185. 9
84
435. 0
212.2
44
488.9
238. 5
05
274.1
133. 7
65
328. 1
160.0
25
382.0
186. 3
85
435. 9
2li!6
45
489.8
238. 9
^06
275. 0
1.34. 1
66
329. 0
160.4
26
382. 9
186.7
86
436.8
213. 0
46
490. 7
239. 3
07
275.9
134. 6
67
329. 9
160.9
27
383.8
187.2
87
437.7
213.5
47
491.6
239. 8
08
276.8
135. 0
68
330.8
161.3
28
384.7
187.6
88
438. 6
213. 9
48
492.5
240.2
09
277.7
135. 5
69
331. 7
161.8
29
385.6
188. 1
89
4.39. 5
214.4
49
493.4
240. 7
10
278.6
135. 9
136. 3
70
-37r
332. 6
162.2
30
431
386. 5
387.4
188. 5
188.9
90
491
440.4
441. 3
214.8
215.2
50
494.3
241.1
311
279.5
333.5
162.6
551
495.2
241. 5
12
280.4
136.8
72
334.4
163.1
32
388.3
189.4
92
442.2
215.7
52
496.1
242.0
13
281. 3
137.2
73
335.3
163.5
33
389.2
189.8
93
443. 1
216.1
53
497. 0
242.4
14
282.2
137. 7
74
336.2
164.0
34
390.1
190.3
94
444.0
216.6
54
497.9
242.9
15
283.1
138.1
75
337.1
164.4
35
391.0
190.7
95
444.9
217.0
55
498. 8
243. 3
16
284.0
138.5
76
338.0
164.8
36
391.9
191.1
96
445.8
217.4
56
499.7
243. 7
17
284.9
139.0
77
338. 9
165.3
37
392. 8
191.6
97
446.7
217.9
57
500.6
244.2
18
285.8
139.4
78
339.8
165.7
38
393.7
192.0
98
447.6
218.3
58
501.5
244.6
19
286.7
139.8
79
340.7
166.2
39
394,6
192.4
99
448.5
218.7
59
502.4
245.0
20
321
287.6
288. 5
140.3
80
341.5
166.6
40
441
395.5
396.4
192.9
500
449.4
219.2
60
503.3
504.2
245.5
245.9
140.7
381
342.4
167. 0
193. 3
501
450. 3
219. 6
561
22
289.4
141.2
82
343.3
167. 5
42
397.3
193.8
02
451.2
220. 1
62
505.1
246. 4
23
290. 3
141.6
83
344.2
167.9
43
398.2
194.2
03
452.1
220.5
63
506.0
246.8
24
291.2
142.0
84
345. 1
168.3
44
399.1
194.7
04
453.0
221.0
64
506. 9
247.3
25
292.1
142.5
85
346.0
168.8
45
400.0
195.1
05
453.9
221.4
65
507. 8
247.7
26
293.0
142.9
86
346.9
169.2
46
400.9
195.5
06
454.8
221.8
• 66
508. 7
248. 1
27
293. 9
143. 4
87
347.8
169.7
47
401.8
196.0
07
455.7
222.3
67
509.6
248.6
28
294.8
143. 8
88
348.7
170.1
48
402.7
196.4
08
456.6
222.7
68
510. 5
249.0
29
295. 7
144.2
89
349. 6
170. 5
49
403.6
196.8
09
457.5
223.1
69
511.4
249.4
30
331
296.6
297. 5
144.7
145. 1
90
391
350. 5
171.0
50
451
404.5
405.4
197.3
197.7
10
458.4
223.6
70
512.3
249.9
351.4
171.4
511
459.3
224.0
571
513.2
250.3
32
298.4
145.6
92
352.3
171.8
52
406.3
198.1
12
460.2
224.4
72
514.1
250.8
33
299. 3
146.0
93
353.2
172.3
53
407.2
198.6
13
461.1
224.9
73
515. 0
251.2
34
300.,2
146.4
94
354. 1
172.7
54
408. 1
199.0
. 14
462.0
225.3
74
515.9
251.6
35
301.1
146.9
95
355.0
173.2
55
409.0
199.5
15
462.9
225.8
75
516.8
252.1
36
302.0
147.3
96
355.9
173.6
56
409.9
199.9
16
463.8
226.2
76
517. 7
252. 5
37
302.9
147.7
97
356. 8
174.0
57
410.8
200.3
17
464.7
226.6
77
518.6
252.9
38
303.8
148.2
98
357. 7
174.5
58
411.7
200.8
18
465.6
227.1
78
519.5
253. 4
39
304,7
148.6
99
358.6
174.9
59
412.6
201.2
19
466.5
227.5
79
520.4
253.8
40
305.6
306.5
149.0
149. 5
400
401
359.5
175.4
60
413.5
201.7
202.1
20
521
467.4
468.3
228.0
228.4
80
521.3
254. 3
341
360. 4
175.8
461
414.4
581
522.2
254.7
42
307.4
149.9
02
361.3
176.2
62
415.2
202.5
22
469.2
228.8
82
523.1
255.1
43
308.3
150.4
03
362. 2
176.7
63
416.1
203.0
23
470.1
229.3
83
524.0
255.6
44
309.2
150. 8
04
363. 1
177.1
64
417.0
203.4
24
471.0
229.7
84
524.9
256. 0
45
310. 1
151. 2
05
364.0
177.5
65
417.9
203.8
25
471.9
230. 1
85
525.8
256. 4
46
311.0
151.7
06
364.9
178.0
66
418.8
204.3
26
472.8
230.6
86
526. 7
256.9
47
311.9
152.1
07
365.8
178.4
67
419.7
204.7
27
473.7
231.0
87
527. 6
257.3
48
312. 8
152. 6
08
366.7
178.9
68
420. 6
205.2
28
474.6
231.5
88
528.5
257.8
49
313. 7
153.0
09
367.6
179. 3
69
421.5
205.6
29
475.5
231.9
89
529.4
258.2
50
314.6
315. 5~
153.4
10
368.5
179.7
70
422.4
206.0
206.5
30
476.4
232. 3
90
530.3
258.6
259. 1
351
153.9
411
369.4
180.2
471
423.3
531
477.3
232. 8
591
531.2
52
316.4
154.3
12
370. 3
180.6
72
424.2
206.9
32
478.2
233.2
92
532.1
259. 5
53
317. 3
154.7
13
371.2
181.1
73
425.1
207.3
33
479.1
233. 6
93
533.0
259.9
54
318.2
155. 2
14
372.1
181.5
74 I 426.0
207.8
34
480.0
234.1
94
533.9
260. 4
55
319.1
155. 6
15
373.0
181.9
75 1 426.9
208.2
35
480.9
234.5
95
534.8
260.8
56
320. 0
156.1
16
373. 9
182.4
76
427.8
208.7
36
481.8
235.0
96
535.7
261. 3
57
320.9
156.5
17
374. 8
182.8
77
428.7
209.1
37
482.7
235.4
97
536. 6
261.7
58
321.8
156.9
18
375.7
183.2
78.
429.6
209.5
38
483.6
235.8
98
537.5
262.1
59
322. 7
157.4
19
376. 6
183.7
79
430.5
210.0
39
484.5
236.3
90
538.4
262.6
60
323.6
157.8
20
377. 5
184.1
80
431.4
210.4
40
485.3
236.7
600
539.3
263. 0
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
64°
(116°, 244°, 296°).
Page 420
TABLE
2.
Difference of Latitude and Departure. for 27° (153°, 207
°, 333°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
54.4
27.7
121
107.8
54.9
181 161.3
82.2
241
214.7
109.4
2
1.8
0.9
62
55.2
28.1
22 108. 7
55. 4
82 162.2
82.6
42
215.6
109.9
3
2.7
1.4
63
56.1
28.6
•23
109.6
55.8
83 i 163. 1
83.1
43
216.5
110.3
4
3.6
1.8
64
57.0
29.1
24
110.5
56.3
84 163.9
83.5
44
217.4
110.8
5
4.5
2.3
65
57.9
29.5
25
111.4
56.7
85 164. 8
84.0
45
218.3
111.2
6
5.3
2.7
%S
58.8
30.0
26
112.3
57.2
86 165. 7
84.4
46
219.2
111.7
7
6.2
3.2
67
59.7
30.4
27
113.2
57.7
87 166. 6
84.9
47
220.1
112.1
8
7.1
3.6
68
60.6
30.9
28 ' 114.0
58.1
88 167. 5
85.4
48
221.0
112.6
9
8.0
4.1
69
61.5
31.3
29 114.9
58.6
89 { 168.4
85.8
49
221.9
113.0
10
8.9
4.5
5.0
70
62.4
31.8
30
115.8
116. 7
59.0
59.5
90
169.3
170. 2
86.3
86.7
50
251
222.8
223.6
113.5
11
9.8
71
63.3
32.2
131
191
114.0
12
10.7
5.4
72
64.2
32.7
32
117.6
59.9
92 171. 1
87.2
52
224.5
114.4
13
11.6
5.9
73
65.0
33.1
33
118.5
60.4
93 172. 0
87.6
53
225.4
114.9
14
12.5
6.4
74
65.9
33.6
34
119.4
60.8
94 172.-9
88.1
54
226.3
115. 3
15
13.4
6.8
75
66.8
34.0
35
120.3
61.3
95
173.7
88.5
55
227.2
115.8
16
14.3
7.3
76
67.7
34.5
36
121.2
61.7
96
174.6
89.0
56
228.1
116.2
17
15.1
7. 7
77
68.6
35.0
37
1^2.1
62.2
97
175.5
89.4
57
229.0
116.7
18
16.0
8.2
78
69.5
35.4
38
123.0
62.7
98
176.4
89.9
58
229.9
117.1
19
16.9
8.6
79
70.4
35.9
39
123.8
63.1
99
177.3
90.3
59
230.8
117.6
20
17.8
9.1
80
71.3
36.3
40
124.7
63.6
.200 178. 2
90.8
60
231.7
118.0
21
18.7
9.5
81
72.2
36.8
141
1%.6
64.0
201 179.1
91.3
261
232.6
118.5
22
19.6
10.0
82
73.1
37.2
42
126.5
64.5
02 180.0
91.7
62
233. 4
118.9
23
20.5
10.4
83
74.0
37.7
43
127.4
64.9
03 180.9
92.2
63
234. 3
119.4
24
21.4
10.9
84
74.8
38.1
44
128.3
65.4
04 j 181. 8
92.6
64
235.2
119.9
25
22.3
11.3
85
75.7
38.6
45
129.2
65.8
05 i 182. 7
93.1
65
236.1
120.3
26
23.2
11.8
86
76.6
39.0
46
130.1
66.3
06 ! 183.5
93.5
66
237.0
120.8
27
24.1
12.3
87
77.5
39.5
47
131.0
66.7
07 ! 184.4
94.0
67
237.9
121.2
28
24.9
12.7
88
78.4
40.0
48
131.9
67.2
08
1«5.3
94.4
68
238.8
121.7
29
25.8
13.2
89
79.3
40.4
49
132.8
67.6
09
186.2
94.9
69
239.7
122.1
30
26.7
13.6
90
80.2
40.9
50
133.7
68.1
10
187.1
188.0
95.3
70
240.6
241. 5
122.6
31
27.6
14.1
91
81.1
41.3
151
134.5
68.6
211
95.8'
271
123.0
32
28.5
14.5
92
82.0
41.8
52
135. 4
69.0
12
188.9
96.2
72
242.4
123.5
33
29.4
15.0
93
82.9
42.2
53
136.3
69.5
13
189.8
96.7
73
243.2
123.9
34
30.3
15.4
94
83.8
42.7
54
137.2
69.9
14
190.7
97.2
74
244.1
124.4
35
31.2
15.9
95
84.6
43.1
55
138.1
70.4
15
191.6
97.6
75
245.0
124.8
36
32.1
16.3
96
85.5
43.6
56
139.0
70.8
16
192.5
98.1
76
245.'9
125.3
37
33.0
16.8
97
86.4
44.0
57
139.9
71.3
17
193.3
98.5
77
246.8
125.8
38
33.9
17.3
98
87.3
44.5
58
140.8
71.7
18
194.2
99.0
78
247.7
126.2
39
34.7
17.7
99
88.2
44.9
59
141.7
72.2
19
195. 1
99.4
79
248.6
126.7
40
35.6
18.2
100
89.1
45.4
60
142.6
143.5
72.6
20
196.0
196.9
99.9
80
249.5
250.4
127.1
127.6
41
36.5
18.6
101
90.0
45.9
161
73. 1
221
100.3
281
42
37.4
19.1
02
90.9
46.3
62
144.3
73.5
22
197.8
100.8
82
251.3
128.0
43
38.3
19.5
03
91.8
46.8
63
145.2
74.0
23
198.7
101.2
83
252.2
128.5
44
39.2
20.0
04
92.7
47.2
64
146.1
74.5
24
199.6
101.7
84
253.0
128.9
45
40.1
20.4
05
93.6
47.7
65
147.0
74.9
25
200.5
102.1
85
253.9
129.4
46
41.0
20.9
06
94.4
48.1
66
147.9
75.4
26
201.4
102.6
86
254.8
129.8
47
41.9
21.3
07
95.3
48.6
67
148.8
75.8
27
202.3
103.1
87
255.7
130.3
48
42.8
21.8
08
96.2
49.0
68
149.7
76.3
28
203.1
103.5
88
256.6
130.7
49
43.7
22.2
09
97.1
49.5
69
150.6
76.7
29 204.0
104.0
89
257. 5
131.2
50
44.6
22.7
10
111
98.0
49.9
70
151.5
152. 4
77.2
77.6
30 204.9
104.4
90
258.4
131.7
51
45.4
23.2
98.9
50.4
171
231 205.8
104.9
291
259.3
132.1
52
46.3
23.6
12
99.8
50.8
72
153. 3
78.1
32 206.7
105.3
92
260.2
132.6
53
47.2
24.1
13
100.7
51.3
73
154.1
78.5
33 207.6
105.8
93
261.1
133.0
54
48.1
24.5
14
101.6
51.8
74
155. 0
79.0
34 208.5
106.2
94
262.0
133.5
55
49.0
25.0
15
102.5
52.2
75
155. 9
79.4
35 209.4
106.7
95
262.8
133.9
56
49.9
25.4
16
103.4
52.7
76
156.8
79.9
36 210.3
107.1
96
263.7
134.4
57
50.8
25.9
17
104.2
53.1
77
157.7
80.4
37 211.2
107.6
97
264.6
134. 8
58
51.7
26.3
18
105.1
53.6
78
158.6
80.8
38 i 212. 1
108.0
98
265.5
135.3
59
52.6
26.8
19
106.0
54.0
79
159.5
81.3
39
213.0
108.5
99
266.4
135.7
60
53.5
27.2
20
106.9
54.5
80
160.4
81.7
40
213.8
109.0
300
267. 3
136.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
63° (117°, 243
°, 297°).
TABLE 2.
[Page
421
Difference of Latitude and Departure for 27° (153°, 207°, 333°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
268.2
136.7
361
321.7
163.9
421
375. 1
191.1
481
428.6
218.3
541
482.0
245.6
02
269.1
137.1
62
322.5
164.4
22
376.0
191.6
82
429.4
218.8
42
482.9
246.1
03
270.0
137. 6
63
323.4
164.8
23
376.9
192.0
83
430.3
219.2
43
483.8
246.5
04
270.9
138. 0
64
324.3
165.3
24
377.8
192.5
84
431.2
219.7
44
484.7
247.0
05
271.8
138. 5
65
325.2
165.7
25
378.7
193.0
85
432.1
220.1
45
485.6
247.4
06
272.7
138.9
66
326.1
166.2
26
379.6
193.4
86
433.0
220.6
46
486.4
247.9
07
273.5
139.4
67
327.0
166.6
27
380.5
193.9
87
433.9
221.1
47
487.3
248.4
08
274.4
139.8
68
327.9
167.1
28
381.4
194.3
88
434.8
221.5
48
488.2
248.8
09
275.3
140.3
69
328.8
167.5
29
382.2
194.8
89
435.7
222.0
49
489.1
249.2
10
311
276.2
277. 1
140.7
141.2
70
329.7
330.6
168.0
30
431
383.1
384.0
195.2
90
436.6
222.4
222. 9
50
551
490.0
249.7
371
168.4
195.7
491
437.5
490.9
250.1
12
278.0
141.7
72
331.5
168.9
32
384.9
196.1
92
438.3
223.3
52
491.8
250.6
13
278. 9
142. 1
73
332. 3
169.3
33
385.8
196.6
93
439.2
223.8
53
492.7
251.0
14
279.8
142.6
74
333. 2
169.8
34
386.7 j 197.0
94
440.1
224.2
54
493.6
251.5
15
280.7
143. 0
75
334.1
170.3
35
387. 6 197. 5
95
441.0
224.7
55
494.5
252.0
16
281.6
143. 5
76
335.0
170.7
36
388. 5 ' 197. 9
96
441.9
225.2
56
495.4
252.4
17
282.5
143.9
77
335.9
171.2
37
389. 4 198. 4
97
442.8
225.6
57
496.3
252.9
18
283.3
144.4
78
336. 8
171.6
38
390.3 198.9
98
443.7
226.1
58
497.2
253.3
19
284.2
144.8
79
337. 7
172.1
39
391.2 199.3
99
444.6
226.5
59
498.1
253.8
20
321
285.1
286.0
145.3
80
338.6
172.5
173.0^
40
441
392.0 199.8
392.9 200.2
500
501
445.5
446. 4
227.0
227.5
60
561
499.0
499.8
254.2
145. 7
381
339. 5
254.7
22
286.9
146.2
82
340.4
173.4
42
393.8 200.7
02
447.3
227.9
62
500.7
255.1
23
287.8
146.6
83
341.3
173. 9
43
394.7
201.1
03
448.2
228.4
63
501.6
255.6
24
288.7
147.1
84
342.1
174.3
44
395.6
201.6
04
449.0
228.8
64
502.5
256.0
25
289.6
147.6
85
343.0
174.8
45
396.5
202.0
05
449.9
229.3
65
503.4
256.5
26
290.5
148.0
86
343. 9
175.2
46
397.4
202.5
06
450. 8
229.8
66
504. 3
257.0
27
291.4
148.5
87
344.8
175. 7
47
398.3
202.9
07
451.7
230.2
67
505.2
257.4
28
292.3
148.9
88
345.7
176.2
48
399.2
203.4
08
452. 6
230.6
68
506.1
257. 9
29
293.2
149.4
89
346.6
176.6
49
400.1
203.8
09
453.5
231.0
69
507.0
258.3
30
294.0
294.9
149.8
150. 3
90
391
347. 5
348.4
177.1
177.5
50
451
401.0
401.8
204.3
204.7
10
511
454.4
455.3
231.5
70
507.9
258.8
259.2
331
231.9
571
508.7
32
295. 8
150.7
92
349. 3
178.0
52
402.7
205. 2
12
456.2
232.4
72
509.6
259.7
33
296.7
151.2
93
350.2
178.4
53
403.6
205. 7
13
457.1
232.9
73
510.5
260.1
34
297.6
151.6
94
351.1
178.9
54
404.5
206.1
14
458.0
233.3
74
511.4
260.6
35
298.5
152.1
95
352. 0
179.3
55
405.4
206.6
15
458.8
233.8
75
512.3
261.1
36
299.4
152. 5
96
352.8
179.8
56
406.3
207.0
16
459.7
234.2
76
513.2
261.5
37
300.3
153.0
97
353. 7
180.2
57
407.2
207.5
17
460.6
234.7
77
514.1
262.0
38
301.2
153.5
98
354.6
180.7
58
408. 1
207.9
18
461.5
235. 2
78
515.0
262.4
39
302.1
153.9
99
355. 5
181.2
59
409.0
208.4
19
462.4
235.7
79
515.9
262.9
40
341
302.9
154.4
154. 8
400
401
356.4
357.3
181.6
182.1
60
461
409.9
410.8
208.8
209.3
20
521
463.3
464.2
236.1
80
581
516.8
517.7
263.4
303.8
236.6
263.8
42
304.7
155.3
02
358.2
182.5
62
411.6
209. 8
22
465.1
237. 0
82
518.5
264.3
43
305.6
155.7
03
359.1 183.0
63
412.5
210.2
23
466.0
237.5
83
519. 4
264.7
44
306.5
156. 2
04
360. 0 183. 4
64
413.4
210.7
24
466.9
237.9
84
520.3
265.2
45
307.4
156.6
05
360.9 183.9
65
414.3
211.1
25
467.8
238. 4
85
521. 2
265.6
46
308.3
157.1
06
361. 8 ' 184. 3
66
415.2
211.6
26
468.7
238.8
86
522.1
266.0
47
309.2
157. 5
07
362. 6 : 184. 8
67
416.1
212.0
27
469.5
239.3
87
523.0
266.5
48
310.1
158.0
08
363. 5 185. 2
68
417.0
212.5
28
470.4
239. 7
88
523.9
267.0
49
311.0
158.5
09
364.4 185.7
69
417.9
212.9
29
471.3
240.2
89
524.8
267.4
50
311.9
158.9
159.4
10
365. 3 ! 186. 1
70
418.8
213.4
30
531
472.2
473.1
240.6
90
525.7
267.9
268.3
351
312.7
411
366. 2 j 186. 6
471
419.7
213.8
241.1
591
526.6
52
313.6
159.8
12
367.1 Il87. 1
72
420.6
214. 3
32
474.0
241.5
92
527.5
268.8
53
314.5
160.3
13
368. 0 i 187. 5
73
421.4
214.7
33
474.9
242.0
93
528.4
269.2
54
315.4
160.7
14
368.9 188.0
74
422.3
215.2
34
475.8
242.4
94
529.3
269.7
55
316.3
161.2
15
369.8 188.4
75
423.2
215. 7
35
476.7
242.9
95
530.1
270.1
56
317.2
161.6
16
370.7 188.9
76
424.1
216.1
36
477.6
243.4
96
531.0
270.6
57
318.1
162.1
17
371.6 189.3
77
425.0
216.6
37
478.4
243.8
97
531.9
271.1
58
319.0
162.5
18
372.4 189.8
78
425.9
217.0
38
479.3
244.3
98
532. 8
271.5
59
319.9
163.0
19
373.3 190.2
79
426.8
217.5
39
480.2
244.7
99
533. 7
272.0
60
320.8
163.4
20
374.2 190.7
80
427.7
217.9
40
481.1
245.2
600
534.6
272.4
Dist.
Dep.
Lat.
Dist.
Dep. 1 Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
(
J3° (1
17°, 243°, 297°,
.
1 Page 422]
TABLE 2.
Difference of Latitude and Departure for 28° (152°, 208°, 332°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
i)ep.
1
0.9
0.5
61
53.9
28.6
121 106.8
56.8
181
159.8
85.0
241
212.8
113.1
2
1.8
0.9
62
54.7
29.1
22 107. 7
57.3
82
160.7
85.4
42
213.7
113.6
3
2.6
1.4
63
55.6
29.6
23 108.6
57.7
83
161.6
85.9
43
214.6
114.1
4
3.5
1.9
64
56.5
30.0
24
109. 5
58.2
84
162.5
86.4
44
215. 4
114.6
5
4.4
2.3
65
57.4
30.5
25
110.4
58.7
85
163.3
86.9
45
216.3
115.0
6
5.3
2.8
66
58.3
31.0
26
111. 3
59.2
m
164.2
87.3
46
217.2
115.5
7
6.2
3.3
^67
59.2
31.5
27
112.1
59.6
87
165.1
87.8
47
218.1
116.0
8
7.1
3.8
•68
60.0
31.9
28
113. 0
60.1
88
166.0
88.3
48
219.0
116.4
9
7.9
4.2
69
60.9
32.4
29
113.9
60.6
89
166.9
88.7
49
219.9
116.9
10
8.8
4.7
70
71
61.8
62.7
32.9
33.3
30
114.8
61.0
61.5
90
167.8
89.2
50
220.7
117.4
117.8
11
9.7
5.2
131
115.7
191
168.6
89. 7
251
221.6
12
10.6
5.6
72
63.6
33.8
32
116.5
62.0
92
169.5
90.1
52
222.5
118.3
13
11.5
6.1
73
64.5
34.3
33
117.4
62.4
93
170.4
90.6
53
223.4
118.8
14
12.4
6.6
74
65.3
34.7
34
118. 3
62.9
94
171.3
91.1
54
224.3
119.2
15
13.2
7.0
75
66.2
35.2
35
119.2
63.4
95
172.2
91.5
55
225.2
119.7
16
14.1
7.5
76
67.1
35.7
36
120.1
63.8
96
173.1
92.0
56
226.0
120.2
17
15.0
8.0
77
68.0
36.1
37
121.0
64.3
97
173.9
92.5
57
226.9
120.7
18
15.9
8.5
78
68.9
36.6
38
121.8
64.8
98
174.8
93.0
58
227.8
121.1
19
16.8
8.9
79
69.8
37.1
39
122.7
65.3
99
175.7
93.4
59
228.7
121.6
20
17.7
9.4
80
70.6
37.6
38.0
40
141
123. 6 -
124.5
65.7
200
176.6
93.9
60
229.6
230.4
122.1
21
18.5
9.9
81
71.5
66.2
201
177.5
94.4
261
122.5
22
19.4
10.3
82
72.4
38.5
42
125. 4
66.7
02
178.4
94.8
62
231.3
123.0
23
20.3
10.8
83
73.3
39.0
43
126.3
67.1
03
179.2
95.3
63
232.2
123.5
24
21.2
11.3
84
74.2
39.4
44
127.1
67.6
04
180.1
95.8
64
233.1
123.9
25
22.1
11.7
85
75.1
39.9
45
128.0
68.1
05
181.0
96.2
()5
234.0
124.4
26
23.0
12.2
86
75.9
40.4
46
128.9
68.5
06
181.9
96.7
66
234.9
124.9
27
23.8
12.7
87
76.8
40.8
47
129.8
69.0
07
182.8
97.2
67
235. 7
125.3
28
24.7
13.1
88
77.7
41.3
48
130.7
69.5
08
183.7
97.7
68
236.6
125.8
29
25.6
13.6
89
78.6
41.8
49
131.6
70.0
09
184.5
98.1
69
237.5
126.3
30
26.5
14.1
14.6
90
79.5
42.3
42.7
50
151
132.4
70.4
10
185.4
98.6
99.1
70
271
238.4
239.3
126.8
127.2
31
27.4
91
80.3
133.3
70.9
211
186.3
32
28.3
15.0
92
81.2
43.2
52
134.2
71.4
12
187.2
99.5
72
240.2
127.7
33
29.1
15.5
93
82.1
43.7
53
135. 1
71.8
13
188.1
100.0
73
241.0
128.2
34
30.0
16.0
94
83.0
44.1
54
136.0
72.3
14
189.0
100.5
74
241.9
128.6
35
30.9
16.4
95
83.9
44.6
55
136.9
72.8
15
189.8
100.9
75
242.8
129.1
36
31.8
16.9
96
84.8
4.5.1
56
137.7
73.2
16
190.7
101.4
76
243.7
129.6
37
32.7
17.4
97
85.6
4.5.5
57
138.6
73.7
17
191.6
101.9
77
244.6
130.0
38
33.6
17.8
98
86.5
46.0
58
139.5
74.2
18
192.5
102.3
78
245.5
130.5
39
34.4
18.3
99
87.4
46.5
59
140.4
74.6
19
193.4
102.8
79
246.3
131.0
40
35.3
36. 2
18.8
19. 2
100
88.3
46.9
60
141.3
142.2
75.1
75.6
20
221
194.2
195.1
103.3
103.8
80
281
247.2
248. i
131.5
41
101
89.2
47.4
161
131.9
42
37.1
19.7
02
90.1
47.9
62
143.0
76.1
22
196.0
104.2
82
249.0
132.4
43
38.0
20.2
03
90.9
48.4
63
143.9
76.5
23
196.9
104.7
83
249.9
132.9
44
38.8
20.7
04
91.8
48.8
64
144.8
77.0
24
197.8
105.2
84
250. 8
133.3
45
39.7
21.1
05
92.7
49.3
65
145. 7
77. 5
25
198.7
105. 6
85
251.6
133.8
46
40.6
21.6
06
93.6
49.8
66
146. 6
77.9
26
199. 5
106. 1
86
252. 5
134.3
47
41.5
22.1
07
94.5
50.2
67
147.5
78.4
27
200.4
106.6
87
253.4
134.7
48
42.4
22.5
08
95.4
50.7
68
148.3
78.9
28
201.3
107.0
88
254.3
135.2
49
43.3
23.0
09
96.2
51.2
69
149.2
79.3
29
202.2
107. 5
89
255.2
135.7
50
44.1
23.5
10
97.1
51.6
70
150.1
151.0
79.8
80.3
30
231
203.1
204.0
108.0
108.4
90
256.1
256. 9"
136. 1
51
45.0
23.9
111
98.0
52.1
171
291
136. 6
52
45.9
24.4
12
98.9
52.6
72
151.9
80.7
32
204.8
108.9
92
257.8
137.1
53
46.8
24.9
13
99.8
53.1
73
152.7
81.2
33
205.7
109.4
93
258.7
137.6
54
47.7
25.4
14
100.7
53.5
74
153. 6
81.7
34
206.6
109.9
94
259.6
138. 0
55
48.6
25.8
15
101.5
54.0
75
154.5
82.2
35
207.5
110. 3
95
260. 5
138. 5
56
49.4
26.3
16
102.4
54.5
76
155.4
82.6
36
208.4
110.8
9f)
261.4
139. 0
57
50. 3
26.8
17
103.3
54.9
77
156. 3
83.1
37
209.3
111.3
97
262. 2
139. 4
58
51. 2
27.2
18
104.2
55.4
78
157.2
83.6
38
210.1
111.7
98
263.1
139.9
59
52.1
27.7
19
105.1
55.9
79
158.0
84.0
39
211.0
112.2
99
264.0
140.4
60
53.0
28.2
20
106.0
56.3
80
158.9
84.5
40
211.9
112.7
300
264.9
140.8
Dist.
Dep.
Lat.
Dist.
Dep.
l^t.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
62° (118°, 242°, 298°
)•
TABLE 2.
[Page 423 |
Dist.
Difference of Latitude and Departure for 28° (152°, 208°, 332=
).
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. ; Lat.
Dep.
Di.st.
Lat.
Dep.
301
265.7
141.3
361
318.7
169.5
421
371.7
197.7
481
424.7
225.8
541
477. 7
254.0
02
266.6
141.8
62
319.6
170.0
22
372.6
198.1
82
425. 6
226.3
42
478.6
254.5
03
267.5
142. 3
63
320. 5
170.4
23
373. 5
198.6
83
426.5
226.8
43
479.4
255. 0
04
268.4
142.7
64
321.4
170.9
24
374. 3
199.1
84
427.4
227.3
44
480.3
255. 5
05
269.3
143. 2
65
322.2
171.4
25
375.2
199.5
85
428.3
227.7
45
481.1
255. 9
06
270.2
143.7
66
323.1
171.8
26
376.1
200.0
86
429.2
228.2
46
482.0
256. 4
07
271.0
144.1
67
324.0
172.3
27
377.0
200. 5
87
430.1
228.6
47
482.9
256.9
08
271.9
144.6
68
324.9
172.8
28
377.9
200.9
88
430.9
229.1
48
483.8
257.3
09
272.8
145.1
69
325.8
173.2
29
378.8
201.4
89
431.8
229.6
49
484.7
257. 8
10
273.7
274.6
145.5
70
326.7
173.7
30
379.6
201.9
90
432.6
230.0
230.5
50
551
485.6
258.2
258. 7
311
146.0
371
327.5
174.2
431
380. 5
202.3
491
433.5
486.5
12
275. 5
146.5
72
328.4
174.6
32
381.4
202.8
92
434.4
231.0
52
487.4
259.1
13
276.3
146.9
73
329.3
175.1
33
382.3
203.3
93
435.3
231.4
53
488.3
259.6
14
277.2
147.4
74 ! 330.2
175.6
34
383.2
203.8
94
436.2
231.9
54
489.2
260.1
15
278.1
147.9
75
331. 1
176.1
35
384.1
204.2
95
437.1
232.4
55
490.1
260.6
16
279.0
148.4
76
332.0
176.5
36
384.9
204.7
96
437.9
232.9
56
490.9
261.0
17
279.9
148.8
77
332.8
177.0
37
385.8
205.2
97
438.8
233.4
57
491.8
261.5
18
280.7
149.3
78
333.7
177.5
38
386.7
205.6
. 98
439.7
233.8
58
492.7
262.0
19
281.6
149.8
79
334.6
177.9
39
387.6
206.1
99
440.6
234.3
59
493.5
262.5
20
321
282.5
150.2
80
335. 5
336.4
178.4
40
388.5
206.6
500
441.5
234.7
235. 2
60
494.4
262.9
283.4
150. 7
381
178.9
441
389.4
207. 0
501
442.3
561
495.3
263.4
22
284.3
151.2
82
337.3
179.3
42
390.2
207.5
02
443.2
235.6
62
496.2
263.8
23
285.2
151.6
83
338.1
179.8
43
391.1
208.0
03
444.1
236.1
63
497.1
264.3
24
286.0
152. 1
84
339. 0
180.3
44
392.0
208.4
04
445.0
236.6
64
498.0
264.7
25
286.9
152.6
85
339.9
180.8
45
392.9
208.9
05
445.9
237.1
65
498.9
265.2
26
287.8
153. 1
86
340.8
181.2
46
393.8
209.4
06
446.8
237. 5
66
499.8
265.7
27
288.7
153. 5
87
341. 7
181.7
47
394.6
209.9
07
447.6
238.0
67
500.7
266.2
28
289.6
154.0
88
342.6
182.2
48
395.5
210.3
08
448.5
238.5
68
501.6
266.6
29
290.5
154.5
89
343.4
182.6
49
396.4
210.8
09
449.4
239.0
69
502.4
267.1
30
291.3
154.9
155.4
90
391
344.3
183.1
50
397.3
398. 2"
211.3
10
450.3
239.4
239. 9
70
571
503.3
267.6
268.0
331
292.2
345.2
183.6
451
211. 7
511
451.2
504.2
32
293.1
155.9
92
346.1
184.0
52
399.1
212.2
12
452.1
240.4
72
505.1
268.5
33
294.0
156.3
93
347.0
184.5
53
399.9
212.7
13
452.9
240.8
73
505.9
269.0
34
294.9
156.8
94
347.9
185.0
54
400.8
213.1
14
453.8
241.3
74
506.8
269.4
35
295.8
157.3
95
348. 7
185.4
55
401.7
213.6
15
454.7
241.8
75
507.7
269.9
36
296.6
157.7
96
349.6
185.9
56
402.6
214.1
16
455.6
242.2
76
508.6
270.4
37
297.5
158.2
97
350.5
186.4
57
403.5
214.6
17
456.4
242.7
77
509.4
270.9
38
298.4
158.7
98
351.4
186.9
58
404.4
215.0
18
457. 3
243.2
78
510.3
271.3
39
299.3
159. 2
99
352.3
187.3
59
405.2
215.5
19
458.2
243.7
79
511.2
271.8
40
341
300.2
301.0
159.6
400
401
353. 1
187.8
60
406. 1
407.0
216.0
20
521
459.1
460.0
244.1
80
512.1
513.0
272.3
272. 7
160.1
354 . 0
188.3
461
216.4
244.6
581
42
301.9
160.6
02
354.9
188.7
62
407.9
216.9
22
460.9
245. 0
82
513. 9
273.2
43
302.8
161.0
03
355.8
189.2
63
408.8
217.4
23
461.8
245.5
83
514.8
273.7
44
303.7
161.5
04
356. 7
189.7
64
409.7
217.8
24
462.7
246.0
84
515.7
274.2
45
304.6
162.0
05
357. 6
190.1
65
410.5
218.3
25
463.5
246.5
85
516.5
274.7
46
305.5
162.4
06
358.4
190. 6
66
411.4
218.8
26
464.4
246.9
86
517.4
275.1
47
306.4
162.9
07
359.3
191.1
67
412.3
219.2
27
465.3
247.4
87
518.3
275.5
48
307.2
163.4
08
360.2
191.5
68
413.2
219.7
28
466.2
247.9
88
519.2
276.0
49
308.1
163.8
09
361. 1
192.0
69
414.1
220.2
29
467.1
248.3
89
520.1
276.5
50
309.0
164.3
10
411
362.0
362.9
192.5
193. 0
70
471
415.0
415.8
220.7
30
531
468.0
248.8
90
521. 0
521.8
277.0
351
309.9
164.8
221.1
468.9
249.3
591
277.4
52
310.8
165.3
12
363.7
193.4
72
416.7
221.6
32
469.8
249.8
92
522.6
277.9
53
311.7
165.7
13
364. 6
193. 9
73
417.6
222.1
33
470.7
250. 2
93
523.5
278.4
54
312.5
166.2
14
365. 5
194.4
.74
418.5
222.5
34
471.5
250. 7
94
524.4
278.8
55
313. 4
166.7
15
366. 4
194.8
75
419.4
223.0
35
472.4
251.1
95
525. 3
279.3
56
314. 3
167.1
16
367.3
195. 3
76
420.3
223.5
36
473.3
251.6
96
526.2
279.8
57
315.2
167.6
17
368. 2
195.8
77
421. 1
223.9
37
474.2
252. 1
97
527.1
280.3
58
316.1
168.1
18
369.0
196.2
78
422.0
224.4
38
475.1
252.6
98
528.0
280.8
59
316.9
168.5
19
369.9
196.7
79
422.9
224.9
39
476.0
253.1
99
528.9
281.3
60
317.8
169.0
20
370.8
197.2
80
423.8
225.3
40
476.8
253.6
600
529.8
281.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
(
52° (118°, 242°, 298°
).
Page 424]
TABLE 2.
Difference of Latitude and Departure for 29° (151°, 209°, 331°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
53.4
29.6
121
105.8
58.7
181
158.3
87.8
241
210.8
116.8
2
1.7
1.0
62
54.2
30.1
22
106.7
59.1
82
159.2
88.2
42
211.7
117.3
3
2.6
1.5
63
55.1
30.5
23
107.6
59.6
83
160.1
88.7
43
212.5
117.8
4
3.5
1.9
64
56.0
31.0
24
108.5
60.1
84
160.9
89.2
44
213.4
118.3
5
4.4
2.4
65
56.9
31.5
25
109.3
60.6
85
161.8
89.7
45
214.3
118.8
6
5.2
2.9
66
57.7
32.0
26
110.2
61.1
86
162.7
90.2
46
215.2
119.3
7
6.1
3.4
^7
58.6
32.5
27
111.1
61.6
87
163.6
90.7
47
216.0
119.7
8
. 7.0
3.9
68
59.5
33.0
28
112.0
62.1
88
164.4
91.1
48
216.9
120.2
9
7.9
4.4
69
60.3
33.5
29
112.8
62.5
89
165.3
91.6
49
217.8
120.7
10
8.7
4.8
70
61.2
33.9
30
113.7
63.0
90
166.2
92.1
50
218.7
"219. 5
121.2
11
9.6
5.3
71
62.1
34.4
131
114.6
63.5
191
167.1
92.6
251
121.7
12
10.5
5.8
72
63.0
34.9
32
115.4
64.0
92
167.9
93.1
52
220.4
122.2
13
11.4
6.3
73
63.8
35.4
33
116.3
64.5
93
168.8
93.6
53
221.3
122.7
14
12.2
6.8
74
64.7
35.9
34
117.2
65.0
94
169.7
94.1
54
222.2
123.1
15
. 13.1
7.3
75
65.6
36.4
35
118.1
65.4
95
170.6
94.5
55
223.0
123.6
16
14.0
7.8
76
66.5
36.8
36
118.9
65.9
96
171.4
95.0
56
223.9
124.1
17
14.9
8.2
77
67.3
37.3
37
119.8
66.4
97
172.3
95.5
57
224.8
124.6
18
15.7
8.7
78
68.2
37.8
38
120.7
66.9
98
173.2
96.0
58
225.7
125.1
19
16.6
9.2
79
69.1
38.3
39
121.6
67.4
99
174.0
96.5
59
226.5
125.6
20
17.5
9.7
80
70.0
38.8
40
122.4
67.9
200
201
174.9
97.0
60
227.4
126. 1
126.5
21
18.4
10.2
81
70.8
39.3
141
123.3
68.4
175.8
97.4
261
228.3
22
19.2
10.7
82
71.7
39.8
42
124.2
68.8
02
176.7
97.9
62
229.2
127.0
23
20.1
11.2
83
72.6
40.2
43
125.1
69.3
03
177.5
98.4
63
230.0
127.5
24
21.0
11.6
84
73.5
40.7
44
125.9
69.8
04
178.4
98.9
64
230.9
128.0
25
21.9
12.1
85
74.3
41.2
45
126.8
70.3
05
179.3
99.4
65
331.8
128.5
26
22.7
12.6
86
75.2
41.7
46
127.7
70.8
06
180.2
99.9
66
232.6
129.0
27
23.6
13.1
87
76.1
42.2
47
128.6
71.3
07
181.0
100.4
67
233. 5
129.4
28
'24.5
13.6
88
77.0
42.7
48
129.4
71.8
08
181.9
100.8
68
234.4
129.9
29
25.4
14.1
89
77.8
43.1
49
130.3
72.2
09
182.8
101.3
69
235.3
130.4
30
31
26.2
14.5
90
78.7
43.6
50
131.2
72.7
10
183.7
101.8
70
236.1
130.9
27.1
15.0
91
79.6
44.1
151
132.1
73.2
211
184.5
102.3
271
237.0
131.4
32
28.0
15.5
92
80.5
44.6
52
132.9
73.7
12
185.4
102.8
72
237.9
131. 9
33
28.9
16.0
93
81.3
45.1
53
133.8
74.2
13
186.3
103.3
73
238.8
132.4
34
29.7
16.5
94
82.2
45.6
54
134.7
74.7
14
187.2
103.7
74
239.6
132.8
35
30.6
17.0
95
83.1
46.1
55
135.6
75.1
15
188.0
104.2
75
240.5
133. 3
36
31.5
17.5
96
84.0
46.5
56
136.4
75.6
16
188.9
104.7
76
241.4
1.33. 8
37
32.4
17.9
97
84.8
47.0
57
137.3
76.1
17
189.8
105.2
77
242.3
134.3
38
33.2
18.4
98
85.7
47.5
58
138.2
76.6
18
190.7
105.7
78
243.1
134.8
39
34.1
18.9
99
86.6
48.0
59
139.1
77.1
19
191.5
106.2
79
244.0
135. 3
40
' 35.0
19.4
100
87.5
48.5
60
139.9
140.8
77.6
20
192.4
106.7
80
244.9
245.8
135.7
41
35.9
19.9
101
88.3
49.0
161
78.1
221
193.3
107.1
281
136.2
42
36.7
20.4
02
89.2
49.5
62
141.7
78.5
22
194.2
107.6
82
246.6
136. 7
43
37.6
20.8
03
90.1
49.9
63
142.6
79.0
23
195. 0
108.1
83 ' 247.5
137.2
44
38.5
21.3
04
91.0
50.4
64
143.4
79.5
24
195.9
108.6
84
248.4
137.7
45
39.4
21.8
05
91.8
50.9
65
144.3
80.0
25
196.8
109.1
85
249.3
138.2
46
40.2
22.3
06
92.7
51.4
66
145.2
80.5
26
197.7
109.6
86
250. 1
138.7
47
41.1
22.8
07
93.6
51.9
67
146.1
81.0
27
198.5
110.1
87
251.0
139.1
48
42.0
23.3
08
94.5
52.4
68
146.9
81.4
28
199.4
110.5
88
251.9
139.6
49
42.9
23.8
09
95.3
52.8
69
147.8
81.9
29
200.3
111.0
89
252.8
140.1
50
43.7
24.2
10
96.2
53.3
70
148.7
82.4
30
201.2
111.5
90
253.6
140.6
141.1
51
44.6
24.7
111
97.1
53.8
171
149.6
82.9
231
202.0
112.0
291
254.5
52
45.5
25.2
12
98.0
54.3
72
150.4
83.4
32
202.9
112.5
92
255.4
141.6
53
46.4
25.7
13
98.8
54.8
73
151.3
83.9
33
203.8
113.0
93
256.3
142.0
54
47.2
26.2
14
99.7
55.3
74
152.2
84.4
34
204.7
113.4
94
257.1
142.5
55
48.1
26.7
15
100.6
55.8
75
153. 1
84.8
35
205. 5
113.9
95 1 258.0
143.0
56
49.0
27.1
16
101.5
56.2
76
153. 9
85.3
36
206.4
114.4
96 1 258.9
143.5
57
49.9
27.6
17
102.3
56.7
77
154.8
85.8
37
207.3
114.9
97
259.8
144.0
58
50.7
28.1
18
103.2
57.2
78
155.7
86.3
38
208.2
115.4
98
260.6
144.5
59
51.6
28.6
19
104.1
57.7
79
156.6
86.8
39
209.0
115.9
99
261.5
145.0
60
52.5
29.1
20
105.0
58.2
80
157.4
87.3
40
209.9
116.4
300
262.4
145. 4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
61° (1
19°, 241
°, 299=
).
TABLE 2.
[Page 425
Difference of Latitude and Departure for 29° (151°, 209°, 331°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
' Lat.
Dep.
Dist.
481
Lat.
Dep.
Dist.
Lat.
Dep.
301
263.2
145.9
361
315. 7
175.0
421
368.2
204.1
420.7
233.2
541
473. 2
262.3
02
264.1
146.4
62
316.6
175. 5
22
369.1
204.6
82
421.6
233.7
42
474.0
262.8
03
265.0
146.9
63
317.5
176.0
23
369.9
205.1
83
422.4
234.2
43
474.9
263.2
04
265.9
147.4
64
318. 3
176.5
24
370.8
205. 6
84
423. 3
234. 6
44
475.8
263.7
05
266.7
147.9
65
319.2
177.0
25
371.7
206.0
85
424.2
235.1
45
476.6
264.2
06
267. 6
148.4
66
320.1
177.4
26
372.6
206.5
86
425.0
235. 6
46
477.5
264.7
07
268.5
148.8
67
321.0
177.9
27
373.4
207.0
87
425.9
236. 1
47
478.4
265. 2
08
269.4
149.3
68
321.8
178.4
28
374.3
207.5
88
426.8
236.6
48
479.3
265.7
09
270.2
149.8
69
322.7
178.9
29
375.2
208.0
89
427. 7
237.1
49
480.1
266.2
10
311
271.1
150.3
150.8
70
323.6
324.5
179.4
30
376.1
376.9
208.5
90
428.5
429.4
237.6
50
481.0
266.6
272.0
371
179.9
431
209.0
491
238.0
551
481.9
267.1
12
272.9
151.3
72
325.3
180.4
32
377.8
209.4
92
430.3
238.5
52
482.8
267.6
13
273.7
151.7
73
326.2
180.8
33
378.7
209.9
93
431.2
2.39. 0
53
483. 6
268.1
14
274.6
152.2
74
327.1
181.3
34
379.6
210.4
94
432.0
239.5
54
484.5
268.6
15
275.5
152.7
75
328.0
181.8
35 380.4
210.9
95
432.9
240.0
55
485. 4
269.1
16
276.3
153. 2
76
328.8
182.3
36 381.3
211.4
96
433.8
240. 5
56
486.3
269.5
17
277.2
153. 7
77
329.7
182.8
37
382.2
211.9
97
434.7
240.9
57
487.1
270.0
18
278.1
154.2
78
230.6
183.3
38
383.1
212.3
98
435.5
241.4
58
488.0
270.5
19
279.0
154.7
79
331.4
183.7
39
383.9 j212.8
99
436.4
241.9
59
488.9
271.0
20
321
279.8
280.7
155. 1
80
332.3
333. 2
184.2
40
384.8 1213.3
500
437.3
242.4
60
489.8
271.5
155. 6
381
184.7
441 1 385.7 1213.8
501
438.2
242.9
561
490.6
272.0
22
281.6
156.1
82
334.1
185.2
42
386.6 i214.3
02
439.0
243. 4
62
491.5
272. 5
23
282.5
156. 6
83
334.9
185.7
43
387.4 214.8
03
439.9
243.9
63
492.4 272.9
24
283. 3
157. 1
84
335. 8
186.2
44
388.3 215.3
04
440.8
244.3
64
493.2 273.4
25
284.2
157. 6
85
336. 7
186.7
45
389.2 215.7
05
441.6
244.8
65
494.1 , 273.9
26
285.1
158.1
86
337. 6
187.1
46
390.0 216.2
06
442. 5
245. 3
66
495.0
274.4
27
286.0
158. 5
87
338.4
187.6
47 390.9 216.7
07
443.4
245. 8
67
495.9
274.9
28
286.8
159.0
88
339. 3
188.1
48 391. 8
217.2
08
444.3
246.3
68
496.8 275.4
29
287.7
159. 5
89
340.2
188.6
49 392. 7
217.7
09
445.2
246.8
69
497.7 275.9
30
288.6
160.0
160.5
90
341.1
341.9
189.1
50 393. 5
218.2
218.7
10
511
446.1
247.3
70
498.5 276.3
31
289.5
391
189.6
451
394.4
447.0
247.8
571
499.4
276.8
32
290.3
161.0
92
.342. 8
190.0
52
395.3
219.1
12
447.8
248.2
72
500.3
277.3
33
291.2
161.4
93
343. 7
190. 5
53
396.2
219.6
13
448.6
248.7
73
501.1
277.8
34
292.1
161.9
94
344. 6
191.0
54
397.0
220.1
14
449.5
249.2
74
502.0
278.3
35
293.0
162.4
95
345. 4
191.5
55
397.9
220.6
15
450.4
249.7
75
502.9
278.8
36
293.8
162.9
96
346. 3
192.0
56
398.8
221.1
16
451.3
250.2
76
503.7
279.2
37
294.7
163.4
97
347.2
192.5
57
399.7
221.6
17
452.2
250. 6
77
504.6
279.7
38
295.6
163.9
98
348.1
193. 0
58
400.5
222.0
18
453.1
251. 1
78
505. 5
280.2
39
296.5
164.4
99
348. 9
193.4
59
401.4
222.5
19
253.9
251.6
79
506.4
280.7
40
297.3
298.2
164.8
165.3
400
401
349.8
350. 7
193.9
194.4
60
461
402.3
403.2
223.0
20
454.8
252. 1
80
507.2
281.2
341
223.5
521
455.6
252.6
581
508.1 ! 281.7 1
42
299.1
165.8
02
351.6
194.9
62
404.0
224.0
22
456.5
253. 1
82
509. 0 282. 2 I
43
300.0
166.3
03
352. 4
195.4
63
404.9
224.5
23
457.4
253.6
83
509.9
282.7
44
300.8
166.8
04
353.3
195.9
64
405.8
225. 0
24
458.3 1254.0
84
510.7
283.2
45
301.7
167.3
05
354.2
196. 3
65
406.7
225. 4
25
459.1 254.5
85
511.6
283.6
46
302.6
167.7
06
355. 1
196. 8
66
407.5
225. 9
26
460.0 255.0
86
512.5
284.1
47
303.5
168.2
07
355. 9
197.3
67
408.4
226.4
27
460.9 255.5
87
513.4
284.6
48
304.3
168.7
08
356.8
197.8
68
409.3
226.9
28
461.8 256.0
88
514.3
285.0
49
305.2
169.2
09
357.7
198.3
69
410.2
227.4
29
462. 6 256. 5
89
515.1
285. 5
50
306.1
169.7
10
358.6
359.4
198.8
199. 3
70
471
411.0
411.9
227.9
228. 3
30
531
463. 5 i 256. 9
90
516.0
286.0
351
307.0
170.2
411
464.4
257.4
591
516.9
286.5
52
307.8
170.7
12
360. 3
199.7
72
412.8
228.8
32
465.3
257.9
92
517.7
287.0
53
308.7
171.1
13
361.2
200.2
73
413. 7
229.3
33
466.1
258.4
93
518.6
287. 5
54
309.6
171.6
14
362.1
200.7
74
414. 5
229.8
34
467.0
258.9
94
519.5
288.0
55
310.5
172.1
15
362.9 -
201.2
75
415.4
230. 3
35
467.9
259.4
95
520.4
288.5
56
311. 3
172.6
16
363.8 ;
201.7
76
416.3
230.8
36
468.8
259.9
96
521.2
288.9
57
312.2
173.1
17
364.7
202.2
77
417.2
231. 3
37
469. 6
260.3
97
522.1
289.4
58
313.1
173.6
18
365.6
202.7
78
418.0
231.7
38
470.5
260.8
98
523.0
289.9
59
314.0
174.0
19
366.4
203. 1
79
418.9
232. 2
39
471.4
261.3
99
523. 9
290.4
60
314.8
174.5
20
367.3
i
203.6
80
419.8
232.7
40
472.3
261.8
600
524.8
290.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
6
1° (119°, 241°, 299°)
Page 426
TABLE 2.
•
Difference of Latitude and Departure for 30° (150°, 210
°, 330°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Di.st.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
52.8
30.5
121
104.8
60.5
181
156.8
90.5
241
208.7
120.5
2
1.7
1.0
62
53. 7
31.0
22
105. 7
61.0
82
157. 6
91.0
42
209.6
121.0
3
2.6
1.5
63
54.6
31.5
23
106.5
61.5
83
158. 5
91.5
43
210.4
121.5
4
3.5
2.0
64
55.4
32.0
24
107.4
62.0
84
159. 3
92.0
44
211.3
122.0
5
4.3
2.5
65
56.3
32.5
25
108. 3 62. 5
85
160.2
92.5
45
212.2
122.5
6
5.2
3.0
66
57.2
33.0
26
109.1 '. 63.0
86
161.1
93.0
46
213. 0
123.0
7
6.1
3.5
^7
58.0
33.5
27
110.0 63.5
87
161.9
93.5
47
213.9
123.5
8
6.9
4.0
B8
58.9
34.0
28
110.9 : 64.0
88
162. 8
94.0
48
214.8
124.0
9
7.8
4.5
69
59. 8
34.5
29
111. 7 ! 64. 5
89
163.7
94.5
49
215. 6
124.5
10
8.7
5.0
70
60.6
35. 0
30
112.6 65.0
90
164.5
95.0
50
216. 5
125.0
125.5
11
9.5
5.5
71
61.5
35.5
131
113. 4
65. 5
191
165.4
95.5
251
217.4
12
10.4
6.0
72
62.4
36.0
32
114.3
66.0
92
166.3
96.0
52
218.2
126.0
13
11.3
6.5
73
63.2
36.5
33
115.2
66.5
93
167. 1
96.5
53
219.1
126.5
14
12.1
7.0
74
64.1
37.0
34 i
116.0
67.0
94
168.0
97.0
54
220.0
127.0
15
13.0
7. 5
75
65.0
37.5
35
116.9 i 67.5
95
168.9
97.5
55
220.8
127. 5
16
13.9
8.0
76
65.8
38.0
36
117.8 i 68.0
96
169.7
98.0
56
221.7
128.0
17
14.7
8.5
77
66.7
38.5
37
118.6 i 68.5
97
170.6
98.5
57
222.6
128.5
18
15.6
9.0
78
67.5
39.0
38
119.5 : 69.0
98
171. 5
99.0
58
223.4
129.0
19
16.5
9.5
79
68.4
39.5
39
120.4 1 69.5
99
172. 3
99.5
59
224.3
129.5
20
17.3
10.0
10.5
80
69.3
70.1
40.0
40
121.2 ' 70.0
122.1 70.5
200
201
173.2
174.1
100.0
100. 5"
60
261
225.2
130.0
21
18.2
81
40.5
141
226.0
130.5
22
19.1
11.0
82
71.0
41.0
42
123.0 71.0
02
174.9
101.0
62
226.9
131.0
23
19.9
11.5
83
71.9
41.5
43
123.8 71.5
03
175.8
101.5
63
227.8
131.5
24
20.8
12.0
84
72.7
42.0
44
124.7
72.0
04
176.7
102.0
64
228.6
132.0
25
21.7
12.5
85
73.6
42.5
45
125. 6
72.5
05
177.5
102. 5
65
229.5
132. 5
26
22.5
13.0
86
74.5
43.0
46
126.4
73.0
06
178.4
103.0
66
230.4
133.0
27
23.4
13.5
87
75.3
43.5
47
127. 3
73.5
07
179.3
103.5
67
231.2
133.5
28
24.2
14.0
88
76.2
44.0
48
128.2
74.0
08
180.1
104.0
68
232. 1
134.0
29
25.1
14.5
89
77.1
44.5
49
129.0
74.5
09
181.0
104.5
69
233. 0
134.5
30
26.0
15.0
15. 5
90
77.9
78.8
45.0
50
129.9
130.8
75.0
10
181.9
105.0
70
271
233. 8
234.7
135.0
135.5
31
26.8
91
45.5
151
75. 5
211
182.7
105.5
32
27.7
16.0
92
79.7
46.0
52
131.6
76.0
12
183.6
106.0
72
233. 6
136.0
33
28.6
16.5
93
80.5
46.5
53
132.5
76.5
13
184.5
106. 5
73
236.4
136. 5
34
29.4
17.0
94
81.4
47.0
54
133.4
77.0
14
185.3
107.0
74
237.3
137.0
35
30.3
17.5
95
82.3
47.5
55
134.2
77.5
15
186.2
107.5
75
238.2
137.5
36
31.2
18.0
96
83.1
48.0
56
135.1
78.0
16
187.1
108.0
76
239.0
138.0
37
32.0
18.5
97
84.0
48.5
57
136. 0
78.5
17
187.9
108. 5
77
239.9
138.5
38
32.9
19.0
98
84.9
49.0
58
136.8
79.0
18
188.8
109. 0
78
240.8
139.0
39
33.8
19.5
99
85.7
49.5
59
137.7
79.5
19
189.7
109. 5
79
241.6
139.5
40
41
34.6
35.5
20.0
20.5
100
101
86.6
50.0
50.5
60
138.6
139.4
80.0
80.5
20
190.5
191.4
110.0
80
242.5
243.4
140.0
140.5'
87.5
161
221
110.5
281
42
36.4
21.0
02
88.3
51.0
62
140.3
81.0
22
192.3
111.0
82
244.2
141.0
43
37.2
21.5
03
89.2
51.5
63
141.2
81.5
23
193.1
111.5
83
245. 1
141.5
44
38.1
22.0
04
90.1
52.0
64
142.0
82.0
24
194.0
112.0
84
246.0
142.0
45
39.0
22.5
05
90.9
52.5
65
142.9
82.5
25
194.9
112. 5
85
246.8
142. 5
46
39.8
23.0
06
91.8
53.0
66
143.8
83.0
26
195. 7
113.0
86
247.7
143. 0
47
40.7
23.5
07
92.7
53.5
67
144.6
83.5
27
196.6
113.5
87
248. 5
143.5
48
41.6
24.0
08
93.5
54.0
68
145. 5
84.0
28
197. 5
114.0
88
249.4
144.0
49
42.4
24.5
09
94.4
54.5
69
146.4 ' 84.5
29
198. 3
114.5
89
250. 3
144.5
50
43.3
25.0
10
111
95.3
96.1
55. 0
70
147.2
85.0
30
199.2
115.0
115.5
90
291
251.1
252. 0
145. 0
51
44.2
25.5
55. 5
171
148.1
85.5
231
200.1
145. 5
52
45.0
26.0
12
97.0
56.0
72
149.0
86.0
32
200.9
116.0
92
252.9
146.0
53
45.9
26.5
13
97.9
56.5
73
149.8
86.5
33
201.8
116.5
93
253. 7
146.5
54
46.8
27.0
14
98.7
57.0
74
150. 7
87.0
34
202.6
117.0
94
254. 6
147.0
55
47.6
27.5
15
99.6
57.5
75
151.6
87.5
35
203. 5
117.5
95
255. 5
147. 5
56
48.5
28.0
10
100. 5
58.0
76
152. 4
88.0
36
204.4
118. 0
96
256. 3
148.0
57
49.4
28.5
17
101.3
58.5
77
153. 3
88. 5 •■
37
• 205. 2
118.-5
97
257. 2
148. 5
58
50.2
29.0
18
102.2
59.0
78
154. 2
89.0
38
206.1
119.0
98
2.58. 1
149.0
59
51.1
29.5
19
103. 1
59.5
79
155. 0
89.5
39
207.0
119.5
99
258.9
149.5
60
Dist.
52.0
30.0
20
103.9
60.0
80
155. 9
90.0
40
207.8
120.0
300
259.8
150.0
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
80° (120°, 240°, 300°).
TABLE 2.
[Page 427
Difference of Latitude and Departure for 30
° (150°, 210°. .330°).
Dist.
Lat,
Dep.
Dist. 1 Lat. 1 Dep.
Dist. Lat.
Dep.
Dist. Lilt. : Dep.
Dist.
Lat.
Dep.
301
260.7
150.5
361 312. 6
180.5
421
364.6
210.5
481 416. 6
240.5
541
468.5
270.5
02
261.5
151.0
62 i 313.5
181.0
22
365. 5
211.0
82 417. 4
241.0
42
469.4
271.0
03
262.4
151.5
63 314.4
181.5
23 j 366.3
211.5
83 418. 3
241.5
43
470.3
271.5
04
263. 3
152.0
64 315. 2
182.0
24 j 367.2
212.0
84 419.2
242.0
44
471.1
272. 0
05
264. 1
152.5
65 316. 1
182.5
25 , 368. 1
212.5
85 420. 0
242.5
45
472.0
272.5
0()
265.0
153.0
66 317.0
183. 0
26 368.9
213.0
86 420. 9
243. 0
46
472.9
273.0
07
2(i5. 9
153. 5
67 317.8
183. 5
27 . 369. 8 1 213. 5
87 421.8
243. 5
47
473.7
273. 5
08
266. 7
154.0
68 318. 7
184.0
28 1 370. 7 1 214. 0
88 : 422.6
244.0
48
474.6
274.0
09
267.6
154.5
6!) 319.6
184. 5
29 371.5 i214.5
89 ; 423.5
244.5
49
475.5
274. 5
10
268.5
155.0
70 320. 4 185. 0
30 ! 372.4
215.0
215. 5
90
491
424.4
245.0
245. 5
50
551
476.3
477.2
275.0
311
269.3
155. 5
371 321. 3 185. 5
431 373.3
425.2
275. 5
12
270.2
156.0
72 322. 2 i 186. 0
32 374.1 ,216.0
92
426.1
246.0
52
478.1
276.0
13
271.1
156.5
73 323. 0
186.5
33 375.0
216. 5
93
426.9
246.5
53
478.9
276. 5
14
271.9
157.0
74 32.3.9
187.0
34 375.9
217.0
94 427. 8
247.0
54
479.8
277.0
15
272.8
157.5
75 324.8
187.5
35 I 376.7
217.5
95 428. 7
247. 5
55
480.7
277.5
16
273.7
158.0
76 325.6
188.0
36 377.6
218.0
96 429. 6
248.0
56
481.5
278.0
17
274.5 ; 158.5
77 326.5
188.5
37 i 378.5
218.5
97 430. 4
248. 5
57
482. 4
278.5
18
275. 4 ! 159. 0
78 327. 4
189.0
38 379.3
219.0
98 431. 3
249.0
58
483.3
279.0
19
276. 3 159. 5
79 328. 2
189.5
39 1 380.2
219.5
99 432.2
249.5
59
484.1
279.5
20
321
277.1 160.0
80 .329. 1
381 330. 0
190.0
40 381. 1
220.0
500 433. 0 ! 250. 0
60
561
485.0
485.9
280.0
278. 0 1 160. 5
190. 5
441 381.9
220.5
501 433. 9 250. 5
280.5
22
278.9 161.0
82 .330. 8
191.0
42 382. 8.
221. 0
02 434.8
251. 0
62
486.7
281.0
23
279.7 161.5
83 331.7
191.5
43 383. 7
221.5
03 435.6
251.5
63
487.6
281.5
24
280. 6 1 162. 0
84 332. 6
192.0
44 384.5 ,222.0
04 1 436.5
252. 0
64
488.5
282.0
25
281.5 '162.5
85 333. 4
192.5
45 385.4 222.5
05
437.4
252.5
65
489.3
282.5
26
282.3
163. 0
86 334.3
193.0
46 386.3 223.0
06
438.2
253. 0
66
490.2
283.0
27
283.2
163.5
87 335. 2
193.5
47 387.1 223.5
07
439.1
253.5
67
491.1
283.5
28
284.1
164.0
88 336.0
194.0
48 388. 0 1 224. 0
08 \ 440.0
254.0
68
491.9
284.0
29
284.9
164.5
89 336. 9
194.5
49 388. 9 2^4. 5
09 ' 440.8
2.54. 5
69
492.8
284.5
30
331
285.8
286.7
165.0
90 337. 8
195.0
195. 5
50 389. 7
451 390.6
225.0
10 i 441. 7
511 1 442.6
255.0
70
571
493.6
494.5
285.0
285. 5
165. 5
391 338.6
225.5
255.5
32
287.5
166.0
92 339. 5
196.0
52 391.5 226.0
12 i 443.4
256.0
72
495.4
286.0
33
288.4
166.5
93 340.4
196.5
53 392.3 226.5
13 ; 444.3
256. 5
73
496.3
286.5
34
289.3
167. 0
94 341.2 ; 197.0
54 393. 2 ' 227. 0
14 445.2
257. 0
74
497.1
287.0
35
290.1
167.5
95 342. 1
197. 5
55 394.0 227.5
15 I 446.0
257. 5
75
497.9
287.5
36
291.0
168.0
96 , 343.0
198.0
56 394.9 ,228.0
. 16 [ 446.9
258.0
76
498.8
288.0
37
291.9
168.5
97 34.3.8
198. 5
57 395.8 '228.5
17 1 447.8
258. 5
77
499.7
288. 5
38
292.7
169.0
98 344.7
199.0
58 396. 6 229. 0
18 448.6 i 2.59.0
78
500.5
289.0
39
293.6
169.5
99 345.6
199. 5
59 397. 5 ; 229. 5
19 449. 4 259. 5
79
501.3
289.5
40
341
294.5
295. 3
170.0
400 .346. 4
200.0
200.5
60
461
398. 4 1 230. 0
20
521
450. 3 j 260. 0
80
581
502.2
503. 1
290.0
290.5
170.5
401 347.3
399.2 230.5
451. 2 1 260. 5
42
296.2
171.0
02 348.1 201.0
62 400. 1 ; 231. 0
22
452.1 1261.0
82
504. 0
291.0
43
297.1
171.5
03 .349.0
201. 5
63 401.0 231.5
23 i 452. 9 1 261. 5
83
504.9
291.5
44
297.9
172.0
04 349. 9
202.0
64 401.8 1232.0
24
453.8 1 262.0
84
505. 8
292.0
45
298.8
172.5
05 350.7
202. 5
65 i 402.7 232.5
25
454.7 |262.5
85
506.6
292.5
46
299.7
173.0
06 351. 6
203. 0
66 403.6 233.0
26
455.5 263.0
86
507.5
293.0
47
300. 5
173.5
07 352.5
203. 5
67 404.4 2.33.5
27
456.4
263.5
87
508.4
293. 5
48
301.4
174.0
08 353.3 i 204.0
68 405. 3 234. 0
28
457.3
264.0
88
509.2
294.0
49
302.3
174. 5
09 354. 2 ! 204. 5
69 406.2 234.5
29
458.1
264.5
89
510.1
294.5
50
351
303. 1
"304. 0
175.0
10 355. 1
205.0
205. 5
70 407.0
471 407. 9
235. 0
30 i 459.0
265.0
90
591
511.0
511.8
295.0
175. 5
411 355.9
235. 5
531 j 459.9
265.5
295.5
52
304. 8
176.0
12 356.8 1206.0
72 408.8 236.01
32 ' 460.7 266.0
92
512.7
296.0
53
305.7 176.51
13 357.7 J206.5
73 409.6
236.5
33 461.6 266.5
93
513.6
296.5
54
306. 6
177.0
14 358.5 207.0
74 410.5
237. 0
34
462.5 267.0
94
514.4
297.0
55
307.4
177.5
15 359.4 207.5
75 411.4
237.5
35
463. 3 ; 267. 5
95
515.3
297.5
5(3
308. 3
178.0
16 360.3 208.0
76 412.2
238.0
36
464. 2 1 268. 0
96
516.2
298.0
57
309.2
178.5
17 361.1 I-208.5
77 413.1
238.5
37
465.1 1268.5
97
517.0
298.5
58
310.0
179.0
18 .362.0
209.0
78 414.0
239.0
38
465.9
269.0
98
517.9
299.0
59
310.9
179.5
19 i 362.9
209.5
79 ! 414.8
239.5
39
466.8
269.5
99
518.8
299.5
60
311. 8
180. 0'
20 1 363.7
i
210.0
80 j 415. 7
240.0
40
467.7
270.0
600
519.6
300.0
Dist.
Dep.
Lat.
Dist. j Dep. Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
6
0° (120°, 240°, 300°
).
Page 428
TABLE 2.
Difference of latitude and Departure for 31° (149°, 211°, 329°
).
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
52.3
31.4
121
103.7
62.3
181
155.1
93.2
241
206.6
124.1
2
1.7
1.0
62
53.1
31.9
22
104.6
62.8
82
156. 0
93.7
42
207.4
124.6
3
2.6
1.5
63
54 0
32.4
23
105.4
63.3
83
156.9
94.3
43
208.3
125.2
4
3.4
2.1
64
54.9
33.0
21
106.3
63.9
84
157. 7
94.8
44
209.1
125.7
5
4.3
2.6
65
55.7
33.5
25
107.1
64.4
85
158.6
95.3
45
210.0
126.2
6
5.1
3.1
^
56.6
34.0
26
108.0
64.9
86
159.4
95.8
46
210.9
126.7
7
6.0
3.6
57.4
34.5
27 108. 9
65.4
87
160.3
96.3
47
211.7
127.2
8
6.9
4.1
68
58.3
35.0
28 109.7
65.9
88
161.1
96.8
48
212.6
127.7
9
7.7
4.6
69
59.1
35.5
29
110.6
66.4
89
162.0
97.3
49
213.4
128.2
10
8.6
5.2
70
71
60.0
60.9
36.1
30
111.4
112; 3
67.0
90
162.9
97.9
50
214.3
128.8
129.3
11
9.4
5. 7
36.6
131
67.5
191
163.7
98.4
251
215.1
12
10.3
6.2
72
61.7
37.1
32
118:1
68.0
92
164.6
98.9
52
216. 0
129.8
13
11.1
6.7
73
62.6
37.6
33
114.0
68.5
93
165.4
99.4
53
216.9
130. 3
14
12.0
7.2
74
63.4
38.1
34
114.9
69.0
94
166.3
99.9
54
217.7
130.8
15
12.9
7. 7
75
64.3
38.6
35
115.7
69.5
95
167.1
100.4
55
218.6
131.3
16
13.7
8.2
76
65.1
39.1
36
116.6
70.0
96
168.0
100.9
56
219.4
131.8
17
14.6
8.8
77
66.0
39.7
37
117.4
70.6
97
168.9
101.5
57
220.3
132.4
18
15.4
9.3
78
66.9
40.2
38
118.3
71.1
98
169.7
102.0
58
221.1
132.9
19
16.3
9.8
79
67.7
40.7
39 119.1
71.6
99
170.6
102.5
59
222.0
133.4
20
17.1
10.3
10.8
80
81
68.6
69.4
41.2
40
120.0
120.9
72.1
200
171.4
103.0
60
261
222.9
223.>
133. 9
134.4
21
18.0
41.7
141
72.6
201
172.3 103.5
22
18.9
11.3
82
70.3
42.2
42 121. 7
73.1
02
173. 1 104. 0
62
224.6
134. 9
23
19.7
11.8
83
71.1
42.7
43 122. 6
73.7
03
174. 0 104. 6
63
225.4
135.5
24
20.6
12.4
84
72.0
43.3
44 123.4
74.2
04
174.9 ! 105.1
64
22H. 3
136. 0
25
21.4
12.9
85
72.9
43.8
45
124.3
74.7
05
175.7
105. 6
65
227.1
136.5
26
22.3
13.4
86
73.7
44.3
46
125.1
75.2
06
176.6
-106. 1
66
228.0
137.0
27
23.1
13.9
87
74.6
44.8
47
126.0
75.7
07
177.4
106. 6
67
228.9
137.5
28
24.0
14.4
88
75.4
45.3
48 I 126.9
76.2
08
178.3 107.1
68
229.7
138.0
29
24.9
14.9
89
76.3
45.8
49 127.7
76.7
09
179.1 107.6
69
230.6
138.5
30
25.7
15.5
16.0
90
. 77.1
46.4
46.9
50 ' 128.6
151 ; 129.4
77.3
10
180.0 !l08.2
180.'9 108.7
70
271
231.4
139.1
31
26.6
91
78.0
77.8
211
232.3
139.6
32
27.4
16.5
92
78.9
47.4
52 1 130.3
78.3
12
181.7
lo;-^. 2
72
233. 1
140.1
33
28.3
17.0
93
79.7
47.9
53 : 131. 1
78.8
13
182.6
109.7
73
234. 0
140.6
34
29.1
17.5
94
80.6
48.4
54 132.0
79.3
14
183. 4
110.2
74
234. 9
141.1
35
30.0
18.0
95
81.4
48.9
55 i 132.9
79.8
15
184.3
110.7
75
235.7
141.6
36
30.9
18.5
96
82.3
49.4
56
133. 7
80.3
16
185.1
111.2
76
236.6
142.2
37
31.7
19.1
97
83.1
50.0
57
134.6
80.9
17
186.0
111.8
77
237. 4
142.7
38
32.6
19. 6
98
84.0
50. 5
58
135.4
81.4
18
186.9
112.3
78
238.3
143.2
39
33.4
20.1
99
84.9
51.0
59
136.3
81.9
19
187.7'
112.8
79
239.1
143. 7
40
34.3
20.6
21. i"
100
101
85.7
51.5
60
137.1
82.4
82. 9~
20
221
188.6
113. 3
80
240.0
144.2
41
35.1
86.6
52.0
161
138.0
"189. 4
113. 8
281
240.9
144.7
42
36.0
21.6
02
87.4
52.5
62
138.9
83.4
22
190.3
114.3
82
241.7
145.2
43
36.9
22.1
03
88.3
53.0
63
139.7
84.0
23
191.1
114.9
83
242.6
145.8
44
37.7
22.7
04
89.1
53.6
64
140.6
84.5
24
192.0
115.4
84
243.4
146.3
45
38.6
23.2
05
90.0
54.1
65
141.4
85.0
25
192.9
115.9
85
244.3
146.8
46
39.4
23.7
06
90.9
54.6
66
142.3
85.5
26
193.7
116.4
86
245.1
147.3
47
40.3
24.2
07
91.7
55.1
67
143.1
86.0
27
194.6
116.9
87
246.0
147.8
43
41.1
24.7
08
92.6
55.6
68
144.0
86.5
28
195.4
117.4
88-
246.9
148.3
49
42.0
25.2
09
93.4
56.1
69
144.9
87.0
29
196.3
117.9
89
247.7
148.8
50
42.9
25.8
10
94.3
56.7
70
145.7
146.6
87.6
30
197.1
198.0
118.5
90
291
248.6
149.4
51
43.7
26.3
111
95.1
57.2
171
88.1
231
119.0
249.4
149.9
52
44.6
26.8
12
96.0
57.7
72
147.4
88.6
32
198.9
119.5
92
250.3
150. 4
53
45.4
27.3
13
96.9
58.2
73
148.3
89.1
33
199.7
120.0
93
251.2
150.9
54
46.3
27.8
14
97.7
58.7
74
149.1
89.6
34
200.6
120.5
94
252.0
151.4
55
47.1
28.3
15
98.6
59.2
75
150.0
90.1
35
201.4
121.0
95
252. 9
151.9
56
48.0
28.8
16
99.4
59.7
76
150. 9
90.6
36
202.3
121.5
96
253.7
152.5
57
48.9
29.4
17
100.3
60.3
77 '-151.7
91.2
37
203. 1
122.1
97
254.6
153.0
58
49.7
29.9
18
101.1
60.8
78 152.6
91.7
38
204.0
122.6
98
255.4
153.5
59
50.6
30.4
19
102.0
61.3
79 153. 4
92.2
39
204.9
123.1
99
256.3
154.0
60
51.4
30.9
20
102.9
61.8
80
154.3
92.7
40
205.7
123.6
300
257. 1
154.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
39° (121°, 239
°,. 301°
).
^■-
TABLE 2.
[Page 429
Difference of Latitude and Departure for 31° (149°, 211°, 329'
')•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
301
258.0
155.0
361
309.4
185.9
421
360. 9
216.8
481
412.3 247.7
541
463.7
278.6
02
258.9
155.5
62
310.3
186.4
22
361.7
217.3
82
413.2 248.2
42
464.6
279.1
03
259. 7
156.1
63
311.2
187.0
23
362.6
217. 9
83
414.0 1248.8
43
465.4
279.7
04
260.6
156.6
64
312.0
187 5
24
363.4
218.4
84
414.9 1249.3
44
466.3
280.2
05
261.4
157.1
65
312.9
188.0
25
364.3
218.9
85
415.7 249.8
45
467.2
280.7
06
262.3
157.6
66
313.7
188.5
26
365.2
219.4
86
416.6
250. 3
46
468.0
281.2
07
263.2
158.1
67
314.6
189.0
27
366.0
219.9
87
417.4
250. 8
47
468.9
281.7
08
264.0
158. 6
68
315.4
189.5
28
366.9
220.4
88
418.3 251.3
48
469.7
282.3
09
264.9
159.2
69
316. 3
190.1
29
367.7
221.0
89
419.2 '251.9
49
470.6
282.8
10
311
265. 7
266.6
159.7
70
317.2
190.6
30
431
368.6
369.4
221.5
90
420.0 1252.4
420.9 ,252.9
50
551
471.4
472.3
2B3.3
160.2
371
318. 0
191.1
222.0
491
283.8
12
267.4
160.7
72
318.9
191.6
32
370. 3
222.5
92
421. 7 ! 253. 4
52
473.2
284.3
13
268. 3
161.2
73
319.7
192.1
33
371.2
223.0
93
422. 6 1 253. 9
53
474.0
284.8
14
269.2
161.7
74
320.6
192.6
34
372. 0
223.5
94
423.4
254. 4
54
474.9
285. 3
15
270. 0
162.2
75
321.4
193.1
35
372.9
224.0
95
424. 3
254. 9
55
475.7
285.8
16
270.9
162.8
76
322.3
193. 7
36
373. 7
224.6
96
425. 2
255. 5
56
476.6
286.4
17
271.7
163.3
77
323.2
194.2
37
374.6
225.1
97
426.0
256. 0
57
477.4
286.9
18
272.6
163.8
78
324.0
194.7
38
375. 4
225.6
98
426.9
256.5
58
478.3
287.4
19
273.4
164.3
79
324.9
195.2
39
376. 3
226.1
99
427.7
257. 0
59
479.2
287.9
20
321
274.3
275. 2~
164.8
80
325.7
195.7
40
441
377.2
378. 0
226.6
500
428.6
257.5
60
480. 0 i 288. 4 |
165. 3
381
326. 6
196.2
227.1
501
429.4
258.0
561
480.9
288.9
22
276.0
165.8
82
327.4
196.7
42
378.9
227.7
02
430.3
258.6
62
481.7
289.5
23
276.9
166.4
83
328.3
197.3
43
379.7
228.2
03
431.2
259.1
63
482.6
290.0
24
277.7
166.9
84
329.2
197.8
44
380.6
228.7
04
432.0
259. 6
64
483.4
290.5
25
278.6
167.4
85
330.0
198.3
45
381.4
229.2
05
432. 9
260.1
65
484.3 1 291.0
26
279.4
167.9
86
3S0.9
198.8
46
382. 3
229.7
06
433.7
260.6
66
485.2 291.5
27
280. 3
168.4
87
331.7
199.3
47
383.2
230.2
07
434.6
261.1
67
486.0 i 292.0
28
281.2
168.9
88
332. 6
199.8
48
384.0
230.7
08
435.4
261.6
68
486.9 i 292.5
29
282.0
169.5
89
333.4
200.4
49
384. 9
231.3
09
436. 3
262.2
69
487.7 ( 293.1
30
282 9
170.0
"170. 5
90
391
334.3
335.2
200.9
50
385.7
231.8
.10
437.2
262.7
70
488.6 ' 293.6
331
283.7
201.4
451
386.6
232.3
511
438.0
263. 2
571
489.4 294.1
32
284.6
171.0
92
336.0
201.9
52
387.4
232.8
12
438.9
263.7
72
490.3 294.6
33
285.4
171.5
93
336.9
202.4
53
388.3
233. 3
13
439.7
264.2
73
491. 2 1 295. 1
34
286.3
172.0
94
337.7
202.9
54 1 389.2
233.8
14
440.6
264.7
74
492. 0 295. 6
35
287.2
172.5
95
338.6
203.4
55 1 390.0
234.3
15
441.4
265.2
75
492.9
296.1
36
288.0
173.1
96
339. 4
204.0
56 1 390.9
234. 9
16
442.3
265.8
76
493.7
296.7
37
288.9
173.6
97
340.3
204.5
57 391. 7
235.4
17
443. 2
266.3
77
494.6
297.2
38
289.7
174.1
98
341.2
205.0
58 392. 6
235. 9
18
444.0
266.8
78
495.4
297.7
39
290.6
174.6
99
342.0
205. 5
59 393. 4
236.4
19
444.9
267. 3
79
496.3
298.2
40
291.4
175.1
400
342.9
206.0
60 394. 3
236.9
237. 4
20
521
445. 7
267.8
80
497.2
298.7
299.2
341
292.3
175.6
.401
343.7
206.5
461 395. 2
446.6
268.3
581
498.0
42
293.2
176.1
02
344. 6
207.0
62
396.0
238.0
22
447.4
268.9
82
498.9
299.8
43
294.0
176.7
03
345.4
207.6
63
396.9
238.5
23
448.3
269.4
83
499.7
300.3
44
294.9
177.2
04
346. 3
208.1
64
397.7
239.0
24
449.2
269.9
84
500.6
300.8
45
295.7
177.7
05
347.2
208.6
65
398.6
239. 5
25
450. 0
270. 4
85
501.4
301.3
46
296.6
178.2
06
348.0
209.1
66 399.4
240.0
26
450.9 270.9
86
502.3
301.8
47
297.4
178.7
07
348.9
209.6
67 400.3
240.5
27
451.7 1271.4
87
503. 2
302.3
48
298.3
179. 2
08
349.7
210.1
68 : 401.2
241.0
28
452.6 i271.9
88
504.0
302.8
49
299.2
179.8
09
350. 6
210.7
69 402.0
241.5
29
453. 4
272.4
89
504.9
303.3
50
300.0
180.3
10
351. 4
352.3
211.2
211.7
70 402.9
471 403! 7
242.1
242. 6
30
531
454.3
273.0
90
591
505.7
303.9
304. 4
351
300.9
180.8
411
455. 2
273.5
506.6
52
301.7
181.3
12
353.2
212.2
72 404.6
243.1
32
456. 0
274.0
92
507.4
304.9
53
302.6
181.8
13
354.0
212.7
73 ' 405.4
243.6
33
456.9
274.5
93
508.3
305. 4
54
303.4
182.3
14
354.9
213. 2
74 , 406.3
244.1
34
457. 7
275. 0
94
509.2
305. 9
55
304..3
182.8
15
355.7
213.7
75
407.2
244.6
35
458. 6
275. 5
95
510.0
306.4
56
305.2
183.4
16
356.6
214.3
76
408.0
245.2
36
459. 4
276.1
96
510.9
307.0
57
306.0
183. 9
17
357. 4
214.8
77
408.9
245.7
37
460. 3
276.6
97
511.7
307. 5
58
306.9
184.4
18
358. 3
215. 3
78 409. 7
246.2
38
461.2
277.1
98
512.6
308.0
59
307.7
184.9
19
359.2
215.8
79
410.6
246.7
39 1
462.0
277.6
99
513. 4
308.5
60
■
308.6
185.4
20
360.0
216. 3
80
411.4
247.2
40
462.9
278.1
600
514.3
309.0
Dist.
Dep. !
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
K
9° (121°, 239°, 301°
).
Page 430
TABLE .2. .
Difference of Latitude and
Departure for 32° (148°, 212°, 328°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. ! Dep.
Dist. i
Lat.
Dep.
1
0.8
0.5
61
51.7
32.3
121
102.6
64.1
181
153.5 95.9
241
204.4
127.7
2
1.7
1.1
62
52.6
32.9
22
103.5
64.7
82
154.3
96.4
42
205.2
128.2
3
2.5
1.6
63
53. 4
33.4
23
104.3
65.2
83
155.2
97.0
43
206. 1
128. 8
4
3.4
2.1
64
54.3
33.9
24
105.2
65.7
84
156. 0
97.5
44
206.9
129.3
5
4.2
2.6
^
55.1
34.4
25
106.0
66.2
85
156.9
98.0
45
207.8
129.8
6
5.1
3.2
66
56.0
35.0
26
106. 9
66.8
86
157. 7
98.6
46
208.6
130.4
7
5.9
3.7
67
56.8
35.5
27
107.7
67.3
87
158.6
99.1
47
209.5
130.9
8
6.8
4.2
68
57.7
36.0
28
108.6
67.8
88
159. 4
99.6
48
210. 3
131.4
9
. 7.6
4.8
69
58.5
36.6
29
109.4
68.4
89
160. 3
100.2
49
211.2
131. 9
10
8.5
5.3
70
59.4
60.2
37.1
30
110.2
68.9
90
161.1
162. 0
100.7
101:2
50
212.0
212.9
132.5
11
9.3
5.8
71
37.6
131
111.1
69.4
191
251
133.0
12
10.2
6.4
72
61.1
38.2
32
111.9
69.9
92
162.8
101.7
52
213. 7
133. 5
13
11.0
6.9
73
61.9
38.7
33
112.8
70.5
93
163.7
102.3
53
214. 6
134. 1
14
11.9
7.4
74
62.8
39.2
34
113.6
71.0
94
164.5
102.8
54
215.4
134. 6
15
12.7
7.9
75
63.6
39.7
35
114.5
71.5
95
165. 4
103. 3
55
216. 3
135. 1
16
13.6
8.5
76
64.5
40.3
36
115.3
72.1
96
166.2
103. 9
56
217. 1
135. 7
17
14.4
9.0
77
65.3
40.8
37
116.2
72.6
97
167. 1
104.4
57
217.9
136. 2
18
15.3
9.5
78
66.1
41.3
.38
117.0
73.1
98
167.9
104.9
58
218.8
136.7
19
16.1
10.1
79
67.0
41.9
39
117.9
73.7
99
168.8
105. 5
59
219. 6
137.2
20
21
17.0
10.6
80
67.8
42.4
40
118.7
74.2
200
169.6
106.0
60
220.5
137. 8
17.8
11.1
81
68.7
42.9
141
119.6
74.7
201
170. 5 1 106. 5
261
221.3
138.3
22
18.7
11.7
82
69.5
43.5
42
120.4
75.2
02
171.3 107.0
62
222.2
138.8
23
19.5
12.2
83
70.4
44.0
43
121.3
75.8
03
172.2 107.6
63
223. 0
139. 4
24
20.4
12.7
84
71.2
44.5
44
122.1
76.3
04
173.0
108.1
64
223.9
139.9
25
21.2
13.2
85
72.1
45.0
45
123.0
76.8
05
173.8
108.6
65
224.7
140.4
26
22.0
13.8
86
72.9
45.6
46
123.8
77.4
06
174. 7
109.2
66
225.6
141.0
27
22.9
14.3
87
73.8
46.1
47
124.7
77.9
07
175.5
109.7
67
226.4
141.5
28
23.7
14.8
88
74.6
46.6
48
125.5
78.4
08
176.4
110.2
68
227. 3
142.0
29
24.6
15.4
89
75.5
47.2
49
126.4
79.0
09
177.2 |110.8
69
228.1
142.5
30
25.4
15.9
90
76.3
47.7
50
127.2
79.5
10
178.1 !lll.3
70
229.0
143.1
31
26.3
16.4
91
77.2
48.2
151
128.1
80.0
211
178.9
111.8
271
229.8
143.6
32
27.1
17.0
92
78.0
48.8
52
128.9
80.5
12
179.8
112.3
72
230.7
144.1
33
28.0
17.5
93
78.9
49.3
53
129.8
81.1
13
180.6
112.9
73
231.5
144.7
34
28.8
18.0
94
79.7
49.8
54
130.6
81.6
14
181.5
113.4
74
232.4
145.2
36
29.7
18.5
95
80.6
50.3
55
131.4
82.1
15
182.3
113.9
/o
233.2
145. 7
36
30.5
19.1
96
81.4
50.9
56
132.3
82.7
16
183.2
114.5
76
234.1
146.3
37
31.4
19.6
97
82.3
51.4
57
133.1
83.2
17
184.0
115.0
77
234.9
146.8
38
32.2
20.1
98
83.1
51.9
58
134. 0
83.7
18
184.9
115.5
78
235. 8
147.3
39
33.1
20.7
99
84.0
52.5
59
134.8
84.3
19
185.7
116.1
79
236.6
147.8
40
33.9
21.2
21.7
100
84.8
53.0
60
135.7
136.5
84.8
85.3
20
221
186.6
187. 4"
116.6
80
237.5
238. 3
148.4
41
34.8
101
85.7
53.5
161
117. 1
281
148.9
42
35.6
22.3
02
86.5
54.1
62
137.4
85.8
22
188. 3
117.6
82
239.1
149.4
43
36.5
22.8
03
87.3
54.6
63
138.2
86.4
23
189.1
118.2
83
240.0
150. 0
44
37.3
23. 3
04
88.2
55.1
64
139.1
86.9
24
190.0
118.7
84
240.8
150.5
45
38.2
23.8
05
89.0
55.6
65
139.9
87.4
25
190.8
119.2
85
241.7
151.0
46
39.0
24.4
06
89.9
56.2
66
140.8
88.0
26
191.7
119.8
86
242. 5
151.6
47
39.9
24.9
07
90.7
56.7
67
141.6
88.5
27
192.5
120.3
87
243.4
152.1
48
40.7
25.4
08
91.6
57.2
68
142.5
89.0
28
193. 4
120.8
88
244.2
152. 6
49
41.6
26.0
09
92.4
57.8
69
143.3
89.6
29
194.2
121.4
89
245. 1
153. 1
50
42.4
26.5
27.0
10
93.3
94.1
58.3
70
144.2
90.1
30
195.1
195.9
121.9
90
245. 9
153.7
154. 2
51
43.3
111
58.8
171
145.0
90.6
231
122.4
291
246. 8
52
44.1
27.6
12
95.0
59.4
72
145. 9
91.1
32
196.7
122.9
92
247.6
154.7
53
44.9
28.1
13
95.8
59.9
73
146.7
91.7
33
197.6
123.5
93
248. 5
155. 3
54
45.8
28.6
14
96.7
60.4
74
147.6
92.2
34
198.4
124.0
94
249.3
155.8
55
46.6
29.1
15
97.5
60.9
75
148.4
92.7
35
199. 3
124.5
95
250. 2
156. 3
56
47.5
29.7
16
98.4
61.5
76
149. 3
93.3
36
200.1
125. 1
96
251.0
156.9
57
48.3
30.2
17
99.2
62.0
77
150.1
93.8
37
201.0
125.6
97
251. 9
157. 4
58
49.2
.30.7
18
100.1
62.5
78
151.0
94.3
38
201.8
126.1
98
252.7
157.9
59
50.0
31.3
19
100.9
63.1
79
151. 8
94.9
39
202. 7
126.7
99
253. 6
158. 4
60
50.9
31.8
20
101.8
63.6
80
152. 6
95.4
40
203. 5
127.2
300
254.4
159.0
Lat.
DIst.
Dep.
Lat.
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
)8° (1
22°, 2.38
°, 302°
)•
TABLE
- 2.
[Page
(431
Difference of Latitude and
Departure for 32° (148°, 212
°, 328=
)•
IDist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
255.3
159.5
361
.306. 2
191.3
421
357.0
223.1
481
407. 9
254.9
641
458.8
286.7
02
256.1
160.0
62
307. 0
191.8
22
357.9
223.6
82
408.8
255. 4
42
459. 6
287.2
03
257.0
160.5
63
307.9
192.3
23
358. 7
224.1
83
409.6
255.9
43
460.5
287.7
04
257.8
161.1
64
308.7
192.9
24
359. 6
224.7
84
410. 5
256. 5
44
461.3
288. 3
05
258.7
161.6
65
309. 5
193.4
25
360.4
225.2
85
411.3
257. 0
45
462. 2
288.8
06
259.5
162.1
66
310. 4
193.9
26
361.3
225. 7
86
412.2
257. 5
46
463. 0
289.3
07
260.4
162.7
67
311. 2
194.5
27
362.1
226. 3
87
413. 0
258. 1
47
463.9
289.9
08
261.2
163.2
68
312. 1
195. 0
28
363.0
226.8
88
41,3. 9
258. 6
48
464.7
290. 4
09
262.1
163.7
69
312.9
195. 5
29
363. 8
227.3
89
414.7
259.1
49
465. 6
290.9
10
311
262.9
263. 8
164.3
164.8
70
371
313. 8
314.6
196.0
196. 6"
30
431
364.7
365. 5
227.8
228.4
90
415.6
259.6
50
466.4
467.3
291.5
491
416.4
260.2
551
292.0
12
264.6
165.3
72
315.5
197.1
32
366.4
228.9
92
417.3
260.7
52
468.1
292.5
13
265. 4
165.8
73
316.3
197.6
33
367.2
229.4
93
418.1
261.2
53
469.0
293.0
14
266.3
166.4
74
317.2
198.2
34
368.1
230.0
94
419.0
261.8
54
469.8
293.6
15
267.1
166.9
75
318.0
198.7
35
368.9
230.5
95
419.8
262.3
55
470.7
294.1
16
268.0
167.4
76
318.9
199.2
36
369.8
231.0
96
420.6
262.8
56
471.5
294.6
17
268.8
168.0
77
319.7
199.8
37
370.6
231.6
97
421. 5
263. 4
57
472.4
295. 2
18
269.7
168.5
78
320.6
200.3
38
371.5
232.1
98
422.3
263.9
58
473.2
295.7
19
270.5
169.0
79
321.4
200.8
39
372.3
232. 6
99
423. 2
264.4
59
474.1
296.2
20
321
271.4
272. 2
169.6
170". 1
80
381
322.3
201.3
40
373.2
233. 1
500
424.0
424.9
26.5.0
"265. 5
60
561
474.9
475. 8
296.7
297. 3
323.1
201.9
441
374.0
233.7
501
22
273.1
170.6
82
324. 0
202.4
42
374.8
234.2
02
425. 7
266.0
62
476.6
297.8
23
273.9
171.1
83
324. 8
202.9
43
375.7
234.7
03 426. 6
266. 5
63
477.5
298.3
24
274.8
171.7
84
325. 7
203.5
44
376.5
235.3
04 427. 4
267.1
64
478.3
298.9
25
275.6
172.2
85
326. 5
204.0
45
377.4
235. 8
05 428. 3
267.6
65
479.2
299.4
26
276.5
172.7
86
327.4
204. 5
46
378.2
236. 3
06 i 429.1
268.1
66
480.0
299.9
27
277.3
173.3
87
328.2
205. 1
47
379.1
236.9
07 ! 430.0
268.7
67
480.9
300.5
28
278.2
173.8
88
329. 1
205.6
48
379.9
237. 4
08 ! 430.8
269.2
68
481.7
301.0
29
279.0
174.3
89
329.9
206.1
49
380.8
237.9
09 t 431.7
269.7
69
482.6
301.5
30
279.9
280.7
*174. 9
90
330.8
331.6
206.6
50
381.6
382.5
238.4
10
432.5 1270.3
433.4 1270.8
70
483.4
.302. 1
331
175.4
391
207.2
451
239.0
511
571
484. 3'
302.6
32
281.6
175.9
92
332.5
207.7
52
383.3
239.5
12 434. 2
271.4
72
485. 1
303.2
33
282.4
176.4
93
333.3
208.2
53
384.2
240.0
13 435. 1
271.9
73
486.0
303.7
34
283.3
177.0
94
334. 2
208.8
54
385. 0
240.6
14 435. 9
272.4
74
486.8
304.2
35
284.1
177.5
95
335.0
209.3
55
385. 9
241.1
15 436. 8
272. 9
75
487.7
304.7
36
285.0.
178.0
96
335. 8
209.8
56
386. 7
241.6
16 437. 6
273.5
76
488.5
305.3
37
285.8
178.6
97
336. 7
210.4
57
387.6
242.2
17 i 438.5
274.0
77
489.4
305.8
38
286.7
179.1
98
337.5
210.9
58
388.4
242.7
18 439. 3
274.5
78
490.2
306.3
39
287.5
179.6
99
338.4
211.4
59
389.3
243.2
19
440.2
275. 0
79
491.1
306.8
40
341
288.3
180.2
400
339.2
211.9
60
390.1
391.0
243.8
20
441.0
275. 6
80
581
491.9
492.8
307.4
289.2
180.7
401
340.1
212.5
461
244.3
521
441.9
276.1
307.9
42
290.0
181.2
02
340.9
213.0
62
391.8
244.8
22
442.7
276.6
82
493.6
308.4
43
290.9
181.7
03
341.8
213. 5
63
.392. 7
245.4
23
443.6
277.2
83
494.5
309.0
44
291.7
182.3
04
342. 6
214.1
64
393.5
245.9
24
444.4
277.7
84
495.3
309. 5
45
292.6
182.8
05
343. 5
214.6
65
394.4
246.4
25
445. 3
278.2
85
496.2
310.0
46
293. 4
183.3
06
344.3
215.1
66
395.2
246.9
26
446.1
278.7
86
497.0
310.6
47
294.3
183.9
07
345.2
215.7
67
396. 0
247.5
27
446.9
279.3
87
497.8
311.1
48
295. 1
184.4
08
346.0
216.2
68
396.9
248.0
28
447.8
279.8
88
498.7
311.6
49
296.0
184. 9
09
346.9
216.7
69
397.7
248.5
29
448.6
280.3
89
499.5
312. 1
50
296.8
185.4
10
347.7
217.2
70
398.6
249.0
30
449.5
280.9
90
500.3
312.6
361
297.7
186.0
411
348.6
217.8
471
399.4
249.6
531
450. 3
281.4
591
501. 2
313.2
52
298.5
186.5
12
349.4
218.3
72
400.3
250.1
32
451.1
281.9
92
502.0
313.7
53
299.4
187.0
13
350.3
218.8
73
401.1
250.6
33
452.0
282.4
93
502.9
314.2
54
300.2
187.6
14
351.1
219.4
74
402.0
251.2
34
452.8
283.0
94
503. 7
314.8
55
301.1
188.1
15
352.0
219.9
75
402.8
251.7
35
453.7
283. 5
95
504.6
315. 3
56
301.9
188.6
16
:^2.8
220.4
76
403.7
252.2
36
454. 5
284.0
96
505. 4
315.8
57
302. 8
189.2
17
353. 6
221.0
77
404.5
252.8
37
455.4
284.6
97
506.2
316.4
58
303.6
189.7
18
354. 5
221.5
78
405.4
253. 3
38
456.2
285.1
98
507.1
316.9
59
304.5
190.2
19
355.3
222.0
79
406.2
253.8
39
457.1
285.6
99
508.0
317.4
60
305.3
190.8
20
356.2
222.5
80
407.1
254.3
40
467.9
286.2
600
508.8
318.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
•Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
5
8° (1
22°, 238
= , 302°
).
/
Page 432]
TABLE 2.
Difference of Latitude and Departure for
33° (147°, 213°, 327°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.5
61
51.2
33.2
121
101.5
65.9
181
151. 8
98.6
241
202.1
131. 3
2
1.7
1.1
62
52.0
33.8
22
102.3
66.4
82
152.6
99.1
42
203.0
131.8
3
2.5
1.6
63
52.8
34.3
23
103.2
67.0
83
153.5
99.7
43
203. 8
132. 3
4
3.4
2. 2
64
53.7
34. 9
24
104.0
67.5
84
154.3 100.2
44
204. 6
132.9
5
4.2
2.7
65
54.5
35.4
25
104. 8
68.1
85
155. 2
100.8
45
205.5
133.4
6
5.0
3.3
m
55.4
35.9
26
105.7
68.6
86
156.0
101.3
46
206.3
134.0
7
5.9
3.8
67
56.2
36. 5
27
106.5
69.2
87
156.8
101.8
47
207.2
134. 5
8
6.7
4.4
68
57.0
37.0
28
107.3
69.7
88
157. 7
102.4
48
208.0
135. 1
9
7.5
4.9
69
57.9
37.6
29
108.2
70.3
89
158.5
102.9
49
208.8
135. 6
10
8.4
5.4
70
58.7
38.1
30
109.0
70.8
90
159.3
103. 5
50
209.7
210. 5
136.2
136.7
11
9.2
6.0
71
59.5
38.7
131
109.9
71.3
191
160.2
104.0
251
12
10.1
6.5
72
60.4
39.2
32
110.7
71.9
92
.161.0
104.6
52
211.3
137. 2
13
10.9
7.1
73
61.2
39.8
33
111.5
72.4
93
161.9
105.1
53
212.2
137.8
14
11.7
7.6
74
62.1
40.3
34
112.4
73. 0
94
162.7
105.7
54
213.0
138.3
15
12.6
8.2
75
62.9
40.8
35 i 113.2
73. 5
95
163. 5
106.2
55
213.9
138.9
16
13.4
8.7
76
63.7
41.4
36 114. 1
74.1
96
164.4
106.7
56
214.7
139.4
17
14.3
9.3
/ 1
64.6
41.9
37
114.9
74.6
97
165. 2
107.3
57
215. 5
140.0
18
15.1
9.8
78
65.4
42.5
38
115. 7
75.2
98
166.1 107.8
58
216.4
140.5
19
15.9
10.3
79
66.3
43.0
39
116. 6
75.7
99
166. 9 108. 4
59
217.2
141.1
20
16.8
10.9
80
67.1
43.6
40
117.4
118.3
76.2
200
201
167. 7 108. 9
168.6 109.5
60
261
218.1
218.9
141.6
142.2
21
17,6
11.4
81
67.9
44.1
141
76.8
22
18.5
12.0
82
68.8
44.7
42 119. 1
77.3
02
169.4 1110.0
62
219. 7
142.7
23
19.3
12.5
83
69.6
45.2
43 119.9
77.9
03
170.3 1110.6
63
220.6
143.2
24
20.1
13.1
84
70.4
45.7
44 120.8
78.4
04
171.1 111.1
64
221.4
143.8
25
21.0
13.6
85
71.3
46.3
45 121.6
79.0
05
171.9 111.7
65
222.2
144.3
26
21.8
14.2
86
72.1
46.8
46 1 122.4
79.5
06
172.2 112.2
66
223. 1
144.9
27
22.6
14.7
87
73.0
47.4
47 123.3
80.1
07
173.6 112.7
67
223. 9
145. 4
28
23.5
15.2
88
73.8
47.9
48 124. 1
80.6
08
174.4 113.3
68
224.8
146.0
29
24.3
15.8
89
74.6
48.5
49
125.0
81.2
09
175. 3 , 113. 8
69
225. 6
146.5
30
31
25.2
26.0
16.3
16.9
90
75.5
76.3
49.0
50
125.8
81.7
82.2
10
211
176.1
177.0
114.4
70
226.4
147.1
147.6
91
49.6
151
126.6
114.9
271
227. 3
32
26.8
17.4
92
77.2
50.1
52 1 127.5
82.8
12
177.8 115.5
72
228.1
148.1
33
27.7
18.0
93
78.0
50.7
53 ! 128.3
83.3
13
178.6
116.0
73
229.0
148.7
34
28.5
18.5
94
78.8
51.2
54 129.2
83.9
14
179.5
116.6
74
229.8
149.2
35
29.4
19.1
95
79.7
51.7
55 130.0
84.4
15
180. 3
117.1
75
230.6
149.8
36
30.2
19.6
96
80.5
52.3
56 j 130.8
85.0
16
181.2
117.6
76
231.5
150. 3
37
31.0
20.2
97
81.4
52.8
57 ! 131.7
85.5
17
182.0
118.2
77
232.3
150.9
38
31.9
20.7
98
82.2
53. 4
58,
132. 5
86.1
18
182.8
118.7
78
233. 2
151.4
39
32.7
21.2
99
83.0
53.9
59
133. 3
86.6
19
183.7
119.3
79
234. 0
152. 0
40
33.5
21.8
100
83. 9
54. 5
60
134.2
135. 0
87.1
20
184.5
119.8
80
234.8
235.7
152. 5
153.0
41
34.4
22.3
101
84.7
55.0
161
87.7
221
185.3
120.4
281
42
35.2
22.9
02
85.5
55.6
62
135.9
88.2
22
186.2
120.9
82
236. 5
153.6
43
36.1
23.4
03
86.4
56.1
63 136.7
88.8
23
187.0
121.5
83
237.3
154.1
44
36.9
24.0
04
87.2
56.6
64 ; 137.5
89.3
24
187.9
122.0
84
238. 2
154.7
45
37.7
24.5
05
88.1
57.2
65 138. 4
89.9
25
188.7
122.5
85
239. 0
155.2
46
38.6
25.1
06
88.9
57.7
66 139. 2
90.4
26
189.5
123.1
86
239.9
155.8
47
39.4
25.6
07
89.7
58.3
67
140.1
91.0
27
190.4
123.6
87
240.7
156.3
48
40.3
26.1
08
90.6
58.8
68
140.9
91.5
28
191.2
124.2
88
241.5
156.9
49
41.1
26.7
09
91.4
59.4
69
141.7
92.0
29
192.1
124.7
89
242.4
157.4
50
51
41.9
27.2
10
92.3
93.1"
59.9
60. 5 "
70
142.6
92.6
30
192.9
193.7
125. 3
90
291'
243.2
244.1
157.9
42.8
27.8
111
171
143. 4
93.1
231
125. 8
158.5
52
43.6
28.3
12
93.9
61.0
72
144.3
93.7
32
194.6
126.4
92
244.9
159.0
53
44.4
28.9
13
94.8
61.5
73
145. 1
94.2
33
195.4
126.9
93
245.7
159.6
54
45.3
29.4
14
95.6
62.1
74
145.9
94.8
34
196.2
127.4
94
246.6
160.1
55
46.1
30.0
15
96.4
62.6
75
146.8
95.3
35
197.1
128.0
95
247.4
160.7
56
47.0
•30.5
16
97.3
63.2
76
147,6
95.9
36
197.9
128.5
96
248.2
161.2
57
47.8
31.0
17
98.1
63.7
77
148.4
96.4
37
198.8
129.1
97
249.1
161.8
58
48.6
31.6
18
99.0
64.3
78
149. 3
96.^-
' 38
199. 6
129.6
98
249.9
162.3
59
49.5
32.1
19
99.8
64.8
79
150.1
97.5
39
200.4
130.2
99
250. 8
162.8
60
50.3
32.7
20
100.6
65.4
80
151.0
98.0
40
201.3
130.7
300
251.6
163.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
lAt.
Dist.
Dep.
Lat.
e.
7° (123°, 237°, 303°
.
TABLE 2.
[Page 433 |
Difference of Latitude and Departure for 33° (147°, 213°, 327'
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
252.4
163.9
361
302.8
196.6
421
353.1
229.3
481
403.4
262.0
541
453.7
294.6
02
253.3
164.4
62
303.6
197.1
22
353.9
229.8
82
404.2
262. 5
42
454.6
295. 2
03
254.1
165.0
63
304. 4
197.7
23
354.7
230. 4
83
405. 1
263. 1
43
455. 4
295.7
04
255. 0
165. 5
64
305. 3
198.2
24
355. 6
230. 9
84
405. 9
263. 6
44
456.2
296.2
05
255. 8
166.1
65
306.1
198. 8
25
356.4
231. 4
85
406.7
264.1
45
457.1
296.8
06
256.6
166. 6
66
307. 0
199.3
26
357.3
232.0
86
407.6
264.7
46
457.9
297.3
07
257. 5
167.2
67
307.8
199.8
27
358.1
232. 5
87
408.4
265.2
47
458.8
297. 9
08
258.3
167.7
68
308.6
200.4
28
359.0
233.1
88
409.3
265.8
48
1 459.6
298.4
09
259.2
168.3
69
309.5
200.9
29
359.8
233.6
89
410.1
266.3
49
460.4
299.0
10
311
260.0
260.8
168.8
169.3
70
371
310. 3
311.2
201.5
30
360.6
361.5
234.2
90
411.0
266.8
50
461.3
299.5
202.0
431
234.7
491
411.8
267.4
551
462.1
300. 1
12
261.7
169.9
72
312. 0
202.6
32
362.3
235.2
92
412.6
267.9
52
463.0
300.6
13
262.5
170.4
73
312. 8
203. 1
33
363.1
235.8
93
413. 5
268. 5
53
463. 8
301.2
14
263.3
171.0
74
313. 7
203.7
34
364.0
236.3
94
414.3
269.0
54
464. 6
301.7
15
264.2
171.5
75
314.5
204.2
35
364.8
236.9
95
415. 1
269.6
55
465. 5
302.3
16
265.0 i 172.1
76
315.3
204.7
36
365.7
237.4
96
416.0
270.1
56
466. 3
302. 9
17
265.9 172.6
77
316.2
205.3
37
366. 5
238.0
97
416.8
270.7
57
467.2
303.4
18
266.7 173.2
78
317. 0
205.8
38
367.3
238. 5
98
417.6
271.2
58
468.0
303. 9
19
267.5 173.7
79
317.9
206.4
39
368.2
239.1
99
418.5
271.8
59
468.8
304.5
20
321
268.4 174.2
269.2 174.8
80
381
318.7
206.9
40
369.0
239.6
5C0
501
419.3
420.2
272.3
60
561
469.7
470.5
305. 0
319.5
207.5
441
369. 9
240.1
272.8
305.5
22
270.1 175.3
82
320.4
208.0
42
370.7
240.7
02
421.0
273.4
62
471.3
306.1
23
270. 9 1 175. 9
83 [ 321.2
208.6
43
371. 5
241.2
03
421.9
273.9
63
472.2
306.6
24
271.7
176.4
84
322.1
209.1
44
372.4
241.8
04
422.7
274.5
64
473.0
307. 2
25
272. d
177.0
85
322.9
209.6
45
373. 2
242.3
05
423. 5
275. 0
65
473.8
307.7
26
273.4
177.5
86
323. 7
210.2
46
374. 1
242.9
06
424.4
275. 6
66
474.7
308. 3
27
274.2
178.1
87
324.6
210.7
47 374. 9
243.4
07
425. 2
276.1
67
475. 5
308.8
28
275.1
178. 6
88
325.4
211.3
48 375. 7
244.0
08
426.0
276.7
68
476.4
309.4
29
275.9
179.1
89
326.2
211.8
49 376.6
244.5
09
426.9
277.2
69
477.2
309.9
30
331
276.8
277.6
179.7
90
327.1
212.4
212.9
50 1 377.4
245.1
10
427.7
277.8
70
478.0
310.4
311.0
180.2
391
327.9
451
378.2
245. 6
511
428.5
278.3
571
478.9
32
278.4
180.8
92
328.8
213.5
52
379.1
246.1
12
429.4
278.8
72
479.7
311.5
33
279.3
181.3
93
329.6
214.0
53
379.9
246.7
13
430.2
279.4
73
480.6
312.0
34
280.1
181.9
94
330.4
214.6
54
380.8
247.2
14
431.1
279.9
74
481.4
312.6
35
281,0
182.4
95
331.3
215.1
55
381.6
247.8
15
431.9
280.4
75
482.2
313.1
36
281.8
183. 0
96
332. 1
215.6
56
382.4
248.3
16
432.7
281.0
76
483.1
313.7
37
282.6
183.5
97
333.0
216.2
57
383.3
248.9
17
433.6
281.5
77
483. 9
314.2
38
283.5
184.1
98
333.8
216.7
58
384.1
249.4
18
434.4
282.1
78
484.7
314. 8
39
284.3
184.6
99
334.6
217.3
59
385.0
250. 0
19
435. 3
282.6
79
485.6
315. 3
40
285.2
286.0
185.1
185. 7
400
401
335. 5
217.8
60
461
385.8
386.6
250. 5
20
436.1
436.9
283. 2
80
486.4
487. 2
315. 9
341
336. 3
218.4
251.0
521
283.7
581
316.4
42
286.8
186.2
02
337.1
218.9
62 387. 5
251.6
22
437.8
284.3
82
488.1
317.0
43
287.7
186.8
03
338.0
219. 5
63
388.3
252. 1
23
438.6
284.8
83
488.9
317.5
44
288.5
187.3
04
338.8
220.0
64
389.1
252.7
24
439.4
285.4
84
489.8
318.1
45
289.3
187.9
05
339.7
220.5
65
390.0
253.2
25
440.3
285.9
85
490.6
318.6
46
290.2
188.4
06
340.5
221.1
66
390.8
253.8
26
441.1
286.5
86
491.5
319.2
47
291.0
189.0
07
341.3
221.6
67
391.7
254.3
27
442.0
287.0
87
492.3
319. 7
48
291.9
189.5
08
342.2
222.2
68
392.5
254.9
28
442.8
287.5
88
493.1
320.2
49
292. 7
190.0
09
343.0
222.7
69
393.3
255. 4
29
443.6
288.1
89
494.0
320.8
50
293.5
190.6
10
343. 9
344.7
223. 3
223. 8
70
471
394.2
395.0
255.9
30
444.5
288.6
289.2
90
494.8
321.3
351
294.4
191.1
411
256.5
531
445.3
591
495.7
321.9
52
295.2
191.7
12
345. 5
224.4
72
395. 8
257.0
32
446.1
289.7
92
496. 5
322.4
53
296.1
192.2
13
346.4
224.9
73
396.7
257.6
33
447.0
290.3
93
497. 3
322. 9
54
296.9
192.8
14
347.2
225.4
74
397. 5
258.1
34
447.8
290.8
94
498.1
323.5
55
297.7
193.3
15
348.1
226.0
75
398.3
258.7
35
448.7
291.4
95
499.0
324.1
56
298.6
193.9
16
348.9
226.5
76 399.2
259.2
36
449.5
291.9
96
499.8
324.6
57
299.4 194.4
17
349.7
227.1
77 400.0
259.8
37
450.3
292. 5
97
500.6
325. 1
58
300.2 194.9
18
350.6
227.6
78 400. 9
260.3
38
451.2
293. 0
98
501.5
325. 7
59
301.1 195.5
19
351.4
228.2
79 401. 7
260.9
39
452.0
293.6
99
502.3
326.2
60
301. 9 196. 0
20
352.2
228.7
80
402.6
261.4
40
452.9
294.1
600
503.2
326.8
Dist.
Dep. 1 Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
57° (123°, 237'
', 303°)
.
22489—03 28
Page 434;
TABLE 2.
Difference of Latitude and Departure for 34° (146°, 214°, 326°
)■
DIst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. 1 Lat.
Dep.
Dist.
Lat.
Dep.
Dist. t Lat.
Dep.
1
0.8
0.6
61
50.6
34.1
121 ! 100.3
67.7
181
150.1
101.2
241 199.8
134.8
2
1.7
1.1
62
51.4
34.7
22 1 101.1
68.2
82
150.9 101.8
42 ' 200.6
135.3
3
2.5
1.7
63
52.2
35.2
23 1 102. 0 i 68. 8 1
83
151.7 102.3
43 '< 201.5
135.9
4
3.3
2.2
64
53.1
35.8
24
102.8 69.3
84
152. 5
102.9
44 ! 202.3
136.4
5
4.1
2.8
i
53.9
36.3
25
103. 6 69. 9
85
153.4
103. 5
45 1 203. 1
137.0
6
5.0
3.4
54.7
36.9
26
104. 5 70. 5
86
154.2
104.0
46 203. 9
137.6
7
5.8
3.9
67
55.5
37.5
27
105.3 ! 71.0
87
155. 0
104.6
47 204. 8
138.1
» 8
6.6
4.5
68
56.4
38.0
28
106.1 i 71.6
88
155.9
105.1
48 205. 6
138.7
9
7.5
5.0
69
57.2
38.6
29
106.9 1 72.1
89
156.7 105.71
49 206. 4
139.2
10
8.3
5.6
70
58.0
58.9
39.1
30
107.8 1 72.7
90
157.5
158. 3
106.2
50 207. 3
139.8
11
9.1
6.2
71
39.7
131
108.6 1 73.3
191
106.8
251
208.1
140.4
12
9.9
6.7
72
• 59.7
40.3
32 109.4 ' 73.8
92
159. 2 107. 4
52
208.9
140.9
13
10.8
7.3
73
60.5
40.8
33 110.3 i 74.4
93
160. 0 107. 9
53
209.7
141. 5
14
11.6
7.8
74
61.3
41.4
34 111.1 ' 74.9
94
160. 8 108. 5
54 210. 6
142.0
15
12.4
8.4
75
62.2
41.9
35 111. 9 i 75. 5
95
161.7 109.0
55 1 211.4
142.6
16
13.3
8.9
76
63.0
42.5
36 112.7 76.1
96
162.5
109.6
56 212.2
143.2
17
14.1
9.5
77
63.8
43.1
37 113.6 76.6
97
163.3
110.2
57 213. 1
143.7
18
14.9
10.1
78
64.7
43.6
38 114.4 77.2
98
164.1
110.7
58 213.9
144.3
19
15.8
10.6
79
65.5
44.2
39 115. 2 i 77. 7
99
165. 0
111.3
59 ; 214. 7
144.8
20
21
16.6
17.4
11.2
11.7
80
81
66.3
44.7
40 116. 1
78.3
78.'8
200
165.8 111.8
166.6 ill2.4
60 215.5
261 216.4
145.4
145. 9
67.2
45.3
141 1 116.9
201
22
18.2
12.3
82
68.0
45.9
42 117.7 1 79.4
02
167.5 113.0
62 217.2
146.5
23
19.1
12.9
83
68.8
46.4
43 118. 6 80. 0
03
168.3 113.5
63 218.0
147.1
24
19.9
13.4
84
69.6
47.0
44 119.4 80.5
04
169.1 114.1
64 218.9
147.6
25
20.7
14.0
85
70.5
47.5
45 120.2 81.1
05
170.0 |114.6
65 219.7
148.2
26
21.6
14.5
86
71.3
48.1
46 121.0 81.6
06
170. 8 1 115. 2
66 220. 5
148.7
27
22.4
15.1
87
72.1
48.6
47 121.9 82.2
07
171.6 115.8
67 221.4
149.3
28
23.2
15.7
88
73.0
49.2
48 1 122. 7 ; 82. 8
08
172.4 116.3
68 222.2
149.9
29
24.0
16.2
89
73.8
49.8
49 123.5 83.3
09
173.3 116.9
69 i 223.0
150.4
30
24.9
16.8
90
74.6
75.4
50.3
50 124.4 1 83.9
10
174.1
174.9
117.4
70 ! 223.8
151.0
151.5
31
25.7
17.3
91
50.9
151 125.2 1 84.4
211
118.0
271 224.7
32
26.5
17.9
92
76.3
51.4
52 i 126.0 1 85.0
12
175.8 118.5
72 225.5
152. 1
33
27.4
18.5
93
77.1
52.0
53 ' 126.8 85.6
13
176.6 119.1
73 226. 3
152.7
34
28.2
19.0
94
77.9
52.6
54 127.7 ' 86.1
14
177.4 ill9. 7
74
227.2
153.2
35
■ 29.0
19.6
95
78.8
53.1
55 128.5 ■ 86.7
15
178.2
120.2
75
228.0
153.8
36
29.8
20.1
96
79.6
53.7
56 129.3 : 87.2
16
179.1
120.8
76
228.8
154. 3
37
30.7
20.7
97
80.4
54.2
57 130.2 87.8
17
179.9
121.3
77
229.6
154. 9
38
31.5
21. 2
98
81.2
54.8
58 1 131.0 ' 88.4
18
180.7
121.9
78
230. 5
155. 5
39
32.3
21! 8
99
82.1
55. 4
59 1 131.8 1 88.9
19
181.6
122.5
79
231.3
156.0
40
33.2
22.4
100
82.9
83.7
55.9
60
161
132.6 1 89.5
20
182.4
123.0
80
232.1
156.6
157.1
41
34.0
22.9
101
56.5
133.5 1 90.0
221
183.2
123.6
281
233.0
42
34.8
23.5
02
84.6
57.0
62 134.3 ! 90.6
22
184.0
124.1
8S ' 233.8
157. 7
43
35.6
24.0
03
85.4
57.6
63 135.1 91.1
23
184.9
124.7
83 1 234.6
158. 3
44
36.5
24.6
04
86.2
58.2
64 136. 0 91. 7
24
185. 7
125. 3
84 1 235.4
158.8
45
37.3
25.2
05
87.0
58.7
65 136.8 t 92.3
25
186.5
125.8
85
236.3
159.4
46
38.1
25.7
06
87.9
59.3
66 137.6
92.8
26
187.4
126.4
86
237.1
159.9
47
39.0
26.3
07
88.7
59.8
67
138.4
93.4
27
188.2
126.9
87
237. 9
160.5
48
39.8
26.8
08
89.5
60.4
68
139.3
93.9
28
189.0
127.5
88
238. 8
161.0
49
40.6
27.4
09
90.4
61.0
69
140.1
94.5
29
189.8
128.1
89
239.6
161.6
50
41.5
28.0
10
91.2
92.0
61.5
70
140.9
95.1
30
190.7
128.6
90
240.4
162.2
162.7
51
42.3
28.5
111
62.1
171
141.8
95.6
231
191.5 129.2
291
241.2
52
43.1
29.1
12
92.9
62.6
72 i 142.6
96.2
32
192.3 fl29.7
92
242.1
163. 3
53
43.9
29.6
13
93.7
63.2
73 143. 4 ; 96. 7
33
193.2 130.3
93 1 242.9
163.8
54
44.8
30.2
14
94.5
63.7
74 144.3 ' 97.3
34
194.0 130.9
94 243.7
164.4
55
45.6
30.8
15
95.3
64.3
75 145. 1 * 97. 9
35
194. 8 1 131. 4
95 244.6
165.0
56
46.4
31.3
16
96.2
64.9
76 1 145. 9 1 98. 4
36
195. 7
132.0
96
245.4
165. 5
57
47.3
31.9
17
97.0
65.4
77 146. 7 99. 0
37
196.5
132.5
97
246.2
166.1
58
48.1
32.4
18
97.8
66.0
78 147.6 99.5
38
197.3
133. 1
98
247.1
166.6
59
48.9
33.0
19
98.7
66.5
79 148. 4 100. 1
39
198.1
133. 6
99
247.9
167.2
60
49.7
33.6
20
99.5
67.1
80 ! 149. 2 100. 7
40
199.0
134.2
300
248.7
167.8
Dist.
Dep.
■Lat.
Dist.
Dep.
' Lat.
Dist. 1 Dep. Lat.
Dist.
Dep. '■ Lat.
Dist.
Dep.
Lat.
56° (124°, 236", 304°).
TABLE 2.
[Page
435
Difference of Latitude and Departure for 34° (146°, 214
=, 326°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat. 1
Dep.
Dist.
Lat.
Dep.
301
249.5
168.3
361
299.3
201.9
421
349.0
235:4
481
398.8
269.0
541
448.5
302.5
02
250.4
168.9
62
300.1
202.4
22
349.9
236.0
82
399.6 !
269.5
42
449.4
303.1
03
251.2
169.4
63
300.9
203.0
23 350.7
236. 5
83
400.4
270.1
43
450.2
303.6
04
252. 0
170.0
64
301.8
203.5
24 351. 5
237.1
84
401.3 ;
270.6
44 451.0 1
304. 2
05
252. 9
170.6
65
302.6
204.1
25 352. 3
237.7
85
402.1 !
271.2
45
451.8
304.8
06
253.7
171.1
66
303.4
204.7
26 1 353. 2
238.2
86 402.9
271.8
46
452.6
305.3
07
254.5
171.7
67
304.3
205.2
27 1 354.0
238.8
87 403.8 i
272.3
47
453.5
305. 9
08
255.3
172.2
68
305.1
205.8
28 , 354.8
239.3
88 404.6 1
272.8
48 1 454.3
306.4
09
256. 2
172.8
69
305. 9
206.3
29 : 355.7
239.9
89 405.4 *
273.4
49
455.2
307.0
10
257.0 173.3
70
306.7
206.9
30 356.5 240.4
90 406.2
274.0
50
456.0
307. 5
311
257.8 173.9
371 307.6
207.5
431 357.3 241.0
491 407.1
274.6
551
456.8
308.1
^?.
258.7 174.5
72 308.4
208.0
32 358.1 241.6
92 407.9 [
275.1
52
457.6
308.7
13
259.5 175.0
73 ; 309.2
208.6
33 359. 0 242. 1
93
408.7 ;
275.7
53
458.4
309.2
14
260.3
175.6
74 1 310. 1
209.1
■ 34 ; 359. 8 242. 7
94
409.5 i
276.2
54
459. 3
309.8
15
261.2
176.1
75
310.9
209.7
35 i 360.6 243.2
95
410.4 1
276.8
55
460.1
310.3
16
262.0
176.7
76
311.7
210.3
36 361. 5 243. 8
96 411. 2 1
277.4
56
460.9
310.9
17
262.8
177.3
77
312.6
210.8
37 362.3 !244.4
97 412.0 1
277.9
57 461. 7
311.5
18
263.7
177.8
78
313.4
211.4
38 363.1 244.9
98
412.8 1
278.4
58
462.6
312.0
19
264.5
178.4
79
314.2
211.9
39 364.0 245.5
99
413.7
279.0
59
463.4
312.6
20
265.3
266.1
178.9
80
315.0
212.5
213.0
40 \ 364.8
441 365. 6
246.0
500
501
414.5
415.3
279.6
280.1
60
464.2
313.1
313.7
321
179.5
381
315.9
246.6
561 465. 1
22
267.0
180.1
82
316.7
213. 6
42 366. 4
247.2
02
416.2
280.7
62 465. 9
314.3
23
267.8
180.6
83 1 317.5
214.2
43 : 367.3
247.7
03
417.0
281.3
63 466. 8
314.8
24
268.6
181.2
84 318. 4
214.7
44 j 368. 1
248.3
04
417.8
281.8
64 467.6
315.4
25
269.5
181.7
85
319.2
215. 3
45 368.9 J 248. 8
05
418. 6
282.4
65 ! 468.4
315.9
26
270.3
182.3
86
320.0
215.8
46 369.8 '249.4
06 419. 4
282.9
66 i 469.2
316.5
27
271.1
182.9
87
320.8
216.4
47 ; 370. 6 250. 0
07 ! 420.3
283.5
67 ! 470. 1
317.1
28
271.9
183.4
88
321.7
217.0
48 371.4 250.5
08 421. 1
284.1
68 ' 470.9
317.6
29
272.8
184.0
89
322. 5
217.5
49 1 372.2 251.1
09
421.9
284.6
69 471. 7
318.2
30
273.6
274.4
184.5
90
323.3
324.2
218.1
218.6
50 373. 1 251. 6
451 i 373. 9 1 252. 2
10
422. 8
285.2
70 472.6
571 473.4
318.7
319.3
331
186.1
391
511
423.6
285.8
32
275.2
185.6
92
325.0
219.2
52 ' 374. 7 252. 8
12
424.4
286.3
72 ; 474.2
319.9
33
276.1
186.2
93
325.8
219.8
53 375. 6 253. 3
13
425.3
286.9
73
475.0
320.4
34
276.9
186.8
94
326.6
220.3
54 376.4 253.9
14
426.1
28r.4
74
475.9
321.0
35
277.7
187.3
95
327.5
220.9
55 377.2 i254.4
15
426.9
288.0
75
476.7
321.5
36
278.6
187.9
96 ! 328.3
221.4
56 ' 378.0 255.0
16
427.8
288.5
76
477.5
322.1
37
279.4
188.4
97
329.1
222.0
57 378.9 255.5
17 ' 428.6
289.1
77
478.3
322.7
38
280.2
189.0
98
330.0
222.6
58 379. 7 256. 1
18 i -429.4
289.6
78
479.2
323.2
39
281.0
189.6
99
330.8
223.1
59 380.5 256.7
19 430. 3
290.2
79 1 480.0
323.8
40
281.9
190.1
400
331.6
332.4
223.7
224.2
60
461
381.3 257.2
382.2 '257.8
20 431.1
290.8
80
480.8
324.3
324.9
341
282.7
190.7
401
521
431.9
291.3
581
481.6
42
283.5
191.2
02
333.3
224.8
62
383.0 1258.3
22
432.8
291.9
82
482.5
325.4
43
284.4
191.8
03
334.1
225.4
63
383.8 258.9
23
433.6
292.5
83
483.3
326.0
44
285. 2
192.4
04
334.9
225.9
64
384.7 259.5
24
434.4
293.0
84
484.1
326.6
45
286.0
192.9
05
335.8
226. 5
65 385.5 260.0
25
435.3
293.6
85
485.0
327.2
46
286.9
193. 5
06
336.6
227.0
66 \ 386.3 260.6
26
436.1
294.1
86
485.8
327.7
47
287. 7 ' 194. 0
07
337.4
227.6
67
387.2 [261.1
27
436.9
294.7
87
486.6
328.2
48
288. 5 ' 194. 6
08
338.3
228.1
68
388. 0 i 261. 7
28
437.8
295. 3
88
487.5
328.8
49
289.3 !195.2
09
339. 1
228.7
69
388. 8 262. 3
29
438.6
295.8
89
488.3
329.4
50
290.2
195. 7
10
339. 9
229.3
70
389.7 262.8
30
439.4
296.4
90
489.2
329. 9
351
291.0
196. 3
411
340.7
229.8
471
390.5
263.4
531
440.3
296. 9
591
490.0
330.5
52
291.8
196.8
12
341.6
230. 4
72
391.3
263.9
32
441.1
297.4
92
490.8
331.0
53
292.7
197.4
13
342.4
230.9
73
392.1
264.5
33 i 441.9
298. 0
93
491.6
331.6
54
293.5
198.0
14
343. 2
231. 5
74
393.0
265.0
34
442.7
298.6
94
492.5
332.2
55
294.3
198.5
15
344.1
232.1
75
393.8
265.6
35
443.6
299.1
95
493.3
332.7
56
295. 1
199.1
16
344.9
232.6
76
394.6
266.2
36
444.4
299.7
96
494.1
333.3
57
296.0
199.6
17
345.7
233.2
77
395.5
266.7
37
445.3
300.2
97
494.9
333. 8
58
296.8
200.2
18
346. 5
233.7
78
396.3
267.3
38
446.1
300.8
98
495.8
334.4
59
297.6
200.7
19
347.4
234. 3
79
397.1
267.9
39
446.9
301.4
99
496.6
334. 9
60
298.5
201.3
20
348.2
234.9
80
397.9
268.4
40
447.7
302.0
600
497.4
335. 5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
56° (124°, 236°, 304°
)•
Page 436]
TABLE
2.
Difference of Latitude and
Departure for
35° (145°, 215°, 325°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
50.0
.35.0
121
99.1
69.4
181
148.3
103.8
241
197.4
138.2
2
1.6
1.1
62
50.8
35.6
22
99.9
70.0
82
149.1
104.4
42
198.2
138.8
3
2.5
1.7
63
51.6
36.1
23
100.8
70.5
83
149.9
105.0
43
199.1
139.4
4
3.3
2.3
64
52.4
36.7
24
101.6
71.1
84
150.7
105.5
44
199.9
140.0
5
4.1
2.9
65
53.2
37.3
25
102.4
71.7
85
151.5
106.1
45
200.7
140. 5
6
4.9
3.4
«B
54.1
37.9
26
103.2
72.3
86
152.4
106.7
46
201. 5
141.1
7
5.7
4.0
67
54.9
38.4
27
104.0
72.8
87
153. 2 i 107. 3
47
202.3
141.7
8
6.6
4.6
68
55.7
39.0
28
104.9
73.4
88
154. 0 ; 107. 8
48
203.1
142.2
9
7.4
5.2
69
56.5
39.6
29
105.7
74.0
89
154.8 108.4
49
204.0
142.8
10
8.2
5.7
70
71
57.3
58.2
40.2
30
106.5
74.6
75.1
90
191
155.6
109.0
50
204.8
205.6
143.4
144.0
11
9.0
6.3
40.7
131
107.3
156.5
109. H
251
12
9.8
6.9
72
59.0
41.3
32
108.1
75.7
92
157.3
110.1
52
206.4
144.5
13
10.6
7.5
73
- 59.8
41.9
33
108.9
76.3
93
158. 1
110.7
53
207.2
145.1
14
11.5
8.0
74
60.6
42.4
34
109.8
76.9
94
158.9
111.3
54
208.1
145.7
15
12.3
8.6
75
61.4
43.0
35
110.6
77.4
95
159.7
111.8
55
208.9
146.3
16
13.1
9.2
76
62.3
43.6
36
111.4
78.0
96
160.6
112.4
56
209.7
146.8
17
13.9
9.8
77
63.1
44.2
37
112.2
78.6
97
161.4
113.0
57
210.5
147.4
18
14.7
10.3
78
63.9
44.7
38
113.0
79.2
98
162.2
113.6
58
211.3
148.0
19
15.6
10.9
79
64.7
45.3
39
113.9
79.7
99
163.0
114.1
59
212.2
148.6
20
16.4
11.5
12.0
80
65.5
45.9
40
114.7
115.5
80.3
200
201
163.8
164:"6
114.7
60
213.0
149.1
149.7
21
17.2
81
66.4
46.5
141
80.9
115.3
261
213.8
22
18.0
12.6
82
67.2
47.0
42
116.3
81.4
02
165. 5
115.9
62
214.6
150.3
23
18.8
13.2
83
68.0
47.6
43
117.1
82.0
03
166.3
116.4
63
215.4
150.9
24
19.7
13.8
84
68.8
48.2
44
118.0
82.6
04
167.1
117.0
64
216.3
151.4
25
20.5
14.3
85
69.6
48.8
45
118.8
83.2
05
167.9
117.6
65
217.1
152.0
26
21.3
14.9
86
70.4
49.3
46
119.6
83.7
06
168.7
118.2
66
217.9
152.6
27
22.1
15.5
87
71.3
49.9
47
120.4
84.3
07
169.6
118.7
67
218.7
153.1
28
22.9
16.1
88
72.1
50.5
48
121.2
84.9
08
170.4
119.3
68
219.5
153.7
29
23.8
16.6
89
72.9
51.0
49
122.1
85.5
09
171.2
119.9
69
220.4
154. 3
30
24.6
17.2
17.8
90
91
73.7*
74.5
51.6
52.2
50
151
122.9
123.7
86.0
86.6
10
211
172.0
172. 8
120.5
70
221.2
222.0
154.9
155.4
31
25.4
121.0
271
32
26.2
18.4
92
75.4
52.8
52
124. 5
87.2
12
173.7
121.6
72
222.8
156.0
33
27.0
18.9
93
76.2
53.3
53
125.3
87.8
13
174.5
122.2
73
223.6
156. 6
34
27.9
19.5
94
77.0
53.9
54
126.1
88.3
14
175.3
122.7
74
224.4
157.2
35
28.7
20.1
95
77.8
54.5
55
127.0
88.9
15
176. 1
123.3
75
225.3
157.7
36
29.5
20.6
96
78.6
55.1
56
127.8
89.5
16
176.9
123.9
76
226.1
158. 3
37
30.3
21.2
97
79.5
55. 6
57
128.6
90.1
17
177.8
124.5
77
226. 9
158.9
38
31.1
21.8
98
80.3
56.2
58
129.4
90.6
18
178.6
125.0
78
227.7
159.5
39
31.9
22.4
99
81.1
56.8
59
130.2
91.2
19
179.4
125. 6
79
228.5
160.0
40
32.8
22.9
100
81.9
57.4
60
131.1
91.8
20
180.2
126.2
80
229.4
160.6
41
33.6
23.5
101
82.7
57.9
161
131.9
92.3
221
181.0
126.8
281
230.2
161.2
42
34.4
24.1
02
83.6
58.5
62
132.7
92.9
22
181.9
127.3
82
231.0
161.7
43
35.2
24.7
03
84.4
59.1
63
133. 5
93.5
23
182.7 !127.9
83
231.8
162.3
44
36.0
25.2
04
85.2
59.7
64
134.3
94.1
24
183. 5
128.5
84
232.6
162.9
45
36.9
25.8
05
86.0
60.2
65
135.2
94.6
25
184.3
129.1
85
233.5
163. 5
46
37.7
26.4
06
86.8
60.8
66
136.0
95.2
26
185.1
129.6
86
234.3
164.0
47
38.5
27.0
07
87.6
61.4
67
136.8
95.8
27
185.9
130.2
87
235.1
164.6
48
39.3
27.5
08
88.5
61.9
68
137.6
96.4
28
186.8
130.8
88
235.9
165.2
49
40.1
28.1
09
89.3
62.5
69
138.4
96.9
29
187.6
131.3
89
236. 7
165.8
50
41.0
28.7
10
90.1
63.1
70
139.3
97.5
30
188. 4.
189.2
131.9
90
237.6
166.3
51
41.8
29.3
111
90.9
63.7
171
140.1
98.1
231
132.5
291
238.4
166.9
52
42.6
29.8
12
91.7
64.2
72
140.9
98.7
32
190. 0
133.1
92
239.2
167.5
53
43.4
30.4
13
92.6
64.8
73
141.7
- 99.2
33
190.9
133.6
93
240.0
168.1
54
44.2
31.0
14
93.4
65.4
74
142.5
99.8
34
191.7
134.2
94
240.8
168.6
55
45.1
31.5
15
94.2
66.0
75
143.4
100.4
35
192.5
1.34. 8
95
241.6
169.2
56
45.9
32.1
16
95.0
66.5
76
144.2
100.9
36
193. 3
135.4
96
242.5
169.8
67
46.7
32.7
17
95.8
67.1
77
145.0
101.5
37
194.1
135. 9
97
243. 3
170.4
58
47.5
33. 3
18
96.7
67.7
78
145.8
102.1
38
195.0
136. 5
98
244.1
170.9
59
48.3
33.8
19
97.5
68.3
79
146.6
102.7
39
195. 8
137.1
99
244.9
171.5
60
49.1
34.4
20
98.3
68.8
80
147.4
103.2
40
196.6
137.7
300
245.7
172.1
DIst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
)5° (1
25°, 235
°, 305°
)■
TABLE ±
[Page 437
Difference of Latitude and Departure for 35° (145°, 215°, 325°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
JOl
246.6
172.6
361
295.7
207.0
421
344.9
241.5
481
394.0
275.9
541
443.2
310.3
02
247.4
173.2
62
296.5
207.6
22
345. 7
242.0
82
394.8
276.4
42
444.0
310.9
03
248.2
173.8
63
297.4
208.2
23
346.5
242.6
83
395.7
277.0
43
444.8
311.4
04
249.0
174.3
64
298.2
208.8
24
347. 3
243. 2
84
396.5
277.6
44
445.6
312.0
05
249. 9
174.9
65
299.0
209.3
25
348.1
243.8
85
397.3
278.2
45
446.4
312.6
06
250.7
175.5
66
299.8
209.9
26
349.0
244.3
86
398.1
278.7
46
447.3
313.2
07
251.5
176.1
67
300. 6
210. 5
27
349.8
244.9
87
398.9
279.3
47
448.1
313. 7
08
252.3
176.6
68
301.5
211.1
28
350.6
245. 5
88
399.8
279.9
48
448.9
314.3
09
253. 1
177.2
69
302.3
211.6
29
351.4
246.0
89
400.6
280.5
49
449.7 314.9
10
253.9
177.8
70
303.1
212.2
30
352.2
353. 1
246.6
247.2
90
491
401.4
402.2
281.0
281.6
50
551
450.5 1 315.4
451.4 1 316.0
311
254.8
178.4
371
303.9
212.8
431
12
255. 6
178.9
72
304.7
213.4
32 I 353.9
247.8
92
403.0
282.2
52
452.2 1 316.6
13
256.4
179.5
73
305.6
213. 9
33 i a54. 7
248.3
93
403.9
282. 8
53
453.0 i 317.2
14
257.2
180.1
74
306.4
214.5
34
355. 5
248.9
94
404.7
283.3
54
453.8 ! 317.7
15
258.0
180.7
75
307.2
215. 1
35
356.3
249.5
95
405.5
283.9
55
454.6 318.3
16
258.9
181.2
76
308.0
215. 6
36
357.2
250. 1
96
406.3
284.5
56
455.5 318.9
17
259. 7
181.8
77
308.8
216.2
37
358.0
250.6
97
407; 1 :285. 1
57
456.3 319.5
18
260.5
182.4
78
309. 6
216.8
38
358.8
251.2
98
408.0 !285.6
58
457.1 320.0
19
261.3
183.0
79
310.5
217.4
39
359. 6
251.8
99
408.8
286.2
59
457.9 320.6
20
321
262.1
263. 0
183.5
184. 1
80
381
311.3
312.1
217.9
40
360.4
361.3
252.4
252. 9
500
501
409.6
410.4
286.8
60
458.7 321.2
218.5
441
287.4
561
459.6 321.8
22
263. 8
184.7
82
312.9
219.1
42
362.1
253. 5
02
411.2
287.9
62
460.4 322.3
23
264.6
185.2
83 : 313.7
219.7
43
362.9
254.1
03
412.1
288.5
63
461. 2 322. 9
24
265.4
185.8
84 1 314.6
220.2
44
363.7
254. 7
04
412.9
289.1
64
462.0 323.5
25
266.2
186.4
85 315.4
220.8
45
364. 5
255. 2
05
413. 7
289.7
65
462.8 324.1
26
267.1
187.0
86 316.2
221.4
46
365. 4
255. 8
06
414.5
290.2
66
463.7 324.6
27
267.9
187.5
87 317.0
222.0
47
366.2
256. 4
07
415.3
290.8
67
464.5 325.2
28
268.7
188.1
88 317.8
222.5
48
367.0
256.9
08
416.1
291.4
68
465. 3 325. 8
29
269.5
188.7
89 1 318.7
223.1
49
367.8
257.5
09
417. 0
291.9
69
466.1 326.4
30
331
270.3
271. r
189. 3
189.8
90
■391
319.5
223.7
50
368.6
369.4
258.1
258. 7
10
511
417.8
418.6
292.5
70
466.9
326. 9 1
320.3
224. 3
451
293.1
571
467.8
327. 5 1
32
272.0
190.4
92
321.1
224.8
52
370.3
259.2
12
419.4
293.7
72
468. 6 328. 1
33
272.8
191.0
93
321.9
225. 4
53
371.1
259.8
13
420.2 (294.2
73
469.4 328.7
34
273. 6
191.6
94
322.8
226.0
54
371.9 !260.4
14
421.1 '294.8
74
470.2 329.2
35
274.4
192.1
95 323.6 1226.5
55
372.7
261.0
15
421.9 295.4
75
471.0 329.8
36
275.2
192.7
96
324.4 1227.1
56
373.5
261.5
16
422.7 296.0
76
471.9 330.4
37
276.1
193.3
97
325.2 227.7
57
374.4
262.1
17
423.5 296.5
77
472. 7 331. 0
38
276.9
193. 9
98
326.0 228.3
58
375.2
262.7
18
424.3 1297.1
78
473. 5 331. 5
39
277.7
194.4
99
326.9 228.8
59
376.0
263. 3
19
425.2 297.7
79
474.3 ; 332.1
40
341
278.5
279.3
195.0
400
327.7 |229.4
60
461
376.8
377.6
263.8
20
426.0 298.3
80
475. 1 ! 332. 7
476.0 333.3
195.6
401
328.5 230.0
264. 4
521
426.8
298.8
581
42
280.2
196.1
02
329.3 230.6
62
378.5
265.0
22
427.6
299.4
82
476. 8 i 333. 8
43
281.0
196.7
03
330.1 231.1
63
379.3
265.5
23
428.4
300.0
83
477.6 334.4
44
281.8
197.3
04
330.9 !231.7
64
380.1
266.1
24
429.3
300.5
84
478.4 335.0
45
282.6
197.9
05
331.8 [232.3
65 1 380.9
266.7
25
430.1
301.1
85
479.2 335.6
46
283.4
198.4
06
332. 6
232. 9
66 381.7
267.3
26
430.9 301.7
86
480. 1 j 336. 1
47
284.3
199.0
07 333.4
233.4
67 1 382.6
267.8
27
431.7 302.3
87
480. 9 \ 336. 7
48
285.1
199.6
08
334.2
234. 0
68 1 383.4
268.4
28
432.5
302.8
88
481. 7 337. 3
49
285.9
200.2
09
335.0
234.6
69 ' 384.2
269.0
29
433.4
303.4
89
482. 5 337. 9
50
351
286: 7
287.5
200.7
201.3
10
411
335. 9
336.7
235.1
235. 7
70 1 385.0
471 , 385.8
269.6
270. 1
30
434.2
304.0
90
483.3 338.4
484.2 339.0
531
435.0
304.5
591
52
288.3
201.9
12
337.5
236.3
72 386. 6
270.7
32
435.8
305.1
92
485.0 ! 339.6
53
289.2
202.5
13
338.3
236. 9
73
387.5
271.3
33
436.6
305.7
93.
485.8 ! 340.2
54
290.0
203.0
14
339. 1
237. 4
74
388.3
271.9
34
437.5
306.3
94
486.6 { 340.7
55
290.8
203. 6
15
340.0
238. 0
75
389.1
272.4
35
438. 3
306.8
95
487.4 ' 341.3
56
291.6
204.2
16
340. 8
238.6
76
389.9
273.0
36
439.1
307.4
96
488.3 \ 341.9
57
292.4
204.7
17 ' 341.6
239.2
77
390.7
273.6
37
439.9
308.0
97
489.1 342.5
58
293.3
205. 3
18 ! 342.4
239.7
78
391.6
274.2
38
440.7
308.6
98
489.9 343.0
59
294.1
205.9
19 I 343.2
240.3
79
392.4
274.7
39
441.5
309.1
99
490. 7 343. 6
60
294.9
206.5
20 344. 1
240.9
80
393.2
275. 3
40
442.3
309.7
600
491. 5 , 344. 1
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. j Lat.
,
>5° (125°, 235°, 305°).
Page 438
]
TABLE 2.
difference of Latitude and
Departure for 36° (144°, 216
°, 324=
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
1
0.8
0.6
61
49.4
35.9
121
97.9
71.1
181
146. 4
106. 4
241 ' 195.0
141.7
2
1.6
1.2
62
50.2
36.4
22
98.7 1 71.7
82
147.2
107.0
42 i 195.8
142.2
3
2.4
1.8
63
51.0
37.0
23
99.5 ! 72.3
83
148.1
107.6
43 i 196.6
142.8
4
3.2
2.4
64
51.8
37.6
24
100.3 1 72.9
84
148.9
108.2
44 I 197.4
143.4
5
4.0
2.9
65
■ 52.6
38.2
25
101.1 1 73.5
85
149.7
108.7
45 1 198.2
144.0
6
4.9
3.5
6»
53.4
.38. 8
26
101.9 1 74.1
86
150.5
109.3
46 '' 199.0
144.6
7
5.7
4.1
67
54.2 39.4
27
102.7 1 74.6
87
151.3
109.9
47 199. 8
145.2
8
6.5
4.7
68
,55; 0 40. 0
28
103.6 1 75.2
88
152. 1
110.5
48 200.6
145.8
9
7.3
5.3
■ 69
55. 8 ■' 40. (5
29
104.4 75.8
89
152.9
111.1
49 201.4
146. 4
10
8.1
5.9
70
56. 6 i 41. 1
30
105.2 76.4
90
153. 7
111.7
112.3
50 i 202.3
251 203. i
146.9
11
8.9
6.5
71
57.4 i 41.7
131 1 106.0 77.0
191
154. 5
147.5
12
9.7
7.1
72
58.2
42.3
32
106.8 77.6
92
155.3
112.9
52 203.9
148.1
13
10.5
7.6
73
59.1
42.9
33
107.6 78.2
93
156.1
113.4
53 204. 7
148.7
14
11.3
8.2
74
59.9
43.5
34
108.4 ' 78.8
94
156. 9
114.0
54 205.5
149.3
15
12.1
8.8
75
60.7
44.1
35
109.2 79.4
95
157. 8
114.6
55 206.3
149.9
16
12.9
9.4
76
61. 5 1 44. 7
36
110.0 79.9
96
158. 6
115. 2
56 207. 1
150.5
17
13.8
10.0
77
62. 3 1 45. 3
37
110.8 80.5
97
159. 4
115. 8
57 207. 9
151.1
18
14.6
10.6
78
63. 1 45. 8
38
111.6 81.1
98
160.2
116.4
58 208. 7
151.6
19
15.4
n.2
79
63.9 1 46.4
39
112.5 81.7
99
161.0
117.0
59 209. 5
152.2
20
21
16.2
11.8
12.3
80
81
64.7 47.0
40
113.3 82.3
200
161.8
162.6
117.6
118.1
60
261
210. 3
152.8
17.0
65.5 47.6
141
114.1 ' 82.9
201
211.2
153.4
22
17.8
12.9
82
66. 3 i 48. 2
42
114.9 83.5
02
163.4
118.7
62 ' 212.0
154.0
23
18.6
13.5
83
67. 1 48. 8
43
115. 7 84. 1
03
164.2
119.3
63 212. 8
154.6
24
19.4
14.1
84
68. 0 49. 4
44
116. 5 84. 6
04
165.0
119.9
64 213. 6
155.2
25
20.2
14.7
85
68. 8 50. 0
45
117.3 85.2
05
165.8
120.5
G5 214.4
155.8
26
21.0
15. 3
86
69. 6 50. 5
46
118.1 ! 85.8
06
166.7
121.1
66 215.2
156.4
27
21.8
15.9
87
70. 4 51. 1
47
118.9 86.4
07
167.5
121.7
67 216.0
156.9
28
22.7
16.5
88
71.2 51.7
48
119.7 87.0
08
16&.3
122.3
68 216. 8
157.5
29
23.5
17.0
89
72. 0 52. 3
49
120.5 ; 87.6
09
169.1
122.8
69 217. 6
158.1
30
31
24.3
17.6
90
72. 8 52. 9
50
121.4
88.2
8'8.8
10
211
169.9
170.7
123.4
70
218.4
219.2
158.7
159.3
25.1
18.2
91
73.6 1 53.5
151
122.2
124.0
271
32
25.9
18.8
92
74.4
54.1
52
123.0 89.3
12
171.5
124.6
72 220. 1
159.9
33
26.7
19.4
93
75.2
54.7
53
123. 8 i 89. 9
13
172.3
125. 2
73 220.9
160. 5
34
27.5
20.0
94
76.0 i 55.3
54
124. 6 90. 5
14
173.1
125.8
74 221.7
161.1
35
28.3
20.6
95
76.9
55.8
55
125. 4 91. 1
15
173.9
126.4
75 222.5
161.6
36
29.1
21. 2
96
77.7
56.4
56
126.2 91.7
16
174.7
127.0
76 223. 3
162.2
37
29.9
2L7
97
78.5
57.0
57
127.0 i 92.3
17
175. 6
127. 5
77 224.1
162.8
38
30.7
22.3
98
79. 3 i 57. 6
58
127.8 92.9
18
176.4
128.1
78 224. 9
163.4
39
31.6
22.9
99
80. 1 1 58. 2
59
128.6 93.5
19
177.2
128.7
79 225.7
164.0
40
32.4
33.2
23.5
100
80. 9 i 58. 8
60
129.4 j 94.0
20
178.0
178.8
129.3
129."9
80 226. 5
281 227.3
164.6
165.2
41
24.1
101
81.7 59.4
161
130.3 i 94.6
221
42
34.0
24.7
02
82.5 60.0
62
131.1 1 95.2
22
179.6
130.5
82 228. 1
165. 8
43
34.8
25.3
03
83. 3 60. 5
63
131.9 j 95.8
23
180.4
131.1
83 : 229.0
166.3
44
35.6
25.9
04
84. 1 61. 1
64
132.7 1 96.4
24
181.2
131.7
84 229.8
166.9
45
36:4
26.5
05
84.9 61.7
65
133.5 97.0
25
182.0
132. 3
85 230. 6
167.5
46
37.2
27.0
06
85.8 j 62.3
66
134.3 97.6
26
182.8
132.8
86 231. 4
168.1
47
38.0
27.6
07
86.6 i 62.9
67
135. 1 98. 2
27
183.6
133.4
87 232.2
168.7
48
38.8
28.2
08
87.4 j 63.5
68
135. 9 98. 7
28
184.5
134.0
88 233. 0
169. 3
49
39.6
28.8
09
88. 2 1 64. 1
69
136. 7 99. 3
29
185.3
134.6
89 233.8
169.9
50
5i
40.5
41.3
29.4
10
89.0
64.7
65.2
70
137.5 1 99.9
30
186.1
135. 2
135. 8
90 234.6
291 235.4
170.5
171.0
30.0
111
89.8
171
138.3
100. 5
231
186.9
52
42.1
30.6
12
90.6 ; 65.8
72
139.2
101.1
32
187.7
136. 4
92 236.2
171.6
53
42.9
31.2
13
91.4 i 66.4
73
140.0
101.7
33
188.5
137.0
93 ' 237. 0
172,2
54
43.7
31. 7
14
92.2 1 67.0
74
140.8
102. 3
34
189.3
137. 5
94
237. 9
172.8
55
44.5
32.3
15
93.0
67.6
75
141.6
102.9
35
190.1
138. 1
95
238. 7
173.4
56
45.3
32. 9
16
93.8
68.2
76
142.4
103. 5
36
190.9
138. 7
96
239. 5
174.0
57
46.1
33.5
17
94.7
68.8
77
143.2
104.0
37
191.7
139.3
97
240.3
174.6
58
46.9
34.1
18
95.5
69.4
78
144.0
104.6
38
192. 5
139.9
98
241. 1
175. 2
59
47.7
34.7
19
96.3
69.9
79
144.8
105.2
39
193. 4
140.5
99
241.9
175. 7
60
48.5
35.3
20
97.1 70.5
80
145.6
105.8
40
194.2
141.1
300
242.7
176.3
Dist.
Dep.
Lat.
Dist.
Dep. j Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
i4° (1
26°, 234°, 306°
)■
TABLE
. 2.
[Page 439
Difference of Latitude and Departure for 36° (144°, 216°, 324°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
243.5
176.9
361
292.1
212.2
421
340.6
247.5
481
389.1
282.7
541
437.7
318.0
02
244.3
177.5
62
292.9
212.8
22
341.4
248.1
82
390.0
283.3
42
438.5
318.6
03
245. 1
178.1
63
293.7
213.4
23
342.2
248.6
83
390.8
283.9
43
439.3
319.1
04
246.0
178.7
64
294.5
214.0
24
343.0
249.2
84
391. 6
284.5
44
440.2
319.7
05
246.8
179.3
65
295.3
214.6
25
343.8
249.8
85
392.4
285.1
45
441.0
320.3
06
247.6
179.9
66
296.1
215. 1
26
344.7
250.4
86
393.2
285.6
46
441.8
320.9
07
248.4
180.5
67
296.9
215.7
27
345.5
251.0
87
394.0
286. 2
47
442.6
321.5
08
249.2
181.1
68
297.7
216.3
28
346. 3
251.6
88
394.8 [286.8
48
443.4
322. 1
09
250.0
181.6
69
298.5
216.9
29
347.1
252.2
89
395.6 1287.4
49
444.2
322.7
10
250.8
251.6
182.2
182. 8
70
299.3
217.5
30
347. 9
252.8
90
396. 4 288. 0
50
445.0
323.3
311
371
300.2
218.1
431
348.7
253.3
491
397.3 288.6
551
445.8
323.8
12
252.4
183.4
72
301.0
218.7
32
349.5
253.9
92
398.1 289.2
52
446.6
324.4
13
253.2
184.0
73
301.8
219.3
33
350.3
254.5
93
398.9 289.8
53
447.4
325.0
14
254.0
184.6
74
302.6
219.8
34
351. 1
255.1
94
399.7 |290.3
54
448.2
325.6
15
254.9
185. 2
75
303.4
220.4
35
351.9
255. 7
95
400.5 ;290.9
55
449.0
326.2
16
255.7
185.8
76
304.2
221.0
36
352.7
256.3
96
401.3
291.5
56
449.8
326.8
17
256.5
186.4
77
305.0
221.6
37
353.6
256.9
97
402.1
292.1
57
450.7
327.4
18
257.3
186.9
78
305.8
222.2
38
354.4
257.5
98
402.9
292.7
58
451.5
328.0
19
258.1
187.5
79
306.6
222.8
39
355.2
258.0
99
403.7
293.3
59
452.3
328.5
20
321
258.9
188.1
80
307.4
308.2
223.4
40
356.0
356.8
258.6
500
404.5
405.3
293.9
60
453.1
329.1
259.7
188.7
381
224.0
441
259.2
501
294.5
561
453.9
329.7
22
260.5
189.3
82
309.1
224.5
42
357.6
259.8
02
406.1
295.0
62
454.7
330.3
23
261. 3
189.9
83
309.9
225. 1
43
358.4
260.4
03
407.0 295.6
63
455.5
330.9
24
262.1
190.5
84
310.7
225. 7
44
359. 2
261.0
04
407.8 296.2
64
456.3
331.5
25
262.9
191.0
85
311.5
226.3
45
360.0
261.6
05
408.6
296. 8
65
457.1
332.1
26
263.7
191.6
86
312.3
226.9
46
360.8
262.2
06
409.4
297.4
66
457.9
332.7
27
264.6
192.2
87
313. 1
227.5
47
361.6
262.8
07
410.2
298.0
67
458.7
333.3
28
265.4
192.8
88
313.9
228.1
48
362.4
263. 3
08
411.0
298.6
68
459.5
333.8
29
266.2
193.4
89
314.7
228.7
49
363.3
263. 9
09
411.8
299.2
69
460.3
334.4
30
267.0
194.0
90
315.5
229.2
50
364.1
364.9
264.5
10
412.6
299.8
70
461.1
335.0
331
267.8
194.6
391
316.3
229.8
451
265.1
511
413.4
300.3
571
462.0
335. 6
32
268.6
195.2
92
317.1
230.4
52
365.7
265.7
12
414.2
300.9
72
462.8
336.2
33
269.4
195. 7
93
318.0
231.0
53
366.5
266.3
13
415.1
301. 5
73
463.6
336.8
34
270.2
196.3
94
318.8
231.6
54
367. 3
266.9
14
415.9
302.1
74
464.4
337.4
35
271.0
196.9
95
319.6
232.2
55
368.1
267.5
15
416.7
302.7
75
4a5.2
338.0
36
271.8
197.5
96
320.4
2.32. 8
56
368.9
268.0
16
417.5
303.3
76
466.0
338. 5
37
272.6
198.1
97
321.2
233.4
57
369.7
268.6
17
418.3
303.9
77
466.8
339.1
38
273.5
198.7
98
322.0
233.9
58
370.5
269.2
18
419.1
304.4
78
467.6
339.7
39
274.3
199. 3
99
322.8
234.5
59
371.3
269. 8
19
419.9
305. 0
79
468.4
340.3
40
275.1
199.9
400
323.6
235. 1
60
372. 2
270.4
20
420.7
305.6
80
469.3
340.9
341
275. 9
200.4
401
324.4
235. 7
461
373.0
271.0
521
421.5
306.2
581
470.1
341.5
42
276.7
201.0
02
325. 2
236. 3
62
373. 8
271.6
22
422.3
306.8
82
470.9
342.1
43
277. 5
201.6
03
326.0
236.9
63
374.6
272.2
23
423.1
307.4
83
471.7
342.7
44
278.3
202.2
04
326.9
237.5
64
375.4
272.7
24
423.9
308.0
84
472.5
343.2
45
279; 1
202.8
05
327.7
238.1
65
376.2
273.3
25
424.7
308.6
85
473.3
343.8
46
279.9
203.4
06
328. 5
238. 7
66
377.0
273. 9
26
425. 5
309.2
86
474.1
344.4
47
280.7
204.0
07
329.3
239. 2
67
377.8
274.5
27
426.4
309.7
87
474.9
345.0
48
281.5
204.6
08
330. 1
239.8
68
378. 6
275.1
28
427.2
310.3
88
475.7
345.6
49
282.4
205.1
09
330.9
240.4
69
379.4
275.7
29
428.0
310.9
89
476.5
346.2
50
351
283.2
205.7
10
331.7
241.0
70
380.2
276.3
30
428.8
311.5
90
477.3
346.8
284.0
206.3
411
332.5
241.6
471
381.1
276.9
531
429.6
312.1
591
478.2
347.4
52
284.8
206.9
12
333. 3
242.2
72
381.9
277.4
32
430.4
312.7
92
479.0
347.9
53
285. 6
207.5
13
334.1
242.8
73
382.7
278.0
33
431. 2
313. 3
93
479.8
348.5
54
286.4
208.1
14
334.9
243.4
74
383. 5
278.6
34
432.0
313.9
94
480.6
349.1
55
287.2
208.7
15
335. 8
243.9
75
384.3
279. 2
35
432.9
314.4
95
481.4
349.7
56
288.0
209.3
16
336.6
244.5
76
385.1
279.8
36
433.7
315. 0
96
482.2
350. 3
57
288.8
209.8
17
337.4
245.1
77
385. 9
280.4
37
434.5
315. 6
97
483.0
350.9
58
289.6
210.4
18
338. 2
245. 7
78
386.7
281.0
38
435.3
316.2
98
483.8
351.5
59
290.4
211.0
19
339. 0
246. 3
79
387. 5 •
281.6
39
436.1
316.8
99
484.6
352.1
60
291.3
211.6
20
339. 8
246.9
80
388.3
282.1
40
436.9
317.4
600
485.4
352.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
DLst.
Dep.
Lat.
Difct.
Dep. Lat.
Dist.
Dep.
Lat.
54° (1
26°, 234
°, 306°
)•
Page 440]
TABLE ±
Difference of Latitude and Departure for c
!7° (143°, 217°, 323°
).
Diet.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
48.7
36.7
121
96.6
72.8
181
144.6
108.9
241
192.5
145.0
2
1.6
1.2
62
49.5
37.3
22
97.4
73.4
82
145. 4
109.5
42
193.3
145. 6
3
2.4
1.8
63
50.3
37.9
23
98.2
74.0
83
146.2
110.1
43
194.1
146. 2
4
3.2
2.4
64
51.1
38.5
24
99.0
74.6
84
146.9
110.7
44
194.9
146.8
5
4.0
3.0
65
51.9
39.1
25
99.8
75.2
85
147.7
111.3
45
195.7
147.4
6
4.8
3.6
m
52.7
39.7
26
100.6
75.8
86
148.5
111.9
46
196.5
148.0
7
5.6
4.2
67
53.5
40.3
27
101.4
76.4
87
149.3
112.5
47
197.3
148.6
8
6.4
4.8
68
54.3
40.9
28
102.2
77.0
88
150.1
113.1
48
198.1
149.3
9
7.2
5.4
69
55.1
41.5
29
103.0
77.6
89
150.9
113.7
49
198.9
149.9
10
8.0
6.0
70
55.9
42.1
30
103.8
78.2
90
151.7
114.3
50
199.7
200.5
150.5
151.1
11
8.8
6.6
71
56.7
42.7
131
104.6
78.8
191
152.5
114.9
251
12
9.6
7.2
72
57.5
43.3
32
105.4
79.4
92
153.3
115.5
52
201.3
151.7
13
10.4
7.8
73
58.3
43.9
33
106.2
80.0
93
154.1
116.2
53
202.1
152.3
14
11.2
8.4
74
59.1
44.5
34
107.0
80.6
94
154.9
116.8
54
202.9
152. 9
15
12.0
9.0
75
59.9
45.1
35
107.8
81.2
95
155.7
117.4
55
203.7
153.5
16
12.8
9.6
76
60.7
45.7
36 ! 108.6
81.8
96
156.5
118.0
56
204.5
154.1
17
13.6
10.2
77
61.5
46.3
37 109.4
82.4
97
157.3
118.6
57
205.2
154.7
18
14.4
10.8
78
62.3
46.9
38 ! 110.2
83.1
98
158.1
119.2
58
206.0
155. 3
19
15.2
11.4
79
63.1
47.5
39 i 111.0
83.7
99
158.9
119.8
59
206.8
155. 9
20
16.0
12.0
80
63.9
48.1
40
111.8
112. 6
84.3
84.9
200
201
159.7
120.4
60 ! 207.6
156.5
21
16.8
12.6
81
64.7
48. 7
141
160.5
121.0
261
208.4
157.1
22
17.6
13.2
82
65.5
49.3
42
113.4
85.5
02
161.3
121.6
62
209.2
157.7
23
18.4
13.8
83
66.3
50.0
43
114. 2
86.1
03
162.1
122.2
63
210.0
158.3
24
19.2
14.4
84
67.1
50.6
44 ' 115.0
86.7
04
162.9
122.8
64
210.8
158.9
25
20.0
15.0
85
67.9
51.2
45 115.8
87.3
05
163.7
123.4
65
211.6
159.5
26
20.8
15.6
86
68.7
51.8
46 116.6
87.9
06
164.5
124.0
66
212.4
160.1
27
21.6
16.2
87
69.5
52.4
47 117.4
88.5
07
165.3
124.6
67
213. 2
160.7
28
22.4
16.9
88
70.3
53.0
48
118.2
89.1
08
166.1
125.2
68
214.0
161.3
29
23.2
17.5
89
71.1
53.6
49
119.0
89.7
03
166.9
125.8
69
214.8
161.9
30
24.0
18.1
18.7
90
71.9
54.2
50
119.8
90.3
10-
167.7
126.4
127.0
70
271
215. 6
216.4
162.5
163.1
31
24.8
91
72.7
54.8
151
120.6
90.9
211
168.5
32
25.6
19.3
92
73.5
55.4
52
121.4
91.5
12
169.3
127.6
72
217.2
163.7
33
26.4
19.9
93
74.3
56.0
53
122.2
92.1
13
170.1
128.2
73
218.0
164.3
34
27.2
20.5
94
75.1
56.6
54
123.0
92.7
14
170.9
128.8
74
218.8
164.9
35
28.0
21.1
95
75.9
57.2
55
123.8
93.3
15
171.7
129.4
75
219.6
165.5
36
28.8
21.7
96
76.7
57.8
56
124.6
93.9
16
172.5
130.0
76
220.4
166.1
37
29.5
22.3
97
77.5
58.4
57
125. 4
94.5
17
173. 3
130.6
77
221.2
166.7
38
30.3
22.9
98
78.3
59.0
58
126.2
95.1
18
174.1
131. 2
78
222. 0
167.3
39
31.1
23.5
99
79.1
59.6
59
127.0
95.7
19
174.9
131.8
79
222.8
167.9
40
31.9
32.7
24.1
100
79.9
60.2
60
127.8
96.3
20
175.7
132.4
133.0
80
281
223.6
224.4
168.5
169. 1
41
24.7
101
80.7
60.8
161
128.6
96.9
221
176.5
42
33.5
25.3
02
81.5
61.4
62
129.4
97.5
22
177. 3
133.6
82
225. 2
169.7
43
34.3
25.9
03
82.3
62.0
63
130.2
98.1
23
178.1
134.2
83
226.0
170.3
44
35.1
26.5
04
83.1
62.6
64
131.0
98.7
24
178.9
134.8
84
226.8
170.9'
45
.35.9
27.1
05
83.9
63.2
65
131.8
99.3
25
179.7
135.4
85
227.6
171.5
46
36.7
27.7
06
84.7
63. 8
66
132.6
99.9
26
180. 5
136.0
86
228.4
172.1
47
37.5
28.3
07
85.5
64.4
67
133.4
100.5
27
181.3
136. 6
87
229.2
172.7
48
38.3
28.9
08
86.3
65.0
68
134. 2
101.1
28
182.1
137.2
88
230.0
173.3
49
39.1
^.5
09
87.1
65.6
69
135. 0
101.7
29
182.9
137.8
89
230.8
173.9
50
39.9
30.1
10
87.8
66.2
70
135.8
136.6
102.3
30
183. 7
138.4
90
231.6
174.5
175. 1
51
40.7
30.7
111
88.6
66.8
171
102.9
231
184. 5 139. 0
291
232.4
52
41.5
31.3
12
89.4
67.4
72
137.4
103.5
32
185. 3 i 139. 6
92
233.2
175.7
53
42.3
31.9
13
90.2
68.0
73
138.2
104.1
33
186. 1 140. 2
93
234.0
176.3
54
43.1
32.5
14
91.0
68.6
74
139.0
104.7
34
186.9' 140.8
94
234.8
176.9
55
43.9
33.1
15
91.8
69.2
75
139.8
105. 3
35
187.7 141.4
95
235. 6
177.5
56
44.7
33.7
16
92.6
69.8
76
140.6
105. 9
36
188. 5 142. 0
96
236.4
178.1
57
45.5
34.3
17
93.4
70.4
77 141.4
106.5
37
189. 3 142. 6
97
237.2
178.7
58
46.3
34.9
18
94.2
71.0
78
142.2
107.1
38
190. 1 143. 2
98
238.0
179.3
59
47.1
35.5
19
95.0
71.6
79
143.0
107.7
39
190.9
143.8
99
238. 8
179.9
60
47.9
36.1
20
95.8
72.2
80
143.8
108.3
40
191.7
144.4
300
239.6
180.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep-.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
53° (127°, 23S
t°, 307=
).
TABLE ±
[Page 441
Difference of Latitude and Departure for 37° (143°, 217°, 323
').
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
{ Dep.
i
Dist.
Lat. Dep.
Dist. i Lat.
Dep.
301
240.4
181.1
361
288. 3
217.3
421
336.2
1
253. 4
481
384.1 289.5
541 432.0
325. 6
02
241.2
181.7
62
289.1
217.9
22 337.0
254. 0
82
384.9 290.0
42 432.8
326.2
03
242.0
182.4
63
289.9
218.5
23 1 337.8
254. 6
83
385.7 290.6
43 433.6
326.8
04
242.7
183.0
64
290.7
219.1
24 338.6
255. 2
84
386.5 ,291.2
44 434.4
327.3
05
243.5
183. 6
65
291.5
219.7
25 : 339.4
255. 8
85
387.3 291.8
45 435.2
327.9
06
244.3
184.2
66
292.3
220.3
26 i 340.2
1 256. 4
86
388.1 292.4
46 436.0
328. 5
07
245.1
184.8
67
293.1
220.9
27 341.0
257. 0
87
388.9 293.0
47 436.8
329.1
08
245.9
185.4
68
293.9
221.5
28 1 341.8
257. 6
88
389.7 293.6
48 437.6
329.7
09
246.7
186.0
69
294.7
222.1
29 342.6
1 258. 2
89
390.5 .294.2
49 438.4
330. 3
10
311
247.5
248.3
186.6
18772
70
295.5
222.7
30
343.4
344. 2
; 258. 8
259.4
90
491
391.3 294.8
50 439.2
330.9
371
296.3
223.3
431
392.1 295.4
551 1 440.0
331.5
12
249.1
187.8
72
297.1
223.9
32 345. 0
260. 0
92
392.9 296.0
52 : 440. 8
332.1
13
249.9
188.4
73
297.9
224.5
33 345. 8
260. 6
93
393.7
296.6
53 ' 441.6
332.7
14
250.7
189.0
74
298.7
225.1
34 346.6
261.2
94
394.5
297. 2
54 442.4 333.3
15
251.5
189.6
75
299.5
225.7
35 347.4
261.8
95
395.3
297.8
55 443.2 333.9
16
252. 3
190.2
76
300.3
226.3
36 1 348.2
i 262. 4
96
396.1
298. 5
56 444.0 334.6
17
253.1
190.8
77
301.1
226.9
37 i 349.0
263.0
97
396. 9
299. 1
57 444.8 235.2
18
253.9
191.4
78
301.8
227.5
38 ! 349.8
263. 6
98
397.7
399. 7
58 445.6 335.8
19
254.7
192.0
79
302.6
228.1
39 i 350.6
264.2
99
398.5
300.3
59 446.4 336.4
20
321
255.5
256.3
192.6
80
381
303. 4
304.2
228.7
40
351.4
352. 2~
264.8
500
399.3
400.1
300.9
60 447.2 337.0
193.2
229. 3
441
265.4
501
301.5
561 448.0 337.6
22
257.1
193.8
82
305.0
229.9
42 353.0
266.0
02
400.9
302. 1
62 448. 8 338. 2
23
257.9
194.4
83
305.8
230.5
43 353.8
266.6
03
401.7
302. 7
63 449. 6 338. 8
24
258.7
195. 0
84
306. 6
231.1
44 354.6
267.2
04
402.5
303.3
64 450.4 339.4
25
259.5
195.6
85
307.4
231.7
45 , 355.4
267.8
05
403.3
303.9
6.5 451. 2 340. 0
26
260.3
196.2
86
308. 2
232.3
46 356.2
268.4
06
404.1
304. 5
66 452.0 340.6
27
261.1
196.8
87
309.0
232.9
47 357.0
269.0
07
404.9
305.1
67 ; 452.8 341.2
28
I 261. 9
197.4
88
309.8
233. 5
48 : 357.8
269.6
08
405.7
305.7
68 453.6 341.8
29
262. 7
198.0
89
310.6
234.1
49 ' 358.6
270.2
09
406. 5
306.3
69 454.4 342.4
30
263.5
264.3
198.6
90
311.4
312.2
234.7
235.3
50 359.4
451 360.1
270.8
271.4
10
511
407. 3
408.1
306.9
307.5
70 , 455.2 343.0
571 456.0 343.6
331
199.2
391
32
265. 1
199.8
92
313.0
235. 9
52 ■ 360.9
272.0
12
408.9
308.2
72 456.8 .344.3
33
265.9
200.4
93
313.8
236. 5
53 361.7
272.6
13
409.7
308.8
73 457.6 344.9
34
266. 7
201.0
94
314.6
237.1
54 362.5
273.2
14
410.5
309. 4
74 458.4 34.5.5
35
267.5
201.6
95
315.4
237.7
55 363.3
273.8
15
411.3
310.0
75 459. 2 346. 1
36
268.3
202.2
96
316.2
238. 3
56 364. 1
274.4
16
412.1
310.6
76 460. 0 346. 7
37
269.1
202.8
97
317.0
238.9
57 364.9
275. 0
17
412.9
311.2
77 460.8 347.3
38
269.9
203.4
98
317.8
239. 5
58 365. 7
^75.6
18
413.7
311.8
78 461.6 347.9
39
270.7
204.0
99
318.6
240.1
59 366.5
276.2
19
414. 5
312.4
79 462.4 348.5
40
341
271. 5
272.3
204.6
400
401
319. 4
320.2
240.7
241.3
60 367.3
461 368. 1
276.8
277. 4
20
521
415.3
416. 1
313.0
313.6
80 463. 2 349. 1
581 464. 0 349. 7
205.2
42
273.1
205.8
02
321.0
241.9
62 368.9
278.0
22
416. 9
314.2
82 464.8 3.50.3
43
273.9
206.4
03
321.8
242.5
63 369. 7
278.6
23
417.7
314.8
83 46.5.6 3,50.9
44
274.7
.207. 0
(4
322.6
243.1
64 370.5
279.2
24
418.5
315. 4
84 466.4 351.5
45
275.5
207.6
05
323. 4
243.7
65 371.3
279.8
25
419.3
316.0
85 467. 2 352. 1
46
276.3
208.2
06
324. 2
244.3
66 1 372. 1
280.4
26
420.1
316.6
86 468. 0 352. 7
47
277.1
208.8
07
325.0
244.9
67 \ 372.9
281.0
27
420.9
317.2
87 468.8 353.3
48
277.9
209.4
08
325.8
245. 5
68 j 373. 7
281.6
28
421.7
317.8
88 469.6 3.53.9
49
278.7
210.0
09
326.6
246.1
69 374.5
282.3
29
422. 5
318.4
89 470.4 3.54.5
50
351
279.5
280.3
210.6
10
327.4
328. 2
246.7
247. 3
70 1 375.3
282.9
30
423. 3
424.1
319.0
319. 6
90 471. 2 355. 1
.591 472. 0 3.55. 7
211.2
411
471 376. 1 283. 5
531
52
281.1
211.8
12
329.0
247.9
72 376. 9 ' 284. 1
32
424.9
320.2
92 , 472.8 3.56.3
53
281.9
212.4
13
329.8
248.5
73 377.7 284.7
33
425. 7
320.8
93 473.6 356.9
54
282.7
213. 0
14
330.6
249.2
74 378.5
285. 3
34 :
426. 5
321.4
94 474.4 357.5
55
283.5
213.6
15
331.4
249.8
75 379.3
285. 9
35
427. 3
322.0
95 475. 2 358. 1
56
284.3
214.2
16
332. 2
250.4
76 380. 1
286. 5
36
428.1
322. 6
96 476. 0 358. 7
57
285.1
214.8
17
333. 0
251. 0
77 380.9 '287.1
37
428.9
323.2
97 ' 476.8 359.3
58
285.9
215.4
18
333.8
251. 6
78 : 381. 7 i 287. 7
38
429.7
323.8
98 477.6 3.59.9
59
286.7
216.1
19
334.6
252. 2
79 382.5 288.3
39
430.5
324.4
99 { 478.4 i 360.5
60
287.5
216.7
20
335.4
252.-8
80 ' 383. 3 1 288. 9
40
431.3
325.0
Lat.
600 i 479. 2 361. 1
Dist.
Dep.
Lat.
Dlst.
Dep.
Lat.
Dist. Dep. Lat.
Dist.
Dep.
Dist. j Dep. Lat.
5
3° (127°, 233°, 307°
.
Page 442]
TABLE 2.
Difference of Latitude and
Departure for 38° (142°, 218°, 322'
)•
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
DLst.
Lat.
Dep.
1
i 0.8
0.6
61
48.1
37.6
121
95.3
74.5
181
142.6
111.4
241
189.9
148.4
2
1.6
1.2
62
48.9
38.2
22
96.1
75.1
82
143.4
112.1
42
190.7
149.0
3
2.4
1.8
63
49.6
38.8
23-
96.9
75.7
83
144.2
112.7
43
191.5
149.6
4
3.2
2.5
64
50.4
39.4
24
97.7
76.3
84
145.0
113.3
44
192.3
150.2
5
3.9
3.1
65
51.2
40.0
25
98.5
77.0
85
145.8
113.9
45
193.1
150.8
6
4.7
3.7
«6
52.0
40.6
26
99.3
77.6
86
146.6
114.5
46
193.9
151.5
7
5.5
4.3
67
52.8
41.2
27
100.1
78.2
87
147.4
115.1
47
194.6
152.1
8
6.3
4.9
68
53.6
41.9
28
100.9
78.8
88
148.1
115.7
48
195. 4
152.7
9
7.1
5.5
69
54.4
42.5
29
101.7
79.4
89
148.9
116.4
49
196.2
153. 3
10
7.9
6.2
70
55.2
43.1
43.7
30
131
102.4
80.0
90
149.7
150. 5
117.0
50
251^
197.0
197.8
153.9
11
8.7
6.8
71
55.9
103.2
80.7
191
117.6
154.5
12
9.5
7.4
72
56.7
44.3
32
104.0
81.3
92
151.3
118.2
52
198. 6
155.1
13
10.2
8.0
73
57.5
44.9
33
104.8
81.9
93
152.1
118.8
53
199.4
155.8
14
11.0
8.6
74
58.3
45.6
34
105.6
82.5
94
152. 9
119.4
54
200.2
156.4
15
11.8
9.2
75
59.1
46.2
35
106.4
83.1
95
153.7
120.1
55
200.9
157.0
16
12.6
9.9
76
59.9
46.8
36
107.2
83.7
96
154.5
120.7
56
201.7
157.6
17
13.4
10.5
77
60.7
47.4
37
108.0
84.3
97
155. 2
121. 3
57
202.5
158.2
18
14.2
11.1
78
61.5
48.0
38
108.7
85.0
98
156.0
121.9
58
203.3
158.8
19
15.0
11.7
79
62.3
48.6
39
109.5
85.6
99
156.8
122. 5
59
204.1
159.5
20
15.8
12.3
12.9
80
63.0
63.8
49.3
40
110.3
86.2
200
201
157.6
123.1
60
204.9
205.7
160.1
21
16.5
81
49.9
141
111.1
86.8
158.4
123.7
261
160.7
22
17.3
13.5
82
64.6
50.5
42
111.9
87.4
02
159.2
124.4
62
206.5
161.3
23
18.1
14.2
83
65.4
51.1
43
112.7
88.0
03
160.0
125.0
63
207.2
161.9
24
18.9
14.8
84
66.2
51.7
44
113.5
88.7
04
160.8
125. 6
64
208.0
162.5
25
19.7
15.4
85
67.0
52.3
45
114.3
89.3
05
161.5
126. 2
65
208.8
163.2
26
20.5
16.0
86
67.8
52.9
46
115.0
89.9
06
162. 3
126.8
66
209.6
163.8
27
21.3
16.6
87
68.6
53.6
47
115.8
90.5
07
163. 1
127.4
67
210. 4
164.4
28
22.1
17.2
88
69.3
54.2
48
116.6
91.1
08
163.9
128.1
. 68
211.2
165. 0
29
22.9
17.9
89
70.1
54.8
49
117.4
91.7
09
164.7
128.7
69
212.0
165.6
30
23.6
18.5
19.1
90
70.9
55.4
50
118.2
119.0
92.3
10
165.5
166.3
129.3
70
212.8
166.2
31
24.4
91
71.7
56.0
151
93.0
211
129.9
271
213.6
166.8
32
25.2
19.7
92
72.5
56.6
52
119.8
93.6
12
167.1
130.5
72
214.3
167.5
33
26.0
20.3
93
73.3
57.3
53
120.6
94.2
13
167.8
131.1
73
215.1
168.1
34
26.8
20.9
94
74.1
57.9
54
121.4
94.8
14
168.6
131.8
74
215.9
168.7
35
27.6
21.5
95
74.9
58.5
55
122.1
95.4
15
169.4
132.4
75
216.7
169.3
36
28.4
22.2
96
75.6
59.1
56
122.9
96.0
16
170.2
133.0
76
217.5
169.9
37
29.2
22.8
97
76.4
59.7
57
123. 7
96.7
17
171.0
133.6
77
218.3
170.5
38
29.9
23.4
98
77.2
60.3
58
124.5
97.3
18
171.8
134. 2
78
219.1
171.2
39
30.7
24.0
99
78.0
61.0
59
125. 3
97.9
19
172.6
134.8
79
219.9
171.8
40
31.5
24.6
100
78.8
61.6
60
126.1
98.5
20
221
173.4
135.4
80
220.6
221.4
172.4
173.0
41
32.3
25.2
101
79.6
62.2
161
126.9
99.1
174.2
136. 1
281
42
33.1
25.9
02
80.4
62.8
62
127.7
99.7
22
174.9
136. 7
82
222.2
173.6
43
33.9
26.5
03
81.2
63.4
63
128.4
100.4
23
175.7
137. 3
83
223.0
174.2
44
34.7
27.1
04
82.0
64.0
64
129.2
101.0
24
176.5
137.9
84
223. 8
174.8
45
35.5
27.7
05
82.7
64.6
65
130.0
101.6
25
177. 3
138.5
85
224.6
175.5
46
36.2
28.3
06
83.5
65.3
66
130.8
102.2
26
178.1
139. 1
86
225.4
176.1
47
37.0
28.9
07
84.3
65.9
67
131.6
102.8
27
178.9
139.8
87
226.2
176.7
48
37.8
29.6
08
85.1
66.5
68
132.4
103.4
28
179.7
140. 4
88
226.9
177.3
49
38.6
30.2
09
85.9
67.1
69
133.2
104.0
29
180.5
141.0
89
227.7
177.9
50
51
39.4
40.2
30.8
10
86.7
87. 5"
67.7
70
134.0
104.7
30
181.2
182.0
141.6
142.2
90
29r
228.5
229.3
178.5
179.2
31.4
111
68.3
171
134. 7
105.3
231
52
41.0
32.0
12
88.3
69.0
72
135.5
105. 9
32
182.8
142.8
92
230.1
179.8
53
41.8
32.6
13
89.0
69.6
73
136. 3
106. 5
33
183.6
143.4
93
230. 9
180.4
54
42.6
33.2
14
89.8
70.2
74
137.1
107.1
34
184.4
144. 1
94
231.7
181.0
55
43.3
.33.9
15
90.6
70.8
75
137. 9
107.7
35
185. 2
144.7
95
232. 5
181.6
56
44.1
34.5
16
91.4
71.4
76
138.7
108.4
36
186.0
145.3
96
233. 3
182.2
57
44.9
35.1
17
92.2
72.0
77
139. 5
109.0
37
186.8
145. 9
97
234. 0
182.9
58
45.7
35.7
18
93.0
72.6
78
140.3
109.6
38
187. 5
146.5
98
234. 8
183. 5
59
46.5
36.3
19
93.8
73.3
79
141.1
110.2
39
188. 3
147.1
99
235. 6
184.1
60
47.3
36.9
20
94.6
73.9
80
141.8
110.8
40
189.1
147.8
300
236.4
184.7
Dist.
Dep.
Lat.
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
52'
(128
°, 232°,
308°).
tablp: 2.
[Page
443 1
Difference of Latitude and Departure for 38° (142°, 218
°, 322°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
801
237.2
185.3
361
284.5
222.3
421
331.8
259.2
481
379.0
296.2
.541
426. 3
333. 1
02
238.0
185.9
62
285.3 1222.9]
22
332. 5
259. 8
82
379.8
296.8
42
427.1
333. 7
03
238.8
186.6
63
286.0
223.5
23
333.3
260.4
83
380.6
297.4
43
427.9
334.3
04
239.6
187.2
64
286.8
224.1
24
334. 1
261.0
84
381.4
298.0
44
428.7
335. 0
05
240.3
187.8
65
287.6
224.7
25
334.9
261.7
a5
382.2
298.6
45
429. 5
335.6
06
241.1
188.4
66
288.4
225. 3
26
3.35. 7
262.3
86
383. 0
299.2
46
430.3
336.2
07
241.9
189.0
67
289.2
226.0
27
336. 5
262.9
87
383.8
299.8
47
431.0
336.8
08
242.7
189.6
68
290.0
226.6
28
337.3
263.5
88
384.5
300.4
48
431.8
337.4
09
243.5
190.2
69
290.8
227.2
29
338. 1
264.1
89
385.3
301.1
49
432.6
338. 0
10
244.3
190.9
70
291.6
227.8
228.4
30
338.8
264.7
90
386.1
301. 7
302.3
50
433.4
338.6
311
245.1
191.5
371
292.4
431
339.6
265.4
491
386.9
551
434.2
339.3
12
245.9
192.1
72
293.1
229.0
32
340.4
266.0
92
387.7
302.9
52
435. 0
339.9
13
246.6
192.7
73
293.9
229.6
33
.341. 2
266.6
93
388. 5
.303. 5
53
435. 8
340. 5
14
247.4
193.3
74
294.7
230.3
34
342.0
267.2
94
389.3
304.2
54
436.6
341.1
15
248.2
193.9
75
295. 5
230.9
35
342.8
267. 8
95
390.1
304.8
55
437.4
341.7
16
249.0
194.6
76
296.3
231.5
36
.343.6 268.4
96
390.9
305. 4
56
438.1
342.3
17
249.8
195. 2
77
297.1
232. 1
37
.344. 4 i 269. 1
97
391.6
,306. 0
57
438.9
343.0
18
250.6
195.8
78
297.9
232.7
38
345. 2 1 269. 7
98
392.4
306.6
58
439.7
343. 6
19
251.4
196.4
79
298.7
2,33. 3
39
345. 9 1 270. 3
99
393.2
.307. 2
59
440.5
344.2
20
252.2
197.0
197.6
80
299.4
234.0
234. 6
40
346. 7
270.9
500
394.0
307. 8
308.4
60
561
441.3
442.1
344.8
321
253.0
381
300.2
441
347.5
271.5
501
394.8
345.4
22
253.7
198.2
82
301.0
235.2
42
348.3
272.1
02
395. 6
309.1
62
442.9
346.0
23
254.5
198.9
83
301.8
235.8
43
.349. 1
272.7
03
396.4
309.7
63
443.7
346.6
24
255.3
199.5
84
302.6
236.4
44
349.9 273.4
04
397.2
310. 3
64
444.4
347. 2
25
256. 1
200.1
85
303.4
2.37. 0
45
350.7 274.0
05
397.9
310.9
65
445. 2
347. 8
26
256.9
200.7
86
304. 2
237.7
46
351.5 274.6
06
398.7
311.6
66
446.0
348.5
27
257.7
201.3
87
305.0
238.3
47
352. 2 275. 2
07
399.5
312.2
67
446.8
,349. 1
28
258.5
201.9
88
305.7
238.9
48
353.0
275.8
08
400.3
312.8
68
447.6
349.7
29
259.3
202.6
89
306. 5
239.5
49
353.8
276.4
09
401.1
313.4
69
448.4
3-50. 3
30
260.0
203.2
90
307.3
240.1
50
451
354.6
355.4
277.1
10
401.9
314.0
70
449.2
350.9
351.6
331
260.8
203.8
391
308.1
240.7
277.7
511
402.7
314.6
571
450.0
32
261.6
204.4
92
308.9
241.3
52
356. 2
278.3
12
403.5
315. 2
72
450. 7
.352. 2
33
262. 4 1 205. 0
93
309.7
242.0
53
.357. 0
278.9
13
404.2
315.8
73
451.5
352.8
34
263.2
205. 6
94
310.5
242.6
54
357.8
279.5
14
405. 0
316.4
74
452. 3
353. 4
35
264.0
206.3
95
311.3
243.2
55
358. 5
280.1
15
405.8
317.1
75
453.1
354. 0
36
264.8
206.9
96
312.1
243.8
56
359. 3
280.7
16
406.6
,317. 7
76
453. 9
354. 6
37
265.6
207.5
97
312.8
244.4
57
360.1 1281.4
17
407.4
318. 3
77
454.7
3.55. 2
38
266.3
208.1
98
313. 6
245. 0
58
360. 9 j 282. 0
18
408.2
318.9
78
455. 5
355. 8
39
267.1
208.7
99
314.4
245.7
59
361. 7 282. 6
19
409.0
319.5
79
456.3
356. 4
40
267.9
209.3
400
.315. 2
246. 3
60
362.5
363.3
283.2
20
409.8
320.2
80
457.1
457.8
357.1
357.7
341
268.7
209.9
401
316.0
246.9
461
283.8
521
410.6
320.8
581
42
269.5
210. 6
02
316.8
247.5
62
364.1
284.4
22
411.3
321.4
82
458.6
358.3
43
270.3
211.2
03
317.6
248.1
63
364.9
285. 1
23
412.1
322.0
83
4.59. 4
358. 9
44
271.1
211.8
04
318.4
248.7
64
365.6
285.7
24
412.9
322.6
84
460.2
359. 5
45
271.9
212.4
05
319.1
249.3
65
366.4
286.3
25
413.7
323.2
85
461.0
360. 2
46
272.7
213. 0
06
319.9
250.0
66
367.2
286. 9
26
414.5
,323. 8
86
461.8
360.8
47
273.4
213.6
07
320.7
250.6
67
368.0
287.5
27
415.3
324. 5
87
462.6
361.4
48
274. 2 I 214. 3
08
321.5
251.2
68
368.8
288.1
28
416.1
.325. 1
88
463. 3
362.0
49
275. 0 214. 9
09
322. 3
251.8
69
369.6
288.7
29
416.9
325. 7
89
464.1
362. 6
50
351
275.8
276.6
215.5
10
323.1
252.4
70
370. 4
289.3
290. 0
30
531
417.6
326.3
90
464.9
363.2
216.1
411
323.9
253.0
471
371.2
418.4
326.9
591
465.7
363.8
52
277.4 ;216.7
12
324.7
253. 7
72
371.9
290.6
32
419.2
327.5
92
466.5
364.4
53
278.2 217.3
13
325.5
254.3
73
372. 7
291.2
33
420.0
328.2
93
467.3
,365. 1
54
279.0 218.0
14
326. 2
254.9
74
373.5
291.8
.34
420.8
328. 8
94
468.1
365.7
55
279.7 218.6
15
327.0
255. 5
75
374.3
292.4
35
421.6
329.4
95
468.9
366.3
56
280.5
219.2
16
327.8
256.1
76
375. 1
293.1
36
422. 4
330. 0
96
469.7
366.9
57
281.3
219.8
17
328.6
256.7
77
375.9
293.7
37
423. 2
330.6
97
470.5
367. 5
58
282.1
220.4
18
329. 4
257.4
78
376.7
294.3
38
424.0
,331. 2
98
471.2
368.1
59
282.9
221.0
19
330.2
258.0
79
.377. 5
294.9
39
424.7
331.8
99
472.0
368.7
60
Dist.
283.7
221.6
20
331.0
258.6
80
378.2
295.5
40
425.5
332.5
600
472.8
369.4
Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
52° (128°, 232°, 308°
).
Page 444J
TABLE
/ '2.
Difference of Latit d
and Departure for 39° (141°, 219°, 321°
)•
Dist.
Lat.
Dep.
0.6
Dist.
Lat.
Dep.
38.4
Dist. j Lat.
Dep.
Dist.
Lat. Dep.
140.7 113.9
Dist.
241
Lat.
Dep.
1
0.8
61
47.4
121 94. 0
76.1
181
187.3
151.7
2
1.6
1.3
62
48. 2 39. 0 1
22
94.8
76.8
82
141.4 114.5
42
188.1
152.3
3
2.3
1.9
63
49.0
39.6
23
95.6
77.4
83
142.2 ill5.2
43
188.8
152. 9
4
3.1
2.5
64
49.7
40.3
24
96.4
78.0
84
143.0 115.8
44
189.6
153.6
5
3.9
3.1
65
50.5
40.9
25
97.1
78.7
85
143.8 116.4
45
190.4
154. 2
6
4.7
3.8
» 66
51.3
41.5
26
97.9
79.3
86
144.5 1117.1
46
191.2
154. 8
7
5.4
4.4
67
52. 1 ! 42. 2
27
98.7
79.9
87
145.3 ill7. 7
47
192.0
155.4
8
6.2
5.0
68
52.8 I 42.8
28
99.5
80.6
88
146.1 ;il8.3
48
192.7
156.1
9
7.0
5.7
69
53. 6 43. 4
29
100.3
81.2
89
146.9
118.9
49
193.5
156.7
10
7.8
6.3
70
71
54. 4 44. 1
55. 2 44. 7
30
131
101. 0
81.8
90
147.7
119.6
50
194.3
157.3
11
8.5
6.9
101.8
82.4
191
148.4
120.2
251
195.1
158.0
12
9.3
7.6
72
56. 0 45. 3
32
102.6
83.1
92
149.2
120.8
52
195.8
158.6
13
10.1
8.2
73
56. 7 45. 9
33
103.4
83.7
93
150.0
121.5
53
196.6
159.2
14
10.9
8.8
74
57.5
46.6
34
104.1
84.3
94
150.8
122.1
54
197.4
159.8
15
11.7
9.4
75
58.3
47.2
35
104.9
85.0
95
151.5
122.7
55
198.2
160.5
16
12.4
10.1
76
59.1
47.8
36
105.7
85.6
96
152.3
123.3
56
198.9
161.1
17
13.2
10.7
( 1
59.8
48.5
37
106.5
86.2
97
153.1
124.0
57
199.7
161.7
18
14.0
11.3
78
60.6
49.1
38
107.2
86.8
98
153.9
124.6
58
200.5
162.4
19
14.8
12.0
79
61.4
49.7
39
108.0
87.5
99
154.7
125.2
59
201.3
163.0
20
15.5
16.3
12.6
13. 2"
80
62.2
50.3
51.0
40
108.8
88.1
200
155.4 125.9
60
261
202.1
202.8
163.6
21
81
62.9
141
109.6
88.7
201
156.2
126.5
164.3
22
17.1
13.8
82
63.7
51.6
42
110.4
89.4
02
157.0
127.1
62
203.6
164.9
23
17.9
14.5
83
64.5
52.2
43
111.1
90.0
03
157.8
127.8
63
204.4
165.5
24
18.7
15.1
84
65.3
52.9
44
111.9
90.6
04
158. 5
128.4
64
205.2
166.1
25
19.4
15.7
85
66.1
53.5
45
112.7
91.3
05
159.3
129.0
65
205.9
166.8
26
20.2
16.4
86
66.8
54.1
46
113.5
91.9
06
160.1
129.6
66
206.7
167.4
27
21.0
17.0
87
67.6
54.8
47
114.2
92.5
07
160.9 130.3
67
207.5
168.0
28
21.8
17.6
88
68.4
55.4
48
115.0
93.1
08
■ 161. 6
130.9
68
208. 3
168. 7
29
22.5
18.3
89
69.2
56.0
49
115.8
93.8
09
162.4
131.5
69
209.1
169.3
30
23.3
18.9
90
69.9
56.6
50
116.6
94.4
10
163.2
164.0
132.2
70
209.8
169.9
170.5
31
24.1
19.5
91
70. 7 57. 3
151
117.3
95.0
211
132. 8
271
210.6
32
24.9
20.1
92
71.5 57.9
52
118.1
95.7
12
164.8
133.4
72
211.4
171.2
33
25.6
20.8
93
72. 3 58. 5
53
118.9
96.3
13
165.5
134.0
73
212.2
171.8
34
26.4
21.4
94
73.1
59.2
54
119.7
96.9
14
166.3
134. 7
74
212.9
172.4
36
27.2
22.0
95
73.8
59.8
55
120.5
97.5
15
167. 1
135. 3
75
213.7
173.1
36
28.0
22.7
96
74.6
60.4
56
121.2
98.2
16
167.9
135. 9
76
214.5
173.7
37
28.8
23.3
97
75.4 i 61.0
57 122. 0
98.8
17
168.6
136.6
77
215.3
174.3
38
29.5
23.9
98
76. 2 61. 7
58 122. 8
99.4
18
169.4
137.2
78
216.0
175.0
39
30.3
24.5
99
76. 9 62. 3
59 123. 6
100.1
19
170.2
137. 8
79
216.8
175. 6
40
41
31.1
25.2
100
77. 7 62. 9
60
124. 3
100.7
20
171.0
138. 5
80
217.6
218.4
176.2
31.9
25.8
101
78.5
63.6
161
125.1
101.3
221
171.7
139.1
281
176.8
42
32.6
26.4
02
79.3
64.2
62
125.9
101.9
22
172. 5
139.7
82
219.2
177.5
43
33.4
27.1
03
80.0
64.8
63
126.7
102.6
23
173. 3
140. 3
83
219.9
178.1
44
34.2
27.7
04
80.8
65.4
64
127. 5
103.2
24
174.1
141.0
84
220.7
178.7
45
35.0
28.3
05
81.6
66.1
65
128. 2
103.8
25
174.9
141,6
85
221.5
179.4
46
35.7
28.9
06
82.4
66.7
66
129.0
104.5
26
175.6
142.2
86
222.3
180.0
47
36.5
29.6
07
83.2
67.3
67
129.8
105.1
27
176.4
142.9
87
223. 0
180.6
48
37.3
30.2
08
83.9
68.0
68
130. 6
105.7
28
177.2
143.5
88
223.8
181.2
49
38.1
30.8
09
84.7
68.6
69
131.3
106.4
29
178.0
144.1
89
224.6
181.9
50
38.9
31.5
10
85.5
69.2
70
132.1
107.0
107.6
30
231
178.7
179.5
144.7
90
225.4
182.5
51
39.6
32.1
111
86.3
69.9
171
132.9
145. 4
291
226.1
183. 1
52
40.4
32.7
12
87.0
70.5
72
133.7
108.2
32
180.3
146.0
92
226.9
183. 8
53
41.2
33.4
13
87.8
71.1
73
134.4
108.9
33
181.1
146.6
93
227.7
184.4
54
42.0
34.0
14
88.6
71.7
74
135.2
109.5
34
181.9
147.3
94
228.5
185. 0
55
42.7
34.6
15
89.4
72.4
75
136.0
110.1
35
182.6
147.9
95
229.3
185. 6
56
43. 5
35.2
16
90.1
73.0
76
136.8
110.8
36
183.4
148.5
96
230.0
186. 3
57
44.3
35.9
17
90.9
73.6
77
137.6
111.4
37
184.2
149.1
97
230.8
186.9
58
45.1
36.5
18
91.7
74.3
78
138.3
112.0
38
185.0
149.8
98
231.6
187.5
59
45.9
37.1
19
92.5
74.9
79
139.1
112.6
39
18.5.7
150. 4
99
232. 4
188.2
60
46.6
37.8
20
93.3
75.5
80
139.9
113.3
40
186.5
151.0
Lat.
300
Dist.
233. 1
Dep.
188.8
Dist.
I)ep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
51° (129°, 23
1°, 309'
').
TABLE 2. [Page 445
Difference of Latitude and Departure for 39° (141°, 219°, 321°). 1
Dlst.
' Lat.
1 Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. ! Dep.
1
Dist.
Lat.
Dep. 1
301
233.9
189.4
361
280.6
227.1
421
327. 2
264.9
481
373.8 .302.6
541
420.4 i 340.4
02
234.7
190.0
62.
281.3
227.8
22
328.0
265. 5
82
374.6 303.3
42
421.2 ! 341.0
03
235. 5
190.6
63
282.1
228.4
23
328.7
266.2
83
375.4 1303.9
43
422.0 1 341.7
04
236.3
191.3
64
282.9
229.0
24
329.5
266.8
84
376. 1 304. 5
44
422.7 342.3
05
: 237.0
191.9
65
283.7
229.7
25
' 330.3
267.4
85
376. 9 305. 2
45
423.5 : 342.9
0(3
237.8
192.5
66
1 284.4
230.3
26
331.1
268.0
86
377.7 1305.8
46
424.3 343.6
07
238.6
193.2
67
285.2
230. 9
27
331.9
268.7
87
378. 5 306. 4
47
425.1 344.2
08
239.4
193.8
68
286.0
231.5
28
332.6
269. 3
88
379.3 [307.1
48
425.9 344.8
09
i 240. 1
194.4
69
286.8
232.2
29
333. 4
269.9
89
380. 0 ; 307. 7
49
426.6 I 345.5
10
311
240.9
i 241.7
195.0
70
287.6
288.3
232.8
233.4
30
431
334.2 1270.6
335. 0 : 271. 2
90
491
380.8
381.6
308.3
308. 9'
50
551
427. 4 1 346. 1
428. 2 1 346. 7
195.7
371
12
i 242.5
196.3
72
289. 1
234.1
32
335.7 |271.8
92
382. 4
309.6
52
429.0 347.4
13
243.3
196.9
73
289.9
234.7
33
336.5 272.5
93
383. 1
310.2
53
429.7 348.0
14
244.0
197.6
74
290.7
235.3
34
337.3 i273. 1
94
383. 9
310.8
54
430.5 1 348.6
15
244.8
198.2
75
291.4
236.0
35
338.1 273.7
95
-384. 7
311.5
55
431.3 ' 349.2
16
245.6
198. 8
76
292.2
236.6
36
338.8 274.3
96
385.5
312.1
56
432. 1 349. 9
17
246.4
199.5
77
293.0
237.2
37
339. 6 275. 0
97
386.2
312. 7
57
432.8 350.5
18
247.1
200.1
78
293.8
237. 8
38
340.4 275.6
98
387. 0 313. 3
58
433.6 351.1
19
247.9
200.7
79
294.5
238.5
39
341.2 276.2
99
387. 8 314. 0
59
434.4 351.7
20
321
248.7
249. 5
201. 3
80
295.3
296.1
239.1
40
342.0 276.9
342.7 277.5
500
501
388.6
389.4
314. 7
60
561
4.35.2 i 352.4
435.9 353.0
202.0
381
239.7
441
315. 3
22
250.3
202.6
82
296.9
240.4
42
343.5 278.1
02
390.1 ;315.9
62
436. 7 353. 6
23
251.0
203.2
83
297.7
241.0
43
344.3 278.7
03
390.9 316.5
63
437.5 354.3
24
251.8
203.9
84
298.4
241.6
44
345.1 |279.4
04
391.7 317.1
64
438. 3 354. 9
25
252.6
204.5
85
299.2
242.2
45
345.8 280.0
05
392.5 317.8
65
439. 1 355. 5
26
253. 4
205.1
86
300. 0
242.9
46
346.6 [280.6
06
393.2 318.4
66
439.8 356.2
27
254.1
205.7
87
300. 8
243.5
47
347. 4
281.3
07
394.0 1319.0
67
440. 6 356. 8
28
254.9
206.4
88
301.5
244.1
48
348.2
281.9
08
394.8 1319.6
68
441.4 ! 357.4
29
255.7
207.0
89
302. 3
244.8
49
349.0
282.5
09
395.6
320.3
69
442. 2 i 358. 1
30
256.5
257.2
207.6
90
303.1 ,245.4
50
349.7
283.2
283. 8"
10
511
396.3
397.1
320.9
70
443. 0 I 358. 7
443. 7 359. 3
331
208.3
391
303.9
246.0
451
350. 5
321. 6
571
32
258.0
208.9
92
304.7
246.7
52
351.3
284.4
12
397.9 i322.2
72
444. 5 359. 9
33
258.8
209. 5
93
305.4
247.3
53
352.1 1285.0
13
398.7 322.8
73
445.3 : 360.6
34
259.6
210.2
94
306.2
247.9
54
352. 8
285.7
14
399.4 323.4
74
446.1 i 361.2
35
260.4
210.8
95
307.0
248.5
55
353. 6
286.3
15
400.2 324.1
75
446.9 1 361.8
36
261.1
211.4
96
307.8
249.2
56
354. 4
286.9
16
401.0 324.7
76
447.6 362.4
37
261.9
212.0
97
308. 5
249.8
57
355. 2
287.6
17
401. 8 i 325. 3
77
448.4
363.1
38
262.7
212.7
98
309. 3
250.4
58
355. 9
288.2
18
402.5 325.9
78
449.2
363. 7
39
263.5
213.3
99
310.1
251.1
59
356. 7
288.8
19
403.3 326.6
79
450.0
364. 3
40
341
264.2
213.9
400
310. 9
251.7
60
357. 5
289.4
20
404.1 i327.2
80
450.7
365. 0
265.0
214.6
401
311.6
252. 3
461
35873
'290. 1
521
404.9
327.8
581
451.5
365. 6
42
265.8
215.2
02
312.4
252.9
62
359.1
290.7
22
405.7
328.5
82
452. 3
366.2
43
266. 6
215.8
03
313.2
253.6
63
359. 8
291.3
23
406.4
329. 1
83
453.1
366.9
44
267.3
216.4
04
314.0
254.2
64
360.6
292.0
24
407.2
329.7
84
453.9
367. 5
45
268.1
217. 1
05
314.8
254.8
65
361.4
292. 6
25
408.0
330. 4
85
454. 6
368. 1
46
268.9
217.7
06
315. 5
255.5
66
362.2
293. 2
26
408.8
331.0
86
455. 4
368.8
47
269.7
218.3
07
316.3
256. 1
67
362.9
293.8
27
409. 5
331. 6
87
456.2
369.4
48
270. 5
219.0
08
317.1
256.7
68
363.7
294.5
28
410.3
332.3
88
457. 0
370.0
49
271.2
219.6
09
317.9
257.3
69
364.5
295. 1
29
411.1
332. 9
89
457. 8
370.6
50
351
272.0
272. 8
220.2
220. 8
10
411
318.6 I
258.0
70
365.3
295. 7
30
411. 9 ! 333. 5
90 i 458.5
371.3
319.4
258.6
471
366.0
296.4
531
412.6 j334. 1
591 459.3
371.9
52
273.6
221.5
12
320.2
259.2
72
366.8
297.0
32
413. 4 1 334. 8
92 460. 1
372.5
53
274.3
222.1
13
321.0
259.9
7.i
367.6
297.6
33
414. 2 1 335. 4
93
460.9
373.2
54
275. 1
222.7
14
321.8
260.5
74
368.4
298.3
34
415. 0 336. 1
94
461.6
373.8
55
275.9
223.4
15
322. 5
261.1
75
369.2
298.9
35
415.8 336.7
95
462.4
374.4
56
276.7
224.0
16
323. 3
261.8
76
369.9
299. 5
36
416. 5 337. 3
96
463.2
375.1
57
277.5 !
224.6
17
324. 1
262.4
77
370.7
300.1
37
417.3 337.9
97
464.0
375. 7
58
278.2
225.3
18
324.9 263.0
78
371.5
300.8
38
418.1 338.5
98
464.8 1
376. 3
59
279.0
225.9
19
325.6 263.6
79
372.3
301.4
39
418. « 339.1
99 465.5 '
376. 9
60
279.8
226.5
20
326. 4 ' 264. 3
80
373.0
302.0
40
419. 6 '• 339. 8 600 466. 3 |
i
377. 6
Dist.
Dep.
Lat.
Dist.
Dep. I Lat.
Dist.
Dep.
Lat.
Dist.
Dep. ' Lat. Di.st. j Dep. j
Lat.
e
c
►1° (11
29°, 231°, 309°).
Page 446J
TABLE 2.
■
Difference of Latitude and Departure for 40° (140°, 220°, 320°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
46.7
39.2
121
92.7
77.8
181
138.7
116.3
241
184.6
154.9
2
1.5 i 1.3
62
47.5
39.9
22
93.5
78.4
82
139.4
117.0
42
1&5.4
155.6
3
2.3 i 1.9
63
48.3
40.5
23
94.2
79.1
83
140.2
117.6
43
186.1
156.2
4
3.1 i 2.6
64
49.0
41.1
24
95.0
79.7
84
141.0
118. 3
- 44
186.9
156.8
5
3.8 ; 3.2
65
49.8
41.8
25
95.8
80.3
85
141.7
118.9
45
187.7
157.5
6
4.6 1 3.9
♦ 66
50.6
42.4
26
96.5
81.0
86
142.5
119.6
46
188.4
158.1
7
5.4
4.5
67
51.3
43.1
27
97.3
81.6
87
143.3
120.2
47
189.2
158. 8
8
6.1
5.1
68
52.1
43.7
28 ! 98.1
82.3
88
144.0
120.8
48
190.0
159. 4
9
6.9
5.8
69
52.9
44.4
29
98.8
82.9
89
144.8
121.5
49
190. 7
160.1
10
7.7
6.4
70
53.6
54.4
45.0
30
99.6
100.4
83.6
84.2
90
145.5
122.1
50
251
191.5
160.7
11
8.4
7.1
71
45.6
131
191
146.3
122.8
192.3
161.3
12
9.2
/. 1
72
55.2
46.3
32
101.1
84.8
92
147.1
123.4
52
193.0
162.0
13
10.0
8.4
73
55.9
46.9
33
101.9
85.5
93
147.8
124.1
53
193.8
162.6
14
10.7 ! 9.0
74
56.7
47.6
34
102.6
86.1
94
148.6
124.7
54
194.6
163.3
15
11.5 9.6
75
57.5
48.2
35
103.4
86.8
95
149.4
125.3
55
195.3
163. 9
16
12. 3 10. 3
76
58.2
48.9
36
104.2
87.4
96
150.1
126.0
56
196.1
164.6
17
13.0
10.9
77
59.0
49.5
37
104.9
88.1
97
150.9
126.6
57
196.9
165.2
18
13.8
11.6
78
59.8
50.1
38
105.7
88.7
98
151.7
127.3
58
197.6
165.8
19
14.6
12.2
79
60.5
50.8
39
106.5
89.3
99
152.4
127.9
59
198.4
166. 5
20
15.3
12.9
80
61.3
51.4
40
107.2
90.0
200
"201
153.2
128.6
60
199.2
199.9
167.1
167. 8
21
16.1
13.5
81
62.0
52.1
141
108.0
90.6
154.0
129.2
261
22
16.9
14.1
82
62.8
52.7
42
108.8
91.3
02
154.7
129.8
62
200.7
168.4
23
17.6
14.8
83
63.6
53.4
43
109.5
91.9
03
155.5
130.5
63
201.5
169.1
24
18.4
15.4
84
64.3
54.0
44
110. 3
92.6
04
156.3
131.1
64
202.2
169.7
25
19.2
16.1
85
65.1
54.6
45
111.1
93.2
05
157.0
131.8
65
203.0
170.3
26
19.9
16.7
86
65.9
55.3
46
111.8
93.8
06
157.8
132.4
66
203.8
171.0
27
20.7
17.4
87
66.6
55.9
47
112.6
94.5
07
158.6
133.1
67
204.5
171.6
28
21.4
18.0
88
67.4
56.6
48
113.4
95.1
08
•159. 3
133.7
68
205. 3
172.3
29
22.2
18.6
89
68.2
57.2
49
114.1
95.8
09
160.1
134.3
69
206. 1
172.9
30
23.0
19.3
90
91
68.9
69.7
57.9
50
114.9
96.4
10
160.9
135.0
70
206.8
207.6
173.6
174.2
31
23.7
19.9
58.5
151
115. 7 1 97. 1
211
161.6
135.6
271
32
24.5
20.6
92
70.5
59.1
52
116.4
97.7
12
162. 4
136.3
72
208.4
174.8
33
25.3
21.2
93
71.2
59.8
53
117.2
98.3
13
163. 2
136.9
73
209.1
175. 5
34
26.0
21.9
94
72.0
60.4
54
118.0
99.0
14
163.9
137.6
74
209.9
176. 1
35
26.8
22.5
95
72.8
61.1
55
118.7
99.6
15
164.7
138.2
75
210.7
176.8
36
27.6
23.1
96
73. 5
61.7
56
119. 5 100. 3
16
165. 5
138. 8
76
211.4
177.4
37
28.3
23.8
97
74.3
62.4
57
120. 3 1 100. 9
17
166.2
139.5
77
212.2
178. 1
38
29.1
24.4
98
75.1
6.3.0
58
121.0
101.6
18
167.0
140.1
78
213.0
178.7
39
29.9
25.1
99
75.8
63.6
59
121.8
102.2
19
167.8
140.8
79
213.7
179.3
40
41
30. 6
31.4
25.7
26.4
100
76.6
64.3
60
161
122.6
102.8
20
168.5
141.4
80
214. 5
180.0
180. 6
101
77.4
64.9
123.3
103.5
221
169.3
142.1
281
215.3
42
32.2
27.0
02
78.1
65.6
62
124.1
104.1
22
170.1
142.7
82
216.0
181.3
43
32.9
27.6
03
78.9
66.2
63
124.9
104.8
23
170.8
143. 3
83
216.8
181.9
44
33.7
28.3
04
79.7
66.8
64
125.6
105.4
24
171.6
144.0
. 84
217.6
182.6
45
34.5
28.9
05
80.4
67. 5
65
126.4
106.1
25
172.4
144.6
85
218.3
183.2
46
35.2
29.6
06
81.2
68.1
66
127.2
106.7
26
173. 1
145.3
86
219.1
183.8
47
36.0
30.2
07
82.0
68.8
67
127.9
107.3
27
173. 9
145.9
87
219.9
184.5
48
36.8
30.9
08
82.7
69.4
68
128.7
108.0
28
174.7
146.6
88
220.6
185.1
49
.37.5
31.5
09
83.5
70.1
69
129. 5
108.6
29
175.4
147.2
89
221.4
185.8
50
38.3 '
39.1
32.1
10
84.3
85.0
70.7
70
130.2
131.0
109.3
30
176.2
147.8
90
222.2
222. 9
186.4
51
32.8
111
71.3
171
109.9
231
177.0
148.5
291
187.1
52
39.8
33.4
12
85.8
72.0
72
131.8
110.6
32
177.7
149.1
92
223.7
187.7
53
40.6 i
34.1
13
86.6
72.6
73
132.5
111.2
33
178.5
149.8
93
224.5
188.3
54
41.4 ;
34.7
14
87.3
73. 3
74
133.3
111.8
34
179.3
150.4
94
225.2
189. 0
55
42.1 i
35. 4
15
88.1
73.9
75
134. 1
112.5
35
180.0
151.1
95
226.0
189. 6
56
42.9 j
36.0
16
88.9
74.6
76
134.8
113.1
36
180.8
151. 7
96
226.7
190. 3
57
43.7
36.6
17
89.6
75.2
77
135.6
113.8
37
181.6
152.3
97
227.5
190.9
58
44.4
37.3
18
90.4
75.8
78
136.4
114.4
38
182.3
153. 0
98
228.3
191.6
59
45.2
37.9
19
91.2
76.5
79 137. 1
115.1
39
183. 1
153. 6
99
229.0
192. 2
60
46.0
38.6
20
91.9
77.1
80 137. 9
115.7
40
183. 9
154.3
300
229.8
192.8
Dist.
Dep. 1
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
'
>0° (130°, 230°, 310°
.
-
TABLE
2.
[Page 447
Difference of Latitude and Departure for
40° (140°, 220
°, 320°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
301
230.6
193.5
361
276. 5
232.1
421
322.5
270.6
481
368.5
309.2
541
414.4
347.7
02
231.3
194.1
62
277.3
232.7
22
323. 3
271.3
82
369. 2
309.8
42
415.2
348.4
03
232.1
194.8
63
278.1
233.3
23
324. 0
271.9
83 I 370.0
310. 5
43
416.0
349.0
04
232.9
195.4
64
278.8
234.0
24
324.8
272.6
84
370. 8
311.1
44
416. 7 349. 7 |
05
233.6
196.1
65
279.6
234.6
25
325. 6
273. 2
85
371.5
311.7
45
417.5
350. 3
06
234.4
196.7
66
280.4
235. 3
26
326.3
273.8
86
372.3
312.4
46
418.3
351.0
07
235.2
197.3
67
281.1
235.9
27
327.1
274. 5
87
373.1
313.0
47
419.0 351.6
08
235.9
198.0
68
281.9
236.6
28
327.9
275. 1
88
373.8
313.6
48
419.8 1 352.2
09
236.7
198. 6
69
282.7
237.2
29
328.6
275. 8
89
374.6
314.3
49
420.6 352.9
10
237.5
199.3
70
283.4
237.8
30
329.4
276.4
90
375.4
314.9
50
421.3
353.5
311
238.2
199.9
371
284.2
238.5
431
330.2
277.1
491
376.1
315.6
551
422.1
354.2
12
239.0
200.6
72
285.0
239.1
32
330.9
277.7
92
376. 9
316.2
52
422.9
354.8
13
239.8
201.2
73
285.7
239.7
33
331.7
278.3
93
37?. 7
316.9
53
423.6
355.5
14
240.5
201.8
74
286.5
240.4
34
332.5
279.0
94
378.4
317.5
54
424.4
356.1
15
241.3
202. 5
75
287.3
241.0
35
333. 2
279.6
95
379.2
318.2
55
425.2 i 356.8
16
242.1
203.1
76
288.0
241.7
36
334. 0
280.3
96
380.0
318.8
56
425.9 357.4
17
242.8
203.8
77
288.8
242.3
37
334. 8
280.9
97
380. 7
319.5
57
426.7 , 358.0
18
243.6
204.4
78
289.6
243. 0.
38
335. 5
281.6
98
381.5
320.1
58
427. 5 358. 7
19
244.4
205.1
79
290.3
243.6
39
336.3
282.2
99
382.3
320. 8
59
428.2 359.3
20
245.1
205.7
80
291.1
291. '9
244.3
40
337.1
282.8
500
383. 0
321.4
60
429.0 i 360.0
321
245.9
206.3
381
244.9
441
337.8
283. 5
501
383. 8
322. 0
561
429.8 1 360.6
22
246.7
207.0
82
292.6
245.6
42
338. 6
284.1
02
384.6
322. 7
62
430.5 , 361.2
23
247.4
207.6
83
293.4
246.2
43
339.4
284.8
03
385.3
323. 3
63
431.3 : 361.9
24
248.2
208.3
84
294.2
246.8
44
340.1
285.4
04
386.1
324.0
64
432. 1 362. 5
25
249.0
208.9
85
294. 9
247.5
45
340.9
286.0
05
386.8
324.6
65
432.8 363.2
26
249.7
209.6
86
295.7
248.1
46
341.7
286.7
06
387.6
325. 2
66
433.6 363.8
27
250.5
210.2
87
296.5
248.8
47
342.4
287.3
07 ' 388.4
325. 9
67
434.3 364.5
28
251.3
210.8
88
297.2
249.4
48
343.2
288.0
08 i 389.2
326.5
68
435.1 365.1
29
252.0
211.5
89
298.0
250.1
49
344.0
288. 6
09 389.9
327. 1
69
435.9 365.8
30
252.8
212.1
90
298.8
250. 7
50
344.7
345.5
289.3
10
390. 7
391. 5
327.8
70
571
436.6 366.4
437.4 367.0
331
253.6
212.8
391
299.5
251.3
451
289.9
511
328.4
32
254.3
213.4
92
300. 3
252.0
52
346.3
290.5
12 392. 2
329. 1
72
438.2 367.7
33
255.1
214.1
93
301.1
252.6
53
.347. 0
291.2
13 393. 0
329. 7
73
438.9 368.3
34
255.9
214.7
94
301.8
253.3
54
347.8
291.8
14 393. 8
330.4
74
439. 7 369. 0
35
256.6
215.3
95
302.6
253.9
55
348.6
292.5
15 394. 5
331. 0
75
440.5 ' 369.6
36
257.4
216.0
96
303.4
254.6
56
349.3
293.1
16 : 395.3
331. 6
76
441. 2 370. 2
37
258.2
216.6
97
304.1
255.2
57
350.1
293.8
17 i 396. 1
332. 3
77
442.0 370.9
38
258. 9
217.3
98
304.9
255.8
58
350.8
294.4
18 i 396.8
332. 9
78
442.8 ( 371.5
39
259.7
217.9
99
305.7
256.5
59
351.6
295.0
19 1 397.6
333. 6
79
443.5 372.2
40
341
260.5
218.6
400
306.4
257.1
60
352. 4
295.7
20 i 398.3
521 i 399. 1
334. 2
334. 9
80
581
444.3 372.8
445. 1 373. 5
261.2
219. 2
401
307.2
257.8
461
353.1
296.3
42
262.0
219.8
02
308.0
258.4
62
353.9
297.0
22 399.9
335. 5
82
445.8 1 374.1
43
262.8
220.5
03
308.7
259. 1
63
354.7
297.6
23 1 400.6
336. 1
83
446. 6 374. 8
44
263. 5
221.1
04
309. 5
259.7
64
355. 4
298.3
24 401.4
336.8
84
447. 4 375. 4
45
264. 3
221.8
05
310.2
260.3
65
356.2
298.9
25 402. 2
337. 4
85
448.1
376.0
46
265.1
222.4
06
311.0
261.0
66
357.0
299.5
26 402. 9
338.1
86
448.9
376.7
47
265.8
223.1
07
311.8
261.6
67
357.7
300. 2
27 403. 7
338.7
87
449.7
377.3
48
266.6
223.7
08
312.5
262.3
68
358.5
300.8
28 404.5
339. 4
88
450.4
378.0
49
267.4
224.3
09
313. 3
262.9
69
359. 3
301. 5
29 1 405.2
340,0
89
451. 2
378. 6
50
268.1
225.0
225.6
10
411
314.1
314.8
263.6
264.2
70
471
360.0
360.8
302. 1
302.8
30 406.0
531 i 406.8
340. 6
"341.3
90
452.0
379.2
351
268.9
591
452. 7
379.9
52
■269.6
226.3
12
315.6
264.8
72
361.6
303. 4
32 407.5
341.9
92
453.5 1 380.5
53
270.4
226.9
13
316.4
265.5
73
362.3
304. 0
33 408. 3
342. 6
93
454.3 381.2
54
271.2
227.6
14
317.1
266.1
74
363. 1
304. 7
34 1 409. 1
343. 2
94
455.0 1 381.8
55
271.9
228.2
15
317.9
266.8
75
363. 9
305. 3
35 ! 409.8
343. 9
95
455.8 : 382.4
56
272.7
228.8
16
318.7
267. 4
76
364. 6
306.0
36 410.6
344.5
96
456.6
383.1
57
273. 5
229.5
17
319. 4
268.1
77
365. 4
306. 6
37 411.4
345.2
97
457.3
383. 7
58
274.2
230. 1
18
320.2
268.7
78
366.2
307. 3
38 412. 1
345. 8
98
458. 1
384.4
59
275.0
230.8
19
321.0
269.3
7^
366.9
307.9
39 ! 412.9
346.4
99
458. 9
385. 0
60
275.8
231.4
20
321.7
270.0
80
367.7
308.5
40 ' 413. 7
347.1
600
459.6
385.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep. Lat.
50° (1
30°, 230
°, 310°
)•
Page 448]
TABLE 2.
Difference of Latitude and Departure for 41° (139°, 221°, 319°
).
Dirt.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.7
61
46.0
40.0
121
91.3
79.4
181
136.6
118.7
241
181.9
158. 1
2
1.5
1.3
62
46.8
40.7
22
92.1
80.0
82
137.4
119.4
42
182.6
158.8
3
2.3
2.0
63
47.5
41.3
23
92.8
80.7
83
138.1
120.1
43
183.4
159. 4
4
3.0
2.6
64
48.3
42.0
24
93.6
81.4
84
138.9
120.7
44
184.1
160.1
5
3.8
3.3
65
49.1
42.6
25
94.3
82.0
85
139.6
121.4
45
184.9
160.7
6
4.5
3.9
» 66
49.8
43.3
26
95.1
82.7
86
140.4
122.0
46
185.7
161.4
7
5.3
4.6
67
50.6
44.0
27
95.8
83.3
87
141.1
122.7
47
186.4
162.0
8
6.0
5.2
68
51.3
44.6
28
96.6
84.0
88
141.9
123. 3
48
187.2
162.7
9
6.8
5.9
69
52.1
45.3
29
97.4
84.6
89
142.6
124.0
49
187.9
163.4
10
7.5
6.6
70
52.8
45.9
30
98.1
98.9
85.3
90
143.4
124.7
50
188.7
164.0
11
8.3
7.2
71
53.6
46.6
131
85.9
191
144.1
125. 3
251
189.4
164.7
12
9.1
7.9
72
54.3
47.2
32
99.6
86.6
92
144.9
126.0
52
190.2
165.3
13
9.8
8.5
73
55.1
47.9
33
100.4
87.3
93
145.7
126.6
53
190.9
166.0
14
10.6
9.2
74
55.8
48.5
34-
101.1
87.9
94
146.4
127.3
54
191.7
166.6
15
11.3
9.8
75
56.6
49.2
35
101.9
88.6
95
147.2
127.9
55
192.5
167.3
16
12.1
10.5
76
57.4
49.9
36
102.6
89.2
96
147.9
128.6
56
193.2
168.0
17
12.8
11.2
77
58.1
50.5
37
103.4
89.9
97
148.7
129.2
57
194.0
168.6
18
13.6
11.8
78
58.9
51.2
38
104. 1
90.5
.98
149.4
129.9
58
194.7
169.3
19
14.3
12.5
79
59.6
51.8
39
104.9
91.2
99
150.2
130.6
59
195.5
169.9
20
15.1
13.1
80
60.4
52.5
40
105.7
91.8
200
'201
150.9
151.7
131.2
60
196.2
170.6
171.2
21
15.8
13.8
81
61.1
53.1
141
106.4
92.5
131.9
261
197.0
22
16.6
14.4
82
61.9
53.8
42
107.2
93.2
02
152. 5
132.5
62
197.7
171.9
23
17.4
15. 1
83
62.6
54.5
43
107.9
93.8
03
153.2
133. 2
63
198.5
172.5
24 '
18.1
15.7
84
63.4
55.1
44
108.7
94.5
04
154.0
133.8
64
199.2
173.2
25
18.9
16.4
85
64.2
55.8
45
109.4
95.1
05
154.7
134.5
65
200.0
173.9
26
19.6
17.1
86
64.9
56.4
46
110.2
95.8
06
155.5
135.1
66
200.8
174.5
27
20.4
17.7
87
65.7
57.1
47
110.9
96.4
07
156.2
135. 8
67
201.5
175.2
28
21.1
18.4
88
66.4
57.7
48
111.7
97.1
08
• 157. 0
136. 5
68
202.3
175.8
29
21.9
19.0
89
67.2
58.4
49
112.5
97.8
09
157. 7
137. 1
69
203.0
176.5
30
22.6
19.7
90
67.9
68.7
59.0
50
113.2
114.0
98.4
10
158.5
137.8
138.4
70
271'
203.8
204.5
177.1
177.8
31
23.4
20.3
91
59.7
151
99.1
211
159.2
32
24.2
21.0
92
69.4
60.4
52
114. 7
99.7
12
160.0
1.39. 1
72
205.3
178.4
33
24.9
21.6
93
70.2
61.0
53
115.5
100.4
13
160. 8
139.7
73
206.0
179.1
34
25.7
22.3
94
70.9
61.7
54
116.2
101.0
14
161.5
140.4
74
206.8
179.8
35
26.4
23.0
95
71.7
62.3
55
117.0
101.7
15
162.3
141.1
75
207.5
180.4
36
27.2
23.6
96
72.5
63.0
56
117.7
102.3
16
1^3.0
141.7
76
208.3
181.1
37
27.9
24.3
97
73.2
63.6
57
118.5
103.0
17
163.8
142.4
77
209.1
181.7
38
28.7
24.9
98
74.0
64.3
58
119.2
103.7
18
164.5
143. 0
78
209.8
182.4
39
29.4
25.6
99
74.7
64.9
59
120.0
104.3
19
165.3
143.7
79
210.6
183.0
40
30.2
26.2
100
75.5
65.6
60
120.8
121.5
105.0
105.6
20
221
166.0
166.8
144.3
145. 0~
80
281
211.3
212.1
183.7
41
30.9
26.9
101
76.2
66.3
161
184.4
42
31.7
27.6
02
77.0
66.9
62
122.3
106. 3
22
167.5
145.6
82
212.8
185.0
43
32.5
28.2
03
77.7
67.6
63
123. 0
106.9
23
168.3
146.3
83
213.6
185. 7
44
33.2
28.9
04
78.5
68.2
64
123. 8
107.6
24
169.1
147.0
84
214.3
186. 3
45
34.0
29.5
05
79.2
68.9
65
124.5
108.2
25
169.8
147.6
' 85
215.1
187.0
46
34.7
30.2
06
80.0
69.5
66
125.3
108.9
26
170.6
148.3
86
215.8
187.6
47
35.5
30.8
07
80.8
70.2
67
126.0
109.6
27
171.3
148.9
87
216.6
188.3
48
.36.2
31.5
08
81.5
70.9
68
126.8
110.2
28
172.1
149.6
88
217.4
188.9
49
37.0
32.1
09
82.3
71.5
69
127.5
110.9
29
172.8'
150. 2
89
218.1
. 189. 6
50
37.7
32.8
10
83.0
72.2
70
128.3
111.5
112. 2
30
231
173.6
174.3
150.9
90
218.9
219.6
190.3
190. 9"
51
38.5
33.5
111
83.8
72.8
171
129.1
151.5
291
52
39.2
34.1
12
84.5
73.5
72
129.8
112.8
32
175.1
152. 2
92
220.4
191.6
53
40.0
34.8
13
85.3
74.1
73
130.6
113.5
33
175.8
152. 9
93
221.1
192.2
54
40.8
35.4
14
86.0
74.8
74
131.3
114.2
34
176.6
153. 5
94
221.9
192.9
55
41.5
36.1
15
86.8
75.4
75
132.1
114.8
35
177.4
154.2
95
222.6
193. 5
56
42.3
36.7
16
87.5
76.1
76
132.8
115.5
36
178.1
154.8
96
223.4
194.2
57
43.0
37.4
17
88.3
76.8
77
133.6
116.1
37
178.9
155.5
97
224.1
194.8
58
43.8
.38.1
18
89.1
77.4
78
134.3
116.8
38
179.6
156. 1
98
224.9
195. 5
59
44.5
38.7
19
89.8
78.1
79
135.1
117.4
39
180.4
156.8
99
225.7
196.2
60
45.3
39.4
20
90.6
78.7
80
135.8
118.1
40
181.1
157.5
300
226.4
196.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
49° (1
31°, 229
°, 311°
).
TABLE 2.
[Page 449 |
Difference of Latitude and Departure for 41° (139°, 221
°, 319°
)•
Dist.
301
Lat.
Dcp.
Dist.
361
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
227.2
197.5
272.5
236.9
421
317.7
276.2
481
363.0
315. 6
541
408.3
354. 9
02
227.9
198.1
62
273.2
237.5
22
318. 5
276.9
82
363.8
316.2
42
409.0
355.6
03
228.7
198.8
63
274.0
238.2
23
319. 2
277.5
83
364.5
316.9
43
409.8
356.2
04
229.4
199.4
64
274.7
238.8
24
320.0
278.2
84
365. 3
317. 5
44
410.6
356.9
05
230.2
200.1
65
275.5
239.5
25
320. 8
278.8
85
366.0
318.2
45
411.3
357.5
08
230.9
200.8
66
276.2
240.1
26
321.5
279.5
86
366.8
318.8
46
412.1
358.2
07
231.7
201.4
67
277.0
240.8
27
322. 3
280.1
87
367.5
319.5
47
412.8
358.8
08
232.5
202.1
68
277.7
241.4
28
323.0
280.8
88
368.3
320.1
48
413.6
359.5
09
233.2
202.7
69
278. 5
242.1
29
323.8
281.5
89
369.0
320.8
49
414.3
360.2
10
234.0
234.7
203.4
70
279.2
242.7
30
431
324. 5
282.1
90
369.8
370.6
321.5
322.1
50
551
415.1
360.8
811
204.0
371
280.0
243.4
325.3
282.8
491
415.8
361.5
12
235.5
204.7
72
280.8
244.1
32
326. 0
283.4
92
371.3
322.8
52
416.6
362.1
13
236.2
205.4
73
281.5
244.7
33
326.8
284.1
93
372.1
323.4
53
417. 3
362.8
14
237.0
206.0
74
282.3
245.4
34
327. 5
284.7
94
372.8
324.1
54
418.1
363.4
15
237.7
206.7
75
283.0
246.0
35
328.3
285.4
95
373.6
324.7
55
418.9
364.1
16
238.5
207.3
76
283.8
246.7
36
329.1
286.0
96
374.3
325.4
56
419.6
364.8
17
239.2
208.0
77
284.5
247.3
37
329.8
286.7
97
375.1
326.0
57
420.4
365.4
18
240.0
208.6
78
285.3
248.0
38
330.6
287.4
98
3^5. 8
326.7
58
421.1
366.1
19
240.8
209.3
79
286.0
248.7
39
331.3
288.0
99
376.6
327.4
59
421.9
366.7
20
241.5
209.9
80
286.8
287.5
249.3
40
332.1
288.7
500
501
377. 3
378.1
328.0
60
422.6
367.4
321
242.3
210.6
381
250.0
441
332. 8 i 289. 3
328.7
561
423.4
368.0
22
243.0
211.3
82
288.3
250. 6
42
333.6 290.0
02
378.9
329.3
62
424.1
368.7
23
243.8
211.9
83
289.1
251.3
43
334. 3
290.6
03
379.6
330.0
63
424.9
369.4
24
244.5
212.6
84
289.8
251. 9
44
335. 1
291.3
04
380.4
330.6
64
425.7
370.0
25
245. 3
213.2
85
290.6
252.6
45
335.8
292.0
05
381.1
331.3
6.5
426.4
370.7
26
246.0
213.9
86
291.3
253. 2
46
336. 6
292.6
06
381.9
332.0
66
427.2
371.3
27
246.8
214.5
87
292.1
253.9
47
337.4
293.3
07
382.6
332.6
67
427.9
372.0
28
247.5
215.2
88
292.8
254.6
48
338.1
293.9
08
383.4
333. 3
68
428.7
372.6
29
248.3
215.9
89
293.6
255. 2
49
338. 9
294.6
09
384.1
333.9
69
429.4
373.3
30
331
249.1
216.5
90
294.3
255.9
256. 5
50
339.6
295.2
10
384.9
385.7
334.6
335.2
70
571
430. 2
374.0
249.8
217.2
391
295.1
451
340.4
295.9
511
430.9
374.6
32
250.6
217.8
92
295.8
257.2
52
341. 1
296.5
■ 12
386.4
335.9
72
431.7
375. 3
33
251.3
218,5
93
296.6
257.8
53
341. 9
297.2
13
387.2
336.5
73
432.4
375. 9
34
252.1
219.1
94
297.4
258. 5
54
342.6
297.9
14
387.9
337.2
74
433.2
376.6
35
252.8
219.8
95
298.1
259. 2
55
343.4
298.5
15
388.7
337.9
75
434. 0
377.2
36
253.6
220.4
96
298.9
259.8
56
344. 1
299.2
16
389.4
338.5
76
434.7
377.9
37
254. 3
221.1
97
299.6
260.5
o/
344.9
299.8
17
390.2
339.2
1 1
435.5
378. 5
38
255.1
221.8
98
300.4
261. 1
58
345. 7
300.5
18
390.9
339. 8
78
436.2
379.2
39
255.8
222.4
99
301.1
261.8
59
346.4
301.1
19
391.7
340.5
79
437.0
379.8
40
256. 6
257.4
223.1
400
301.9
262.4
60
461
347.2
347.9
301.8
302.5
20
392.4
393. 2
341.1
80
437.7
380.5
341
223.7
401
302.6
263.1
521
341. 8
581
438.5
381.2
42
258.1
224.4
02
303.4
263.7
62
348.7
303. 1
22
394.0
342.5
82
439.2
381.8
43
258.9
225.0
03
304.2
264.4
63
349.4
303.8
23
394.7
343.1
83
440.0
382.5
44
259.6
225.7
04
304.9
265.1
64
350. 2
304.4
24
395. 5
343.8
84
440.7
383.2
45
260.4
226.3
05
305.7
265. 7
65
350.9
305. 1
25
396.2
344.4
85
441.5
383.8
46
261.1
227.0
06
306. 4
266.4
66
351. 7
305. 7
26
397.0
345.1
86
442.3
384.5
47
261.9
227.7
07
307.2
267.0
67
352. 5
306.4
27
397.7
345. 7
87
443.0
385. 1
48
262.6
228. 3
08
307.9
267.7
68
353. 2
307.0
28
398.5
346.4
88
443.8
385.8
49
263.4
229.0
09
308.7
268.3
69
354.0
307.7
29
399.2
347.0
89
444.5
386.4
50
264.2
264. 9
229.6
10
309.4
269.0
269.6
70
471
354.7
355:5
308.4
30
531
400.0
400.7
347.7
90
445.3
387.1
351
230.3
411
310.2
309.0
348.4
591
446.0
387.7
52
265.7
230.9
12
310.9
270.3
72
356. 2
309. 7
32
401.5
349. 0
92
446.8
388.4
53
266.4
231.6
13
311.7
271.0
73
357. 0
310. 3
33
402.2
349. 7
93
447.5
389.1
54
267.2
232.3
14
312. 5
271.6
74
357.7
311.0
34
403. 0
350. 3
94
448.3
389.7
55
267.9
232.9
15
313.2
272.3
75
358. 5
311.6
35
403.8
351. 0
95
449.1
390.4
56
268.7
233.6
16
314. 0 , 272. 9
76
359.2
312. 3
36
404.5
351.6
96
449.8
391.0
57
269.4
234.2
17
314.7
273.6
77
360.0
312.9
37
405.3
352. 3
97
450.6
391. 7
58
270.2
234.9
18
315.5
274.2
78
360.8
313.6
38
406.0
352. 9
98
451. 3
392. 3
59
270.9
235. 5
19
316. 2
274.9
79
361.5 1314.3
39
406.8
353. 6
• 99
452.1
393.0
60
271.7
236.2
20
317.0
275.6
80
362.3 314.9
40
407.5
354.3
600
452.8
393.6
Dist.
Dep.
Lat.
Diet.
Dep.
Lat.
Dist.
Dep. 1 Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
49° (1
31°, 229°, 311°
)•
22489—03-
-29
Page 450
1
TABLE '2.
Difference of Latitude and Departure for 42° (138°, 222°, 318°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. 1 Lat.
Dep.
Dist.
Lat. ! Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
45.3
40.8
121
89.9
81.0
181
134.5
121.1
241
179.1
161.3
2
1.5
1.3
62
46.1
41.5
22
90.7
81.6
82
135.3
121.8
42
179.8
161.9
3
2.2
2.0
63
46.8
42.2
23
91.4
82.3
83
136.0
122.5
43
180.6
162.6
4
3.0
2.7
64
47.6
42.8
24 i 92. 1
83.0
84
136. 7
123.1
44
181.3
163.3
5
3.7
3.3
65
48.3
43.5
25
92.9
83.6
85
137.5
123.8
45
182.1
163. 9
6
4.5
4.0
•66
49.0
44.2
26
93.6
84.3
86
138.2 124.5
46
182.8
164.6
7
5.2
4.7
67
49.8
44.8
27
94.4
85.0
87
139. 0 ! 125. 1
47
183.6
165. 3
8
5.9
5.4
68
50.5
45.5
28
95.1
85.6
88
139.7
125.8
48
184.3
165. 9
9
6.7
6.0
69
51.3
46.2
29
95.9
86.3
89
140.5
126.5
49
185.0
166.6
10
7.4
6.7
7.4
70
71"
52.0
46.8
30
96.6
97.4
87.0
90
141.2
141.9
127.1
50
251
185.8
186.5
167.3
11
8.2
52.8
47.5
131
87.7
191
127.8
168.0
12
8.9
8.0
72
53.5
48.2
32
98.1
88.3
92
142.7
128.5
52
187.3
168.6
13
9.7
8.7
73
54.2
48.8
33
98.8
89.0
93
143.4
129.1
53
188.0
169.3
14
10.4
9.4
74
55.0
49.5
34
99.6
89.7
94
144.2 1129.8
54
188.8
170.0
15
11.1
10.0
75
55.7
50.2
35
100.3
90.3
95
144.9
130.5
55
189.5
170.6
16
11.9
10.7
76
56.5
50.9
36
101.1
91.0
96
145.7
131.1
56
190.2
171.3
17
12.6
11.4
77
57.2
51.5
37
101.8
91.7
97
146.4
131.8
57
191.0
172.0
18
13.4
12.0
78
58.0
52.2
38
102.6
92.3
98
147.1
132. 5
58
191.7
172.6
19
14.1
12.7
79
58.7
52.9
39
103.3
93.0
99
147. 9 \ 133. 2
59
192.5
173.3
20
14.9
13.4
80
59.5
53.5
40
104.0
93.7
200
148.6
149.4
133.8
134.5
60
261
193.2
194.0
174.0
21
15.6
14.1
81
60.2
54.2
141
104.8
94.3
201
174.6
22
16.3
14.7
82
60.9
54.9
42
105.5
95.0
02
150.1
135. 2
■62
194.7
175.3
23
17.1
15.4
83
61.7
55.5
43
106.3
95.7
03
150. 9
135.8
63
195.4
176.0
24
17.8
16.1
84
62.4
56.2
44
107.0
96.4
04
151.6
136.5
64
196.2
176.7
25
18.6
16.7
85
63.2
56.9
45
107.8
97.0
05
152. 3
137.2
65
196.9
177.3
26
19.3
17.4
86
63.9
57.5
46
108.5
97.7
06
153. 1
137.8
66
197.7
178.0
27
20.1
18.1
87
64.7
58.2
47
109.2
98.4
07
153.8
138.5
67
198.4
178. 7
28
20.8
18.7
88
65.4
58.9
48
110.0
99.0
08
154. 6
139.2
68
199.2
179.3
29
21.6
19.4
89
66.1
59.6
49
110.7
99.7
09
155.3
139.8
69
199.9
180.0
30
31
22.3
20.1
90
66.9
67.6
60.2
50
111.5
112.2
100.4
10
156.1
156.8
140.5
70
200.6
180.7
23.0
20.7
91
60.9
151
101.0
211
141.2
271
201.4
181.3
32
23.8
21.4
92
68.4
61.6
52
113.0
101.7
12
157.5
141.9
72
202.1
182.0
33
24.5
22.1
93
69.1
62.2
53
.113.7
102.4
13
158.3
142.5
73
202.9
182.7
34
25.3
22.8
94
69.9
62.9
54
114.4
103.0
14
159.0
143.2
74
203.6
183.3
35
26.0
23.4
95
70.6
63.6
55 1 115.2
103.7
15
159.8
143.9
75
204.4
184.0
36
26.8
24.1
96
71.3
64.2
56
115.9
104.4
16
160.5
144.5
76
205.1
184.7
37
27.5
24.8
97
72.1
64.9
57
116.7
105.1
17
161.3
145. 2
77
205.9
185.3
38
28.2
25.4
98
72.8
65.6
58
117.4
105.7
18
162.0
145.9
78
206.6
186.0
39
29.0
26.1
99
73.6
66.2
59
118.2
106.4
19
162.7
146.5
79
207.3
186.7
40
41
29.7
26.8
100
101
74.3
66.9
60
118.9
107.1
20
163. 5
164.2
147.2
80
281
208.1
208.8
187.4
188.0
30.5
27.4
75.1
67.6
161 119.6
107.7
221
147.9
42
31.2
28.1
02
75.8
68.3
62 120.4
108.4
22
165.0
148.5
82
209.6
1"88.7
43
32.0
28.8
03
76.5
68.9
63
121.1
109.1
23
165.7
149.2
83
210.3
189.4
44
32.7
29.4
04
77.3
69.6
64
121.9
109.7
24
166.5
149.9
84
211.1
190.0
45
33.4
30.1
05
78.0
70.3
65
122.6
110.4
25
167.2
150.6
85
211.8
190.7
46
34.2
30.8
06
78.8
70.9
66
123. 4
111.1
26
168.0
151.2
86
212.5
191.4
47
34.9
31.4
07
79.5
71.6
67
124.1
111.7
27
168.7
151.9
87
213.3
192.0
48
35.7
32.1
08
80.3
72.3
68
124. 8 ' 112. 4
28
169.4
152.6
88
214.0
192.7
49
36.4
32.8
09
81.0
72.9
69
125. 6 i 113. 1
29
170.2
153. 2
89
214.8
193.4
50
51
37.2
37.9
33.5
10
81.7
73.6
70
126.3
127.1
113.8
30
170.9
171.7
153.9
90
215.5
194.0
194.7
34.1
111
82.5
74.3
171
114.4
231
154.6
291
216.3
52
38.6
34.8
12
83.2
74.9
72
127.8
115.1
32
172.4
155.2
92
217.0
195.4
53
39.4
35.5
13
84.0
75.6
73
128.6
115.8
33
173.2
155.9
93
217.7
196.1
54
40.1
36.1
14
84.7
76.3
74
129.3
116.4
34
173.9
156.6
94
218.5
196.7
55
40.9
36.8
15
85.5
77.0
75
130.1
117.1
35
174.6
157.2
95
219.2
197.4
56
41.6
37. 5
16
86.2
77.6
76
130.8
117.8
36
175.4
157.9
96
220.0
198.1
57
42.4
38.1
17
86.9
78.3
77
131.5
118.4
37
176.1 158.6
97
220.7
198.7
58
43.1
38.8
18
87.7
79.0
78
132.3
119.1
38
176.9
159.3
98
221.5
199.4
59
43.8
39.5
19
88.4
79.6
79
133.0 119.8
39
177.6
159.9
99
222.2
200.1
60
44.6
40.1
20
89.2
80.3
80
133.8 120.4
40
178.4
160.6
300
222.9
200.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep. 1 Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
48° (132°, 228°, 312). 1
TABLE 2.
[Page 451 |
Difference of Latitude and Departure for 42° (138°, 222°, 318°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. ; Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
301
223.7
201.4
361
268.3
241.6
421
312.9
281.7
481
357.5 '321.9
541
402.1
362.0
02
224.4
202.1
62
269.0
242.2
22
313.6
282.4
82
358.2 322.5
42
402.8
362.7
03
225.2
202.8
63
269.8
242.9
23
314.4
283. 0
83
358.9
323. 2
43
403.5
363.3
04
225.9
203.4
64
270.5
243.6
24
315.1
283.7
84
359.7
323.9
44
404.3
364.0
05
226.6
204.1
65
271.2
244.2
25
315.8
284. 4
85
360.4
324.6
45
405.0
364.7
i 06
227.4
204.8
66
272.0
244.9
26
316.6
285.1
86
361.2
325.2
46
405.8
365.4
07
228.1
205.4
67
272.7
245.6
27
317.3
285. 7
87
361.9
325.9
47
406.5
366.0
08
228.9
206.1
68
273.5
246.2
48
318.1
286.4
88
362.7
326.6
48
407.2
366.7
09
229.6
206.8
69
274.2
246.9
29
318.8
287.1
89
363. 4
327.2
49
408.0
367.4
10
311
230.4
231.1
207.4
208.1
70
275.0
247.6
30
319.6
287.7
90
.364.1 :327.9
50
408.7
368. 0
371
275.7
248. 3
431
320.3
288.4
491
364.9 328.6
551
409.5
368.7
12
231.9
208.8
72
276.5
248.9
32
321. 0
289.1
92
365. 6
329.2
52
410.2
369.4
13
232.6
209.4
73
277.2
249.6
33
321.8
289.7
93
366. 4
329.9
53
411.0
370.0
14
233. 3
210.1
74
277.9
250.3
34
322.5
290.4
94
367.1
330.6
54
411.7
370.7
15
234.1
210.8
75
278.7
250.9
35
323.3
291.1
95
367.9
331.3
55
412.4
371.4
16
234.8
211.5
76
279.4
251.6
36
324.0
291.7
96
368.6
331.9
56
413.2
372.0
17
235.6
212.1
77
280.2
252.3
37
324.8
292.4
97
369.3
332.6
57
413. 9
372.7
18
236. 3
212.8
78
280.9
252.9
38
325. 5
293.1
98
370.1
333. 3
58
414.7
373.4
19
237.1
213.5
79
281.7
253.6
39
326.2
293.8
99
370.8
333.9
59
415.4
374.1
20
321
237.8
214.1
80
282.4
254.3
40
327.0
294.4
295.1
500
371.6
334.6
60
416.2
416.9
374.7
238.6
214.8
381
283.1
254.9
441
327.7
501
372.3
335.3
561
375. 4
22
239.3
215.5
82
283. 9
255.6
42
328.5
295.8
02
373. 1
335.9
62
417.6
376.1
23
240.0
216.1
83
284.6
256.3
43
329. 2
296.4
03
373.8
336.6
63
418.4
376.7
24
240.8
216.8
84
285.4
257.0
44
330.0
297.1
04
374.5
337.2
64
419.1
377.4
25
241.5
217.5
85 i 286.1
257.6
45
330.7
297.8
05
375. 3
337.9
65
419.9
378.1
26
242.3
•218. 1
86 286.9
258.3
46
331.4
298.4
06
376.0
338.6
66
420.6
378.7
27
243.0
218.8
87
287.6
259.0
47
332.2
299.1
07
376.8
339.3
67
421.4
379.4
28
243.8
219.5
88
288.3
259.6
48
332.9
299.8
08
377.5
339.9
68
422.1
380.1
29
244.5
220.1
89
289.1
260.3
49
333. 7
300.4
09
378.3
340.6
69
422.8
380.7
30
245.2
220.8
90
289.8
261.0
50
451"
334.4
335.2
301.1
10
379.0
341.3
70
423.6
424.3
381.4
331
246.0
221.5
391
290.6
261.6
301.8
511
379.7
341.9
571
382.1
32
246.7
222.2
92
291.3
262. 3
52
335.9
302.5
12
380.5
342.6
72
425.1
382.8
33
247.5
222.8
93
292.1
263.0
53
336.6
303.1
13
381.2
343.3
73
425.8
383.4
34
248.2
223.5
94
292.8
263.6
54
337.4 1303.8
14
382.0
343.9
74
426.6
384.1
35
249.0
224.2
95
293. 5
264.3
55
338.1
304.5
15
382.7
344.6
75
427.3
384.8
36
249.7
224.8
96
294.3
265.0
56
338.9
305.1
16
383.5
345.3
76
428.0
385.4
37
250.4
225.5
97 ; 295.0
265.7
57
339.6
305. 8
17
384.2
346. 0
77
428.8
386.1
38
251.2
226.2
98 i 295.8
266.3
58
340.4
306.5
18
384.9
346.6
78
429.5
386.8
39
251.9
226.8
99
296.5
267.0
59
341.1
307.1
19
385. 7
347.3
79
430.3
387.4
40
341
252.7
253.4
227.5
400
297. 3
267.7
60
341.8
307.8
20
386.4
348.0
80
431.0
388.1
228.2
401 i 298.0
268.3
461
342.6
308. 5
521
387.2
348.6
581
431.8
388.8
42
254.2
228.8
02 i 298. 7
269.0
62
343.3
309. 1
22
387.9
349.3
82
432.5
389.4
43
254. 9
229.5
03 1 299.5
269.7
63
344.1
309.8
23
388.7
350.0
83
433.2
390.1
44
255.6
230.2
04
300. 2
270.3
64
344. 8
310. 5
24
■389. 4
350.6
84
434.0
390.8
45
256.4
230.9
05
301.0
271.0
65
345.6 311.2
25
390.1
351.3
85
434.7
391.4
46
257.1
231.5
06
301.7
271.7
6(5
346.3
311.8
26
390.9 ; 352.0
86
435.5
392. 1
47
257.9
232.2
07
302.5
272.3
67
347.0
312. 5
27
391. 6
352.6
87
436.2
392.8
48
258.6
232.9
08
303. 2
273. 0
()A
347.8
313. 2
28
392.4
353.3
88
437.0
393.4
49
259.4
233.5
09 303.9
273. 7
69
348.5
313.8
29
393.1
354.0
89
437.7
394.1
50
260.1
234.2
10
304. 7
274.3
70
349.3
350. 0
314.5
315.2
30
393. 9 i 354. 6
90
438.4
394. 8
351
260.8
234.9
411
305. 4
275.0
471
531
394.6
355.3
591
439.2
395.4
52
261.6
235.5
12
306. 2
275.7
72
350.8
315.8
32
395. 3
356.0
92
440.0
396. 1
53
262.3
236.2
13
306. 9
276.4
73
351. 5
316.5
33
396.1
356.6
93
440.7
396. 8
54
263. 1
236.9
14
307. 7
277.0
74
352.3
317. 2
34
396.8
357. 3
94
441.4
397.5
55
263. 8
237.5
15
308. 4
277.7
75
353.0
317.8
35
397.6
358.0
95
442.2
398.1
56
264.6
238.2
16
309. 1
278.4
76
353. 7
318.5
36
398. 3'
358.6
96
442.9
398. 8
57
265.3
238.9
17
309. 9
279.0
77
354.5
319.2
37
399.1
359.3
97
443.7
399.5
58
266.0
239.6
18 i 310.6
279.7
78
355. 2
319. 9
38
399.8
360.0
98
444.4
400.1
59
266.8
240.2
19 i 311.4
280.4
79
356.0
320. 5
39
400.6
360.6
99
445.2
400.8
60
267.5
240.9
20
312. 1
281.0
80
356.7
321.2
40
401.3
361.3
600
445.9
401.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
48° (1
32°, 228°, 312°
).
Page 452
TABLE 2.
Difference of Latitude and Departure for 43° (137°, 223
°, 317°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. { Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
44.6
41.6
121 '\ 88.5
82.5
181
132.4
123.4
241
176.3
164.4
2
1.5
1.4
62
45.3
42.3
22 1 89.2
83.2
82
133.1
124.1
42
177.0
165.0
3
2.2
2.0
63
46.1
43.0
23 i 90.0
83.9
83
133.8
124.8
43
177.7
165.7
4
2.9
2.7
64
46.8
43.6
24 : 90.7
84.6
84
134.6
125.5
44
178.5
166.4
5
3.7
3.4
65
47.5
44.3
25 i 91.4
85.2
85
135. 3
126.2
45
179.2
167.1
6
4.4
4.1
^6
48.3
45.0
26 92.2
85.9
86
136.0
126.9
46
179.9
167.8
7
5.1
4.8
67
49.0
45.7
27 92.9
86.6
87
136. 8
127.5
47
180.6
168.5
8
5.9
5.5
68
49.7
46.4
28 93.6
87.3
88
137.5
128.2
48
181.4
169.1
9
6.6
6.1
69
50.5
47.1
29 94.3
88.0
89
138.2
128.9
49
182.1
169.8
10
7.3
6.8
70
51.2
47.7
30
95.1
95.8
88.7
89.3
90
139.0
129.6
50
182.8
170.5
11
8.0
7.5
71
51.9
48.4
131
191
139.7
130.3
251
183.6
171.2
12
8.8
8.2
72
52.7
49.1
32 96. 5
90.0
92
140.4
130.9
52
184.3
171.9
13
9.5
8.9
73
53.4
49.8
33 i 97.3
90.7
93
141.2
131.6
53
185.0
172.5
14
10.2
9.5
74
54.1
50.5
34
98.0
91.4
94
141.9
132.3
54
185.8
173.2
15
11.0
10.2
75
54.9
51.1
35
98.7
92.1
95
142.6
133.0
55
186.5
173.9
16
11.7
10.9
76
55.6
51.8
36
99.5
92.8
96
143.3
133.7
56
187.2
174.6
17
12.4
11.6
77
56.3
52.5
37
100.2
93.4
97
144.1
134.4
57
188.0
175.3
18
13.2
12.3
78
57.0
53.2
38
100.9
94.1
98
144.8
135.0
58
188.7
176.0
19
13.9
13.0
79
57.8
53.9
39 i 101.7
94.8
99
145.5
135.7
59
189.4
176.6
20
14.6
13.6
80
58.5
54.6
40
102.4
103.1
95.5
96.2
200
146.3
136.4
60
190.2
177.3
21
15.4
14.3
81
59.2
55.2
141
201
147.0
137.1
261
190.9
178.0
22
16.1
15.0
82
60.0
55.9
42 1 103.9
96.8
02
147.7
137.8
62
191.6
178.7
23
16.8
15.7
83
60.7
56.6
43 { 104.6
97.5
03
148.5
138.4
63
192.3
179.4
24
17.6
16.4
84
61.4
57.3
44
105.3
.98.2
04
149.2
139.1
64 ! 193.1
180.0
25
18.3
17.0
85
62.2
58.0
45
106.0
98.9
05
149.9
139.8
65 193.8
180.7
26
19.0
17.7
86
62.9
58.7
46
106.8
99.6
06
150.7
140.5
66 i 194.5
181.4
27
19.7
18.4
87
63.6
59.3
47 ' 107.5
100.3
07
151.4
141.2
67 1 195.3
182.1
28
20.5
19.1
88
64.4
60.0
48
108.2
100.9
08
152. 1
141.9
68
196.0
182.8
29
21.2
19.8
89
65.1
60.7
49
109.0
101.6
09
152.9
142.5
69
196. 7 i 183. 5 1
30
21.9
20.5
90
65.8
61.4
50
109.7
102.3
10
153.6
143.2
70
197.5
198.2
184.1
31
22.7
21.1
91
66.6
62.1
151
110.4
103.0
211
154.3
143.9
271
184.8
32
23.4
21.8
92
67.3
62.7
52
111.2
103.7
12
155.0
144.6
72
198.9
185.5
33
24.1
22.5
93
68.0
63.4
53
111.9
104.3
13
155.8
145.3
73
199.7
186.2
34
24.9
23.2
94
68.7
64.1
54
112.6
105.0
14
156.5
145.9
74
200.4
186.9
35
25.6
23.9
95
69.5
64.8
55
113.4
105.7
15
157.2
146.6
75
201.1
187.5
36
26.3
24.6
96
70.2
65.5
56
114.1
106.4
16
158.0
147.3
76
201.9
188.2
37
27.1
25.2
97
70.9
66.2
57
114.8
107.1
17
158.7
148.0
77
202.6
188.9
38
27.8
25.9
98
71.7
66.8
58
115. 6
107.8
18
159.4
148.7
78
203.3
189.6
39
28.5
26.6
99
72.4
67.5
59
116.3
108.4
19
160.2
149.4
79
204.0
190.3
40
29.3
27.3
100
73.1
68.2
60
117.0
117.7
109.1
20
160.9
150.0
80
281
204.8
191.0
41
30.0
28.0
101
73.9
68.9
161
109.8
221
161.6
150.7
205.5
191.6
42
30.7
28.6
02
74.6
69.6
62
118.5
110.5
22
162.4
151.4
82
206.2
192.3
43
31.4
29.3
03
75.3
70.2
63
119.2
111.2
23
163.1
152.1
83
207.0
193.0
44
32.2
30.0
04
76.1
70.9
64
119.9
111.8
24
163.8
152.8
84
207.7
193.7
45
32.9
30.7
05
76.8
71.6
65
120.7
112.5
25
164.6
153.4
85
208.4
194.4
46
33.6
31.4
06
77.5
72.3
66
121.4
113.2
26
165.3
154.1
86
209.2
195.1
47
34.4
32.1
07
78.3
73.0
67
122.1
113.9
27
166.0
154.8
87
209.9
195.7
48
35.1
32.7
08
79.0
73.7
68
122.9
114.6
28
166.7
155.5
88
210.6
196.4
49
35.8
33.4
09
79.7
74.3
69
123.6
115.3
29
167.5
156.2
89
211.4
197.1
50
36.6
34.1
10
80.4
75.0
70
171
124.3
115.9
30
168.2
156. 9
157.5
90
212.1
197.8
51
37.3
34.8
111
81.2
75.7
125.1
116.6
231
168.9
291
212.8
198.5
52
38.0
35.5
12
81.9
76.4
72
125.8
117.3
32
169.7
158.2
92
213.6
199.1
53
38.8
36.1
13
82.6
77.1
73
126.5
118.0
33
170.4
158.9
93
214.3
199.8
54
39.5
36.8
14
83.4
77.7
74
127.3
118.7
34
171.1
159.6
94
215.0
200.5
55
40.2
37.5
15
84.1
78.4
75
128.0
119.3
35
171.9
160.3
95
215.7
201.2
56
41.0
38.2
16
84.8
79.1
76
128.7
120.0
36
172.6
161.0
96
216.5
201.9
57
41.7
38.9
17
85.6
79.8
77
129.4
120.7
37
173. 3
161.6
97
217.2
202.6
58
42.4
39.6
18
86.3
80.5
78
130.2
121.4
38
174.1
162.3
98
217.9
203.2
59
43.1
40.2
19
87.0
81.2
79
130. 9
122.1
39
174.8
163.0
99
218.7
203.9
60
43.9
40.9
20
87.8
81.8
80
131.6
122.8
40
175.5
163.7
300
219.4
204.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
t7° (133°, 227
°, 313°
).
TABLE 2.
[Page 453
Dist.
Difference of Latitude and Departure for 43° (137°, 223°, 317°
).
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. 1 Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
301
220.1
205.3
361
264.0
246.2
421
307. 9 287. 1
481
351.8
328.1
541
395. 7 369. 0
02
220.9
206.0
62
264.8 1246.9
22
308. 6 j 287. 8
82
352.5
328.7
42
396.4
369.7
03
221.6
206.7
63
265. 5
247.6
23
309.4 288.5
83
353.2
329.4
43
397.1
370.3
04
222.3
207.3
64
266.2
248.3
24
310.1 |289.2
84
354.0
330.1
44
397.9
371.0
05
223.1
208.0
65
267.0
248.9
25
310.8
289. 9
85
354.7
330.8
45
398.6
371.7
06
223. 8
208.7
66
267.7
249.6
26
311.6
290.5
86
355.4
331.4
46
399.3
372.4
07
224.5
209.4
67
268.4
250.3
27
312.3
291.2
87
356.2
332.1
47
400.1
373.1
08
225.3
210.1
68
269.1
251.0
28
313. 0
291.9
88
356.9
332.8
48
400.8
373.7
09
226.0
210.7
69
269.9
251.7
29
313.8
292.6
89
357.7
333.5
49
401.5
374.4
10
311
226.-7
227.5
211.4
70
270.6
252.3
30
431"
314.5
293.3
90
358.4
334.2
50
402.2
403.0
375.1
375.8
212.1
371
271.3
253.0
315.2
293.9
491
359.1
334.9
551
12
228.2
212.8
72
272.1
253.7
32
316.0
294.6
92
359.8
335. 5
52
403.7
376.5
13
228.9
213.5
73
272.8
254.4
33
316. 7
295.3
93
360.6
336.2
53
404.4
377.1
14
229.7
214.2
74
273.5
255.1
34
317.4
296.0
94
361.3
336.9
54
405.2
377.8
15
230.4
214.8
75
274.3
255. 8
35
318.1
296.7
95
362.0
337.6
55
405.9
378.5
16
231.1
215.5
76
275.0
256.4
36
318.9
297.4
96
362.8
338.3
56
406.6
379.2
17
231.8
216.2
77
275.7
257.1
37
319.6
298.0
97
363.5
338.9
57
407.4
379.9
18
232.6
216.9
78
276.5
257.8
38
320.3
298.7
98
364.2 1339.6
58
408.1
380.6
19
233.3
217.6
79
277.2
258.5
39
321.1
299.4
99
364.9 1340.3
59
408.8
381.2
20
321
234.0
218.2
80
381
277.9
278.7
259.2
259. 8
40
321.8
300.1
300.8
500
365.7 i 341.0
60
409.6
381.9
382.6
234.8
218.9
441 1 322.5
501
366.4
341.7
561
410.3
22
235.5
219.6
82
279.4
260.5
42
323.3
301.4
02
367. 1
342.4
62
411.0
383. 3
23
236.2
220.3
83
280.1
261.2
43
324.0
302.1
03
367.8
343.0
63
411.8
384.0
24
237.0
221.0
84
280.8
261.9
44
324.7
302.8
04
368.6
343.7
64
412.5
384.6
25
237.7
221.7
85
281.6
262.6
45
325.5
303.5
05
369.3
344.4
65
413.2
385. 3
26
238.4
222.3
86
282.3
263.3
46
326.2
304.2
06
370.0
345.1
66
414.0
386.0
27
239.2
223.0
87
283.0
263. 9
47
326.9
304.9
07
370.8
345.8
67
414.7
386.7
28
239.9
223.7
88
283.7
264.6
48
327.7
305.5
08
371.5
346.5
68
415.4
387.4
29
240.6
224.4
89
284.5
265.3
49
328.4
306.2
09
372.3
347.1
69
416.2
388.1
30
241.4
225.1
90
285.2
286.0
266.0
50
451
329.1
306.9
10
373.0
347.8
70
416.9
388.7
389.4
331
242.1
225.7
391
266.7
329.9
307.6
511
373.8 348.5
571
417.6
32
242.8
226.4
92
286.7
267.3
52
330.6
308.3
12
374.5 349.2
72
418.3
390.1
33
243. 5
227.1
93
287.4
268.0
53
331.3
309.0
13
375.2 1349. 9
73
419.1
390.8
34
244.3
227.8
94
288.2
268.7
54
332.1
309.6
14
376. 0 { 350. 5
74
419.8
391.5
35
245.0
228.5
95
288.9
269.4
55
332.8
310.3
15
376.6 i351.2
75
420.5
392.2
36
245.7
229.2
96
289.6
270.1
56
333.5
311. 0
16
377.4
351.9
76
421.3
392.8
37
246.5
229.8
97
290.4
270.8
57
334.3
311.7
17
378.2
352.6
77
422.0
393.5
38
247.2
230. 5
98
291.1
271.4
58
335.0
312.4
18
378.9
353.3
78
422.7
394.2
39
247.9
231.2
99
291.8
272.1
59
335.7
313.0
19
379.6
354.0
79
423.5
394.9
40
248.7
249.4
231.9
232.6
400
292.6
272.8
60
336.5
337.2
313.7
20
380.3
354.6
80
424.2
395.6
341
401
293.3
273.5
461
314.4
521
381.1
355.3
581
424.9
396.2
42
250.1
233.2
02
294.0
274.2
62
337.9
315.1
22
381.8
356.0
82
425.7
396.9
43
250.9
233.9
03
294.7
274.9
63
338.7
315.8
23
382.6
356.7
83
426.4
397.6
44
251.6
234.6
04
295.5
275.5
64 ! 339.4
316.5
24
383.3
357. 4
84
427.1
398.3
45
252. 3
235.3
05
296.2
276.2
65
340.1
317.1
25
384.0
358.1
85
427.9
399.0
46
253.1
236.0
06
296.9
276.9
66
340.8
317.8
26
384.7
358.7
86
428.6
399.6
47
253.8
236.7
07
297.7
277.6
67
341.6
318.5
27
385.5 359.4
87
429.3
400.3
48
254.5
237.3
08
298.4
278.3
68
342.3
319.2
28
386.2 360.1
88
430.1
401.0
49
255.3
238.0
09
299. 1
278.9
69
343.0
319.9
29
386. 9
360.8
89
430.8
401.7
50
256.0
238.7
10
299.9
279.6
70
343.7
320.5
321. 2
30
387.6
388. 4
361.5
90
431.5
402.4
351
256.7
239.4
411
300.6
280.3
471
344.5
531
362.1
591
432.3
403.1
52
257.4
240.1
12
301.3
281.0
72
345.2
321.9
32
389.1
362.8
92
433.0
403.7
53
258.2
240.8
13
302.1
281.7
73
345.9
322.6
33
389.9
363.5
93
433.7
404.4
54
258.9
241.4
14
302.8
282.4
74
346.7
323.3
34
390.6
364.2
94
434.5
405.1
55
259.6
242.1
15
303.5
283.0
75
347.4
324.0
35
391.3
364.9
95
435.2
405. 8
56
260.4
242.8
16
304.3
283.7
76
348.1
324.6
36
392.0
365.5
96
435.9
406.5
57
361.1
243.5
17
305.0
284.4
77
348.9
325.3
37
392.8
366.2
97
436.7
407.2
58
261.8
244.2
18
305.7
285.1
78
349.6
326.0
38
393.5
366.9
98
437.4
407.8
59
262.6
244.8
19
306.4
285.8
79
350.3
326.7
39
394.2
367.6
99
438.1
408.5
60
263.3
245.5
20
307.2
286.4
80 ! 351.1
327.4
40
394.9
368.3
600
438.8
409.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. j Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat.
4
7° (133°, 227°, 313°
)•
Page 454
1
TABLE 2.
Difference of Latitude and Departure for
44° (136°, 224°, 316°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
43.9
42.4
121
87.0
84.1
181
130. 2 125. 7
241
173.4
167.4
2
1.4
1.4
62
44.6
43.1
22
87.8
84.7
82
130.9 126.4
42
174.1
168.1
3
2.2
2.1
63
45.3
43.8
23
88.5
85.4
83 i 131. 6 1 127. 1
43
174.8
168.8
4
2.9
2.8
64
46. 0 1 44. 5 1
24
89.2
86.1
84
132. 4 127. 8
44
175.5
169.5
6
3.6
3.5
65
46.8
45.2
25
89.9
86.8
85
133.1
128.5
45
176.2
170.2
6
4.3
4.2
•66
47.5
45.8
26
90.6
87.5
86
13.3.8
129.2
46
177.0
170.9
7
5.0
4.9
67
48.2
46.5
27
91.4
88.2
87
134.5 129.91
47
177.7
171.6
8
5.8
5.6
68
48.9
47.2
28 92. 1
88.9
88
135.2
130.6
48
178.4
172.3
9
6.5
6.3
69
49.6
47.9
29 92. 8
89.6
89
136.0
131.3
49
179.1
173. 0
10
7.2
6.9
70
50.4
48.6
30
93.5
94.2
90.3
90
136.7
137.4
132.0
132.7
50
251
179.8
180.6
173.7
11
7.9
7.6
71
51.1
49.3
131
91.0
191
174.4
12
8.6
8.3
72
51.8
50.0
32 95.0
91.7
92
138.1
133.4
52
181.3
175.1
13
9.4
9.0
73
52.5
50.7
33 95.7
92.4
93
138.8
134.1
53
182.0
175.7
14
10.1
9.7
74
53.2
51.4
34
96.4
93.1
94
139.6
134.8
54
182.7
176.4
15
10.8
10.4
75
54.0
52.1
35
97.1
93.8
95
140.3
135.5
55
183.4
177.1
16
11.5
11.1
76
54.7
52.8
36
97.8
94.5
96
141.0
136.2
56
184.2
177.8
17
12.2
11.8
77
55.4
53.5
37
98.5
95.2
97
141.7
136.8
57
184.9
178.5
18
12.9
12.5
78
56.1
54.2
38
99.3
95.9
98
142.4
137.5
58
185.6
179.2
19
13.7
13.2
79
56.8
54.9
39
100.0
96.6
99
143.1
138.2
59
186.3
179.9
20
14.4
13.9
80
57.5
55.6
40
100.7
97.3
200
143.9
144.6
138.9
60
187. 0
187.7
180.6
21
15.1
14.6
81
58.3
56.3
141
101.4
97.9
201
139.6
261
181.3
22
15.8
15.3
82
59.0
57.0
42
102.1
98.6
02
145.3
140.3
62
188.5
182.0
23
16.5
16.0
83
59.7
57.7
43
102.9
99.3
03
146.0
141.0
63
189.2
182.7
24
17.3
16.7
84
60.4
58.4
44
103.6
100.0
04
146.7
141.7
64
189.9
183.4
25
18.0
17.4
85
61.1
59.0
45
104.3
100.7
05
147. 5
142.4
65
190.6
184.1
26
18.7
18.1
86
61.9
59.7
46
105.0
101.4
06
148.2
143.1
66
191.3
184.8
27
19.4
18.8
87
62.6
60.4
47 1 105. 7
102.1
07
148.9
143.8
67
192.1
185.5
28
20.1
19.5
88
63.3
61.1
48 ! 106.5
102.8
08
149.6
144.5
68
192.8
186.2
29
20.9
20.1
89
64.0
61.8
49 j 107.2
103.5
09
150.3
145.2
69
193.5
186.9
30
21.6
20.8
21.5
90
64.7
62.5
50 ! 107.9
104.2
10
151.1
145. 9
Y46. 6
70
271
194.2
187.6
31
22.3
91
65.5
63.2
151 108. 6
104.9
211
151.8
194.9
188.3
32
23.0
22.2
92
66.2
63.9
52 109. 3
105.6
12
152. 5 i 147. 3
72
195.7
188.9
33
23.7
22.9
93
66.9
64.6
53
110.1
106.3
13
153. 2 148. 0
73
196.4
189.6
34
24.5
23.6
94
67.6
65.3
54
110.8
107.0
14
153. 9 1 148. 7
74
197.1
190.3
35
25.2
24.3
95
68.3
66.0
55
111.5
107.7
15
154. 7 149. 4
75
197.8
191.0
36
25.9
25.0
96
69.1
66.7
56
112.2
108.4
16
155. 4 150. 0
76
198.5
191.7
37
26.6
25.7
97
69.8
67.4
57
112.9
109.1
17
156.1 150.7
77
199.3
192.4
38
27.3
26.4
98
70.5
68.1
58
113. 7
109.8
18
156.8 151.4
78
200.0
193.1
39
28.1
27.1
99
71.2
68.8
59
114.4
110.5
19
157. 5 152. 1
79
200.7
193.8
40
28.8
27.8
28.5
100
101
71.9
72.7
69.5
60
115.1
115.8'
111.1
111.8
20
158.3
152.8
80
201.4
194.5
41
29.5
70.2
161
221
159.0
153. 5
281
202. 1
195.2
42
30.2
29.2
02
73.4
70.9
62
116.5
112.5
22
159.7
154.2
82
202.9
195.9
43
30.9
29.9
03
74.1
71.5
63
117.3
113.2
23
160.4
154.9
83
203.6
196.6
44
31.7
30.6
04
74.8
72.2
64
118.0
113.9
24
161.1
155.6
84
204.3
197.3
45
32.4
31.3
05
75.5
72.9
65
118.7
114.6
25
161.9
156.3
85
205.0
198.0
46
33.1
32.0
06
76.3
73.6
66
119.4
115.3
26
162.6
157.0
86
205.7
198.7
47
33.8
32.6
07
77.0
74.3
67
120.1
116.0
27
163.3
157.7
87
206.5
199.4
48
34.5
33.3
08
77.7
75.0
68
120. 8
116.7
28
164.0
158.4
88
207.2
200.1
49
35.2
34.0
09
78.4
75.7
69
121. 6
117.4
29
164.7
159.1
89
207.9
200.8
50
36.0
36.7
34.7
10
79.1
79.8
76.4
70
122.3
118.1
30
165.4
166.2
159.8
90
208.6
201.5
51
35.4
111
77.1
171
123.0
118.8.
231
160.5
291
209.3
202.1
52
.37.4
36.1
12
80.6
77.8
72 ' 123.7
119. 5
32
166.9
161.2
92
210.0
202.8
53
38.1
36.8
13
81.3
78.5
73 1 124.4
120.2
33
167.6 1161.9
93
210.8
203. 5
54
38.8
37.5
14
82.0
79.2
74 i 125.2
120.9
34
168. 3 162. 6
94
311.5
204.2
55
39.6
38.2
15
82.7
79.9
75
125.9
121.6
35
169. 0 163. 2
95
212.2
204.9
56
40.3
38.9
16
83.4
80.6
76
126.6
122.3
36
169. 8 163. 9
96
212.9
205. 6
57
41.0
39.6
17
84.2
81.3
77
127. 3
123.0
37
170. 5 i 164. 6
97
213.6
206.3
58
41.7
40.3
18
84.9
82.0
78
128.0
123.6
38
171.2 |165.3
98
214.4
207.0
59
42.4
41.0
19
85.6
82.7
79
128.8
124.3
39
171.9
166.0
99
215.1
207.7
60
43.2
41.7
20
86.3
83.4
80
129. 5
125.0
40
172.6
166.7
300
215.8
208.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
16° (134°, 226
°, 314°
)•
TABLE 2.
[Page 455
Dist.
Difference of Latitude and Departure for 44° (136°, 224°, 316
').
Lat.
Dep.
Dist.
Lat.
Dep.
Di.st.
Lat.
Dep.
Dist. Lilt.
Dep.
Dist.
1 Lat.
Dep.
801
216. 5
209. 1
361
259.7
250. 8
421
302. 8
292.5
481
346.0
334. 1
541
1
i 389.2
375.8
02
217.2
209.8
()2
260.4
251. 5
22
303.6
293.2
82
346.7
334. 8
42
389.9
376.5
03
218.0
210.5
(53
261.1
252. 2
23
304.3
293.8
83
347.4
335. 5
43
390.6
377.2
04
218.7
211.2
64
261.8
252. 9
24
305. 0
294.5
84
348.2
336.2
44
391.3
377.9
05
219. 4
211.9
65
262.6
253. 6
25
305. 7
295.2
85
348.9
336. 9
45
392.0
378.6
06
220.1
212.6
66
263.3
254. 3
26
306.4
295.9
86
349. 6
337. 6
46
392.8
379.3
07
220.8
213.3
67
264. "0
254. 9
27
307.2
296.6
87 ! 350.3
338.3
47
393.5
380.0
08
221.6
214.0
68
264.7
255. 6
28
307.9
297.3
88
351.0
339.0
48
394.2
380. 7
09
222. 3-
214.7
69
265.4
256. 3
29
308.6
298.0
89
351.7
339.7
49
394.9
381.4
10
311
223.0
223.7
215.4
70
266.2
266.9
257.0
30
431
309.3
310.0
298.7
299.4
90
491
352.5
353.2
340.4
341.1
50
551
395.6
396.4
382.1
382.7
216.0
371
257.7
12
224.4
216.7
72
267.6
258.4
32
310. 8
300. 1
92 ^ .353.9
341.8
52
397.1
383. 4
13
225. 2
217.4
73
268. 3
259.1
33
311. 5
300. 8
93 354.6
342.5
53
397.8
384.1
14
225. 9
218.1
74
269.0
259.8
34
312. 2
301.5
94 355.3
343.2
54
398.5
384.8
15
226.6
218.8
75
269.8
260.5
35
312. 9
302. 2
95 1 356. 1
343.9
55
399.2
385.5
16
227. 3
219.5
76
270.5
261.2
36
313. 6
302. 9
96 i 356.8
344.6
56
400.0
386. 2
17
228.0
220.2
77
271.2
261.9
37
314. 4
303.6
97 1 357.5
345.2
57
400.7
386.9
18
228.8
220.9
78
271.9
262.6
38
315.1
304.3
98
358.2
345.9
58
401.4
387.6
19
229.5
221.6
79
272.6
263.3
39
315.8
305.0
99
358.9
346. 6
59
402.1
388.3
20
321
230.2
230.9
222.3
80
273.4
264.0
264.7
40
441
316. 5
305.7
500
359.7
360.4
347.3
348.0
60
561
402.8
403.6
389.0
389.7
223.0
381
274.1
317. 2
306. 4
501
22
231.6
223.7
82
274.8
265.4
42
318. 0
307.0
02
361.1
348.7
62
404.3
39D.4
23
232.3
224.4
83
275.5
266.1
43
318. 7
307.7
03
361.8
349.4
63
405.0
391.1
24
233.1
225.1
84
276.2
266.8
44
319.4
308.4
04
362.5
350.1
64
405. 7
391.8
25
233.8
225.8
85
276.9
267.5
45
320. 1
309.1
05
363.3
350.8
65
406.4
392.5
26
234.5
226.5
86
377.7
268.1
46
320.8
309.8
06
364.0
351. 5
66
407.2
393.2
27
235.2
227. 2
87
278.4
268.8
47
321.5
310.5
07
364.7
352.2
67
407.9
393.9
28
235.9
227.9
88
279.1
269.5
48
322. 3
311.2
08
365.4
352.9
68
408.6
394.6
29
236.7
228.6
89
279.8
270.2
49
323. 0
311.9
09
366.1
353.6
69
409.3
395.3
30
331
237.4
238.1
229.2
229.9
90
391
280. 5
270.9
50
323.7
312.6
10
366. 9
354.3
70
410.0
410.7
396.0
396.7
281.3
271.6
451
324.4
313.3
511
367.6
355.0
571
32
238.8
230.6
92
282.0
272.3
52
325.2
314.0
12
368.3
355. 7
72
411.5
397.3
33
239.5
231.3
93
282.7
273.0
53
325.9
314.7
13
369.0
356. 4
73
412.2
398.0
34
240.3
232. 0
94
283.4
273.7
54
326. 6
315.4
14
369.7
357. 1
74
412.9
398.7
35
241. 0
232. 7
95
284.1
274.4
55
327. 3
316.1
15 370.5
357. 8
75
413.6
399.4
36
241.7
233. 4
96
284.9
275. 1
56
328. 0
316.8
16
371.2
358. 4
76
414.3
400.1
37
242.4
234.1
97
285.6
275.8
57
328. 7
317.5
17
371.9
359.1
77
415.1
400.8
38
243.1
234.8
98
286.3
276. 5
58
329.5
318.2
18
372.6
359.8
78
415.8
401.5
39
243.9
335.5
99
287.0
277.2
59
330. 2
318.9
19
373.3
360.5
79
416.5
402.2
40
244.6
2.36. 2
400
287.7
288.5
277.9
60
330.9
319.6
20
374.1
361.2
80
417.2
417.9
402.9
403.6
341
245.3
236.9
401
278.6
461
331.6
320.2
521 374. 8
361.9
581
42
246.0
237. 6
02
289.2
279.3
62
332.3
320.9
22 375. 5
362. 6
82
418.7
404.3
43
246.7
238.3
03
289.9
280.0
63
333. 1
321.6
23 ! 376.2
363.3
83
419.4
405.0
44
247.5
239. 0
04
290.6
280.7
64
333. 8
322.3
24 376.9
364.0
84
420.1
405.7
45
248.2
239.7
05
291.3
281.3
65
334.5
323.0
25
377.7
364.7
85
420.8
406.4
46
248.9
240.4
06
292.1
282.0
66
335.2
323.7
26
378.4
365.4
86
421.5
407.1
47
249.6
241.1
07
292.8
282.7
67
335.9
324.4
27
379.1
366.1
87
422.3
407.8
48
250.3
241.7
08
293.5
283.4
68
336. 7
325.1
28
379.8
366.8
88
423. 0
408.5
49
251.1
242.4
09
294.2
284.1
69
337.4
325.8
29
380.5
367.5
89
423. 7
409.1
50
251.8
243.1
10
294.9
284.8
70
338. 1
326.5
30
381.2
368.2
90
424.4
409.9
351
252.5
243.8
411
295.7
285.5
471
338.8
327.2
531
382.0
368.9
591
425.1
410.5
62
253.2
244.5
12
296.4
286.2
72
339.5
327.9
32
382.7
369.6
92
425.9
411.2
53
253.9
245.2
13
297.1
286.9
73
340.3
328.6
33
383.4
370. 3
93
426.6
411.9
54
254.6
245.9
14
297.8
287.6
74
341.0
329.3
34
384. 1
371.0
94
427.3
412.6
55
255.4
246.6
15
298.5
288.3
75
341.7
330.0
35
384.8
371. 7
95
428.0
413.3
56
256.1
247.3
16
299. 2
289.0
76
342. 4
330.7
36
385. 6
372.4
96
428.7
414.0
57
256.8
248.0
17
300.0
289.7
77
343. 1
331.4
37
386.3
373.1
97
429.5
414.7
58
257.5
248.7
18
300.7
290.4
78
343. 8
332. 1
38
387.0
373.7
98
430.2
415. 4
59
258.2
249.4
19
301.4
291.1
79
344.6
332.7
39
387.7
374.4
99
430.9
416.1
60
259. 0
250.1
20
302.1
291.8
80
345.3
333.4
40
388.4
375,1
600
431.6
416.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. j Lat. 1
46° (134°, 226°, 314°).
Page 456J
TABLE 2.
Difference of Latitude and
Departure for 46° (135", 225°, 315'
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
43.1
43.1
121
85.6
85.6
181
128.0
128.0
241
170.4
170.4
2
1.4
1.4
62
43.8
43.8
22
86.3
86.3
82
128. 7
128.7
42
171.1
171.1
3
2.1
2.1
63
44.5
44.5
23
87.0
87.0
83
129.4
129.4
43
171.8
171.8
4
2.8
2.8
64
45.3
45.3
24
87.7
87.7
84
130.1
130.1
44
172.5
172.5
5
3.5
3.5
65
46.0
46.0
25
88.4
88.4
85
130.8
130.8
45
173.2
173.2
6
4.2
4.2
•66
46.7
46.7
26
89.1
89.1
86
131.5
131.5
46
173.9
173.9
7
4.9
4.9
67
47.4
47.4
27
89.8
89.8
87
132.2
132.2
47
174.7
174.7
8
5.7
5.7
68
48.1
48.1
28
90.5
90.5
88
132.9
132.9
48
175.4
175.4
9
6.4
6.4
69
48.8
48.8
29
91.2
91.2
89
133.6
133.6
49
176.1
176. 1
10
11
7.1
7.1
70
49.5
49.5
30
91.9
91.9
90
134.4
134.4
135.1
50
251
176.8
177.6
176.8
7.8
7.8
71
50.2
50.2
131
92.6
92.6
191
136.1
177.5
12
8.5
8.5
72
50.9
50.9
32
93.3
93.3
92
135.8
135.8
52
178.2
178.2
13
9.2
9.2
73
51.6
51.6
33
94.0
94.0
93
136.5
136.5
53
178.9
178.9
14
9.9
9.9
74
52.3
52.3
34
94.8
94.8
94
137.2
137.2
54
179.6
179.6
15
10.6
10.6
75
53.0
53.0
35
95.5
95.5
95
137.9
137.9
55
180.3
180.3
16
11.3
11.3
76
53.7
53.7
36
96.2
96.2
96
138.6
138.6
56
181.0
181.0
17
12.0 I 12.0
77
54.4
54.4
37
96.9
96.9
97
139.3
139.3
57
181.7
181.7
18
12.7
12.7
78
55.2
55.2
38
97.6
97.6
98
140.0
140.0
58
182.4
182.4
19
13.4
13.4
79
55.9
55.9
39
98.3
98.3
99
140.7
140.7
59
183.1
183.1
20
14.1
14.1
80
56.6
56.6
40
99.0
99.0
200
141.4
141.4
60
183.8
184.6
183.8
21
14.8
14.8
81
57.3
57.3
141
99.7
99.7
201
142.1
142.1
261
184.6
22
15.6
15.6
82
58.0
58.0
42
100.4
100.4
02
142.8
142.8
62
185.3
185.3
23
16.3
16.3
83
58.7
58.7
43
101.1
101.1
03
143.5
143.5
63
186.0
186.0
24
17.0
17.0
84
59.4
59.4
44
101.8
101.8
04
144.2
144.2
64
186.7
186.7
25
17.7
17.7
85
60.1
60.1
45
102.5
102.5
05
145. 0
145.0
65
187.4
187.4
26
18.4
18.4
86
60.8
60.8
46
103.2
103.2
06
145.7
145.7
66
188.1
188.1
27
19.1
19.1
87
61.5
61.5
47
103.9
103.9
07
146.4
146.4
67
188.8
188.8
28
19.8
19.8
88
62.2
62.2
48
104.7
104.7
08
147.1
147.1
68
189.5
189.5
29
20.5
20.5
89
62.9
62.9
49
105.4
105.4
09
147.8
147.8
69
190.2
190.2
30
21.2
21.2
90
63.6
63.6
50
106.1
106.1
10
148.5
148.5
70
190.9
190.9
31
21.9
21.9
91
64.3
64.3
151
106.8
106.8
211
149. 2 1 149. 2
271
191.6
191.6
32
22.6
22.6
92
65.1
65.1
52
107.5
107.5
12
149.9
149.9
72
192.3
192.3
33
23.3
23.3
93
65.8
65.8
53
108.2
108.2
13
150.6
150.6
73
193.0
193.0
34
24.0
24.0
94
66.5
66.5
54
108.9
108.9
14
151.3
151.3
74
193. 7
193.7
35
24.7
24.7
95
67.2
67.2
55
109.6
109.6
15
152.0 152.0
75
194.5
194.5
36
25.5
25.5
96
67.9
67.9
56
110.3
110.3
16
152.7 152.7
76
195.2
195.2
37
26.2
26.2
97
68.6
68.6
57
111.0
111.0
17
153.4 153.4
.77
195.9
195.9
38
26.9
26.9
98
69.3
69.3
58
111.7
111.7
18
154. 1 1 154. 1
78
196.6
196.6
39
27.6
27.6
99
70.0
70.0
59
112. 4
112.4
19
154.9
154.9
79
197.3
197.3
40
28.3
28.3
100
70.7
70.7
60
113.1
113.1
20
155.6
156.3
155.6
80
198.0
198.0
41
29.0
29.0
101
71.4
71.4
161
113.8
113.8
221
156.3
281
198.7
198.7
42
29.7
29.7
02
72.1
72.1
62
114.6
114.6
22
157.0
157.0
82
199.4
199.4
43
30.4
30.4
03
72.8
72.8
63
115.3
115.3
23
157.7
157.7
83
200.1
200.1
44
31.1
31.1
04
73.5
73.5
64
116.0
116.0
24
158.4
158.4
84
200.8
200.8
45
31.8
31.8
05
74.2
74.2
65
116.7
116.7
25
159. 1
159.1
85
201.5
201.5
46
32.5
32.5
06
75.0
75.0
66
117.4
117.4
26 \
159.8
159.8
86
202.2
202.2
47
33.2
33.2
07
75.7
75.7
67
118.1
118.1
27
160.5
160.5
87
202.9
202.9
48
33.9
33.9
08
76.4
76.4
68
118.8
118.8
28
161.2
161.2
88
203.6
203.6
49
34.6
34.6
09
77.1
77.1
69
119.5
119.5
29
161.9
161.9
89
204.4
204.4
50
51
35.4
35.4
10
77.8
77.8
70
120.2
120.2
30
162.6
163. 3
162.6
90
205.1
205.1
36.1
36.1
111
78.5
78.5
171
120.9
120.9
231
163.3
291
205.8
205.8
52
36.8
36.8
12
79.2
79.2
72
121.6
121.6
32
164.0
164.0
92
206.5
206.5
53
37.5
37.5
13
79.9
79.9
73
122.3
122.3
33
164.8
164.8
93
207.2
207.2
54
38.2
38.2
14
80.6
80.6
74
123.0
123.0
34
165.5
165.5
94
207.9
207.9
55
38.9
38.9
15
81.3
81.3
75
123.7
123.7
35
166.2
166.2
95
208.6
208.6
56
39.6
39.6
16
82.0
82.0
76
124.5
124.5
36
166.9
166.9
96
209.3
209.3
57
40.3
40.3
17
82.7
82.7
77
125.2
125.2
37
167.6
167.6
97
210.0
210.0
58
41.0
41.0
18
83.4
83.4
78
125. 9
125.9
38
168. 3
168. 3
98
210.7
210.7
59
41.7
41.7
19
84.1
84.1
79
126.6
126.6
39
169.0
169.0
99
211.4
211.4
60
42.4
42.4
20
84.9
84.9
80
127.3
127.3
40
169.7
169.7
300
212,1
212.1
Dist.
Dep. Lat. |
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
4
5° (i;
J5°, 225°, 315°
.
TABLE 2.
[Page 457
Difference of Latitude and Depart
are for 45° (135°, 225°, 315
= )•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
301
212.8
212.8
361
255.3
255. 3
421
297.7
297.7
481
340.1 !340. 1
541
382.5
382.5
02
213.5
213.5
62
256.0
256.0
22
298.4
298.4
82
340. 8 ' 340. 8
42
383.2
383.2
03
214.3
214.3
63
256.7
256. 7
23
299.1
299.1
83
.341.5 341.5
43
383. 9
383.9
04
215.0
215.0
64
257. 4
257. 4
24
299.8
299.8
84
342.2 342.2
44
384.7
384.7
05
215.7
215.7
65
258. 1
258.1
25
300.5
300.5
85
342.9 342.9
45
385.4
385.4
06
216.4
216.4
66
258.8
258.8
26
301.2
301.2
86
343.6 343.6
46
386.1
386.1
07
217.1
217.1
67
259.5
259. 5
27
301.9
301.9
87
344.3 344.3
47
386. 8
386.8
08
217.8'
217.8
68
260.2
260.2
28
302.6
302.6
88
345.1 34.5.1
48
387.5
387.5
09
218.5
218.5
69
260.9
260.9
29
303. 4
303.4
89
345.8 345.8
49
388.2
388.2
10
219.2
219.2
70
371
261.6
262.3
261.6
30
304.1
304.1
90
346.5
347.2
346.5
50
388.9
388.9
311
219.9
219.9
262.3
431
304.8
304.8
491
347.2
551
389.6
389.6
12
220.6
220.6
72
263.0
263.0
32
305. 5
305.5
92
347.9 347.9
52
390.3
390.3
13
221.3
221.3
73
263.8
263.8
33
306.2
306.2
93
348.6 348.6
53
391.0
391.0
14
222.0
222.0
74
264.5
264.5
34
306.9
306.9
94
349.3 349.3
54
391.7
391.7
15
222.7
222.7
75
265.2
265.2
35
307.6
307.6
95
350.0 350.0
55
392.4
392.4
16
223.4
223.4
76
265.9
265.9
36
308. 3
308.3
96
350.7 350.7
56
393.1
393.1
17
224.2
224.2
77
266.6
266.6
37
309.0
309.0
97
351.4 351.4
57
393.9
393.9
18
224.9
224.9
78
267.3
267.3
38
309.7
309.7
98
352.1 352.1
58
394.6
394.6
19
225.6
225.6
79
268.0
268. 0
39
310.4
310.4
99
352.8 352.8
59
395.3
395.3
20
226.3
227.0
226.3
80
268.7
268.7
269.4
40
311.1
31178
311.1
311.8
500
501
353.5
353.5
354.3
60
561
396. 0 ! 396. 0 |
321
227.0
381
269.4
441
354.3
396.7
396.7
22
227.7
227.7
82
270.1
270.1
42
312.5
312.5
02
355.0 355.0
62
397.4
397.4
23
228.4
228.4
83
270.8
270.8
43
313.3
313.3
03
355.7
355.7
63
398.1
398.1
24
229.1
229.1
84
271.5
271.5
44
314.0
314.0
04
356.4
356.4
64
398.8 1 398.8
25
229.8
229.8
85
272.2
272.2
45
314.7
314.7
05
357.1
357.1
65
399. 5 399. 5
26
230.5
230.5
86
272.9
272.9
46
315. 4
315.4
06
357.8
357. 8
66
400. 2 400. 2
27
231.2
231.2
87
273.7
273.7
47
316.1
316.1
07
358.5
358.5
67
400.9 400.9
28
231.9
231.9
88
274.4
274.4
48
316.8
316.8
08
359.2
359.2
68
401.6 * 401.6
29
232.6
232.6
89
275.1
275.1
49
317.5
317.5
09
359.9
359.9
69
402.3 , 402.3
30
233.3
233.3
90
275.8
276.5
275.8
50
318.2
318.2
10
511
360.6
360.6
70
403.0
403.8
403.0
331
234.1
234.1
391
276.5
451
318.9
318. 9
361.3
361.3
571
403.8
32
234.8
234.8
92
277.2
277.2
52
319.6
319.6
12
362.0
362.0
72
404.5 i 404.5
33
235. 5
235. 5
93
277.9
277.9
53
320.3
320. 3
13
362.7 362.7
73
405.2 , 405.2
34
236.2
236.2
94
278.6
278.6
54
321.0
321.0
14
363. 5 363. 5
74
405.9 405.9
35
236.9
236. 9
95
279.3
279.3
55
321.7
321.7
15
364. 2 364. 2
75
406.6 406.6
36
237.6
237.6
96
280.0
280.0
56
322.4
322.4
16
364.9 364.9
76
407.3 407.3
37
238.3
238.3
97
280.7
280.7
57
323.2
323.2
17
365.6 !365.6
77
408.0 408.0
38
239.0
239.0
98
281.4
281.4
58
323.9
323. 9
18
366.3 366.3
78
408. 7 ' 408. 7
39
239.7
239.7
99
282.1
282.1
59
324.6
324.6
19
367.0 1367.0
79
409.4 409.4
40
240.4
240.4
400
282.8
283.6
282.8
60
325. 3
326.0
325.3
326. 0
20
521
367.7 1367:7
368.4 368.4
80
581
410.1
410.8
410.1
341
241.1
241.1
401
283.6
461
410.8
42
241.8
241.8
02
284.3
284.3
62
326.7
326.7
22
369.1 j 369.1
82
411.5 411.5
43
242.5
242.5
03
285.0
285.0
63
327.4
327.4
23
369. 8 369. 8
83
412. 2 412. 2
44
243.2
243.2
04
285.7
285.7
64
328.1
328.1
24
370.5 [370.5
84
412. 9 412. 9
45
244.0
244.0
05
286.4
286.4
65
328.8
328.8
25
371.2 1371.2
85
413. 7 413. 7
46
244.7
244.7
06
287.1
287.1
66
329.5
329.5
26
371.9 371.9
86
414.4 414.4
47
245.4
245.4
07
287.8
287.8
67
330.2
330.2
27
372. 6 I 372. 6
87
415. 1 415. 1
48
246.1
246.1
08
288.5
288.5
68
330.9
330.9
28
373.4 373.4
88
415.8 ! 415.8
49
246.8
246.8
09
289.2
289.2
69
331.6
331.6
29
374.1 374.1
89
416.5 '. 416.5
50
247.5
248.2
247.5
10
289.9
289.9
290.6
70
332.3
332. 3
30
374.8 374.8
90
591
417.2
417.9
417.2
417.9
351
248.2
411
290.6
471
333. 1
333.1
531
375.5
375.5
52
248.9
248.9
12
291.3
291.3
72
333. 8
333.8
32
376.2
376. 2
92
418.6
418.6
53
249.6
249.6
13
292.0
292.0
73
334. 5
334.5
33
376.9
376.9
93
419.3
419.3
54
250.3
250.3
14
292.7
292.7
74
335. 2
335.2
34
377.6
377.6
94
420.0
420.0
55
251.0
251.0
15
293.5
293.5
75
335. 9
335.9
35
378.3
378.3
95
420.7
420.7
56
251.7
251.7
16
294.2
294.2
76
336. 6
336. 6
36
379.0
379.0
96
421.4
421.4
57
252.4
252.4
17
294.9
294.9
77
337. 3
337.3
37
379.7
379.7
97
422.1
422.1
58
253.1
253.1
18
295.6
295.6
78
338.0
338.0
38
380. 4 ! 380. 4
98
422.8
422.8
59
253. 9
253.9
19
296.3
296.3
79
338.7
338.7
39
381.1 1381.1
99
423.6
423.6
60
254.6
254.6
20
297.0
297.0
80
339.4
339.4
40
381.8
381.8
600
424.3
424.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
45° (■
L35°, 22.
)°, 315<
').
1
Page 458]
TABLE 3.
Meridional Parts, or
Increased Latitudes.
Comp
1
293.465
M.
0°
1°
20
go
4°
5°
6°
JO
8°
90
M.
0
0.0
59.6
119.2
178.9
238.6
298.3
358.2
418.2
478.3
538.6
0
1
1.0
60.6
20.2
79.9
39.6
99.3
59.2.
19.2
79.3
39.6
1
2
2.0
61.J
62;b
21.2
80.8
40.6
300.3
60.2
20.2
80.3
40.6
2
3
3.0
22.2
81.8
41.6
01.3
61.2
21.2
81.3
41.6
3
4
4.0
63.6
23.2
82.8
42.5
02.3
62.2
22.2
82.3
42.6
4
5
5.0
64.6
124.2
183.8
243.5
303.3
363.2
423.2
483.3
543.6
5
6
6.0
65.6
25.2
84.8
44.5
04.3
64.2
24.2
84.3
44.6
6
7
7.0
66.5
26.2
85.8
45.5
05.3
65.2
25.2
85.3
45.6
7
8
7.9
67.5
27.2
86.8
46.5
06.3
66.2
26.2
86.3
46.6
8
9
8.9
68.5
28.2
87.8
47.5
07.3
67.2
27.2
87.3
47.6
9
10
9.9
69.5
129.1
188.8
248.5
308.3
368.2
428.2
488.3
548.6
10
11
10.9
70.5
30.1
89.8
49.5
09.3
69.2
29.2
89.3
49.6
11
12
11.9
71.5
31.1
90.8
50.5
10.3
70.2
30.2
90.4
50.6
12
13
12.9
72.5
32.1
91.8
51.5
11.3
71.2
31.2
91.4
51.7
13
14
13.9
73.5
33.1
92.8
52.5
12.3
72.2
32.2
92.4
52.7
14
15
15
14.9
74.5
134.1
193.8
253.5
313.3
373.2
433.2
493.4
553.7
16
15.9
75.5
35.1
94.8
54.5
14.3
74.2
34.2
94.4
54.7
16
17
16.9
76.5
36.1
95.8
55.5
15.3
75.2
35.2
95.4
55.7
17
18
17.9
77.5
37.1
96.8
56.5
16.3
76.2
36.2
96.4
56.7
18
19
18.9
78.5
38.1
97.8
57.5
17.3
77.2
37.2
97.4
57.7
19
20
19.9
79.5
139.1
198.8
258.5
318.3
378.2
438.2
498.4
558.7
20
21
20.9
80.5
40.1
99.7
59.5
19.3
79.2
39.2
99.4
59.7
21
22
21.9
81.5
41.1
200.7
60.5
20.3
80.2
40.2
500.4
60.7
22
23
22.8
82.4
42.1
01.7
61.5
21.3
81.2
41.2
01.4
61.7
23
24
23.8
83.4
43.1
02.7
62.5
22.3
82.2
42.2
02.4
62.7
24
25
24.8
84.4
144.1
203. 7
263.5
323.3
383.2
443.2
503.4
563.7
25
26
25.8
85.4
45.1
04.7
64.5
24.3
84,2
44.2
04.4
64.7
26
27
26.8
86.4
46.0
05.7
65.5
25.3
85.2
45.2
05.4
65.7
27
28
27.8
87.4
47.0
06.7
66.5
26.3
86.2
46.2
06.4
66.8
28
29
28.8
88.4
48.0
07.7
67.4
27.3
87.2
47.2
07.4
67.8
29
30
29.8
89.4
149.0
208.7
268.4
328.3
388.2
448.2
508.4
568.8
30
31
30.8
90.4
50.0
09.7
69.4
29.3
89.2
49.2
09.4
69.8
31
32
31.8
91.4
51.0
10.7
70.4
30.3
90.2
50.2
10.4
70.8
32
33
32.8
92.4
52.0
11.7
71.4
31.3.
91.2
51.2
11.4
71.8
33
34
33.8
93.4
53.0
12.7
72.4
273.4
32.3
92.2
52.2
12.4
72.8
34
35
34.8
94.4
154.0
213.7
333.3
393.2
453.2
513.4
573.8
35
36
35.8
95.4
55.0
14.7
74.4
34.3
94.2
54.3
14.5
74.8
36
37
36.7
96.4
56.0
15.7
75.4
35.3
95.2
55.3
15.5
75.8
37
38
37.7
97.3
57.0
16.7
76.4
36.2
96.2
56.3
16.5
76.8
38
39
38.7
98.3
58.0
17.7
77.4
37.2
97.2
57.3
17.5
77.8
39
40
40
39.7
99.3
159.0
218.7
278.4
338.2
398.2
458.3
518.5
578.8
41
40.7
100.3
60.0
19.7
79.4
39.2
99.2
59.3
19.5
79.9
41
42
41.7
01.3
61.0
20.6
80.4
40.2
400.2
60.3
20.5
80.9
42
43
42.7
02.3
62.0
21.6
81.4
41.2
01.2
61.3
21.5
81.9
43
44
43.7
03.3
63.0
22.6
82.4
42.2
02.2
62.3
22.5
82.9
44
45
44.7
104.3
164.0
223.6
283.4
343.2
403.2
463.3
523. 5
583.9
45
46
45.7
05.3
65.0
24.6
84.4
44.2
04.2
64.3
24.5
84.9
46
47
46.7
06.3
66.0
25.6
85.4
45.2
05.2
65.3
25.5
85.9
47
48
47.7
07.3
67.0
26.6
86.4
46.2
06.2
66.3
26.5
86.9
48
49
48.7
08.3
68.0
27.6
87.4
47.2
07.2
67.3
27.5
87.9
49
50
49.7
109.3
168.9
228.6
288.4
348.2
408.2
468.3
528.5
588.9
50
51
50.7
10.3
69.9
29.6
89.4
49.2
09.2
69.3
29.5
89.9
51
52
51.6
11.3
70.9
30.6
90.4
50.2
10.2
70.3
30.5
90.9
52
53
52.6
12.3
71.9
31.6
91.4
51.2
11.2
71.3
31.5
91.9
53
54
53.6
13.2
72.9
32.6
92.4
52.2
12.2
72.3
32.5
93.0
54
55
54.6
114.2
173.9
233.6
293.4
353.2
413.2
473.3
533.5
594.0
55
56
55.6
15.2
74.9
34.6
94.4
54.2
14.2
74.3
34.6
95.0
56
57
56.6
16.2
75.9
35.6
95.4
55.2
15.2
75.3
35.6
96.0
57
58
57.6
17.2
76.9
36.6
96.3
56.2
16.2
76.3
36.6
97.0
58
59
58.6
18.2
77.9
37.6
97.3
57.2
17.2
77.3
37.6
98.0
59
M.
0°
1°
2°
8°
4°
5°
6°
7°
8°
9°
M.
TABLE 3.
[Page 459 |
Meridional Parts, or
Increased Latitudes.
Comp
1
293.465
M.
10°
11°
12°
13°
14°
15°
16°
17°
18°
19°
M.
0
599.0
659.6
720.5
781.5
842.8
904.4
966.3
1028. 5
1091.0
1153. 9
0
1
GOO.O
60.6
21.5
82.5
43.9
05.4
67.3
29.5
92.0
54.9
1
2
01.0
61.7
22.5
83.6
44.9
06.5
68.3
30.5
93.1
56.0
2
3
02.0
62.7
23.5
84.6
45.9
07.5
69.4
31.6
94.1
57.0
3
4
03.0
63.7
24.5
85.6
46.9
08.5
70.4
32.6
95.2
58.1
4
5
604.1
664.7
725.5
786.6
847.9
909.6
971.4
1033. 7
1096. 2
1159. 1
5
6
05.1
65.7
26.6
87.6
49.0
10.6
72.5
34.7
97.3
60.2
6
7
06.1
66.7
27.6
88.7
50.0
11.6
73.5
35.7
98.3
61.2
t
8
07.1
67.7
28.6
89.7
51.0
12.6
74.6
36.8
99.4
62.3
8
9
08.1
68.7
29.6
90.7
52.0
13.7
75.6
37.8
1100.4
63.3
9
10
609.1
669.8
730.6
791.7
853.1
914.7
976.6
1038. 9
1101.4
1164. 4
10
11
10.1
70.8
31.6
92.7
54.1
15.7
77.7
39.9
02.5
65.4
11
12
11.1
71,8
32.7
93.8
55.1
16.8
78.7
40.9
03.5
66.5
12
13
12.1
72.8
33.7
94.8
56.1
17.8
79.7
42.0
04.6
67.5
13
14
13.1
73.8
34.7
95.8
57.2
18.8
80.8
43.0
05.6
68.6
14
15
614.1
674.8
735.7
796.8
858.2
919.8
981.8
1044. 1
1106. 7
1169. 7
15
16
15.2
75.8
36.7
97.8
59.2
20.9
82.8
45.1
07.7
70.7
16
17
16.2
76.8
37.7
98.9
60.2
21.9
83.9
46.1
08.8
71.8
17
18
17.2
77.9
38.8
99.9
61.3
22.9
84.9
47.2
09.8
72.8
18
19
18.2
78.9
39.8
800.9
62.3
24.0
925.0
85.9
987.0
48.2
10.9
73.9
19
20
. 619. 2
679.9
740.8
801.9
863.3
1049. 3
1111.9
1174. 9
20
21
20.2
80.9
41.8
02.9
64.3
26.0
88.0
50.3
13.0
76.0
21
22
21.2
81.9
42.8
04.0
65.4
27.1
89.0
51.3
14.0
77.0
22
23
22.2
82.9
43.8
05.0
66.4
28.1
90.1
52.4
15.0
78.1
23
24
23.2
83.9
44.9
06.0
67.4
29.1
91.1
53.4
16.1
79.1
24
25
624.2
684.9
745.9
807.0
868.5
930. 1
992.1
1054. 5
1117. 1
1180. 2
25
26
25.3
86.0
46.9
08.1
69.5
31.2
93.2
55.5
18.2
81.2
26
27
26.3
87.0
47.9
09.1
70.5
32.2
94.2
56.6
19.2
82.3
27
28
27.3
88.0
48.9
10.1
71.5
33.2
95.3
,57.6
20.3
83.3
28
29
28.3
89.0
49.9
11.1
72.6
34.3
96.3
58.6
21.3
84.4
29
30
629.3
690.0
751.0
812.1
873.6
935.3
997.3
1059. 7
1122. 4
1185.5
30
31
30.3
91.0
52.0
13.2
74.6
36.3
98.4
60.7
23.4
86.5
31
32
31.3
92.0
53.0
14.2
75.6
37.4
99.4
61. '8
24.5
87.6
32
33
32.3
93.1
54.0
15.2
76.7
38.4
1000.4
62.8
25.5
88.6
33
34
35
33.3
94.1
55.0
16.2
77.7
39.4
01.5
63.9
1064. 9"
26.6
89.7
1190. 7
34
35
634.3
695.1
756.0
817.3
878.7
940.5
1002.5
1127.6
36
35.4
96.1
57.1
18.3
79.7
41.5
03.6
65.9
28.7
91.8
36
37
36.4
97.1
58.1
19.3
80.8
42.5
04.6
67.0
29.7
92.8
37
38
37.4
98.1
59.1
20.3
81.8
43.6
05.6
68.0
30.8
93.9
38
39
38.4
99.1
60.1
21.3
82.8
44.6
06.7
69.1
31.8
95.0
39
40
639.4
700.2
761.1
822.4
883.8
945.6
1007. 7
1070. 1
1132. 9
1196,0
40
41
40.4
01.2
62.2
23.4
84.9
46.7
08.7
71.2
33.9
97.1
41
42
41.4
02.2
63.2
24.4
85.9
47.7
09.8
72.2
35.0
98.1
42
43
42.4
03.2
64.2
25.4
86.9
48.7
10.8
73.2
36.0
99.2
43
44
43.4
04.2
65.2
26.5
88.0
49.7
11.8
74.3
37.1
1200.2
44
45
644.5
705.2
766.2
827.5
889.0
950.8
1012. 9
1075. 3
1138. 1
1201. 3
45
46
45.5
06.2
67.3
28.5
90.0
51.8
13.9
76.4
39.2
02.3
46
47
46.5
07.3
68.3
29.5
91.0
52.8
15.0
77.4
40.2
03.4
47
48
47.5
08.3
69.3
30.5
92.1
53.9
16.0
78.5
41.3
04.5
48
49
48.5
09.3
70.3
31.6
93.1
54.9
17.0
79.5
42.3
05.5
49
50
649.5
710. 3
771.3
832.6
894.1
955.9
1018. 1
1080. 5
1143. .4
1206. 6
50
51
50.5
11.3
72.3
33.6
95.2
57.0
19.1
81.6
44.4
07.6
51
52
51.5
12.3
73.4
34.6
96.2
58.0
20.2
82.6
45.5
08.7
52
53
52.5
13.4
74.4
35.7
97.2
59.0
21.2
83.7
46.5
09.7
53
54
53.6
14.4
75.4
36.7
98.2
60.1
22.2
84.7
47.6
10.8
54
55
654.6
715.4
776.4
837.7
899.3
961.1
1023. 3
1085. 8
1148. 6
1211.8
55
56
55.6
16.4
77.4
38.7
900.3
62.1
24.3
86.8
49.7
12.9
56
57
56.6
17.4
78.5
39.8
01.3
63.2
25.3
87.9
50.7
14.0
57
58
57.6
18.4
79.5
40.8
02.3
64.2
26.4
88.9
51.8
15.0.
58
59
58.6
19.4
80.5
41.8
03.4
65.2
27.4
89.9
17°
52.8
16.1
59
M.
10°
11°
12°
13°
14°
15°
lfi°
1S°
1J.°
M.
Page 460]
TABLE 3.
Meridional Parts, or Increased Latitudes.
Comp. 293.466
M.
2©°
210
22°
28°
24°
26°
26°
27°
28°
29°
M.
0
1217. 1
1280. 8
1344. 9
1409.5
1474. 5
1540.1
1606. 2
1672. 9
1740. 2
1808.1
0
1
18.2
81.9
46.0
10.6
75.6
41.2
07.3
74.0
41.3
09.2
1
%
19.3
82.^
84.^
47.1
11.6
76.7
42.3
08.4
75.1
42.4
10.4
2
3
20.3
48.1
12.7
77.8
43.4
09.5
76.2
43.6
11.5
3
4
21.4
85.1
49.2
13.8
78.9
44.5 10.6 1
77.4
44.7
12.6
4
5
1222. 4
1286. 1
1350. 3
1414. 9
1480. 0
1545.6
1611.7
1678. 5
1745.8
1813. 8
5
6
23.5
87.2
51.4
16.0
81.1
46.7
12.9
79.6
46.9
14.9
6
7
24.5
88.3
52.4
17.1
82.2
47.8
14.0
80.7
48.1
16.1
7
8
25.6
89.3
53.5
18.1
83.3
48.9
15.1
81.8
49.2
17.2
8
9
26.7
90.4
54.6
19.2
84.3
50.0
16.2
82.9
50.3
18.3
9
10
1227. 7
1291.5
1355.7
1420. 3
1485.4
1551. 1
1617. 3
1684. 1
1751.5
1819. 5
10
11
28.8
92.5
56.7
21.4
86.5
52.2
18.4
85.2
52.6
20.6
11
12
29.8
93.6
57.8
22.5
87.6
53.3
19.5
86.3
53.7
21.8
12
13
30.9
94.7
58.9
23.5
88.7
54.4
20.6
87.4
54.8
22.9
13
14
32.0
95.7
59.9
24.6
89.8
55.5
21.7
88.5
56.0
24.0
14
15
1233. 0
1296. 8
1361. 0
1425. 7
1490. 9
1556. 6
1622. 8
1689. 7
1757. 1
1825. 2
15
16
34.1
97.9
62.1
26.8
92.0
57. 7 23. 9 1
90.8
58.2
26.3
16
17
35.1
98.9
63.2
27.9
93.1
58.8
25.0
91.9
59.4
27.5
17
18
36.2
1300.0
64.2
29.0
94.2
59.9
26.2
93.0
'60.5
28.6
18
19
37.3
01.1
65.3
30.0
95.2
61.0
27.3
94.1
61.6
29.7
19
20
20
1238. 3
1302. 1
1366.4
1431. 1
1496. 3
1562. 1
1628. 4
1695. 3
1762. 7
1830. 9
21
39.4
03.2
67.5
32.2
97.4
63.2
29.5
96.4
63.9
32.0
21
22
40.4
04.3
68.5
33.3
98.5
64.3
30.6
97.5
65.0
33.2
22
23
41.5
05.3
69.6
34.4
99.6
65.4
31.7
98.6
66.1
34.3
23
24
42.6
06.4
70.7
36.4
1500.7
66.5
32.8.
99.7
67.3
35.4
24
25
1243. 6
1307. 5
1371.8
1436. 5
1501. 8
1567. 6
1633. 9
1700.9
1768. 4
1836. 6
25
26
44.7
08.5
72.8
37.6
02.9
68.7
35.0
02.0
69.5
37.7
26
27
45.7
09.6
73.9
38.7
04.0
69.8
36.1
03.1
70.7
38.9
27
28
46.8
10.7
75.0
39.8
05.1
70.9
37.3
04.2
71.8
40.0
28
29
47.9
11.7
76.1
40.9
06.2
72.0
38.4
05.3
72.9
41.2
29
30
30
1248. 9
1312. 8
1377. 1
1442.0
1507. 3
1573. 1
1639. 5
1706.5
1774. 1
1842.3
31
50.0
13.9
78.2
43.0
08.4
74.2
40.6
07.6
75.2
43.4
31
32
51.0
14.9
79.3
44.1
09.4
75.3
41.7
08.7
76.3
44.6
32
33
52.1
16.0
80.4
45.2
10.5
76.4
42.8
09.8
77.4
45.7
33
34
53.2
17.1
81.5
46.3
11.6
77.5
43.9
10.9
78.6
46.9
34
35
1254. 2
1318. 2
1382. 5
1447.4
1512. 7
1578. 6
1645.0
1712. 1
1779.7
1848. 0
35
36
55.3
19.2
83.6
48.5
13.8
79.7
46.2
13.2
80.8
49.2
36
37
56.4
20.3
84.7
49.5
14.9
80.8
47.3
14.3
82.0
50.3
37
38
57.4
21.4
85.8
50.6
16.0
81.9
48.4
15.4
83.1
51.4
38
39
58.5
22.4
86.8
51.7
17.1
83.0
49.5
16.6
84.2
52.6
39
40
1259. 5
1323. 5
1387. 9
1452. 8
1518. 2
1584. 1
1650. 6
1717.7
1785.4
1853.7
40
41
60.6
24.6
89.0
53.9
19.3
85.2
51.7
18.8
86.5
54.9
41
42
61.7
25.6
90.1
55.0
20.4
86.3
52.8
19.9
87.6
56.0
42
43
62.7
26.7
91.1
56.1
21.5
87.4
53.9
21.1
88.8
57.2
43
44
63.8
27.8
92.2
57.1
22.6
88.5
55.1
22.2
89.9
58.3
44
45
1264.9
1328. 9
1393. 3
1458.2
1523. 7
1589. 6
1656.2
1723. 3
1791. 1
1859.5
45
46
65.9
29.9
94.4
59.3
24.8
90.7
57.3
24.4
92.2
60.6
46
47
67.0
31.0
95.5
60.4
25.9
91.8
58.4
25.5
93.3
61.8
47
48
68.0
32.1
96.5
61.5
27.0
92.9
59.5
26.7
94.5
62.9
48
49
69.1
33.1
97.6
62.6
28.0
94.1
60.6
27.8
95.6
64.0
49
50
1270. 2
1334. 2
1398. 7
1463. 7
1529.1
1595. 2
1661. 7
1728. 9
1796. 7
1865.2
50
51
71.2
35.3
99.8
64.8
30.2
96.3
62.9
30.0
97.9
66.3
51
52
72.3
36.3
1400.9
65.8
31.3
97.4
64.0
31.2
99.0
67.5
52
53
73.4
37.4
01.9
66.9
32.4
98.5
65.1
32.3
1800.1
68.6
53
54
74.4
38.5
03.0
68.0
33.5
99.6
66.2
33.4
01.3
69.8
54
55
1275. 5
1339. 6
1404. 1
1469. 1
1534. 6
1600. 7
1667. 3
1734. 5
1802. 4
1870. 9
55
56
76.6
40.6
05.2
70.2
35.7
01.8
68.4
35.7
03.5
72.1
56
57
77.6
41.7
06.2
71.3
36.8
02.9
69.5
36.8
04.7
73.2
57
58
78.7
42.8
■ 07.3
72.4
37.9
04.0
70.7
37.9
05.8
74.4
58
59
79.7
43.8
08.4
73.5
39.0
05.1
71.8
39.1
07.0
75.5
59
M.
20°
21°
22°
28°
24°
26°
26°
27°
28°
29°
M.
TABLE 3.
[Page 461 |
Meridional Parts, or
Increased Latitudes.
Comp.
1
293.465
M.
80°
31°
82°
38°
34°
35° 36°
87°
38°
39°
M.
0
1876. 7
1946. 0
2016. 0
2086. 8
2158. 4
2230. 9
2304. 2
2378. 5
2453. 8
2530. 2
0
1
77.8
47.1
17.2
88.0
59.6
32.1
05.5
79.8
55.1
31.5
1
2
79.0
48.3
18.3
89.2
60.8
33.3
06.7
81.0
56.4
32.8
2
3
80.1
49.4
19.5
90.3
62.0
34.5
07.9
82.3
57.6
34.0
3
4
81.3
50.6
20.7
91.5
63.2
35.7
09.2
83.5
58.9
35.3
4
5
1882. 4
1951. 8
2021.9
2092. 7
2164.4
2236. 9
2310. 4
2384. 8
2460. 2
2536. 6
5
6
83.6
52.9
23.0
93.9
65.6
38.2
11.6
86.0
61.4
37.9
6
7
84.7
54.1
24.2
95.1
66.8
39.4
12.9
87.3
62.7
39.2
7
8
85.9
55.3
25.4
96.3
68.0
40.6
14.1
88.5
64.0
40.5
8
9
87.0
56.4
26.6
97.5
69.2
41.8
15.3
89.8
65.2
41.7
9
10
1888. 2
1957. 6
2027. 7
2098. 7
2170. 4
2243.0
2316. 5
2391. 0
2466. 5
2543. 0
10
11
89.3
58.7
28.9
99.8
71.6
44.2
17.8
92.3
67.8
44.3
11
12
90.5
59.9
30.1
2101. 0
72.8
45.5
19.0
93.5
69.0
45.6
12
13
91.6
61.1
31.3
02.2
74.0
46.7
20.3
94.8
70.3
46.9
13
14
92.8
62.2
32.4
03.4
75.2
47.9
21.5
96.0
71.6
48.2
14
15
1893. 9
1963. 4
2033. 6
2104. 6
2176. 4
2249. 1
2322. 7
2397. 3
2472. 8
2549. 5
15
16
95.1
64.6
34.8
05.8
77.6
50.3
24.0
98.5
74.1
50.7
16
17
96.2
65.7
36.0
07.0
78.8
51.6
25.2
99.8
75.4
52.0
17
18
97.4
66.9
37.1
08.2
80.0
52.8
26.4
2401. 0
76.6
53.3
18
19
98.5
68.1
38.3
09.4
81.2
54.0
27.7
02.3
77.9
54.6
19
20
1899. 7
1969. 2
2039. 5
2110. 6
2182. 5
2255. 2
2328. 9
2403. 5
2479. 2
2555. 9
20
21
1900. 8
70.4
40.7
11.8
83.7
56.4
30.1
04.8
80.4
57.2
21
22
02.0
71.5
41.8
12.9
84.9
57.7
31.4
06.0
81.7
58.5
22
23
03.1
72.7
43.0
14.1
86.1
58.9
32.6
07.3
83.0
59.8
23
24
04.3
73.9
44.2
15.3
87.3
60.1
33.8
08.5
84.3
61.0
24
25
1905. 5
1975. 0
2045.4
2116.5
2188. 5
2261. 3
2335.1
2409. 8
2485. 5
2562. 3
25
26
06.6
76.2
46.6
17.7
89.7
62.5
36.3
11.1
86.8
63.6
26
27
07.8
77.4
47.7
18.9
90.9
63.8
37.6
12.3
88.1
64.9
27
28
08.9
78.5
48.9
20.1
92.1
65.0
38.8
13.6
89.3
66.2
28
29
10.1
79.7
50.1
21.3
93.3
66.2
40.0
14.8
90.6
67.5
29
30
1911.2
1980. 9
2051. 3
2122. 5
2194. 5
2267. 4
2341. 3
2416. 1
^91.9
2568. 8
30
31
12.4
82.0
52.5
23.7
95.7
68.7
42.5
17.3
^ 93.2
70.1
31
32
13.5
83.2
53.6
24.9
96.9
69.9
43.7
18.6
94.4
71.4
32
33
14.7
84.4
54.8
26.1
98.1
71.1
45.0
19.8
95.7
72.7
33
34
35
15.8
85.5
56.0
27.3
99.4
72.3
46.2
2347. 5
21.1
97.0
73.9
34
1917.0
1986. 7
2057. 2
2128. 5
2200.6
2273. 5
2422. 3
2498. 3
2575. 2
35
36
18.2
87.9
58.4
29.6
01.8
74.8
48.7
23.6
99.5
76.5
36
37
19.3
89.1
59.5
30.8
03.0
76.0
49.9
24.9
2500.8
77.8
37
38
20.5
90.2
60.7
32.0
04.2
77.2
51.2
26.1
02.1
79.1
38
39
21.6
91.4
61.9
33.2
05.4
78.4
52.4
27.4
03.4
80.4
39
40
1922. 8
1992. 6
2063.1
2134. 4
2206. 6
2279. 7
2353. 7
2428. 6
2504.6
2581.7
40
41
23.9
93.7
64.3
35.6
07.8
80.9
54.9
29.9
05.9
83.0
41
42
25.1
94.9
65.5
36.8
09.0
82.1
56.1
31.2
07.2
84.3
42
43
26.3
96.1
66.6
38.0
10.2
83.3
57.4
32.4
08.5
85.6
43
44
27.4
97.2
67.8
39.2
11.5
84.6
58.6
33.7
09.7
86.9
44
45
1928. 6
1998. 4
2069. 0
2140. 4
2212. 7
2285. 8
2359. 9
2434. 9
2511. 0
2588. 2
45
46
29.7
99.6
70.2
41.6
13.9
87.0
61.1
36.2
12.3
89.5
46
47
30.9
2000.7
71.4
42.8
15.1
88.3
62.4
37.4
13.6
90.8
47
48
32.0
01.9
72.6
44.0
16.3
89.5
63.6
38.7
14.8
92.1
48
49
33.2
03.1
73.7
45.2
17.5
90.7
64.8
40.0
16.1
93.4
49
50
1934. 4
2004. 3
2074. 9
2146. 4
2218. 7
2291.9
2366. 1
2441.2
2517. 4
2594. 7
50
51
35.5
05.4
76.1
47.6
19.9
93.2
67.3
42.5
18.7
96.0
51
52
36.7
06.6
77.3
48.8
21.1
94.4
68.6
43.7
20.0
97.3
52
53
37.8
07.8
78.5
50.0
22.4
95.6
69.8
45.0
21.2
98.5
53
54
39.0
08.9
79.7
51.2
23.6
96.9
71.1
2372. 3
46.3
2447.5
22.5
99.8
2601. 1
54
55
55
1940. 2
2010. 1
2080. 8
2152. 4
2224. 8
2298. 1
2523. 8
56
41.3
11.3
82.0
53.6
26.0
99.3
-^73.6
48.8
25.1
02.4
56
57
42.5
12.5
83.2
54.8
27.2
2300. 5
74.8
50.1
26.4
03.7
57
58
43.6
13.6
84.4
56.0
28.4
01.8
76.1
51.3
27.6
05.0
58
59
44.8
14.8
85.6
57.2
29.6
03.0
77.3
52.6
28.9
06.3
59
M,
30°
81°
32°
88°
34°
35°
36°
87°
88°
39°
M.
Page 462J
TABLE 3.
Meridional Parts, or Increased Latitudes.
\
Con^P- 29065
M.
40°
41°
42°
48°
44°
45°
46°
47°
48°
49°
M.
0
2607.6
2686.2
2766. 0
2847.1
2929.5
3013. 4
3098. 7
3185. 6
3274. 1
3364. 4
0
1
08.9
87.6
67.4
48.5
30.9
14.8
3100.1
87.1
75.6
65.9
1
2
10.2
88-9
68.7
49.9
32.3
16.2
01.6 88.5
77.1
67.4
2
3
11.5
90.2
70.1
51.2
33.7
17.6
03.0 ! 90.0
78.6
69.0
3
4
12.8
91.5
71.4
52.6
35.1
19.0
04.4
91.4
80.1
70.5
4
5
2614. 1
2692. 8
2772. 8
2853. 9
2936. 5
3020. 4
3105. 9
3192. 9
3281. 6
3372.0
5
6
15.4
94.2
74.1
55.3
37.9
21.8
07.3 94.4
83.1
73.5
6
7
16.8
95.5
75.4
56. 7 39. 3
23.3
08.8 i 95.8
84.6
75.1
7
8
18.1
96.8
76.8
58. 0 40. 6
24.7
10.2 ; 97.3
86.1
76.6
8
9
19.4
98.1
2699. 5
78.1
59. 4 42. 0
26.1
11. 6 : 98. 8
87.6
78.1
9
10
2620. 7
2779. 5
2860.8 2943.4
3027. 5
3113.1 1 3200.2
3289. 0
3379. 6
10
11
22.0
2700.8
80.8
62.1 44.8
28.9
14.5 01.7
90.5
81.2
11
12
23.3
02.1
82.2
63.5 I 46.2
30.3
16.0 03.2
92.0
82.7
12
13
24.6
03.4
83.5
64.9 47.6
31.7
17.4 , 04.6
93.5
84.2
13
14
25.9
2627.2"
04.8
84.8
66.2 1 49.0
33.2
18.8 1 06.1
95.0
85.7
14
15
2706.1
2786. 2
2867. 6
2950. 4
3034. 6
3120. 3 3207. 6
3296. 5
3387. 3
15
16
28.5
07.4
87.5
69.0
51.8
36.0
21.7 09.0
98.0
88.8
16
17
29.8
08.7
88.9
70.3
53.2
37.4
23.2 10.5
99.5
90.3
17
18
31.1
10.1
90.2
71.7
54.5
38.8
24.6 j 12.0
3301. 0
91.8
18
19
20
32.4
11.4
91.6
73.1
55.9
40.2
26.0 1 13.4
02.5
93.4
19
20
2633. 7
2712. 7
2792. 9
2874.4 ! 2957.3
3041. 7
3127.5 ! 3214.9
3304. 0
3394. 9
21
35.0
14.0
94.3
75. 8 58. 7
43.1
28.9
16.4
05.5
96.4
21
22
36.3
15.4
95.6
77.2 60.1
44.5
30.4
17.9
07.0
98.0
22
23
37.6
16.7
97.0
78.6
61.5
45.9
31.8
19.3
08.5
99.5
23
24
25
38.9
2640. 2
18.0
98.3
79.9
62.9
47.3
33.3.
20.8
10.0
3401.0
24
25
2719. 3
2799. 7
2881. 3
2964.3
3048. 7
3134. 7
3222. 3
3311.5
3402. 6
26
41.6
20.7
2801.0
82.7
65.7
50.2
36.2
23.7
13.0
04.1
26
27
42.9
22.0
02.4
84.0
67.1
51.6
37.6
25.2
14.5
05.6
27
28
44.2
23.3
03.7
85.4
68.5
53.0
39.0
26.7
16.0
07.2
28
29
45.5
24.7
05.1
86.8 i 69.9
. 54.4
40.5
28.2
17.5
08.7
29
30
30
2646. 8
2726. 0
2806. 4
2888.2 2971.3
3055. 9
3141. 9
3229. 6
3319. 0
3410. 2
31
48.1
27.3
07.8
89.5 1 72.7
57.3
43.4
31.1
20.5
11.8
31
32
49.4
28.6
09.1
90. 9 1 74. 1
58.7
44.8
32.6
22.1
13.3
32
33
50.7
30.0
10.5
92.3 75.5
60.1
46.3
34.1
23.6
14.8
33
34
52.0
31.3
11.8
93.7
76.9
61.5
47.7
35.6
25.1
16.4
34
35
2653. 3
2732. 6
2813. 2
2895. 0
2978. 3
3063. 0
3149. 2
3237. 0
3326. 6
3417. 9
35
36
54.7
34.0
14.5
96.4
79.7
64.4
50.6
38.5
28.1
19.5
36
37
56.0
35.3
15.9
97.8
81.1
65.8
52.1
40.0
29.6
21.0
37
38
57.3
36.6
17.2
99.2 1 82.5
67.2
53.5
41.5
31.1
22.5
38
39
58.6
38.0
18.6
2900.5 83.9
68.7
55.0
42.9
32.6
24.1
39
40
2659. 9
2739. 3
2820. 0
2901.9 2985.3
3070. 1
3156. 4
3244. 4
3334. 1
3425. 6
40
41
61.2
40.6
21.3
03.3 86.7
71.5
57.9
45.9
35.6
27.2
41
42
62.5
42.0
22.7
04. 7 88. 1
72.9
59.4
47.4
37.1
28.7
42
43
63.9
43.3
24.0
06.1 89.5
74.4
60.8
48.9
38.6
30.2
43
44
65.2
44.6
25.4
07.4 90.9
75.8
62.3
50.3
40.2
31.8
44
45
2666. 5
2746. 0
2826. 7
2908. 8 2992. 3
3077. 2
3163. 7
3251.8
3341. 7
3433. 3
45
46
67.8
47.3
28.1
10.2 93.7
78.7
65.2
53.3
43.2
34.9
46
47
69.1
48.6
29.4
11.6 95.1 ! 80.1
66.6
54.8
44.7
36.4
47
48
70.4
50.0
30. 8
13. 0 96. 5
81.5
68.1
56.3
46.2
38.0
48
49
71.7
51.3
32.2
14.3 97.9
82.9
69.5
57.8
47.7
39.5
49
50
2673. 1
2752. 7
2833. 5
2915. 7 2999. 3
3084. 4
3171.0
3259. 3
3349. 2
3441.0
50
51
74.4
54.0
34.9
17. 1 - 3000. 7
85.8
72.5
60.7
50.8
42.6
51
52
75.7
55.3
36.2
18. 5 02. 1
87.2
73.9
62.2
52.3
44.1
52
53
77.0
56.7
37.6
19.9 ! 03.5
88.7
75.4
63.7
53.8
45.7
53
54
78.3
58.0
39.0
21.2
2922. 6
04.9
90.1
76.8
65.2
55. 3
47.2
54
55
2679. 6
2759. 3
2840. 3
3006.3
3091.5
3178. 3
3266. 7
3356. 8
3448. 8
55
56
81.0
60.7
41.7
^4.0 07.7
93.0
79.7
68.2
58. 3
50.3
56
57
82.3
62.0
43.0
25.4 09.2
94.4
81.2
69.7
59.9
51.9
57
58
83.6
63.4
44.4
26.8 I 10.6
95.8
82.7
71.1
61.4
53.4
58
59
84.9
64.7
45.8
28.2 12.0
97.3
84.1
72.6
62.9
55.0
59
M.
40°
41°
42°
48° 44°
46°
46°
47°
48°
49°
M.
TABLE 3.
[Page 463 |
Meridional Parts, or
Increased Latitudes.
Com p.
1
293.465
M.
50°
51°
62°
58°
54°
55°
56°
67°
58°
59°
M.
0
3456. 5
3550. 6
3646. 7
3745. 1
3845. 7
3948. 8
4054. 5
4163. 0
4274. 4
4389. 1
0
1
58.1
52.2
48.4
46.7
47.4
50.5
56.3
64.8
76.3
91.0
1
2
59.6
53.8
50.0
48.4
49.1
52.3
58.1
66.6
78.2
92.9
2
3
61.2
55.4
51.6
50.0
50.8
54.0
59.8
68.5
80.1
94.9
3
4
62.7
56.9
53.2
51.7
52.5
55.7
61.6
70.3
82.0
96.8
4
5
3464. 3
3558.5
3654. 8
3753. 4
3854. 2
3957. 5
4063. 4
4172. 1
4283. 9
4398. 8
5
6
65.9
60.1
56.5
55.0
55.9
59.2
65.2
74.0
85.7
4400. 7
6
,7
67.4
61.7
58.1
56.7
57.6
61.0
67.0
75.8
87.6
02.6
7
8
69.0
63.3
59.7
58.3
59.3
62.7
68.8
77.7
89.5
04.6
8
9
70.5
64.9
61.3
60.0
61.0
64.5
70.6
79.5
91.4
06.5
9
10
3472. 1
3566. 5
3663. 0
3761. 7
3862. 7
3966. 2
4072. 4
4181.3
4293. 3
4408. 5
10
11
73.6
68.1
64.6
63.3
64.4
68.0
74.2
83.2
95.2
10.4
11
12
75.2
69.7
66.2
65.0
66.1
69.7
76.0
85.0
97.1
12.4
12
13
76.7
71.3
67.9
66.7
67.8
71.5
77.7
86.9
99.0
14.3
13
14
78.3
72.8
69.5
68.3
69.5
73.2
79.5
88.7
4300.9
16.3
14
15
3479. 9
3574. 4
3671. 1
3770. 0
3871. 2
3975. 0
4081. 3
4190. 6
4302. 8
4418. 2
15
16
81.4
76.0
72.7
71.7
72.9
76.7
83.1
92.4
04.7
20.2
16
17
83.0
77.6
74.4
73.3
74.6
78.5
84.9
94.2
06.6
22.1
17
18
84.5
79.2
76.0
75.0
76.3
80.2
86.7
96.1
08.5
24.1
18
19
86.1
80.8
77.6
76.7
78.1
82.0
88.5
97.9
10.4
26.1
19.
20
3487. 7
3582. 4
3679. 3
3778. 3
3879. 8
3983. 7
4090. 3
4199. 8
4312. 3
4428. 0
20
21
89.2
84.0
80.9
80.0
81.5
85.5
92.1
4201. 6
14.2
30.0
21
22
90.8
85.6
82.5
81.7
83.2
87.2
93.9
03.5
16.1
31.9
22
23
92.4
87.2
84.2
83.3
84.9
89.0
95.7
05.3
18.0
33.9
23
24
93.9
88.8
85.8
85.0
86.6
90.7
97.5
07.2
19.9
35.8
24
25
3495.5
3590. 4
3687. 4
3786. 7
3888. 3
3992. 5
4099.3
4209. 0
4321. 8
4437. 8
25
26
97.1
92.0
89.1
88.4
90.0
94.3
4101.1
10.9
23.7
39.8
26
27
98.6
93.6
90.7
90.0
91.8
96.0
02.9
12.8
25.6
41.7
27
28
3500. 2
95.2
92.3
91.7
93.5
97.8
04.8
14.6
27.5
43.7
28
29
01.8
96.8
94.0
93.4
95.2
99.5
06.6
16.5
29.4
45.7
29
30
3503. 3
3598. 4
3695. 6
3795. 1
3896. 9
4001.3
4108. 4
4218. 3
4331. 3
4447.6
30
31
04.9
3600. 0
97.3
96.8
98.6
03.1
10.2
20.2
33.2
49.6
31
32
06.5
01.6
98.9
98.4
3900.4
04.8
12.0
22.0
35.2
51.6
32
33
08.0
03.2
3700. 5
3800.1
02.1
06.6
13.8
23.9
37.1
53.5
33
34
09.6
04.8
02.2
01.8
03.8
08.3
15.6
25.8
39.0
55.5
34
35
3511. 2
3606.4
3703. 8
3803. 5
3905. 5
4010. 1
4117.4
4227. 6
4340. 9
4457. 5
35
36
12.7
08.0
05.5
05.1
07.2
11.9
19.2
29.5
42.8
59.4
36
37
14.3
09.6
07.1
06.8
09.0
13.6
21.0
31.3
44.7
61.4
37
38
15.9
11.2
08.7
08.5
10.7
15.4
22.9
33.2
46.6
63.4
38
39
17.5
12.8
10.4
10.2
12.4
17.2
24.7
35.1
48.6
65.4
39
40
3519. 0
3614. 5
3712. 0
3811. 9
3914. 1
4018. 9
4126. 5
4236. 9
4350. 5
4467. 3
40
41
20.6
16.1
13.7
13.6
15.9
20.7
28.3
38.8
52.4
69.3
41
42
22.2
17.7
15.3
15.2
17.6
22.5
30.1
40.7
54.3
71.3
42
43
23.7
19.3
17.0
17.0
19.3
24.3
31.9
42.5
56.2
73.3
43
44
25.3
20.9
18.6
18.6
21.0
26.0
33.8
44.4
58.2
75.3
44
45
3526. 9
3622. 5
3720. 3
3820. 3
3922. 8
4027. 8
4135. 6
4246. 3
4360. 1
4477. 2
45
46
28.5
24.1
21.9
22.0
24.5
29.6
37.4
48.1
62.0
79.2
46
47
30.1
25.7
23.6
23.7
26.2
31.4
39.2
50.0
63.9
81.2
47
48
31.6
27.3
25.2
25.4
28.0
33.1
41.0
51.9
65.9
83.2
48
49
33.2
29.0
26.9
27.1
29.7
34.9
42.9
53.8
67.8
85.2
49
50
3534. 8
3630. 6
3728. 5
3828. 7
3931. 4
4036. 7
4144. 7
4255. 6
4369. 7
4487. 2
50
51
36.4
32.2
30.2
30.4
33.2
38.5
46.5
57.5
71.7
89.1
51
52
37.9
33.8
31.8
32.1
34.9
40.2
48.3
59.4
73.6
91.1
52
53
39.5
35.4
33.5
33.8
36.6
42.0
50.2
61.3
75.5
93.1
53
54
41.1
37.0
35.1
35.5
38.4
43.8
52.0
63.1
77.4
95.1
54
55
55
3542. 7
3638. 6
3736. 8
3837. 2
3940. 1
4045. 6
4153. 8
4265. 0
4379. 4
4497.1
56
44.3
40.3
38.4
38.9
41.8
47.4
55.7
66.9
81.3
99.1
56
57
45.9
41.9
40.1
40.6
43.6
49.1
57.5
68.8
83.2
4501. 1
57
58
47.4
43.5
41.7
42.3
45.3
50.9
59.3
70.7
85.2
03.1
58
59
49.0
45.1
43.4
45.0
47.0
52.7
61.1
72.5
87.1
05.1
59
M.
60°
51°
52°
53°
54°
55°
66°
67°
58°
59°
M.
Page 464j
TABLE 3.
Meridional Parts, or
Increased Latitudes.
Comp
1
293.46.5
M.
60°
61°
02°
03°
04°
05°
66°
67°
68°
69°
M.
0
4507. 1
4628. 7
4754. 3
4884. 1
5018. 4
5157. 6
5302. 1
5452. 4
5609. 1
5772. 7
0
1
09.1
30.8
56.4
86.3
20.6
59.9
04.6
55.0
11.8
75.5
1
2
11.1
32^9
34ri9
58.6
88.5
22.9
62.3
07.0
57.6
14.4
78.3
2
3
13.1
60.7
90.7
25.2
64.7
09.5
60.1
17.1
81.1
3
4
15.1
37.0
62.8
92.9
27.5
67.0
11.9
62.7
19.8
83.8
4
5
5
4517.1
4639. 0
4764.9
4895. 1
5029.8
5169. 4
5314. 4
5465. 2
5622. 4
5786. 6
6
19.1
41.1
67.1
97.3
32.1
71.8
16.9
67.8
25.1
89.4
6
7
21.1
43.2
69.2
99.5
34.3
74.2
19.3
70.4
27.8
92.2
/
8
23.1
45.2
71.3
4901. 7
36.6
76.5
21.8
72.9
30.5
95.1
8
9
25.1
47.3
73.5
03.9
38.9
78.9
24.3
75.5
33.2
9%Ji
9
10
10
4527. 1
4649. 4
4775. 6
4906. 1
5041. 2
5181. 3
5326. 7
5477. 1
5635. 9
5800.7
11
29.1
51.5
77.8
08.3
43.5
83.7
29.2
80.7
38.5
03.5
11
12
31.1
53.5
79.9
10.5
45.8
86.0
31.7
83.2
41.2
06.3
12
13
33.1
55.6
82.0
12.8
48.1
88.4
34.2
85.8
43.9
09.1
13
14
35.1
57.7
84.2
15.0
50.4
90.8
36.6
88.4
46.6
11.9
14
15
4537.1
4659. 7
4786. 3
4917. 2
5052. 7
5193. 2
5339. 1
5491.0
5649. 3
5814. 7
15
16
39.2
61.8
88.5
19.4
55.0
95.6
41.6
93.6
52.0
17.6
16
17
41.2
63.9
90.6
21.6
57.3
98.0
44.1
96.2
54.7
20.4
17
18
43.2
66.0
92.8
23.9
59.6
5200.4
46.6
98.7
57.4
23.2
18
19
20
45.2
68.1
94.9
26.1
61.9
02.7
49.1
5501. 3
60.1
26.0
19
4547. 2
4670. 1
4797. 1
4928. 3
5064.2
5205. 1
5351. 5
5503. 9
5662. 8
5828. 9
20
21
49.2
72.2
99.2
30.5
66.5
07.5
54.0
06.5
65.5
31.7
21
22
51.3
74.3
4801.4
32.8
68.8
09.9
56.5
09.1
68.2
34.5
22
23
53.3
76.4
03.5
35.0
71.1
12.3
59.0
11.7
70.9
37.4
23
24
55.3
78.5
05.7
37.2
73.4
14.7
61.5
14.3
73.7
40.2
24
25
4557. 3
4680. 6
4807. 8
4939. 4
5075. 7
5217. 1
5364. 0
5516. 9
5676. 4
5843. 0
25
26
59.3
82.6
10.0
41.7
78.1
19.5
66.5
19.5
79.1
45.9
26
27
61.4
84.7
12.1
43.9
80.4
21.9
69.0
22.1
81.8
48.7
27
28
63.4
86.8
14.3
46.1
82.7
24.3
71.5
24.7
84.5
51.6
28
29
65.4
88.9
16.5
48.4
85.0
26.7
74.0
27.3
87.3
54.4
29
30
4567. 4
4691. 0
4818. 6
4950. 6
5087. 3
5229. 1
5376. 5
5529. 9
5690. 0
5857. 3
30
31
69.5
93.1
20.8
52.9
89.6
•31.6
79.0
32.5
92.7
60.1
31
32
71.5
95.2
23.0
55.1
92.0
34.0
81.5
35.2
95.4
63.0
32
33
73.5
97.3
25.1
57.3
94.3
36.4
84.0
37.8
98.2
65.9
33
34
75.6
99.4
27.3
59.6
96.6
38.8
86.5
40.4
5700. 9
68.7
34
35
4577. 6
4701. 5
4829. 5
4961.8
5098. 9
5241. 2
5389. I
5543. 0
5703. 6
5871. 6
35
36
79.6
03.6
31.6
64.1
5101.3
43.6
91.6
45.6
06.4
74.4
36
37
81.7
05.7
33.8
66.3
03.6
46.0
94.1
48.3
09.1
77.3
37
38
83.7
07.8
36.0
68.6
05.9
48.5
96.6
50.9
11.9
80.2
38
39
85.7
09.9
38.1
70.8
08.3
50.9
99.1
53.5
14.6
83.1
39
40
4587. 8
4712. 0
4840. 3
4973. 1
5110. 6
5253. 3
5401. 6
5556. 1
5717. 3
5885. 9
40
41
89.8
14.1
42.5
75.3
12.9
55.7
04.2
58.8
20.1
88.8
41
42
91.8
16.2
44.7
77.6
15.3
58.2
06.7
61.4
22.8
91.7
42
43
93.9
18.3
46.8
79.8
17.6
60.6
09.2
64.0
25.6
94.6
43
44
95.9
20.4
49.0
82.1
19.9
63.0
11.8
66.7
28.3
97.4
44
45
4598. 0
4722. 5
4851. 2
4984. 3
5122. 3
5265. 4
5414. 3
5569.3
5731. 1
5900. 3
45
46
4600. 0
24.6
53.4
86.6
24.6
67.9
16.8
71.9
33.9
03.2
46
47
02.1
26.7
55.6
88.9
27.0
70.3
19.3
74.6
36.6
06.1
47
48
04.1
28.9
57.8
91.1
29.3
72.8
21.9
77.2
39.4
09.0
48
49
50
06.1
31.0
59.9
93.4
31.7
75.2
24.4
79.9
42.1
11.9
49
4608. 2
4733. 1
4862. 1
4995. 6
5134. 0
5277. 6
5427. 0
5582. 5
5744. 9
5914. 8
50
51
10.2
35.2
64.3
97.9
36.4
80.1
29.5
85.2
47.7
17.7
51
52
12.3
37.3
66.5
5000.2
38.7
82.5
32.0
87.8
50.4
20.6
52
53
14.3
39.4
68.7
02.4
41.1
85.0
34.6
90.5
53.2
23.5
53
54
16.4
41.6
70.9
04.7
43.4
87.4
37.1
93.1
56.0
26.4
54
55
4618. 5
4743. 7
4873. 1
5007. 0
5145. 8
5289. 8
5439. 7
5595. 8
5758. 8
5929. 3
55
56
20.5
45.8
75.3
09.3
48.1
92.3
42.2
98.4
61.5
32.2
56
57
22.6
47.9
77.5
11.5
50.5
94.7
44.8
5601. 1
64.3
35.1
57
58
24.6
50.0
79.7
13.8
52.8
97.2
47.3
03.8
67.1
38.1
58
59
26.7
52.2
81.9
16.1
55.2
99.7
49.9
06.4
69.9
41.0
59
M.
«0°
61°
62°
68°
64°
65°
66°
67°
68°
09°
M.
TABLE 3.
[Page
465
IMeridional Parts, or Increased Latitudes.
Comp.
1
^
'293.4d5
M.
70°
71°
72°
78°
74° 1 75°
76°
77°
78°
79°
M.
0
5943. 9
6123. 5
6312. 5
6512. 0
6723. 2
6947. 7
7187. 3
7444. 4
7721. 6
8022. 7
0
1
46.8
26.6
15.8
15.4
26.8
51.6
91.5
48.8
26.4
27.9
1
2
49.7
29.7
19.0
18.9
30.5
55.4
95.6
53.3
31.3
33.2
2
3
52.7
32.8
22.3
22.3
34.1
59.3
99.7
57.7
36.1
38.5
3
4
55.6
35.8
25.5
25.7
37.7
63.2
7203. 9
62.2
40.9
43.7
4
5
5958. 5
6138. 9
6328. 8
6529. 1
6741.4
6967. 1
7208. 0
7466. 7
7745. 8
8049. 0
5
6
61.5
42.0
32.0
32.6
45.0
70.9
12.2
71.1
50.6
54.3
6
7
64.4
45.1
35.3
36.0
48.7
74.8
16.4
75.6
55.5
59.6
7
8
67.3
48.2
38.5
39. 5
52.3
78.7
20.5
80.1
60.3
64.9
8
9
vj«.3
51.3
41.8
42.9
56.0 ' 82.6
24.7
84.6
65.2
70.2
9
10
5973. 2
6154. 4
6345. 0
6546. 4
6759. 7 6986. 5
7228. 9
7489. 1
7770. 1
8075. 5
10
11
76.2
57.5
48.3
49.8
63.3 90.4
33.1
93.6
74.9
80.8
11
12
79.1
60.6
51.6
53.3
67.0 : 94.3
37.3
98.1
79.8
86.1
12
13
82.1
63,7
54.8
56.7
70.7 ! 98.3
41.5
7502. 6
84.7
91.5
13
14
85.0
66.8
58.1
60.2
74.3
7002.2
45.7
07.1
89.6
96.8
14
15
5988. 0
6169. 9
6361. 4
6563. 7
6778. 0
7006.1
7249. 9
7511.7
7794. 5
8102. 2
15
16
90.9
73.0
64.7
67.1
81.7
10.0
54.1
16.2
99.4
07.5
16
17
93.9
76.1
67.9
70.6
85.4
14.0
58.3
20.7
7804. 3
12.9
17
18
96.9
79.2
71.2
74.1
89.1
17.9
62.5
25.3
09.3
18.3
18
19
99.8
82.3
74.5
77.6
92.8
21.8
66.7
29.8
14.2
23.7
19
20
6002.8
6185. 5
6377. 8
6581. 0
6796. 5 7025. 8
7270. 9
7534. 4
7819. 1
8129. 1
20
21
05.8
88.6
81.1
84.5
6800.2 : 29.7
75.2
38.9
24.1
34.5
21
22
08.7
91.7
84.4
88.0
03. 9 33. 7
79.4
43.5
29.0
39.9
22
23
11.7
94.8
87.7
91.5
07.6 ! 37.7
83.7
48.1
34.0
45.3
23
24
14.7
98.0
91.0
95.0
11.3 41.6
87.9
52.7
39.0
50.8
24
25
6017. 7
6201.1
6394. 3
6598. 5
6815.0 7045.6
7292. 2
7557. 3
7844. 0
8156. 2
25
26
20.7
04.2
97.6
6602. 0
18.8 49.6
96.4
61.8
48.9
61.6
26
27
23.6
07.4
6400. 9
05.5
22. 5 53. 5
7300. 7
66.4
53.9
67.1
27
28
26.6
10.5
04.3
09.0
26. 2 57. 5
05.0
71.0
58.9
72.6
28
29
29.6
13.7
07.6
12.5
.30.0 61.5
09.2
75.7
63.9
78.0
29
30
6032. 6
6216. 8
6410. 9
6616. 1
6833. 7 7065. 5
7313. 5
7580. 3
7868. 9
8183. 5
30
31
35.6
20.0
14.2
19.6
37.4 69.5
17.8
84.9
74.0
89.0
31
32
38.6
23.1
17.6
23.1
41.2 73.5
22.1
89.5
79.0
94.5
32
33
41.6
26.3
20.9
26.6
44.9
77.5
26.4
94.2
84.0
8200.0
33
34
44.6
29.4
24.2
30.2
48.7
81.5
30.7
98.8
89.1
05.5
34
35
6047. 6
6232. 6
6427.6
6633. 7
6852. 4 7085. 5
7335.0
7603. 4
7894. 1
8211. 1
35
36
50.6
35.8
30.9
37.2
56. 2 89. 5
39.3
08.1
99.2
16.6
36
37
53.6
38.9
34.2
40.8
60. 0 93. 5
43.6
12.8
7904. 2
22.1
37
38
56.6
42.1
37.6
44.3
63.7
97.6
47.9
17.4
09.3
27.7
38
39
59.7
45.3
40.9
47.9
67.5
7101.6
52.3
22.1
14.4
33.3
39
40
6062.7
6248. 4
6444.3
6651.4
6871. 3 7105. 6
7356. 6
7626. 8
7919. 4
8238. 8
40
41
65.7
51.6
47.6
55.0
75.1
09.7
60.9
31.4
24.5
44.4
41
42
68.7
54.8
51.0
58.5
78.9
13.7
65.3
36.1
29.6
50.0
42
43
71.7
58.0
54.4
62.1
82.6
17.8
69.6
40.8
34.7
55.6
43
44
45
74.8
61.2
57.7
65.7
86.4
21.8
74.0
45.5
39.9
61.2
44
6077. 8
6264. 4
6461.1
6669.2
6890. 2
7125. 9
7378. 3
7650. 2
7945. 0
8266. 8
45
46
80.8
67.6
64.5
72.8
94.0
29.9
82.7
55.0
50.1
72.4
46
47
83.9
70.8
67.8
76.4
97.8
34.0
87.1
59.7
55.2
78.1
47
48
86.9
74.0
71.2
80.0
6901. 7
38.1
91.4
64.4
60.4
83.7
48
49
89.9
77.2
74.6
83.5
05.5
42.2
95.8
69.1
65.5
89.3
49
50
6093. 0
6280. 4
6478. 0
6687. 1
6909. 3
7146. 2
7400. 2
7673. 9
7970. 7
8295. 0
50
51
96.0
83.6
81.4
90.7
13.1
50.3
04.6
78.6
75.9
8300. 7
51
52
99.1
86.8
84.8
94.3
16.9
54.4
09.0
83.4
81.0
06.4
52
53
6102. 1
90.0
88.2
97.9
20.8
58.5
13.4
88.1
86.2
12.0
53
54
05.2
93.2
91.6
6701. 5
24.6
62.6
17.8
92.9
91.4
17.7
54
55
6108. 2
6296. 4
6495. 0
6705. 1
6928. 4
7166. 7
7422. 2
7697. 7
7996. 6
8323. 4
55
56
11.3
99.6
98.4
08.7
32.3
70.8
26.6
7702. 5
8001.8
29.2
56
57
14.3
6302. 9
6501.8
12.4
36.1
75.0
31.1
07.2
07.0
34.9
57
58
17.4
06.1
05.2
16.0
40.0
79.1
35.5
12.0
12.2
40.6
58
59
20.5
09.3
08.6
19.6
43.8
83.2
39.9
16.8
17.5
46.4
59
M.
70°
71°
72°
78°
74°
75°
76°
77°
78°
79°
M.
22489—03-
-BO-
Page 466]
TABLE 4.
1
Length of
a Degree in Latitude and .
Longitude.
Degree of Long.
Degree of Lat. 1
Lat.
Naut. miles.
statute miles.
Meters.
Naut. miles.
Statute miles.
Meters.
0
0
60.068
69. 172
Ill 321
59. 661
68. 704
110 567
o
0
1
0.059
9.162
1 304
.661
.704
568
1
2
0.^1
59. { 86
9.130
1 253
.662
.705
569
2
3
9.078
1 169
.663
.706
570
3
4
9.922
9.005
1 051
.664
.708
573
4
5
59. 840
68. 911
110 900
59. 666
68. 710
110 576
5
6
9.741
8.795
0 715
.668
.712
580
6
7
9.622
8.660
0 497
.670
.715
584
7
8
9.487
8.504
0 245
.673
.718
589
8
9
9.333
8.326
109 959
.676
.721
595
9
10
59. 161
68.129
109 641
59. 680
68. 725
110 601
10
11
8.971
7.910
9 289
.684
.730
608
11
12
8.764
7.670
8 904
.687
.734
616
. 12
13
8.538
7.410
8 486
.692
.739
624
13
14
8.295
7.131
8 036
.697
.744
633
14
15
58. 034
66. 830
107 553
59. 702
68. 751
110 643
15
16
7.756
6.510
7 036
.707
.757
653
16
17
7.459
6.169
6 487
.713
.764
663
17
18
7.146
5.808
5 906
.719
.771
675
18
19
6.816
5.427
5 294
.725
.778
686
19
20
56. 468
65.026
104 649
59. 732
68. 786
110 699
20
21
6.102
4.606
3 972
.739
.794
712
21
22
5.720
4.166
3 264
.746
.802
725
22
23
5.321
3.706
2 524
.754
.811
739
23
24
4.905
3.228
1 754
.761
.820
68.829
753
24
25
54. 473
62. 729
100 952
59. 769
110 768
25
26
4.024
2.212
0 119
• .777
.839
783
26
27
3.558
1.676
99 257
.786
.848
799
27
28
3.076
1.122
8 364
.795
.858
815
28
29
2.578
0.548
7 441
.804
.869
832
29
30
52.064
59. 956
96 488
59. 813
68. 879
110 849
30
31
1.534
9.345
5 506
.822
.890
866
31
32
0.989
8.716
4 495
.831
.901
883
32
33
0.428
8.071
3 455
.841
.912
901
33
34
49.851
7.407
2 387
.851
.923
919
34
35
49. 259
56. 725
91 290
59. 861
68. 935
110 938
35
36
8.653
6.027
0 166
.871
.946
956
36
37
8.031
5.311
89 014
.881
.958
975
37
38
7.395
4:579
7 835
.891
.969
994
38
39
6.744
3.829
6 629
.902
.981
111 013
39
40
46. 079
53.063
85 396
59. 912
68. 993
111 033
40
41
5.399
2.281
4 137
.923
69.006
052
41
42
4.706
1.483
2 853
.933
.018
072
42
43
4.000
0.669
1 543
.944
.030
091
43
44
3.280
49. 840
0 208
.954
.042
111
44
45
2.546
8.995
78 849
.965
.054
131
45
TABLE 4.
[Page 467 |
Length of
a Degree in Latitude and Longitude.
Degree of Long.
Degree of Lat.
Lat.
Naut. miles.
Statute miles.
Meters.
Naut. miles.
Statute miles.
Meters.
0
46
42. 546
48. 995
78 849
59. 965
69. 054
Ill 131
o
45
46
1.801
8.136
7 466
.976
.066
151
46
47
1.041
7.261
6 058
.987
.079
170
47
48
0.268
6.372
4 628
.997
.091
190
48
49
39. 484
5.469
3 174
60. 008
.103
210
49
50
50
38. 688
44.552
71 698
60. 019
69. 115
111 229
51
7.880
3.621
0 200
.029
.127
249
51
52
7.060
2.676
68 680
.039
.139
268
52
53
6.229
1.719
7 140
.050
.151
287
53
54
5.386
0.749
5 578
.060
.163
306
54
55
34. 532
39. 766
63 996
60. 070
69. 175
111 325
55
56
3.668
8.771
2 395
.080
.086
343
56
57.
2.794
7.764
0 774
.090
.197
362
57
58
1.909
6.745
59 135
.100
.209
380
58
59
1.015
5.716
7 478
.109
.220
397
59
60
30. 110
34. 674
55 802
60. 118
69. 230
111 415
60
61
29. 197
3.623
4 110
.128
.241
432
61
62
8.275
2.560
2 400
.137
.251
448
62
63
7.344
1.488
0 675
,145
.261
464
63
64
6.404
0.406
48 934
.154
.271
480
64
65
25. 456
29. 315
47 177
60.162
69. 281
111 496
65
66
4.501
8.215
5 407
.170
.290
511
66
67
3.538
7.106
3 622
.178
.299
525
67
68
2.567
5.988
1 823
.186
.308
539
68
69
1.590
4.862
0 012
.193
.316
553
69
70
20. 606
23. 729
38 188
60.200
69. 324
111 566
70
71
19. 616
2.589
6 353
.207
.332
578
71
72
8.619
1.441
4 506
.213
.340
590
72
73
7.617
0.287
2 648
.220
.347
602
73
74
6.609
19. 127
0 781
.225
.354
613
74
75
15. 596
17. 960
28 903
60. 231
69. 360
111 623
75
76
4.578
6.788
7 017
.236
.366
633
76
77
3.556
5.611
5 123
.241
.372
642
77
78
2.529
4. 428
3 220
.246
.377
650
78
79
1.499
3.242
1 311
.250
.382
658
79
80
10. 465
12. 051
19 394
60.254
69. 386
111 665
80
81
9.428
10.857
7 472
.257
.390
671
81
82
8.388
9.659
5 545
.260
.394
677
82
83
7.345
8.458
3 612
,263
.397
682
83
84
6.300
7.255
1 675
.265
.400
687
84
85
5.253
6.049
9 735
60.268
69. 402
111 691
85
86
4.205
4.842
7 792
.269
.404
694
86
87
3.154
3.632
5 846
.270
,405
696
87
88
2.103
2.422
3 898
.271
,407
698
88
89
1.052
1.211
1 949
.272
.407
699
89
90
0
0
0
.272-
.407
699
90
Page 468]
TABLE
5A.
Distance of an Object by Two Bearings.
Difference
between
Difference between the course and first bearing?, in
points.
the course
and second
bearing, in
points.
2
2K
2H
2
%
» 1
8Ji
^% 1
3
1.96
1.09
3i
1.57
0.94
'2.19
1.31
3J
1.32
0.84
1.76
1.12
2.42
1. 58
3f
1.14
0.76
1.47
0.99
1.94
1.30
2.64
1.77
4
1.00
0.71
1.27
0.90
1.62
1.15
2.12
1.50
2.85
2.01
%
4i
0.90
0.66
1.12
0.83
1.40
1.04
1.77
1.31
2.29
1.69
3.05
2.26
4J
0.81
0.63
1.00
0.77
1.23
0.95
1.53
1.18
1.91
1.48
2.45
1.90
3.25
2.51
4|
0.74
0.60
0.91
0.73
1.10
0.89
1.34
1.08
1.65
1.32
2.05
1.65
2.61
2.10
5
0.69
0.57
0.83
0.69
1.00
0.83
1.20
1.00
1.45
1.21
1.77
1.47
2.19
1.82
5\
0.64
0.55
0.77
0.66
0.92
0.79
1.09
0.94
1.30
1.11
1.56
1.34
1.88
1.62
5J
0.60
0.53
0.72
0.63
0.85
0.75
1.00
0.88
1.18
1.04
1.39
1.23
1.66
1.46
5|
0.57
0.52
0.68
0.61
0.79
0.72
0.93
0.84
1.08
0.98
1.26
1.14
1.48
1.34
6
0.54
0.50
0.64
0.59
0.74
0.69
0.86
0.80
1.00
0.92
1.16
1.07
1.35
1.24
6}
0.52
0.49
0.60
0.57
0.70
0.66
0.81
0.76
0.93
0.88
1.07
1.01
1.23
1.16
6J
0.50
0.47
0.58
0.55
0.67
0.64
0.77
0.73
0.88
0.84
1.00
0.96
1.14
1.09
6|
0.48
0.46
0.55
0.54
0.64
0.62
0.73
0.71
0.83
0.80
0.94
0.91
1.06
1.03
7
0.46
0.45
0.53
0.52
0.61
0.60
0.69
0.68
0.79
0.77
0.89
0.87
1.00
0.98
7k
0.45
0.44
0.51
0.51
0.59
0.58
0.67
0.66
0.75
0.74
0.84
0.83
0.94
0.93
n
0.43
0.43
0.50
0.50
0.57
0.56
0.64
0.64
0.72
0.72
0.80
0.80
0.90
0.89
n
0.42
0.42
0.48
0.48
0.55
0.55
0.62
0.62
0.69
0.69
0.77
0.77
0.86
0.86
8
0.41
0.41
0.47
0.47
0. 53
0.53
0.60
0.60
0.67
0.67
0.74
0.74
0.82
0.82
8J
0.41
0.41
0.46
0.46
0.52
0.52
0.58
0.58
0.65
0.65
0.72
0.72
0.79
0.79
8J
0.40
0.40
0.45
0.45
0.51
0.51
0.57
0.57
0.63
0.63
0.69
0.69
0.76
0.76
8f
0.39
0.39
0.45
0.44
0.50
0.50
0.56
0.55
0.61
.0.61
0.68
0.67
0.74
0.73
9
0.39
0.38
0.44
0.43
0.49
0.48
0.55
0.54
0.60
0.59
0.66
0.65
0.72
0.71
n
0.39
0.38
0.44
0.42
0.49
0.47
0.54
0.52
0.59
0.57
0.64
0.63
0.70
0.68
n
0.38
0.37
0.43
0.41
0.48
0.46
0.53
0. 51
0.58
0.56
0.63
0.61
0.69
0.66
91
0.38
0.36
0.43
0.40
0.48
0.45
0.52
0.49
0.57
0.54
0.62
0.59
0.67
0.63
10
0.38
0.35
0.43
0.40
0.47
0.44
0.52
0.48
0.57
0.52
0.61
0.57
0.66
0.61
lOJ-
0.38
0.35
0.43
0.39
0.47
0.43
0.52
0.47
0.56 '\ 0.51
0.61
0.55
0.&5
0.59
m
0.38
0.34
0.43
0.38
0.47
0.42
0.51
0.45
0.56
0.49
0.60
0.53
0.65
0.57
10|
0.39
0.33
0.43
0.37
0.47
0.40
0.51
0.44
0.56
0.48
0.60
0.51
0.64
0.55
11
0.39
0.32
0.43
0.36
0.47
0. 39
0.51
0.43
0.56
0.46
0.60
0.50
0.64
0.53
lU
0.39
0.31
0.44
0.35
0.48
0.38
0.52
0.41
0.56
0.45
0.60
0.48
0.64
0.51
iij
0.40
0.31
0.44
0.34
0.48
0.37
0.52
0.40
0.56
0.43
0.60
0.46
0.63
0.49
111
0.41
0.30
0.45
0.33
0.49
0.36
0.52
0.39
0.56
0.42
0.60
0.44
0.64
0.47
12
0.41
0.29
0.45
0.32
0.49
0. 35
0.53
0.37
0.57
0.40
0.60
0.43
0.64
0.45
12i
0.42
0.28
0.46
0.31
0.50
0.34
0.54
0.36
0.57
0.38
0.61
0.41
0.64
0.42
12J
0.43
0.28
0.47
0.30
0.51
0.32
0.55
0.35
0.58
0.37
0.61
0.39
0.65
0.41
12|
0.45
0.27
0.48
0.29
0.52
0.31
0.56
0.33
0.59
0. 35
0.62
0.37
0.65
0.39
13
0.46
0.26
0.50
0.28
0.53
0.30
0.57
0.32
0.60
0.33
0.63
0. 35
0.66
0.37
n\
0.48
0.24
0.51
0.26
0. 55
0.28
0.58
0.30
0.61
0.32
0.64
0.33
0.67
0.35
l^
0.50
0.23
0.53
0.25
0.57
0.27
0.60
0.28
0.63
0.30
0.66
0.31
0.69
0.32
13|
0.52
0.22
0.55
0.24
0.59
0.25
0.62
0.26
0.65
0.28
0.68
0.29
0.70
0.30
14
0.54
0.21
0.58
0.22
0.61
0. 23
0.64
0.24
0.67
0.26
0.69
0.27
0.72
0.28
TABLE
5A.
[Page 469 |
Distance of an Object by Two Bearings.
Difference
between
the course
Difference between the course and first bearing, in points.
and second
bearing, in
points.
8K
4
*V*
4M
*r*
5
5K 1
4f
3.44
2.76
5
2.76
2.30
3.62
3.01
5i
2.31
1.98
2.91
2.50
3.80
3.26
5^
1.99
1.76
2.44
2.15
3.05
2.69
3.96
3.49
5f
1.75
1.59
2.10
1.90
2.55
2.31
3.18
2.88
4.12
3.72
6
1.57
1.45
1.85
1.71
2.20
2.03
2.66
2.46
3.31
3. 05
4.26
.3.94
6i
1.42
1.34
1.65
1.56
1.94
1.82
2.29
2. 16
2.77
2.61
,3.42
3.22
4.40
4.14
6^
1.31
1.25
1.50
1.44
1.73
1.66
2.02
1.93
2.38
2.28
2.86
2.74
3.53
3.38
6|
1.21
1.17
1.38
1.33
1.57
1. 52
1.81
1.75
2.10
2.04
2.47
2.39
2.95
2.87
7
1.13
1.11
1.27
1.25
1.44
1.41
1.64
1.61
1.88
1.84
2.17
2.13
2.55
2.50
7i
1.06
1.05
1. 19
1.17
1.33
1.32
1.50
1.49
1.70
1.69
1.94
1.92
2.24
2.22
7i
1.00
1.00
1.11
1.11
1.24
1.24
1.39
1. 38
1.56
1.55
1.76
1.76
2.01
2.00
71
0.95
0.95
1.05
1.05
1.17
1.17
1.30
1.30
1.45
1.44
1.62
1.62
1.82
1.82
8 ■
0.91
0.91
1.00
1.00
1.10
1.10
1.22
1.22
1.35
1.35-
1.50
1.50
1.67
1.67
8i
0.87
0.87
0.95
0.95
1.05
1.05
1.15
1.15
1.27
1.26
1.40
1.39
1.54
1.54
8i
0.84
0.83
0.91
0.91
1.00
1.00
1.09
1.09
1.20
1.19
1.31
1.30
1.44
1.43
8|
0.81
0.80
0.88
0.87
0.96
0.95
1.04
1.03
1.14
1.12
1.24
1.22
1.35
1.34
9
0.78
0.77
0.85
0.83
0.92
0.90
1.00
0.98
1.08
1.06
1.18
1.15
1.28
1.25
9i
0.76
0.74
0.82
0.80
0.89
0.86
0.96
0.93
1.04
1.01
1.12
1.09
1.21
1.18
9i
0.74
0.71
0.80
0.77
0.86
0.83
0.93
0.89
1.00
0.96
1.08
1.03
1.16
1.11
91
0.73
0.68
0.78
0.74
0.84
0.79
0.90
0.&5
0.97
0.91
1.04
0.97
1.11
1.04
10
0.71
0.66
0.77
0.71
0.82
0.76
0.88
0.81
0.94
0.87
1.00
0.92
1.07
0.99
lOi
0.70
0.63
0.75
0.68
0.80
0.72
0.86
0.77
0.91
0.82
0.97
0.88
1.03
0.93
m
0.69
0.61
0.74
0.65
0.79
0.69
0.84
0.74
0.89
0.78
0.94
0.83
1.00
0.88
101
0.68
0.59
0.73
0.63
0.77
0.66
0.82
0.70
0.87
0.75
0.92
0.79
0.97
0.83
11
0.68
0.56
0.72
0.60
0.76
0.64
0.81
0.67
0.85
0.71
0.90
0.75
0.95
0.79
lU
0.67
0.54
0.71
0.57
0.76
0.61
0.80
0.64
0.84
0.67
0.88
0.71
0.93
0.75
lU
0.67
0.52
0.71
0.55
0.75
0.58
0.79
0.61
0.83
0.64
0.87
0.67
0.91
0.70
111
0.67
0.50
0.71
0.52
0.74
0.55
0.78
0.58
0.82
0.61
0.86
0.64
0.90
0.66
12
0.67
0.48
0.71
0.50
0.74
0.52
0.78
0.55
0.81
0.57
0.85
0.60
0.88
0.63
12i
0.67
0.45
0.71
0.48
0.74
0.50
0.77
0.52
0.81
0.54
0.84
0.56
0.87
0.59
m
0.68
0.43
0.71
0.45
0.74
0.47
0.77
0.49
0.80
0.51
0.84
0.53
0.87
0.55
12|
0.68
0.41
0.71
0.43
0.74
0.44
0.77
0.46
0.80
0.48
0.83
0.50
0.86
0.51
13
0.69
0.38
0.72
0.40
0.75
0.42
0.78
0.43
0.80
0.45
0.83
0.46
0.86
0.48
131^
0.70
0.36
0.73
0.37
0.76
0.39
0.78
0.40
0.81
0.41
0.83
0.43
0.86
0.44
13J
0.71
0.34
0.74
0. 35
0.76
0.36
0.79
0.37
0.81
0.38
0.84
0.39
0.86
0.41
131
0.73
0.31
0.75
0..32
0.77
0.33
0.80
0.34
0.82
0.35
0.84
0.36
0.86
0.37
14
0.74
0.28
0.77
0.29
0.79
0.30
0.81
0.31
0.83
0.32
0.85
0.32
0.87
0.33
o%
oVa
6
«^
6^
6K
' 1
6J
4.52
4.33
6|
3.63
3.52
4.63
4.49
7
3.04
2.98
3.72
3.65
4.74
4.64
7i
2.62
2.59
3.11
3.08
3.80
3.76
4.83
4.77
7i
2.30
2.29
2.68
2.67
3.18
3.17
3.87
3.86
4.91
4.88
7f
2.06
2.06
2.36
2.36
2.74
2.74
3.24
3.24
3.94
3.93
4.97
4.97
8
1.87
1.87
2.11
2.11
2.41
2.41
2.79
2.79
3.30
3.30
.3.99
3.99
5.03
5.03
8i
1.72
1.71
1.92
1.92
2.16
2.16
2.46
2. 46
2.84
2.84
3.34
3.34
4.04
4.03
8^
1.59
1.58
1.76
1.75
1.96
1.95
2.20
2.19
2.50
2.49
2.88
2.87
3.38
3.36
8f
1.48
1.46
1.63
1.61
1.80
1.78
2.00
1.98
2.24
2.21
2.53
2.51
2.91
2.88
9
1.39
1.36
1.52
1.49
1.66
1.63
1.83
1.80
2.03
1.99
2.27
2.23
2.56
2.51
9i
1.31
1.27
1.42
1.38
1.55
1.50
1.69
1.64
1.86
1.81
2.06
2.00
2.29
2.23
9^
1.25
1.19
1.35
1.29
1.46
1.39
1.58
1.51
1.72
1.65
1.89
1.81
2.08
1.99
9|
1.19
1.12
1.28
1.20
1.38
1.30
1.48
1.40
1.61
1.51
1.75
1.64
1.91
1.80
10
1.14
1.05
1.22
1.13
1.31
1.21
1.40
1.30
1.51
1.39
1.62
1.50
1.77
1.63
lOi
1.10
0.99
1.17
1.06
1.25
1.13
1.33
1.20
1.42
1.29
1.53
1.38
1.65
1.49
lOi
1.06
0.94
1.13
0.99
1.20
1.05
1.27
1.12
1.35
1.19
1.44
1.27
1.55
1.36
101
1.03
0.88
1.09
0.93
1.15
0.99
1.22
1.04
1.29
1.11
1.37
1.18
1.46
1.25
11
1.00
0.83
1.05
0.88
1.11
0.92
1.17
0.97
1.24
1.03
1.31
1.09
1.39
1.15
lU
0.98
0.78
1.03
0.82
1.08
0.87
1.13
0.91
1.19
0.96
1.25
1.01
1.32
1.06
lU
0.95
0.73
1.00
0.77
1.05
0.81
1.10
0.85
1.15
0.89
1.21
0.93
1.27
0.98
111
0.94
0.69
0.98
0.72
1.02
0.76
1.07
0.79
1.12
0.83
1.17
0.86
1.22
0.90
12
0.92
0.65
0.96
0.68
1.00
0.71
1.04
0.73
1.09
0.77
1.13
0.80
1.18
0.83
12i
0.91
0.61
0.94
0.63
0.98
0.66
1.02
0.68
1.06
0.71
1.10
0.74
1.14
0.77
12J
0.90
0.57
0.93
0.59
0.97
0.61
1.00
0.63
1.04
0.66
1.07
0.68
1.11
0.71
12|
0.89
0.53
0.92
0.55
0.95
0.57
0.98
0.59
1.02
0.61
1.05
0.63
1.08
0.65
13
0.89
0.49
0.91
0.51
0.94
0.52
0.97
0.54
1.00
0.56
1.03
0.57
1.06
0.59
13i
0.88
0.45
0.91
0.47
0.93
0.48
0.96
0.49
0.99
0.51
1.01
0.52
1.04
0.54
13J
0.88
0.42
0.91
0.43
0.93
0.44
0.95
0.45
0.98
0.46
1.00
0.47
1.02
0.48
13|
0.88
0.38
0.90
0.39
0.92
0.40
0.95
0.41
0.97
0.41
0.99
0.42
1.01
0.43
14
0.89
0.34
0.91
0.35
0.92
0.35
0.94
0.36
0.90
0.37
0.98
0.38
1.00
0.38
Page 470] TABLE 5A.
Distance of an Object by Two Bearings.
Difference
between
Difference between the course and first bearing, in points.
the course
and second
bearing, in
points.
IK
J^
7K
8
W*
»%
m
9
8i
5.07
5.06
•
'
8J
4.07
4.05
5.10
5.08
8|
3.41
3.37
4.10
4.06
5.12
5.06
9
2.94
2.88
3.43
3.36
4.11
4.03
5.13
5.03
n
2.58
2.51
2.95
2.87
3.44
3.34
4.12
3.39
5.12
4.97
H
2.31
2.21
2.60
2.49
2.96
2.84
3.44
3.30
4.11
3.93
5.10
4.88
n
2.10
1.98
2.33
2.19
2.61
2.46
2.97
2.79
3.44
3.24
4.10
3.86
5.07
4.77
10
1.92
1.78
2.11
1.95
2.34
2.16
2.61
2.41
2.96
2.74
3.43
3.17
4.07
3.76
5.03
4.64
10^
1.78
1.61
1.93
1.75
2.12
1.92
2.34
2.11
2.61
2.36
2.95
2.67
3.41
3.08
4.04
3.65
10^
1.66
1.46
1.79
1.58
1.94
1.71
2.12
1.87
2.34
2.06
2.60
2.29
2.94
2.59
3.38
2.98
10|
1.56
1.34
1.67
1.43
1.80
1.54
1.95
1.67
2.12
1.82
2.33
2.00
2.58
2.22
2.91
2.50
11
1.47
1.22
1.57
1.30
1.68
1.39
1.80
1.50
1.94
1.62
2.11
1.76
2.31
1.92
2.56
2.13
lU
1.40
1.12
1.48
1.19
1.57
1.26
1.68
1.35
1.80
1.44
1.93
1.55
2.10
1.69
2.29
1.84
lu
1.34
1.03
1.41
1.09
1.49
1.15
1.58
1.22
1.68
1.30
1.79
1.38
1.92
1.49
2.08
1.61
111
1.28
0.95
1.34
1.00
1.41
1.05
1.49
1.10
1.57
1.17
1.67
1.24
1.78
1.32
1.91
1.41
12
1.23
0.87
1.29
0.91
1.35
0.95
1.41
1.00
1.49
1.05
1.57
1.11
1.66
1.17
1.77
1.25
m
1.19
0.80
1.24
0.83
1.29
0.87
1.35
0.91
1.41
0.95
1.48
1.00
1.56
1.05
1.65
1.11
12i
1.15
0.73
1.20
0.76
1.24
0.79
1.29
0.82
1.35
0.86
1.41
0.89
1.47
0.93
1.55
0.98
12|
1.12
0.67
1.16
0.69
1.20
0.72
1.25
0.74
1.29
0.77
1.34
0.80
1.40
0.83
1.46
0.87
13
1.09
0.61
1.13
0.63
1.16
0.65
1.20
0.67
1.24
0.69
1.29
0.72
1.34
0.74
1.39
0.77
m
1.07
0.55
1.10
0.57
1.13
0.58
1.17
0.60
1.20
0.62
1.24
0.64
1.28
0.66
1.32
0.68
m
1.05
0.50
1.08
0.51
1.10
0.52
1.13
0.53
1.16
0.55
1.20
0.56
1.23
0.58
1.27
0.60
131
1.03
0.44
1.06
0.45
1.08
0.46
1.11
0.47
1.13
0.48
1.16
0.50
1.19
0.51
1.22
0.52
14
1.02
0.39
1.04
0.40
1.06
0.41
1.08
0.41
1.10
0.42
1.13
0.43
1.15
0.44
1.18
0.45
»K
95^
9%
10
lOK
im
lOK
» 1
lOi
4.97
4.50
10^
3.99
3.52
4.91
4.33
101
3.34
2.87
3.94
3.38
4.83
4.14
11
2.88
2.39
3.30
2.74
3.87
3.22
4.74
3.94
lU
2.53
2.04
2.84
2.28
3.24
2.61
3.80
3.05
4.63
3.72
lU
2.27
1.75
2.50
1.93
2.79
2.16
3.18
2.46
3.72
2.88
4.52
3.49
111
2.06
1.52
2.24
1.66
2.46
1.82
2.74
2.03
3.11
2.31
3.63
2.69
4.40
3.20
12
1.89
1.33
2.03
1.44
2.20
1.56
2.41
1.71
2.68
1.90
3.04
2.15
3.53
2.50
4.26
3.01
m
1.75
1.18
1.86
1.25
2.00
1.34
2.16
1.45
2.36
1.59
2.62
1.76
2.95
1.98
3.42
2.30
m
1.62
1.03
1.72
1.09
1.83
1.16
1.96
1.24
2.11
1..34
2.30
1.46
2.55
1.62
2.86
1.82
121
1.53
0.91
1.61
0.96
1.69
1.01
1.80
1.07
1.92
1.14
2.06
1.23
2.24
1.34
2.47
1.47
13
1.44
0.80
1.51
0.84
1.58
0.88
1.66
0.92
1.76
0.98
1.87
1.04
2.01
1.11
2.17
1.21
m
1.37
0.71
1.42
0.73
1.48
0.76
1.55
0.80
1.63
0.84
1.72
0.88
1.82
0.94
1.94
1.00
m
1.31
0.62
1.35
0.64
1.40
0.66
1.46
0.69
1.52
0.72
1.59
0.75
1.67
0.79
1.76
0.83
13|
1.25
0.54
1.29
0.55
1.33
0.57
1.38
0.59
1.42
0.61
1.48
0.63
1.54
0.66
1.62
0.69
14
1.21
0.46
1.24
0.47
1.27
0.49
1.31
0.50
1.35
0.52
1.39
0.53
1.44
0.55
1.50
0.57
UK
11
'A
llji
12
I'zy, 1
t'2%
12'/i
u 1
12i
4.12
2.77
i
m
3.31
2.10
3.96
2.51
12|
2.77
1.65
3.18
1.90
3.80
2.26
13
2.38
1.32
2.66
1.48
3.05
1.69
3.62
2.01
m
2.10
1.08
2.29
1.18
2.55
1.31
2.91
1.50
3.44
1.77
13i
1.88
0.89
2.02
0.95
2.20
1.04
2.44
1.15
2.76
1.30
3.25
1.53
13|
1.70
0.73 1.81
0.77
1.94
0.83
2.10
0.90
2.31
0.99
2.61
1.12
3.05
1.31
14
1.56
0.60 1.64
0.63
1.73
0.66
1.85
0.71
1.99
0.76
2.19
0.84
2.45
0.94
2.85
1.09
TABLE
5B.
[Page 471 |
Distance of an Object by Two Bearings.
Difference
between
the course
and second
bearing.
Difference between the course and first bearing.
20°
22°
24°
26°
28°
80°
a
2°
30°
1.97
0.98
32
1.64
0.87
2.16
1.14
34
1.41
0.79
1.80
1.01
2.34
1.31
36
1.24
0.73
1.55
0.91
1.96
1.15
2.52
1,48
38
1.11
0.68
1.36
0.84
1,68
1.04
2.11
1,30
2.70
1.66
40
1.00
0.64
1.21
0.78
1.48
0.95
1.81
1,16
2.26
1,45
2.88
1.85
42
0.91
0.61
1.10
0.73
1.32
0.88
1.59
1.06
1.94
1,30
2.40
1.61
3.05
2,04
44
0.84
0.58
1.00
0.69
1.19
0.83
1.42
0.98
1.70
1.18
2.07
1.44
2.55
1,77
46
0.78
0.56
0.92
0.66
1.09
0.78
1.28
0.92
1.52
1.09
1.81
1.30
2.19
1,58
48
0.73
0.54
0.85
0.64
1.00
0.74
1.17
0.87
1.37
1.02
1.62
1.20
1,92
1,43
50
0.68
0.52
0.80
0.61
0.93
0.71
1.08
0.83
1.25
0.96
1.46
1.12
1.71
1.31
52
0.65
0.51
0.75
0.59
0.87
0.68
1.00
0.79
1.15
0.91
1.33
1.05
1.55
1.22
54
0.61
0.49
0.71
0.57
0.81
0.66
0.93
0.76
1.07
0.87
1.23
0.99
1.41
1.14
56
0.58
0.48
0.67
0.56
0.77
0.64
0.88
0.73
1.00
0.83
1.14
0.95
1.30
1.08
58
0.56
0.47
0.64
0.54
0.73
0.62
0.83
0.70
0.94
0.80
1.07
0.90
1.21
1.03
60
0.53
0.46
0.61
0.53
0.69
0.60
0.78
0.68
0.89
0.77
1.00
0.87
1.13
0.98
62
0.51
0.45
0.58
0.51
0.66
0.58
0.75
0.66
0.84
0,74
0.94
0.83
1.06
0.94
64
0.49
0.44
0.56
0.50
0.63
0.57
0.71
0.64
0.80
0.72
0.89
0.80
1.00
0.90
66
0.48
0.43
0.54
0.49
0.61
0.56
0.68
0.62
0.76
0.70
0.85
0.78
0.95
0.87
68
0.46
0.43
0.52
0.48
0.59
0.54
0.66
0.61
0,73
0.68
0.81
0,75
0.90
0.84
70
0.45
0.42
0.50
0.47
0.57
0.53
0.63
0.59
0.70
0.66
0.78
0.73
0.86
0.81
72
0.43
0.41
0.49
0.47
0.55
0.52
0.61
0.58
0.68
0.64
0.76
0.71
0.82
0.78
74
0.42
0.41
0.48
0.46
0.53
0.51
0.59
0.57
0.65
0.63
0.72
0.69
0.79
0.76
76
0.41
0.40
0.46
0.45
0.52
0.50
0.57
0.56
0.63
0.61
0.70
0.67
0.76
0.74
78
0.40
0.39
0.45
0.44
0.50
0.49
0.56
0.54
0,61
0.60
0.67
0.66
0.74
0.72
80
0.39
0.39
0.44
0.44
0.49
0.48
0.54
0.53
0.60
0.59
0.65
0.64
0.71
0.70
82
0.39
0.38
0.43
0.43
0.48
0.47
0.53
0.52
0,58
0,57
0.63
0,63
0.69
0.69
84
0.38
0.38
0.42
0.42
0.47
0.47
0.52
0.51
0.57
0,56
0.62
0,61
0.67
0.67
86
0.37
0.37
0.42
0.42
0.46
0.46
0.51
0.51
0.55
0.55
0.60
0,60
0.66
0.65
88
0.37
0.37
0.41
0.41
0.45
0.45
0.50
0.50
0.54
0.54
0.59
0,59
0.64
0.64
90
0.36
0.36
0.40
0.40
0.45
0.45
0.49
0.49
0.53
0.53
0.58
0.58
0.62
0.62
92
0.36
0.36
0.40
0.40
0.44
0.44
0.48
0.48
0.52
0.52
0.57
0.57
0.61
0.61
94
0.36
0.35
0.39
0.39
0.43
0.43
0.47
0.47
0.51
0.51
0.56
0.55
0.60
0.60
96
0.35
0.35
0.39
0.39
0.43
0.43
0.47
0.46
0.51
0.50
0.55
0.54
0.59
0.59
98
0.35
0.35
0.39
0.38
0.42
0.42
0.46
0.46
0,50
0.50
0.54
0.53
0.58
0.57
100
0.35
0.34
0.38
0.38
0.42
0.41
0.46
0.45
0,49
0.49
0.53
0.52
0.57
0.56
102
0.35
0.34
0.38
0.37
0.42
0.41
0.45
0.44
0.49
0.48
0.53
0.51
0.56
0.55
104
0.34
0.33
0.38
0.37
0.41
0.40
0.45
0.43
0.48
0.47
0.52
0.50
0.56
0.54
106
0.34
0.33
0.38
0.36
0.41
0.39
0.45
0.43
0.48
0.46
0.52
0.50
0.55
0.53
108
0.34
0.32
0.38
0.36
0.41
0.39
0.44
0.42
0.48
0.45
0.51
0.49
0.55
0.52
110
0.34
0.32
0.37
0.35
0.41
0.38
0.44
0.41
0.47
0.44
0.51
0.48
0.54
0,51
112
0.34
0.32
0.37
0.35
0.41
0.38
0.44
0.41
0,47
0.44
0.50
0.47-
0.54
0,50
114
0.34
0.31
0.37
0.34
0.41
0.37
0.44
0.40
0,47
0.43
0:50
0.46
0.54
0.49
116
0.34
0.31
0.38
0.34
0.41
0.37
0.44
0.39
0,47
0.42
0.50
0.45
0.53
0.48
118
0.35
0.31
0.38
0.33
0.41
0.36
0.44
0.39
0.47
0.41
0.50
0.44
0.53
0.47
120
0.35
0.30
0.38
0.33
0.41
0.36
0.44
0.38
0.47
0.41
0.50
0.43
0.53
0,46
122
0. 35
0.30
0.38
0.32
0.41
0.35
0.44
0.37
0,47
0,40
0.50
0.42
0.53
0,45
124
0.35
0.29
0.38
0.32
0.41
0.34
0.44
0.37
0.47
0.39
0.50
0.42
0.53
0.44
126
0.36
0.29
0.39
0.31
0.42
0.34
0.45
0.36
0.47
0.38
0.50
0,41
0.53
0.43
128
0.36
0.28
0.39
0.31
0.42
0.33
0.45
0,35
0.48
0.38
0.50
0,40
0.53
0.42
130
0.36
0.28
0.39
0.30
0.42
0.32
0.45
0.35
0.48
0.37
0.51
0.39
0.54
0.41
132
0.37
0.27
0.40
0.30
0,43
0.32
0.46
0.34
0.48
0.36
0.51
0.38
0.54
0.40
134
0.37
0.27
0.40
0.29
0.43
0.31
0.46
0.33
0.49
0.35
0.52
0.37
0.54
0.39
136
0.38
0.26
0.41
0.28
0.44
0.30
0.47
0.32
0.49
0.34
0.52
0.36
0.55
0.38
138
0.39
0.26
0.42
0.28
0.45
0.30
0.47
0.32
0.50-
0. 33
0.53
0.35
0.55
0.37
140
0.39
0.25
0.42
0.27
0.45
0.29
0.48
0.31
0.51
0. 33
0.53
0.34
0.56
0.36
142
0.40
0.25
0.43
0.27
0.46
0.28
0.49
0.30
0.51
0.32
0.54
0.33
0.56
0.35
144
0.41
0.24
0.44
0.26
0.47
0.28
0.50
0.29
0.52
0.31
0.55
0.32
0.57
0.34
146
0.42
0.24
0.45
0.25
0.48
0.27
0.51
0.28
0.53
0.30
0.56
0.31
0.58
0,32
148
0.43
0 23
0.46
0.25
0.49
0.26
0.52
0.27
0.54
0.29
0.57
0,30
0.59
0.31
150
0.45
0.22
0.48
0.24
0.50
0.25
0.53
0.26
0.55
0.28
0.58
0,29
0.60
0.30
152
0.46
0.22
0.49
0.23
0.52
0.24
0.54
0.25
0.57
0.27
0.59
0,28
0.61
0.29
154
0.48
0.21
0.50
0.22
0.53
0.23
0.56
0.24
0.58
0.25
0.60
0 26
0. 62
0.27
156
0.49
0.20
0.52
0.21
0.55
0.22
0.57
0.23
0.60
0.24
0.62
0 25
0.64
0.26
158
0.51
0.19
0.54
0.20
0.57
0.21
0.59
0.22
0.61
0.23
0.63
0.24
0.66
0.25
160
0.53
0.18
0.56
0.19
0.59
0.20
0.61
0.21
0.63
0,22
0.65
0.22
0.67
0.23
1 Page 472]
TABLE 5B.
Distance of an Object by Two Bearings.
Difference
between
the cours*
and secoiu
bearing.
Difference between the course and first bearing.
a:°
Z6°
i>
8°
40°
42°
44°
46°
44°
3.22
i
2.24
46
2.69^ 1.93
3.39
2.43
48
2.31 1 1.72
2.83
2.10
3.55
2.63
50
2. 03 i 1. 55
2.43
1.86
2.96
2.27
.3.70
2.84
52
1.81 ! 1.43
2.13
1.68
2.54
2.01
3.09
2.44
3.85
3.04
54
1.63| 1.32
1.90
1.54
2.23
1.81
2.66
2.15
3.22
2.60
4.00
3.24
56
1.49 1 1.24
1.72
1.42
1.99
1.65
2. .33
1.93
2.77
2: 29
3.34
2.77
4.14
3.43
58
1.37
1.17
1.57
1.33
1.80
1.53
2.08
1.76
2.43
2.06
2.87
2.44
3.46
2.93
60
1.28
1.10
1.45
1.25
1.64
1.42
1.88
1.63
2.17
1.88
2.52
2.18
2.97
2.57
62
1.19
1.05
1.34
1.18
1.51
1.34
1.72
1.52
1.96
1.73
2.25
1.98
2.61
2.30
64
1.12
1.01
1.25
1.13
1.40
1.26
1.58
1.42
1.79
1.61
2.03
1.83
2.33
2.09
66
1.06
0.96
1.18
1.07
1.31
1.20
1.47
1.34
1.65
1.51
1.85
1.69
2.10
1.92
68
1.00
0.93
1.11
1.03
1.23
1.14
1.37
1.27
1.53
1.42
1.71
1.58
1.92
1.78
70
0.95
0.89
1.05
0.99
1.16
1.09
1.29
1.21
1.43
1.34
1.58
1.49
1.77
1.66
72
0.91
0.86
1.00
0.95
1.10
1.05
1.21
1.15
1.34
1.27
1.48
1.41
1.64
1.56
74
0.87
0.84
0.95
0.92
1.05
1.01
1.15
1.10
1.26
1.21
1.39
1.34
1.53
1.47
76
0.84
0.81
0.91
0.89
1.00
0.97
1.09
1.06
1.20
1.16
1.31
1.27
1.44
1.40
78
0.80
0.79
0.88
0.86
0.96
0.94
1.04
1.02
1.14
1.11
1.24
1.22
1.36
1.33
80
0.78
0.77
0.85
0.83
0.92
0.91
1.00
0.98
1.09
1.07
1.18
1.16
1.28
1.27
82
0.75
0.75
0.82
0.81
0.89
0.88
0.96
0.95
1.04
1.03
1.13
1.12
1.22
1.21
84
0.73
0.73
0.79
0.79
0.86
0.85
0.93
0.92
1.00
0.99
1.08
1.07
1.17
1.16
86
0.71
0.71
0.77
0.77
0.83
0.83
0.89
0.89
0.96
0.96
1.04
1.04
1.12
1.12
88
0.69
0.69
0.75
0.75
0.80
0.80
0.86
0.86
0.93
0.93
1.00
1.00
1.08
1.07
90
0.67
0.67
0.73
0.73
0.78
0.78
0.84
0.84
0.90
0.90
0.97
0.97
1.04
1.04
92
0.66
0.66
0.71
0.71
0.76
0.76
0.82
0.82
0.87
0.87
0.93
0.93
1.00
1.00
94
0.65
0.64
0.69
0.69
0.74
0.74
0.79
0.79
0.85
0.85
0.91
0.90
0.97
0.97
96
0.63
0.63
0.68
0.67
0.73
0.72
0.78
0.77
0.83
0.82
0.88
0.88
0.94
0.93
98
0.62
0.62
0.67
0.66
0.71
0.70
0.76
0.75
0.81
0.80
0.86
0.85
0.91
0.90
100
0.61
0.60
0.65
0.64
0.70
0.69
0.74
0.73
0.79
0.78
0.84
0.83
0.89
0.88
102
0. 60 ' 0. 59
0.64
0.63
0.68
0.67
0.73
0.71
0.77
0.76
0.82
0.80
0.87
0.85
104
0. 60 0. 58
0.63
0.61
0.67
0.65
0.72
0.69
0.76
0.74
0.80
0.78
0.85
0.82
106
0. 59 1 0. 57
0.63
0.60
0.66
0.64
0.70
0.68
0.74
0.72
0.79
0.76
0.83
0.80
108
0. 58 ' 0. 55
0.62
0.59
0.66
0.62
0.69
0.66
0.73
0.70
0.77
0.74
0.81
0.77
110
0. 58 1 0. 54
0.61
0.57
0.65
0.61
0.68
0.64
0.72
0.68
0.76
0.71
0.80
0.75
112
0. 57 1 0. 53
0.61
0.56
0.64
0.59
0.-68
0.63
0.71
0.66
0.75
0.69
0.79
0.73
114
0. 57 i 0. 52
0.60
0.55
0.63
0.58
0.67
0.61
0.70
0.64
0.74
0.68
0.78
0.71
116
0. 56 1 0. 51
0.60
0.54
0.63
0.57
0.66
0.60
0.70
0.63
0.73
0.66
0.77
0.69
118
0. 56 1 0. 50
0.59
0.52
0.63
0.55
0.66
0.58
0.69
0.61
0.72
0.64
0.76
0.67
120
0. 56 I 0. 49
0.59
0.51
0.62
0.54
0.65
0.57
0.68
0.59
0.72
0.62
0.75
0.65
122
0.56
0.47
0.59
0.50
0.62
0.53
0.65
0.55
0.68
0.58
0.71
0.60
0.74
0.63
124
0.56
0.46
0.59
0.49
0.62
0.51
0.65
0.54
0.68
0.56
0.71
0.58
0.74
0.61
126
0. 56 0. 45
0.59
0.48
0.62
0.50
0.64
0.52
0.67
0.54
0.70
0.57
0.73
0.59
128
0.56
0.44
0.59
0.46
0.62
0.49
0.64
0.51
0.67
0.53
0.70
0.55
0.73
0.57
130
0.56
0.43
0.59
0.45
0.62
0.47
0.64
0.49
0.67
0.51
0.70
0.53
0.72
0.55
132
0.56
0.42
0.59
0.44
0.62
0.46
0.64
0.48
0.67
0.50
0.70
0.52
0.72
0.54
134
0.57
0.41
0.59
0.43
0.62
0.45
0.64
0.46
0.67
0.48
0.69
0.50
0.72
0.52
136
0.57
0.40
0.60
0.41
0.62
0.43
0.65
0.45
0.67
0.47
0.70
0.48
0.72
0.50
138
0. 58 : 0. 39
0.60
0.40
0.63
0.42
0.65
0.43
0.67
0.45
0.70
0.47
0.72
0.48
140
0. 58 0. 37
0.61
0.39
0.63
0.40
0.65
0.42
0.68
0.43
0.70
0.45
0.72
0.46
142
0. 59 0. 36
0.61
0.38
0.63
0.39
0.66
0.41
0.68
0.42
0.70
0.43
0.72
0.45
144
0. 60 0. 35
0.62
0.36
0.64
0.38
0.66
0.39
0.68
0.40
0.71
0.41
0.73
0.43
146
0.60
0.34
0.63
0.35
0.65
0.36
0.67
0.37
0.69
0..39
0.71
0.40
0.73
0.41
148
0.61
0.32
0.63
0.34
0.66
0..35
0.68
0.36
0.70
0.37
0.72
0.38
0.74
0.39'
150
0.62
0.31
0.64
0.32
0.66
0.33
0.68
0.34
0.70
0.35
0.72
0.36
0.74
0.37
152
0.63
0.30
0.65
0.31
0.67
0.32
0.69
0.33
0.71
0.33
0.73
0.34
0.75
0.35
154
0.65
0.28
0.67
0.29
0.68
0.30
0.70
0.31
0.72
0.32
0.74
0.32
0.76
0.33
156
0.66
0.27
0.68
0.28
0.70
0.28
0.72
0.29
0.73
0.30
0.75
0.30
0.77
0.31
158
0.67
0.25
0.69
0.26
0.71
0.27
0.73
0.27
0.74
0.28
0.76
0.28
0.78
0.29
160
0.69
0.24
0.71
0.24
0.73
0.25
0.74
0.25
0.76
0.26
0.77
0.26
0.79
0.27
TABLE 5B.
[Page 473 |
Distance of an Object by Two Bearings.
Difference
Difference between the course and first bearing.
between
the course
and second
bearing.
48°
50°
5
2°
54°
56°
58°
60°
58°
4.28
3.63
60
3.57
3.10
4.41
3.82
62
3.07
2.71
3.68
3.25
4.54
4.01
64
2.70
2.42
3.17
2.85
3.79
3.41
4.66
4.19
66
2.40
2.20
2.78
2.54
3.26
2.98
3.89
3.55
4.77
4.36
68
2.17
2.01
2.48
2.30
2.86
2.65
3.34
3.10
3.99
3.71
4.88
4.53
70
1.98
1.86
2.24
2.10
2.55
2.39
2.94
2.76
3.43
3.22
4.08
3.83
4.99
4.69
>72
1.83
1.74
2.04
1.94
2.30
2.19
2.62
2.49
3.01
2.86
3.51
3.33
4.17
3.96
74
1.70
1.63
1.88
1.81
2.10
2.02
2.37
2.27
2.68
2.58
3.08
2.96
3.58
3.44
76
1.58
1.54
1.75
1.70
1.94
1.88
2.16
2.10
2.42
2.35
2.74
2.66
3.14
3.05
78
1.49
1.45
1.63
1.60
1.80
1.76
1.99
1.95
2.21
2.16
2.48
2.43
2.80
2.74
80
1.40
1.38
1.53
1.51
1.68
1.65
1.85
1.82
2.04
2.01
2.26
2.23
2.53
2.49
82
1.33
1.32
1.45
1.43
1.58
1.56
1.72
1.71
1.89
1.87
2.08
2.06
2.31
2.29
84
1.26
1.26
1.37
1.36
1.49
1.48
1.62
1.61
1.77
1.76
1.93
1.92
2.13
2.12
86
1.21
1.20
1.30
1..30
1.41
1.41
1.53
1.52
1.66
1.65
1.81
1.80
1.98
1.97
88
1.16
1.16
1.24
1.24
1.34
1.34
1.45
1.45
1.56
1.56
1.70
1.70
1.84
1.84
90
1.11
1.11
1.19
1.19
1.28
1.28
1.38
1.38
1.48
1.48
1.60
1.60
1.73
1.73
92
1.07
1.07
1.14
1.14
1.23
1.23
1.31
1.31
1.41
1.41
1.52
1.52
1.63
1.63
94
1.03
1.03
1.10
1.10
1.18
1.17
1.26
1.26
1.35
1.34
1.44
1.44
1.55
1.54
96
1.00
0.99
1.06
1.06
1.13
1.13
1.21
1.20
1.29
1.28
1.38
1.37
1.47
1.47
98
0.97
0.96
1.03
1.02
1.10
1.08
1.16
1.15
1.24
1.23
1.32
1.31
1.41
1.39
100
0.94
0.93
1.00
0.98
1.06
1.04
1.12
1.11
1.19
1.18
1.27
1.25
1.35
1.33
102
0.92
0.90
0.97
0.95
1.03
1.01
1.09
1.06
1.15
1.13
1.22
1.19
1.29
1.27
104
0.90
0.87
0.95
0.92
1.00
0.97
1.06
1.02
1.12
1.08
1.18
1.14
1.25
1.21
106
0.88
0.84
0.92
0.89
0.97
0.94
1.03
0.99
1.09
1.04
1.14
1.10
1.20
1.16
108
0.86
0.82
0.90
0.86
0.95
0.90
1.00
0.95
1.05
1.00
1.11
1.05
1.17
1.11
110
0.84
0.79
0.88
0.83
0.93
0.87
0.98
0.92
1.02
0.96
1.08
1.01
1.13
1.06
112
0.83
0.77
0.87
0.80
0.91
0.84
0.95
0.88
1.00
0.93
1.05
0.97
1.10
1.02
114
0.81
0.74
0.85
0.78
0.89
0.82
0.93
0.85
0.98
0.89
1.02
0.93
1.07
0.98
116
0.80
0.72
0.84
0.75
0.88
0.79
0.92
0.82
0.96
0.85
1.00
0.90
1.04
0.94
118
0.79
0.70
0.83
0.73
0.86
0.76
0.90
0.79
0.94
0.83
0.98
0.86
1.02
0.90
J 20
0.78
0.68
0.82
0.71
0.85
0.74
0.89
0.77
0.91
0.80
0.96
0.83
1.00
0.87
122
0.77
0.66
0.81
0.68
0.84
0.71
0.87
0.74
0.90
0.77
0.95
0.80
0.98
0.83
124
0.77
0.63
0.80
0.66
0.83
0.69
0.86
0.71
0.90
0.74
0.93
0.77
0.96
0.80
126
0.76
0.61
0.79
0.64
0.82
0.66
0.85
0.69
0.88
0.71
0.91
0.74
0.95
0.77
128
0.75
0.59
0.78
0.62
0.81
0.64
0.84
0.66
0.87
0.69
0.90
0.71
0.93
0.74
130
0.75
0.57
0.78
0.60
0.81
0.62
0.83
0.64
0.86
0.66
0.89
0.68
0.92
0.71
132
0.75
0.56
0.77
0.57
0.80
0.59
0.83
0.61
0.85
0.64
0.88
0.66
0.91
0.68
134
0.74
0.54
0.77
0.55
0.80
0.57
0.82
0.59
0.85
0.61
0.87
0.63
0.90
0.65
136
0.74
0.52
0.77
0.53
0.80
0.55
0.82
0.57
0.84
0.58
0.87
0.60
0.89
0.62
138
0.74
0.50
0.77
0.51
0.79
0.53
0.81
0.54
0.84
0.56
0.86
0.58
0.89
0.59
140
0.74
0.48
0.77
0.49
0.79
0.51
0.81
0.52
0.83
0.54
0.86
0.55
0.88
0.57
142
0.74
0.46
0.77
0.47
0.79
0.49
0.81
0.50
0.83
0.51
0.85
0.52
0.87
0.54
144
0.75
0.44
0.77
0.45
0.79
0.46
0.81
0.48
0.83
0.49
0.85
0.50
0.87
0.51
146
0.75
0.42
0.77
0.43
0.79
0.44
0.81
0.45
0.83
0.46
0.85
0.47
0.87
0.49
148
0.76
0.40
0.77
0.41
0.79
0.42
0.81
0.43
•0.83
0.44
0.85
0.45
0.87
0.46
150
0.76
0.38
0.78
0.39
0.80
0.40
0.81
0.41
0.83
0.42
0.85
0.42
0.87
0.43
152
0.77
0.36
0.78
0.37
0.80
0.38
0.82
0.38
0.83
0.39
0.85
0.40
0.87
0.41
154
0.77
0.34
0.79
0.35
0.81
0.35
0.82
0.36
0.84
0.37
0.85
0.37
0.87
0.38
156
0.78
0.32
0.80
0.32
0.81
0.33
0.83
0.34
0.84
0.34
0.86
0.35
0.87
0.35
158
0.79
0.30
0.81
0.30
0.82
0.31
0.83
0.31
0.85
0.32
0.86
0.32
0.87
0.33
160
0.80
0.27
0.82
0.28
0.83
0.28
0.84
0.29
0.85
0. 29
0.86
0.30
0.88
0.30
Page 474] TABLE 5B.
Distance of an Object by Two Bearings.
Difference
between
the course
Difference between the course and first bearing.
and second
bearing.
62°
«4°
66°
68°
70°
72°
74°
76°
72°
5.08
i
4.84
\
74
4.25
4.08
5.18
4.98
76
3.65
3.54
4.32
4.19
5.26
5.10
78
3.20
3.13
3.72
3.63
4.39
4.30
5.34
5.22
80
2.86
2.81
3.26
3.21
3.78
3.72
4.46
4.39
5.41
5.33
82
2.58
2.56
2.91
2.88
3.31
3.28
3.83
3.80
4.52
4.48
5.48
5. 42
84
2.36
2.34
2.63
2.61
2.96
2.94
3.36
3.35
3.88
3.86
4.57
4.55
5.54
5.51
86
2.17
2.17
2.40
2.39
2.67
2.66
3.00
2.99
3.41
3.40
3. 93
3.92
4.62
4.61
5.59
5.57
88
2.01
2.01
2.21
2.21
2.44
2.44
2.71
2.71
3.04
3.04
3.45
3.45
3.97
3.97
4.67
4.66
90
1.88
1.88
2.05
2.05
2.25
2.25
2.48
2.48
2.75
2.75
3.08
3.08
3.49
3.49
4.01
4.01
92
1.77
1.76
1.91
1.91
2.08
2.08
2.28
2.28
2.51
2.51
2.78
2.78
3.11
3.11
3.52
3.52
94
1.67
1.66
1.80
1.79
1.95
1.94
2.12
2.11
2.31
2.30
2.54
2.53
2.81
2.80
3.14
3.13
96
1.58
1.57
1.70
1.69
1.83
1.82
1.97
1.96
2.14
2.13
2.34
2. 33
2.57
2.55
2.84
2.82
98
1.50
1.49
1.61
1.59
1.72
1.71
1.85
1.84
2.00
1.98
2.17
2.15
2.36
2.34
2.59
2.56
100
1.43
1.41
1.53
1.51
1.63
1.61
1.75
1.72
1.88
1.85
2.03
2.00
2.19
2.16
2.39
2.35
102
1.37
1.34
1.46
1.43
1.55
1.52
1.66
1.62
1.77
1.73
1.90
1.86
2.05
2.00
2.21
2.16
104
1.32
1.28
1.40
1.36
1.48
1.44
1.58
1.53
1.68
1.63
L79
1.74
1.92
1.87
2.07
2.01
106
1.27
1.22
1.34
1.29
1.42
1.37
1.51
1.45
1.60
1.54
1.70
1.63
1.81
1.74
1.94
1.87
108
1.23
1.17
1.29
1.23
1.37
1.30
1.44
1.37
1.53
1.45
1.62
1.54
1.72
1.63
1.83
1.74
110
1.19
1.12
1.25
1.17
1.32
1.24
1.39
1.30
1.46
1.37
1.54
1.45
1.64
1.54
1.74
1.63
112
1.15
1.07
1.21
1.12
1.27
1.18
1.33
1.24
1.40
1.30
1.48
1.37
1.56
1.45
1.65
1.53
114
1.12
1.02
1.17
1.07
1.23
1.12
1.29
1.18
1.35
1.24
1.42
1.30
1.50
1.37
1.58
1.44
116
1.09
0.98
1.14
1.03
1.19
1.07
1.25
1.12
1.31
1.17
1.37
1.23
1.44
1.29
1.51
1.36
118
1.07
0.94
1.11
0.98
1.16
1.02
1.21
1.07
1.26
1.12
1.32
1.17
1.38
1.22
1.45
1.28
120
1.04
0.90
1.08
0.94
1.13
0.98
1.18
1.02
1.23
1.06
1.28
1.11
1.34
1.16
1.40
1.21
122
1.02
0.86
1.06
0.90
1.10
0.93
1.15
0.97
1.19
1.01
1.24
1.05
1.29
1.10
1.35
1.14
124
1.00
0.83
1.04
0.86
1.08
0.89
1.12
0.93
1.16
0.96
1.21
1.00
1.25
1.04
1.31
1.08
126
0.98
0.79
1.02
0.82
1.05
0.85
1.09
0.88
1.13
0.92
1.18
0.95
1.22
0.99
1.27
1.02
128
0.97
0.76
1.00
0.79
1.03
0.82
1.07
0.84
1.11
0.87
1. lo
0.90
1.19
0.94
1.23
0.97
130
0.95
0.73
0.98
0.75
1.02
0.78
1.05
0.80
1.09
0.83
1.12
0. 86
1.16
0.89
1.20
0.92
132
0.94
0.70
0.97
0.72
1.00
0.74
1.03
0.77
1.06
0.79
1.10
0.82
1.13
0.84
1.17
0.87
134
0.93
0.67
0.96
0.69
0.99
0.71
1.01
0.73
1.04
0.75
1.08
0.77
1.11
0.80
1.14
0.82
136
0.92
0.64
0.95
0. 66
0.97
0.68
1.00
0.69
1.03
0.71
1. 06
0.74
1.09
0. 76
1.12
0.78
138
0.91
0.61
0.94
0.63
0.96
0.64
0.99
0.66
1.01
0.68
1.04
0.70
1.07
0.72
1.10
0.74
140
0.90
0.58
0.93
0.60
0.95
0.61
0.97
0.63
1.00
0.64
1 . 03
0.66
1.05
0.68
1.08
0.70
142
0.90
0.55
0.92
0.57
0.94
0.58
0.96
0.59
0.99
0.61
1.01
0.62
1.04
0.64
1.06
0.65
144
0.89
0.52
0.91
0.54
0.93
0.55
0.96
0.56
0.98
0.57
1.00
0.59
1.02
0.60
1.05
0. 62
146
0.89
0.50
0.91
0.51
0.93
0.52
0.95
0.53
0.97
0.54
0.99
0.55
1.01
0.57
1.03
0.58
148
0.89
0.47
0.90
0.48
0.92
0.49
0.94
0.50
0.96
0.51
0.98
0.52
1.00
0.53
1.02
0.54
150
0.88
0.44
0.90
0.45
0.92
0.46
0.94
0.47
0.95
0.48
0.97
0.49
0.99
0.50
1.01
0.50
152
0.88
0.41
0.90
0.42
0.92
0.43
0.93
0.44
0.95
0.45
0.97
0.45
0.98
0.46
1.00
0.47
154
0.88
0.39
0.90
0.39
0.91
0.40
0.93
0.41
0.94
0.41
0.96
0.42
0.98
0. 43
0.99
0.43
156
0.89
0.36
0.90
0.37
0.91
0.87
0.93
0.38
0.94
0.38
0.96
0.39
0.97
0. 39
0.99
0.40
158
0.89
0.33
0.90
0.34
0.91
0.34
0.93
0.35
0.94
0. 35
0.95
0. 36
0.97
0. 36
0.98
0.37
160
0.89
0.30
0.90
0.31
0.91
0.31
0.93
0.32
0.94
0.32
0.95
0.33
0.96
0.33
0.98
0.33
TABLE 5B. [Page
475
Distance of an Object by Two Bearings.
Difference
Difference between the course and first bearing.
between
the course
and second
bearing.
78°
80°
82°
84°
86°
88°
90°
92°
88°
5.63
5.63
90
4.70
4.70
5.67
5.67
92
4.04
4.04
4.74
4.73
5.70
5.70
94
3.55
3.54
4.07
4.06
4.76
4.75
5.73
5.71
96
3.17
3.15
3.57
3.55
4.09
4.07
4.78
4.76
5.74
5.71
98
2.86
2.83
3.19
3.16
3.59
3.56
4.11
4.07
4.80
4.75
5.76
5.70
100
2.61
2.57
2.88
2.84
3.20
3.16
3.61
3.55
4.12
4.06
4.81
4.73
5.76
5.67
102
2.40
2.35
2.63
2.57
2.90
2.83
3.22
3.15
3.62
3.54
4.13
4.04
4.81
4.70
5.76
5.63
104
2.23
2.16
2.42
2.35
2.64
2.56
2.91
2.82
3.23
3.13
3.63
3.52
4.13
4.01
4.81
4.66
106
2.08
2.00
2.25
2.16
2.43
2.34
2.65
2.55
2.92
2.80
3.23
3.11
3.63
3.49
4.13
3.97
108
1.96
1.86
2.10
2.00
2.26
2.15
2.45
2.33
2.66
2.53
2.92
2.78
3.24
3.08
3.63
3.45
110
1.85
1.73
1.97
1.85
2.11
1.98
2.27
2.13
2.45
2.31
2.67
2.51
2.92
2.75
3.23
3.04
112
1.75
1.62
1.86
1.72
1.98
1.83
2.12
1.96
2.28
2.11
2.46
2.28
2.67
2.48
2.92
2.71
114
1.66
1.52
1.76
1.61
1.87
1.71
1.99
1.82
2.12
1.94
2.28
2.08
2.46
2.25
2.67
2.44
116
1.59
1.43
1.68
1.51
1.77
1.59
1.88
1.69
2.00
1.79
2.13
1.91
2.28
2.05
2.46
2.21
118
1.52
1.34
1.60
1.41
1.68
1.49
1.78
1.57
1.88
1.66
2.00
1.76
2.13
1.88
2.28
2.01
120
1.46
1.27
1.53
1.33
1.61
1.39
1.69
1.47
1.78
1.54
1.89
1.63
2.00
1.73
2.13
1.84
122
1.41
1.19
1.47
1.25
1.54
1.31
1.62
1.37
1.70
1.44
1.79
1.52
1.89
1.60
2.00
1.70
124
1.36
1.13
1.42
1.18
1.48
1.23
1.55
1.28
1.62
1.34
1.70
1.41
1.79
1.48
1.89
1.56
126
1.32
1.06
1.37
1.11
1.43
1.15
1.48
1.20
1.55
1.26
1.62
1.31
1.70
1.38
1.79
1.45
128
1.28
1.01
1.33
1.04
1.38
1.08
1.43
1.13
1.49
1.17
1.55
1.23
1.62
1.28
1.70
1.34
130
1.24
0.95
1.29
0.98
1.33
1.02
1.38
1.06
1.44
1.10
1.49
1.14
1.56
1.19
1.62
1.24
132
1.21
0.90
1.25
0.93
1.29
0.96
1.34
0.99
1.39
1.03
1.44
1.07
1.49
1.11
1.55
1.16
134
1.18
0.85
1.22
0.88
1.26
0.90
1.30
0.93
1.34
0.97
1.39
1.00
1.44
1.04
1.49
1.07
136
1.15
0.80
1.19
0.83
1.22
0.85
1.26
0.88
1.30
0.90
1.34
0.93
1.39
0.97
1.44
1.00
138
1.13
0.76
1.16
0.78
1.19
0.80
1.23
0.82
1.27
0.85
1.30
0.87
1.35
0.90
1.39
0.93
140
1.11
0.71
1.14
0.73
1.17
0.75
1.20
0.77
1.23
0.79
1.27
0.82
1.31
0.84
1.34
0.86
142
1.09
0.67
1.12
0.69
1.14
0.70
1.17
0.72
1.20
0.74
1.24
0.76
1.27
0.78
1.30
0.80
144
1.07
0.63
1.10
0.64
1.12
0.66
1.15
0.67
1.18
0.69
1.21
0.71
1.24
0.73
1.27
0.75
146
1.05
0.59
1.08
0.60
1.10
0.62
1.13
0.63
1.15
0.64
1.18
0.66
1.21
0.67
1.24
0.69
148
1.04
0.55
1.06
0.56
1.08
0.57
1.11
0.59
1.13
0.60
1.15
0.61
1.18
0.62
1.21
0.64
150
1.03
0.51
1.05
0.52
1.07
0.53
1.09
0.54
1.11
0.55
1.13
0.57
1.15
0.58
1.18
0.59
152
1.02
0.48
1.04
0.49
1.05
0.49
1.07
0.50
1.09
0.51
1.11
0.52
1.13
0.53
1.15
0.54
154
1.01
0.44
1.02
0.45
1.04
0.46
1.06
0.46
1.08
0.47
1.09
0.48
1.11
0.49
1.13
0.50
156
1.00
0.41
1.01
0.41
1.03
0.42
1.05
0.43
1.06
0.43
1.08
0.44
1.09
0.45
1.11
0.45
158
0.99
0.37
1.01
0.38
1.02
0.38
1.03
0.39
1.05
0.39
1.06
0.40
1.08
0.40
1.09
0.41
160
0.99
0.34
1.00
0.34
1.01
0.35
1.02
0.35
1.04
0.35
1.05
0.36
1.06
0.36
1.08
0.37
94°
96°
98°
100°
102°
104°
106°
108° 1
104°
5.74
5.57
106
4.80
4.61
5.78
5.51
108
4.12
3.92
4.78
4.55
5,70
5.42
110
3.62
3.40
4.11
3.86
4.76
4.48
5.67
5.33
112
3.23
2.99
3.61
3.35
4.09
3.80
4.74
4.40
5.63
5.22
114
2.92
2.66
3.22
2.94
3.59
3.28
4.07
3.72
4.70
4.30
5.59
5.10
116
2.66
2.39
2.91
2.61
3.20
2.88
3.57
3.21
4.04
3.63
4.67
4.19
5.54
4.98
118
2.45
2.17
2.65
2.34
2.90
2.56
3.19
2.81
3.55
3.13
4.01
3.54
4.62
4.08
5.48
4.84
120
2.28
1.97
2.45
2.12
2.64
2.29
2.88
2.49
3.17
2.74
3.52
3.05
3. 97 ! 3. 44
4.57
3.96
122
2.12
1.80
2.27
1.92
2.43
2.06
2.63
2.23
2.86
2.43
3.14
2.66
3. 49 1 2. 96
3.93
3.33
124
2.00
1.65
2.12
1.76
2.26
1.87
2. 42 i 2. 01
2.61
2.16
2.84
2.35
3.11
2.58
3.45
2.86
126
1.88
1.52
1.99
1.61
2.11
1.71
2.25
1.82
2.40
1.95
2.59
2.10
2.81
2.27
3.08
2.49
128
1.78
1.41
1.88
1.48
1.98
1.56
2.10
1.65
2.23
1.76
2.39
1.88
2.57
2.02
2.78
2.19
130
1.70
1.30
1.78
1.36
1.87
1.43
1.97
1.51
2.08
1.60
2.21
1.70
2.36
1.81
2.54
1.94
132
1.62
1.20
1.69
1.26
1.77
1.32
1.86
1.38
1.96
1.45
2.07
1.54
2.19
1.63
2.34
1.74
134
1.55
1.12
1.62
1.16
1.68
1.21
1.76
1.27
1.85
1.33
1.94
1.40
2.05
1.47
2.17
1.56
136
1.49
1.04
1.55
1.07
1.61
1.12
1.68 1.16
1.75
1.22
1.83
1.27
1.92
1.34
2.03
1.41
138
1.44
0.96
1.49
0.99
1.54
1.03
1.60
1.07
1.66
1.11
1.74
1.16
1.81
1.21
1.90
1.27
140
1.39
0.89
1.43
0.92
1.48
0.95
1.53
0.98
1.59
1.02
1.65
1.06
1.72
1.10
1.79
1.15
142
1.34
0.83
1.38
0.85
1.43
0.88
1.47
0.91
1.52
0.94
1.58
0.97
1.64
1.01
1.70
1.05
144
1.30
0.77
1.34
0.79
1.38
0.81
1.42
0.83
1.46
0.86
1.51
0.89
1.56
0.92
1.62
0.95
146
1.27
0.71
1.30
0.73
1.33
0.75
1.37
0.77
1.41
0.79
1.45
0.81
1.50
0.84
1.54
0.86
148
1.23
0.65
1.26
0.67
1.29
0.69
1.33
0.70
1.36
0.72
1.40
0.74
1.44
0.76
1.48
0.78
150
1.20
0.60
1.23
0.61
1. 26 ' 0. 63
1.29
0.64
1.32
0.66
1.35
0.67
1.38
0.69
1.42
0.71
152
1.18
0.55
1.20
0.56
1.22
0.57
1. 25 ! 0. 59
1.28
0.60
1.31
0.61
1.34
0.63
1.37
0.64
154
1.15
0.50
1.17
0.51
1.19
0.52
1. 22 0. 53
1.24
0.54
1.27
0.56
1.29
0.57
1.32
0.58
156
1.13
0.46
1.15
0.47
1.17
0.47
1. 19 i 0. 48
1.21
0.49
1.23
0.50
1.2510.51
1.28
0.52
158
1.11
0.42
1.13
0.42
1.14
0.43
1.16
0.44
1.18
0.44
1.20
0.45
1.22
0.46
1.24
0.47
160
1.09
0.37
1.11
0.38
1.12
0.38
1.14
0.39
1.15
0.39
1.17
0.40
1.19
0.41
1.21,
0.41
Page 476J TABLE 5B.
Distance of an Object by Two Bearings.
Difference
between
the course
and second
bearing.
Difference between the course and first bearing.
110°
112°
114°
116°
118°
120°
122°
120°
5.41
4.69
1
'
122
4.52
li
5.34
4.53
124
3.88
4.46
3.70
15.26
4.36
126
3.41
2! 76
3.83
3.10
14.39
3.55
5.18
4.19
128
3.04
2.40
3.36
2.65
13.78
2.98
4.32
3.41
5.08
4.01
130
2.75
2.10
3.00
2.30
3.31
2.54
3.72
2.85
4.25
3.25
4.99
3.82
132
2.51
1.86
2.71
2.01
2.96
2.20
3.26
2.42
3.65
2.71
4.17
3.10
4.88
3.63
134
2.31
1.66
2.48
1.78
2.67
1.92
2.91
2.09
3.20
2.30
3.58
2.57
4.08
2.93
136
2.14
1.49
2.28
1.58
2.44
1.69
2.63
1.83
2.86
1.98
3.14
2.18
3.51
2.44
138
2.00
1.34
2.12
1.42
2.25
1.50
2.40
1.61
2.58
1.73
2.80
1.88
3.08
2.06
140
1.88
1.21
1.97
1.27
2.08
1.34
2.21
1.42
2.36
1.52
2.53
1.63
2.74
1.76
142
1.77
1.09
1.85
h 14
1.95
1.20
2.05
1.26
2.17
1.34
2.31
1.42
2.48
1.53
144
1.68
0.99
1.75
1.03
1.83
1.07
1.91
1.13
2.01
1.18
2.13
1.25
2.26
1.33
146
1.60
0.89
1.66
0.93
1.72
0.96
1.80
1.01
1.88
1.05
1.98
1.10
2.08
1.17
148
1.53
0.81
1.58
0.84
1.63
0.87
1.70
0.90
1.77
0.94
1.84
0.98
1.93
1.03
150
1.46
0.73
1.51
0.75
1.55
0.78
1.61
0.80
. 1. 67
0.83
1.73
0.87
1.81
0.90
152
1.40
0.66
1.44
0.68
1.48
0.70
1.53
0.72
1.58
0.74
1.63
0.77
1.70
0.80
154
1.35
0.59
1.39
0.61
1.42
0.62
1.46
0.64
1.50
0.66
1.55
0.68
1.60
0.70
156
1.31
0.53
1.33
0.54
1.37
0.56
1.40
0.57
1.43
0.58
1.47
0.60
1.52
0.62
158
1.26
0.47
1.29
0.48
1.32
0.49
1.34
0.50
1.37
0.51
1.41 1 0.53
1.44
0.54
160
1.23
0.42
1.25
0.43
1.27
0.43
1.29
0.44
1. 32
0.45
1.35 1 0.46
1.38
0.47
124°
126°
128°
130°
132°
134°
136° 1
134°
4.77
3.43
136
3.99
2.77
4.66
3.23
138
3.43
2.29
3.89
2.60
4.54
3.04
140
3.01
1.93
3.34
2.15
3.79
2.44
4.41
2.84
142
2.68
1.65
2.94
1.81
3.26
2.01
3.68
2.27
4.28
2.63
144
2.42
1.42
2.62
1.54
2.86
1.68
3.17
1.86
3.57
2.10
4.14
2.43
146
2.21
1.24
2.37
1.32
2.55
1.43
2.78
1.55
3.07
1.72
3.46
1.93
4.00
2.24
148
2.04
1.08
2.16
1.14
2.30
1.22
2.48
1.31
2.70
1.43
2.97
1.58
3.34
1.77
150
1.89
0.95
1.99
0.99
2.10
1.05
2.24
1.12
2.40
1.20
2.61
1.30
2.87
1.44
152
1.77
0.83
1.85
0.87
1.94
0.91
2.04
0.96
2.17
1.02
2.33
1.09
2.52
1.18
154
1.66
0.73
1.72
0.76
1.80
0.79
1.88
0.83
1.98
0.87
2.10
0.92
2.25
0.99
156
1.56
0.64
1.62
0.66
1.68
0.68
1.75
0.71
1.83
0.74
1.92
0.78
2.03
0.83
158
1.48
0.56
1.53
0.57
1.58
0.59
1.63
0.61
1.70
0.64
1.77
0.66
1.85
0.69
160
1.41
0.48
1.45
0.49
1.49
0.51
1.53
0.52
1.58
0.54
1.64
0.56
1.71
0.58
138°
140° ; 142°
144° 1 14«°
148°
150° 1
148°
3.85
2.04
150
3.22
1.61
3.70
1.85
152
2.77
1.30
3.09
1.45
3.55 1.66
154
2.43
1.06
2.66
1.16
2. 96 ; 1. 30
3.38
1.48
156
2.17
0.88
2.33
0.95
2. 54 : 1. 04
2.83
1.15
3.22
1.31
158
1.96
0.73
2.08
0.78
2.23 0.84
2.43
0.91
2.69
1.01
3.05
1.14
160
1.79
0.61
1.88
0.64
1.99 0.68
2.13
0.73
2.31
0.79
2.55
0.87
2.88 0.98 1
TABLE
6.
[Page 477
Distance of Visibility of Objects at Sea.
Height,
Nautical
statute
Height,
Nautical
Statute
Height,
Nautical
statute
feet.
miles.
miles.
feet.
miles.
miles.
feet.
miles.
miles.
1
1.1
1.3
100
11.5
13.2
760
31.6
36.4
2
1.7
1.9
105
11.7
13.5
780
32.0
36.9
3
2.0
2.3
110
12.0
13.8
800
32.4
37.3
4
2.3
2.6
115
12.3
14.1
820
32.8
37.8
5
2.5
2.9
120
12.6
14.5
840
33.2
38.3
6
2.8
3.2
125
12.9
14.8
860
33.6
38.7
7
2.9
3.5
130
13.1
15.1
880
34.0
39.2
8
3.1
3.7
135
13.3
15.3
900
34.4
39.6
9
3.5
4.0
140
13.6
15.6
920
34.7
40.0
10
3.6
4.2
145
13.8
15.9
940
35.2
40.5
11
3.8
4.4
150
14.1
16.2
960
35.5
40.9
12
4.0
4.6
160
14.5
16.7
980
35.9
41.3
13
4.2
4.8
170
14.9
17.2
1,000
36.2
41.7
14
4.3
4.9
180
15.4
17.7
1,100
38.0
4.3.8
15
4.4
5.1
190
15.8
18.2
1,200
39.6
45.6
16
4.6
5.3
200
16.2
18.7
1,300
41.3
47.6
17
4.7
5.4
210
16.6
19.1
1,400
42.9
49.4
18
4.9
5.6
220
17.0
19.6
1,500
44.4
51.1
19
5.0
5.8
230
17.4
20.0
1,600
45.8
52.8
20
5.1
5.9
240
17.7
20.4
1,700
47.2
54.4
21
5.3
6.1
250
18.2
20.9
1,800
48.6
56.0
22
5.4
6.2
260
18.5
21.3
1,900
49.9
57.5
23
5.5
6.3
270
18.9
21.7
2,000
51.2
59.0
24
5.6
6.5
280
19.2
22.1
2, 100
52.5
60.5
25
5.7
6.6
290
19.6
22.5
2,200
53.8
61.9
26
5.8
6.7
300
19.9
22.9
2,300
55.0
63.3
27
6.0
6.9
310
20.1
23.2
2,400
56.2
64.7
28
6.1
7.0
320
20.5
23.6
2,500
57.3
66.0
29
6.2
7.1
330
20.8
24.0
2,600
58.5
67.3
30
6.3
7.2
340
21.1
24.3
2,700
59.6
68.6
31
6.4
7.3
350
21.5
24.7
2,800
60.6
69.8
32
6.5
7.5
360
21.7
25.0
2,900
61.8
71.1
33
6.6
7.6
370
22.1
25.4
3,000
62.8
72.3
34
6.7
7.7
380
22.3
25.7
3,100
63.8
73.5
35
6.8
7.8
390
22.7
26.1
3,200
64.9
74.7
36
6.9
7.9
400
22.9
26.4
3,300
65.9
75.9
37
6.9
8.0
410
23.2
26.7
3,400
66.9
77.0
38
7.0
8.1
420
23.5
27.1
3,500
67. 8
78.1
39
7.1
8.2
430
23.8
27.4
3,600
68. 8
79.2
40
7.2
8.3
440
24.1
27.7
3,700
69.7
80.3
41
7.3
8.4
450
24.3
28.0
3, 800
70.7
81.4
42
7.4
8.5
460
24.6
28.3
3,900
71.6
82.4
43
7.5
8.7
470
24.8
28.6
4,000
72.5
83.5
44
7.6
8.8
480
25.1
28.9
4,100
73.4
84.5
45
7.7
8.9
490
25.4
29.2
4,200
74.3
85.6
46
7.8
9.0
500
25.6
29.5
4,300
75.2
86.6
47
7.9
9.0
520
26.1
30.1
4,400
76.1
87.6
48
7.9
9.1
540
26.7
30.7
4, 500
76.9
88.5
49
8.0
9.2
560
27.1
31.2
4,600
77.7
89.5
50
8.1
9.3
580
27.6
31.8
4,700
78.6
90.5
55
8.5
9.8
600
28.0
32.3
4,800
79.4
91.4
60
8.9
10.2
620
'28.6
32.9
4,900
80.2
92.4
65
9.2
10.6
640
29.0
33.4
5,000
81.0
93.3
70
9.6
11.0
660
29.4
33.9
6,000
88.8
102.2
75
9.9
11.4
680
29.9
34.4
7,000
96.0
110.5
80
10.3
11.8
700
30.3
34.9
8,000
102.6
118.1
85
10.6
12.2
720
30.7
35.4
9,000
108. 7
125.2
90
10.9
12.5
740
31.1
35.9
10,000
114.6
132.0
95
11.2
12.9
Page 478]
TABLE 7
For converting Arc into Time,
and the reverse.
o
H. M.
o
H. M.
o
H. M.
o
H. M.
o
H. M.
o
H. M.
'
M. S.
/
M. S.
'
M. S.
'
M. S.
'
M. S.
/
M. S.
II
s. ^
"
s. A
II
s. A
"
8. A
"
s. A
II
S. rfB
1
0 4
61
4 4
121
8 4
181
12 4
241
16 4
301
20 4
2
0 8
62
4 8
122
8 8
182
12 8
242
16 8
302
20 8
3
0 12
h,
4 12
123
8 12
183
12 12
243
16 12
303
20 12
4
0 16
64
4 16
124
8 16
184
12 16
244
16 16
304
20 16
5
0 20
65
4 20
125
8 20
185
12 20
245
16 20
305
20 20
6
0 24
66
4 24
126
8 24
186
12 24
246
16 24
306
20 24
7
0 28
67
4 28
127
8 28
187
12 28
247
16 28
307
20 28
8
0 32
68
4 32
128
8 32
188
12 32
248
16 32
308
20 32
9
0 36
69
4 36
129
8 36
189
12 36
249
16 36
309
20 36
10
0 40
70
4 40
130
8 40
190
12 40
250
16 40
310
20 40
11
0 44
71
4 44
131
8 44
191
12 44
251
16 44
311
20 44
12
0 48
72
4 48
132
8 48
192
12 48
252
16 48
312
20 48
13
0 52
73
4 52
133
8 52
193
12 52
253
16 52
313
20 52
14
0 56
74
4 56
134
8 56
194
12 56
254
16 56
314
20 56
15
1 0
75
5 0
135
9 0
195
13 0
255
17 0
315
21 0
16
1 4
76
5 4
136
9 4
196
13 4
256
17 4
316
21 4
17
1 8
77
5 8
137
9 8
197
13 8
257
17 8
317
21 8
18
1 12
78
5 12
138
9 12
198
13 12
258
17 12
318
21 12
19
1 16
79
5 16
139
9 16
199
13 16
259
17 16
319
21 16
20
1 20
80
5 20
140
9 20
200
13 20
260
17 20
320
21 20
21
1 24
81
5 24
141
9 24
201
13 24
261
17 24
321
21 24
22
1 28
82
5 28
142
9 28
202
13 28
262
17 28
322
21 28
23
1 32
83
5 32
143
9 32
203
13 32
263
17 32
323
21 32
24
1 36
84
5 36
144
9 36
204
13 36
264
17 36
324
21 36
25
1 40
85
5 40
145
9 40
205
13 40
265
17 40
325
21 40
26
1 44
86
5 44
146
9 44
206
13 44
266
17 44
326
21 44
27
1 48
87
5 48
147
9 48
207
13 48
267
17 48
327
21 48
28
1 52
88
5 52
148
9 52
208
13 52
268
17 52
328
21 52
29
1 56
89
5 56
149
9 56
209
13 56
269
17 56
329
21 56
30
2 0
90
6 0
150
10 0
210
14 0
270
18 0
330
22 0
31
2 4
91
6 4
151
10 4
211
14 4
271
18 4
331
22 4
32
2 8
92
6 8
152
aO 8
212
14 8
272
18 8
332
22 8
33
2 12
93
6 12
153
10 12
213
14 12
273
18 12
333
22 12
34
2 16
94
6 16
154
10 16
214
14 16
274
18 16
334
22 16
35
2 20
95
6 20
155
10 20
215
14 20
275
18 20
335
22 20
36
2 24
96
6 24
156
10 24
216
14 24
276
18 24
336
22 24
37
2 28
97
6 28
157
10 28
217
14 28
277
18 28
337
22 28
38
2 32
98
6 32
158
10 32
218
14 32
278
18 32
338
22 32
39
2 36
99
6 36
159
10 36
219
14 36
279
18 36
339
22 36
40
2 40
100
6 40
160
10 40
220
221
14 40
14 44
280
18 40
340
22 40
41
2 44
101
6 44
161
10 44
281
18 44
341
22 44
42
2 48
102
6 48
162
10 48
222
14 48
282
18 48
342
22 48
43
2 52
103
6 52
163
10 52
223
14 52
283
18 52
343
22 52
44
2 56
104
6 56
164
10 56
224
14 56
284
18 56
344
22 56
45
3 0
105
7 0
165
11 0
225
15 0
285
19 0
345
23 0
46
3 4
106
7 4
166
11 4
226
15 4
286
19 4
346
23 4
47
3 8
107
7 8
167
11 8
227
15 8
287
19 8
347
23 8
48
3 12
108
7 12
168
11 12
228
15 12
288
19 12
348
23 12
49
3 16
109
7 16
169
11 16
229
15 16
289
19 16
349
23 16
50
51
3 20
110
7 20
170
11 20
230
15 20
290
19 20
350
23 20
3 24
111
7 24
171
11 24
231
15 24
291
19 24
351
23 24
52
3 28
112
7 28
172
11 28
232
15 28
292
19 28
352
23 28
53
3 32
113
7 32
173
11 32
233
15 32
293
19 32
353
23 32
54
3 36
114
7 36
174
11 36
234
15 36
294
19 36
354
23 36
55
3 40
115
7 40
175
11 40
235
15 40
295
19 40
355
23 40
56
3 44
116
7 44
176
11 44
236
15 44
296
19 44
356
23 44
57
3 48
117
7 48
177
11 48
237
15 48
297
19 48
357
23 48
58
3 52
118
7 52
178
11 52
238
15 52
298
19 52
358
23 52
59
3 56
119
7 56
179
11 56
239
15 56
299
19 56
359
23 56
60
4 0
120
8 0
180
12 0
240
16 0
300
20 0
360
24 0
Note. — When turning seconds of arc into time, and vice versa, it should be remembered that the fractions are sixtieths;
thufi, the value in time oi 42" is not 2^48, but 2»U=2".8.
TABLE 8.
[Page 479
Sidereal into Mean Solar Time.
"3
To be subtracted from a sidereal time interval.
Oh
Ih
2.
Sh
4h
oh
6"
7"
For seconds.
m.
in. 8.
TO. «.
m. «.
TO. 8.
TO. S.
TO. 8.
TO.
8.
m. 8.
8.
8.
0
0 0.000
0 9.830
0 19.659
0 29. 489
0 39. 318
0 49. 148
0 58. 977
1 8. 807
1
0 0. 164
0 9.993
0 19.823 0 29.653
0 39.482
0 49. 312
0
59. 141
1 8. 971
1
0.003
2
0 0. 328
0 10. 157
0 19. 987 0 29. 816 0 39. 646
0 49. 475
0 59. 305
1 9. 135
2
.005
3
0 0. 491
0 10. 321
0 20. 151
0 29. 980
0 39. 810
0 49. 639
0 59. 469
1 9. 298
3
.008
4
0 0. 655
0 10.485
0 20. 314
0 30. 144
0 39. 974
0 49. 803
0
0
59. 633
1 9.462
4
.011
5
0 0. 819
0 10.649
0 20. 478
0 30. 308
0 40. 137
0 49. 967
59. 796
1 9.626
5
.014
6
0 0. 983
0 10. 813
0 20. 642
0 30. 472
0 40. 301
0 50. 131
0 59. 960
1 9.790
6
.016
7
0 1. 147
0 10.976
0 20. 806
0 30. 635
0 40. 465
0 50. 295
0.124
1 9. 954
7
.019
8
0 1.311
0 11. 140
0 20. 970
0 30. 799
0 40. 629
0 50. 458
0.288
1 10.118
8
.022
9
10
0 1.474
0 11. 304
0 21. 134
0 30. 963
0 40. 793
0 50. 622
0.452
1 10.281
9
.025
0 1.638
0 11.468
0 21. 297
0 31. 127
0 40. 956
0 50. 786
0.616
1 10.445
10
.027
11
0 1.802
0 11. 632
0 21.461 i 0 31.291
0 41. 120
0 50. 950
0.779
1 10.609
11
.030
12
0 1.966
0 11. 795
0 21. 625 0 31. 455
0 41. 284
0 51. 114
0.943
1 10.773
12
.033
13
0 2. 130
0 11.959
0 21.789 1 0 31.618
0 41. 448
0 51. 278
1.107
1 10. 937
13
.035
14
0 2. 294
0 12. 123
0 21. 953 0 31. 782
0 41.612
0 51.441
1.271
1 11.100
14
.038
15
0 2. 457
0 12. 287
0 22. 117 1 0 31. 946
0 41. 776
0 51. 605
1.435
1 11.264
15
.041
16
0 2. 621
0 12. 451
0 22. 280 0 32. 110 0 41. 939
0 51. 769
1.599
1 11.428
16
.044
17
0 2. 785
0 12. 615
0 22. 444 0 32. 274 i 0 42. 103
0 51. 933
1.762
1 11.592
17
.046
18
0 2. 949
0 12. 778 0 22. 608 0 32. 438 i 0 42. 267
0 52. 097
1.926
1 11.756
18
.049
19
0 3. 113
0 12. 942 1 0 22. 772 i 0 32. 601 I 0 42. 431
0 52. 260
2.090
1 11.920
19
.052
20
0 3.277
0 13. 106
0 22. 936 i 0 32. 765
0 42. 595
0 52. 424
2.254
1 12.083
20
.055
21
0 3. 440
0 13. 270
0 23. 099 i 0 32. 929
0 42. 759
0 52. 588
2.418
1 12.247
21
.057
22
0 3. 604
0 13.434
0 23. 263 ; 0 33. 093
0 42. 922
0 52. 752
2.582
1 12.411
22
.060
23
0 3. 768
0 13.598
0 23. 427
0 33. 257
0 43. 086
0 52. 916
2.745
1 12.575
23
.063
24
0 3. 932
0 13. 761
0 23. 591
0 33. 420
0 43. 250
0 53. 080
2.909
1 12.739
24
.066
25
0 4. 096
0 13.925
0 23. 755
0 33. 584
0 43. 414
0 53. 243
3.073
1 12.903
25
.068
26
0 4. 259
0 14.089
0 23. 919
0 33. 748
0 43. 578
0 53. 407
3.237
1 13.066
26
.071
27
0 4. 423
0 14. 253
0 24. 082
0 33. 912
0 43. 742
0 53. 571
3.401
1 13.230
27
.074
28
0 4. 587
0 14.417
0 24. 246
0 34. 076
0 43.905
0 53. 735
3.564
1 13.394
28
.076
29
0 4. 751
0 14.581
0 24. 410
0 34. 240
0 44. 069
0 53. 899
0 54. 063
3.728
1 13.558
29
.079
30
0 4.915
0 14. 744
0 24. 574
0 34. 403
0 44. 233
3.892
1 13.722
30
.082
31
0 5. 079
0 14.908
0 24. 738
0 34. 567
0 44. 397
0 54. 226
4.056
1 13.886
31
.085
32
0 5. 242
0 15.072
0 24. 902
0 34. 731
0 44. 561
0 54. 390
4.220
1 14.049
32
.087
33
0 5. 406
0 15.236
0 25.065
0 34. 895
0 44. 724
0 54. 554
4.384
1 14.213
33
.090
34
0 5. 570
0 15.400
0 25. 229
0 35. 059
0 44. 888
0 54. 718
4.547
1 14.377
34
35'
.093
.096
35
0 5. 734
0 15. 563
0 25. 393
0 35. 223
0 45. 052
0 54. 882
4.711
1 14.541
36
0 5. 898
0 15. 727
0 25. 557
0 35. 386
0 45. 216
0 55. 046
4.875
1 14.705
36
.098
37
0 6.062
0 15. 891
0 25. 721
0 35. 550
0 45. 380
0 55. 209
5.039
1 14.868
37
.101
38
0 6. 225
0 16. 055
0 25. 885
0 35. 714
0 45. 544
0 55. 373
5.203
1 15.032
38
.104
39
0 6. 389
0 16. 219
0 16.383
0 26. 048
0 35. 878
0 45. 707
0 55. 537
5.367
1 15.196
39
.106
40
0 6. 553
0 26. 212
0 36. 042
0 45. 871
0 55. 701
5.530
1 15.360
40
.109
41
0 6. 717
0 16.546
0 26. 376
0 36. 206
0 46. 035
0 55. 865
5.694
1 15.524
41
.112
42
0 6. 881
0 16. 710
0 26. 540
0 36. 369
0 46. 199
0 56. 028
5.858
1 15.688
42
.115
43
0 7.045
0 16. 874
0 26. 704
0 36. 533
0 46. 363
0 56. 192
6.022
1 15.851
43
.117
44
0 7. 208
0 17.038
0 26. 867
0 36. 697
0 46. 527
0 56. 356
6.186
1 16.015
44
.120
45
0 7.372
0 17.202
0 27. 031
0 36. 861
0 46. 690
0 56. 520
6.350
1 16.179
45
.123
46
0 7.536
0 17.366
0 27. 195
0 37. 025
0 46. 854
0 56. 684
6.513
1 16.343
46
.126
47
0 7. 700
0 17. 529
0 27. 359
0 37. 188
0 47. 018
0 56. 848
6.677
1 16.507
47
.128
48
0 7.864
0 17.693
0 27. 523
0 37. 352
0 47. 182
0 57. Oil
6.841
1 16.671
48
.131
49
0 8. 027
0 17.857
0 27. 687
0 37. 516
0 47. 346
0 57. 175
7.005
1 16.834
49
.134
50
0 8. 191
0 18.021
0 27. 850
0 37.680
0 47. 510
0 57. 339
7.169
1 16.998
50
.137
51
0 8.355
0 18. 185
0 28.014
0 37. 844
0 47. 673
0 57. 503
7.332
1 17. 162
51
.139
52
0 8.519
0 18. 349
0 28. 178
0 38. 008
0 47. 837
0 57. 667
7.496
1 17.326
52
.142
53
0 8. 683
0 18. 512
0 28. 342
0 38. 171
0 48. 001
0 57. 831
7.660
1 17.490
53
.145
54
0 8. 847
0 18.676
0 28. 506
0 38. 335
0 38.499
0 48. 165
0 57. 994
7.824
1 17.654
54
.147
55
0 9. 010
0 18. 840
0 28. 670
0 48. 329
0 58. 158
7.988
1 17.817
55
.150
56
0 9. 174
0 19.004
0 28. 833
0 38. 663
0 48. 492
0 58. 322
8.152
1 17.981
56
.153
57
0 9. 338
0 19. 168
0 28. 997
0 38. 827
0 48. 656
0 58. 486
8.315
1 18.145
57
.156
58
0 9. 502
0 19. 331
0 29. 161
0 38. 991
0 48. 820
0 58. 650
8.479
1 18.309
58
.158
59
0 9. 666
0 19. 495
0 29. 325
0 39. 154
0 48. 984
0 58. 814
8.643
1 18.473
59
0.161
Page 480]
TABLE 8.
Sidereal into Mean Solar Time.
S
To be subtracted from a sidereal time interval.
8h
flh
lOi-
llh
Igk
18*
14h
IS"
For seconds.!
m.
VI. s.
TO. S.
m. ».
m. s.
TO.
8.
VI. D.
TO. «.
TO. S.
s.
«.
0
1 18.636
1 28.466
1 38.296
1 48. 125
57. 955
2 7. 784
2 17. 614
2 27.443
1
1 18.800
1 28.630
1 38.459
1 48.289
58. 119
2 7. 948 2 17. 778
2 27. 607
1
0.003
2
1 18.964
1 28.t94
1 38.623
1 48.453
58. 282
2 8.112 2 17.941
2 27. 771
2
.005
3
1 19.128
1 28.958
1 38.787
1 48.617
58. 446
2 8. 276 2 18. 105
2 27. 935
3
.008
4
1 19.292
1 29. 121
1 38.951
1 48. 780
1 48.944
58. 610
58. 774
2 8.440 1 2 18.269
2 8.603 2 18.433
2 28. 099
2 28. 263
4
5
.011
.014
5
1 19.456
1 29.285
1 39. 115
6
1 19.619
1 29.449
1 39.279
1 49. 108
58. 938
2 8. 767 2 18. 597
2 28. 426
6
.016
7
1 19.783
1 29. 613
1 39.442
1 49.272 ! 1
59. 101
2 8.931
2 18. 761
2 28. 590
7
.019
8
1 19.947
1 29. 777
1 39.606
1 49.436 1
59. 265
2 9.095
2 18. 924
2 28. 754
8
.022
9
1 20.111
1 29.940
1 30. 104
1 39. 770
1 49.600 1
1 49. 763 1
59. 429
59. 593
2 9.259 2 19.088
2 28. 918
9
.025
10: 1 20,275
1 39.934
2 9.423 2 19.252
2 29. 082
10
.027
11 1 20. 439
1 30.268
1 40.098
1 49.927 1
59. 757
2 9.586 2 19.416
2 29. 245
11
.030
12 1 20.602
1 30.432
1 40.261
1 50.091 1
59. 921
2 9.750 2 19.580
2 29. 409
12
.033
13 1 20. 766
1 30.596
1 40.425 1 1 50.255 2
0.084
2 9. 914 2 19. 744
2 29. 573
13
.035
14 1 20.930
1 30.760
1 40.589 1 1 50.419 2
0.248
2 10.078 2 19.907
2 29. 737
14
.038
15 1 T 21. 094
1 30.923
1 40. 753 1 50. 583 2
0.412
2 10. 242 t 2 20. 071
2 29.901
15
.041
16 1 21.258
1 31. 087
1 40. 917 1 50. 746 2
0.576
2 10. 405 2 20. 235
2 30.065
16
.044
T7
i 21.422
1 31. 251
1 41.081 1 50.910 2
0.740
2 10. 569 2 20. 399
2 30. 228
17
.046
18
i 21.585
1 31.415
1 41.244 1 51.074 2
0.904
2 10. 733 2 20. 563
2 30. 392 18
.049
19 1 21.749
1 31.579
1 41.408 1 51.233 2
1.067
2 10. 897 i 2 20. 727
2 11.061 2 20.890
2 30. 556
19
.052
20 1 21.913
1 31. 743
1 41.572 1 51.402 2
1.231
2 30. 720
20
.055
21 1 1 22. 077
1 31.906
1 41.736 1 51.565 2
1. 395
2 11. 225 2 21. 054
2 30. 884
21
.057
22! 1 22.241
1 32. 070
1 41.900 1 51.729 2
1.559
2 11. 388 ; 2 21. 218
2 31. 048
22
.060
23 1 1 22.404
1 32. 234
1 42. 064 1 51. 893 2
1.723
2 11.552 2 21.382
2 31.211
23
.063
24 ! 1 22. 568
1 32.398
1 42.227 1 52.057
2
2
1.887
2.050
2 11. 716 2 21. 546
2 11. 880 2 21. 709
2 31. 375
2 31. 539
24
.066
25 i 1 22. 732
1 32. 562
1 42. 391 1 52. 221
25
.068
26 1 1 22. 896
1 32.726
1 42. 555 1 52. 385 2
2.214
2 12.044 2 21.873
2 31. 703
26
.071
27 1 1 23. 060
1 32.889
1 42. 719 1 52. 548 2
2.378
2 12.208 2 22.037
2 31.867
27
.074
28 1 1 23.224
1 33.053
1 42. 883 1 52. 712 2
2.542
2 12.371 2 22.201
2 32. 031
28
.076
29
30
1 23.387
1 23.551
1 33.217
1 33.381
1 43. 047 1 52. 876 2
2.706
2 12.535
2 22. 365
2 32. 194
29
.079
1 43.210 1 53.040 . 2
2.869
2 12.699
2 22.529
2 32. 358
30
.082
31
1 23. 715
1 33.545
1 43. 374 1 53. 204 2
3.033
2 12.863
2 22. 692
2 32. 522
31
.085
32
1 23.879
1 33. 708
1 43. 538 : 1 53. 368 2
3.197
2 13. 027 i 2 22. 856
2 32. 686
32
.087
33
1 24.043
1 33.872
1 43. 702 i 1 53. 531 2
3.361
2 13. 191 1 2 23. 020
2 32. 850
33
.090
34
1 24.207
1 34.036
1 43.866
1 53.695
2
3.525
2 13.354
2 23. 184
2 33.013
34
.093
35
1 24.370
1 34.200
1 44. 029
1 53.859
2
3.689
2 13.518
2 23. 348
2 33. 177
35
.096
36
1 24. 534
1 34.364
1 44.193
1 54.023
2
3. 852
2 13.682
2 23.512
2 33.341
36
.098
37
1 24.698
1 34.528
1 44. 357
1 54. 187 2
4.016
2 13.846
2 23.675
2 33.505
37
.101
38
1 24.862
1 34.691
1 44.521
1 54.351 2
4.180
2 14.010
2 23. 839
2 33.669
38
.104
39
1 25.026
1 34.855
1 44. 685
1 54.514 2
4.344
2 14.173
2 14.337
2 24. 003
2 24. 167
2 33. 833
39
.106
40
1 25. 190
1 35.019
1 44.849
1 54. 678 2
4.508
2 33. 996
40
.109
41
1 25.353
1 35. 183
1 45.012
1 54.842
2
4.672
2 14.501
2 24. 331
2 34. 160
41
.112
42
1 25.517
1 35.347
1 45.176
1 55.006
2
4. 835
2 14. 665 ! 2 24. 495
2 34. 324
42
.115
43
1 25.681
1 35.511
1 45.340
1 55. 170
2
4.999
2 14. 829 i 2 24. 658
2 .34. 488
43
.117
44
1 25.845
1 35.674
1 45.504
1 55.333
2
5.163
2 14. 993 i 2 24. 822
2 34. 652
44
.120
45
1 26.009
1 35.838
1 45.668
1 55.497
2
5.327
2 15. 156
2 24. 986
2 34. 816
45
.123
46
1 26. 172
1 36.002
1 45.832
1 55.661
2
5.491
2 15. 320
2 25. 150
2 34. 979
46
.126
47
1 26.336
1 36. 166
1 45.995
1 55.825
2
5.655
2 15.484
2 25. 314
2 35. 143
47
.128
48
1 26.500
1 36.330
1 46. 159
1 55.989
2
5.818
2 15.648
2 25.477
2 35. 307
48
.131
49
1 26.664
1 36.493
1 46.323
1 56. 153
2
5.982
2 15.812
2 25. 641
2 35. 471
49
.134
50
1 26. 828
1 36.657
1 46.487
1 56.316
2
6.146
2 15.976
2 25. 805
2 35. 635
50
.137
51
1 26.992
1 36.821
1 46.651
1 56.480
2
6.310
2 16.139 2 25.969
2 35. 798
51
.139
52
1 27. 155
1 36.985
1 46.815
1 56.644
2
6.474
2 16.303
2 26. 133
2 35. 962
52
.142
53
1 27. 319
1 37. 149
1 46.978
1 56.808
2
6.637
2 16.467
2 26. 297
2 36.126
53
.145
54
1 27.483
1 37.313
1 47.142
1 56.972
2
6.801
2 16.631
2 26.460
2 36. 290
64
.147
55
1 27.647
1 37.476
1 47.306
1 57.136
2
6.965
2 16. 795
2 26. 624
2 36. 454
55
.150
56
1 27.811
1 37. 640
1 47. 470 i 1 57. 299
2
7.129
2 16.959
2 26. 788
2 36.618
56
.153
57
1 27.975
1 37.804
1 47.634 1 57.463
2
7.293
2 17. 122
2 26. 952
2 36. 781
57
.156
58
1 28. 138
1 37.968
1 47.797 1 57.627
2
7.457
2 17.286
2 27. 116
2 36. 945
58
.158
59
1 28.302
1 38. 132
1 47. 961 1 57. 791
2
7.620
2 17.450
2 27. 280
2 37. 109
59
0.161
TABLE 8.
[Page 481
Sidereal into Mean Solar Time.
"3
2
"2
m.
0
1
2
3
4
5
6
7
8
9
To be subtracted from a sidereal time interval.
m. s.
2 37. 273
2 37. 437
2 37. 601
2 37. 764
2 37. 928
2 38. 092
2 38. 256
2 38. 420
2 38. 584
2 38. 747
17h
m. s.
2 47. 102
2 47. 266
2 47. 430
2 47. 594
2 47. 758
2 47. 922
2 48. 085
2 48.249
2 48. 413
2 48. 577
181-
19«>
ao"
•21h
2 SI"
2S^
For seconds.!
m. s.
2 56. 932
2 57. 096
2 57. 260
2 57.424
2 57. 587
m.
3
3
3
3
3
6.762
6.925
7.089
7.253
7.417
m. s.
3 16.591
3 16. 755
3 16.919
3 17.083
3 17.246
m. 8.
3 26.421
3 26. 585
3 26. 748
3 26. 912
3 27. 076
TO. 8.
3 36. 250
3 367414
3 36. 578
3 36. 742
3 36.906
TO. «.
3 46. 080
3 46. 244
3 46. 407
3 46. 571
3 46. 735
1
2
3
4
8.
0. 003
.005
.008
.011
2 57. 751
2 57.915
2 58. 079
2 58. 243
2 58. 406
3
3
3
3
3
7.581
7.745
7.908
8.072
8.236
3 17.410
3 17.574
3 17. 738
3 17.902
3 18.066
3 27. 240
3 27.404
3 27.568
3 27. 731
3 27.895
3 37. 069
3 37. 233
3 37.397
3 37.561
3 37. 725
3 46. 899
3 47. 063
3 47. 227
3 47. 390
3 47. 554
5
6
7
8
9
.014
.016
.019
.022
.025
10
11
12
13
14
2 38. 911
2 39. 075
2 39. 239
2 39. 403
2 39. 566
2 48. 741
2 48. 905
2 49. 068
2 49. 232
2 49. 396
2 58. 570
2 58. 734
2 58. 898
2 59. 062
2 59. 226
3
3
3
3
3
8.400
8.564
8.728
8.891
9.055
3 18.229
3 18.393
3 18.557
3 18. 721
3 18.885
3 28. 059
3 28. 223
3 28. 387
3 28. 550
3 28. 714
3 37. 889
3 38. 052
3 38. 216
3 38. 380
3 38. 544
3 47. 718
3 47. 882
3 48. 046
3 48. 210
3 48. 373
10
11
12
13
14
.027
.030
.033
.035
.038
15
16
17
18
19
2 39. 730
2 39.894
2 40. 058
2 40. 222
2 40. 386
2 49.560
2 49. 724
2 49. 888
2 50. 051
2 50. 215
2 59. 389
2 59. 553
2 59. 717
2 59.881
3 0.045
3
3
3
3
3
9.219
9.383
9.547
9.710
9.874
3 19.049
3 19.212
3 19. 376
3 19.540
3 19. 704
3 28.878
3 29.042
3 29. 206
3 29. 370
3 29. 533
3 38. 708
3 38. 871
3 39.035
3 39. 199
3 39. 363
3 48. 537
3 48. 701
3 48. 865
3 49. 029
3 49. 193
15
16
17
18
19
.041
.044
.046
.049
.052
20
21
22
23
24
2 40. 549
2 40. 713
2 40. 877
2 41.041
2 41. 205
2 50. 379
2 50. 543
2 50. 707
2 50. 870
2 51. 034
3
3
3
3
3
0.209
0.372
0. 536
0.700
0.864
3
3
3
3
3
10. 038
10. 202
10. 366
10. 530
10. 693
3 19.868
3 20.032
3 20. 195
3 20. 359
3 20. 523
3 29. 697
3 29. 861
3 30.025
3 30. 189
3 30. 353
3 39.527
3 39. 691
3 39. 854
3 40. 018
3 40. 182
3 49. 356
3 49. 520
3 49. 684
3 49. 848
3 50.012
20
21
22
23
24
.055
.057
.060
.063
.066
25
26
27
28
29
2 41.369
2 41.532
2 41.696
2 41.860
2 42. 024
2 51. 198
2 51. 362
2 51.526
2 51. 690
2 51.853
3
3
3
3
3
1.028
1.192
1. 355
1.519
1.683
3
3
3
3
3
10. 857
11. 021
11. 185
11. 349
11.513
3 20.687
3 20. 851
3 21.014
3 21. 178
3 21. 342
3 30. 516
3 30. 680
3 30. 844
3 31.008
3 31. 172
3 40.346
3 40. 510
3 40. 674
3 40. 837
3 41.001
3 50. 175
3 50. 339
3 50. 503
3 50. 667
3 50. 831
25
26
27
28
29
.068
.071
.074
.076
.079
30
31
32
33
34
2 42. 188
2 42. 352
2 42. 515
2 42. 679
2 42. 843
2 52.017
2 52. 181
2 52. 345
2 52. 509
2 52. 673
3
3
3
3
3
1.847
2.011
2.174
2.338
2.502
3
3
3
3
3
11.676
11. 840
12. 004
12. 168
12. 332
3 21. 506
3 21. 670
3 21. 834
3 21. 997
3 22. 161
3 31. 336
3 31.499
3 31. 663
3 31. 827
3 31.991
3 41. 165
3 41. 329
3 41. 493
3 41. 657
3 41. 820
3 50. 995
3 51. 158
3 51. 322
3 51. 486
3 51. 650
30
31
32
33
34
35
36
37
38
39
.082
.085
.087
.090
.093
35
36
37
38
39
2 43. 007
2 43. 171
2 43. 334
2 43. 498
2 43. 662
2 52. 836
2 53. 000
2 53. 164
2 53. 328
2 53. 492
3
3
3
3
3
2.666
2.830
2.994
3. 157
3.321
3
3
3
3
3
12. 496
12. 659
12. 823
12. 987
13. 151
3 22. 325
3 22. 489
3 22. 653
3 22.817
3 22. 980
3 32. 155
3 32. 318
3 32. 482
3 32. 646
3 32. 810
3 41. 984
3 42. 148
3 42. 312
3 42. 476
3 42. 639
3 51.814
3 51. 978
3 52. 141
3 52. 305
3 52. 469
.096
.098
.101
.104
.106
40
41
42
43
44
2 43. 826
2 43.990
2 44. 154
2 44. 317
2 44. 481
2 53. 656
2 53. 819
2 53. 983
2 54. 147
2 54. 311
3
3
3
3
3
3. 485
3. 649
3.813
3.977
4.140
3
3
3
3
3
13. 315
13. 478
13. 642
13. 806
13. 970
3 23. 144
3 23. 308
3 23. 472
3 23.636
3 23. 800
3 32.974
3 33. 138
3 33. 301
3 33.465
3 33. 629
3 42. 803
3 42. 967
3 43. 131
3 43. 295
3 43. 459
3 52. 633
3 52. 797
3 52. 961
3 53. 124
3 53. 288
3 53. 452
3 53. 616
3 53. 780
3 53. 943
3 54. 107
40
41
42
43
44
45
46
47
48
49
.109
.112
.115
.117
.120
.123
.126
.128
.131
.134
45
46
47
48
49
2 44. 645
2 44. 809
2 44. 973
2 45. 137
2 45. 300
2 54. 475
2 54. 638
2 54. 802
2 54. 966
2 55. 130
3
3
3
3
3
4.304
4.468
4.632
4.796
4.960
3
3
3
3
3
14. 134
14.298
14.461
14. 625
14. 789
3 23.963
3 24.127
3 24. 291
3 24. 455
3 24. 619
3 33. 793
3 33. 957
3 34. 121
3 34. 284
3 34. 448
3 43.622
3 43. 786
3 43. 950
3 44. 114
3 44. 278
50
51
52
53
54
2 45.464
2 45. 628
2 45. 792
2 45. 956
2 46. 120
2 55. 294
2 55. 458
2 55. 621
2 55. 785
2 55.949
3
3
3
3
3
5.123
5.287
5.451
5.615
5.779
3
3
3
3
3
3
3
3
3
3
14. 953
15. 117
15. 281
15. 444
15.608
15. 772
15. 936
16. 100
16. 264
16. 427
3 24. 782
3 24.946
3 25.110
3 25. 274
3 25. 438
3 34. 612
3 34. 776
3 34.940
3 35. 104
3 35. 267
3 44. 442
3 44. 605
3 44. 769
3 44. 933
3 45.097
3 54. 271
3 54. 435
3 54. 599
3 54. 763
3 54. 926
50
51
52
53
54
.137
.139
.142
.145
.147
55
56
57
58
59
2 46.283
2 46. 447
2 46. 611
2 46. 755
2 46. 939
2 56. 113
2 56. 277
2 56. 441
2 56. 604
2 56. 768
3
3
3
3
3
5.942
6.106
6.270
6.434
6.598
3 25.602
3 25. 765
3 25.929
3 26. 093
3 26. 257
3 35.431
3 35. 595
3 35. 759
3 35. 923
3 36. 086
3 45. 261
3 45. 425
3 45. 588
3 45. 752
3 45. 916
3 55. 090
3 55. 254
3 55. 418
3 55. 582
3 55. 746
55
56
57
58
59
.150
.153
.156
.158
0.161
22489—03-
-31
Page 482] TABLE 9.
Mean Solar into Sidereal Time.
To be added to a mean time interval. 1
Oh
Ik
21. 8"
4b
oh
[«"
Jh
For seconds. 1
m.
0
1
2
3
4
m.
0
0
0
0
0
0.000
0.164
0. 329
0.493
0.657
m. B.
0 9.856
0 10.021
0 la 185
0 10.349
0 10.514
m. s.
0 19. 713
0 19.877
0 20. 041
0 20. 206
0 20. 370
m. s.
0 29. 569
0 29. 734
0 29. 898
0 30. 062
0 30. 227
m. s.
0 39. 426
0 39.590
0 39. 754
0 39.919
0 40. 083
0 40. 247
0 40. 412
0 40. 576
0 40. 740
0 40. 904
in. s.
0 49. 282
0 49. 447
0 49. 611
0 49. 775
0 49. 939
m. s.
0 59. 139
0 59. 303
0 59. 467
0 59. 632
0 59. 796
TO. 8.
1 8.995
1 9.160
1 9. 324
1 9. 488
1 9. 652
s.
1
2
.3
4
s.
0.003
.005
.008
.011
5
6
7
8
9
0
0
0
0
0
0.821
0.986
1.150
1.314
1.478
0 10.678
0 10.842
0 11.006
0 11.171
0 11. 335
0 20. 534
0 20.699
0 20. 863
0 21. 027
0 21. 191
0 30. 391
0 30. 555
0 30. 719
0 30. 884
0 31.048
0 50. 104
0 50. 268
0 50. 432
0 50. 597
0 50. 761
0 59. 960
1 0. 124
1 0. 289
1 0. 453
1 0.617
1 9. 817
1 9.981
1 10.145
1 10.310
1 10.474
5
6
7
8
9
.014
.016
.019
.022
.025
10
11
12
13
14
0
0
0
0
0
1.643
1.807
1.971
2.136
2.300
0 11.499
0 11.663
0 11.828
0 11.992
0 12. 156
0 21.356
0 21.520
0 21. 684
0 21. 849
0 22. 013
0 31.212
0 31. 376
0 31. 541
0 3i. 705
0 31. 869
0 41. 069
0 41. 233
0 41. 397
0 41:561
0 41. 726
0 50. 925
0 51.089
0 51. 254
0 51.418
0 51. 582
0.782
0.946
1.110
1.274
1. 439
1 10.638
1 10.802
1 10.967
1 11.131
1 11.295
10
11
12
13
14
.027
.030
.033
.036
.038
15
16
17
18
19
0
0
0
0
0
2.464
2.628
2. 793
2.957
3.121
0 12.321
0 12.485
0 12. 649
0 12.813
0 12. 978
0 22. 177
0 22. 341
0 22. 506
0 22. 670
0 22. 834
0 32. 034
0 32. 198
0 32. 362
0 32. 526
0 32. 691
0 41. 890
0 42. 054
0 42. 219
0 42. 383
0 42. 547
0 51. 746
0 51.911
0 52. 075
0 52. 239
0 52. 404
0 52. 568
0 52. 732
0 52. 896
0 53. 061
0 53. 225
0 53. 389
0 53. 554
0 53. 718
0 53. 882
0 54. 046
^-
1.603
1.767
1.932
2.096
2.260
1 11.459
1 11.624
1 11.788
1 11.952
1 12.117
1 12.281
1 12.445
1 12.609
1 12.774
1 12.938
1 13.102
1 13.266
1 13.431
1 13.595
1 13.759
15
16
17
18
19
20
21
22
23
24
25"
26
27
28
29
.041
.044
.047
.049
.052
.6.55
.057
.060
.063
.066
.068
.071
.074
.077
.079
20
21
22
23
24
0
0
0
0
0
3.285
3.450
3.614
3.778
3.943
0 13. 142
0 13.306
0 13.471
0 13.635
0 13. 799
0 22. 998
0 23. 163
0 23. 327
0 23. 491
0 23. 656
0 32. 855
0 33. 019
0 33. 183
0 33. 348
0 33.512
0 42. 711
0 42. 876
0 43. 040
0 43. 204
0 43. 368
2.424
2.589
2.753
2.917
3.081
25
26
27
28
29
0
0
0
0
0
4.107
4.271
4.435
4.600
4.764
0 13.963
0 14. 128
0 14.292
0 14.456
0 14.620
0 23. 820
0 23. 984
0 24. 148
0 24. 313
0 24. 477
0 33. 676
0 33. 841
0 34.005
0 34. 169
0 34. 333
0 43. 533
0 43. 697
0 43. 861
0 44. 026
0 44. 190
1
3.246
3. 410
3.574
3.739
3.903
30
31
32
33
34
35
36
37
38
39
0
0
0
0
0
0
0
0
0
0
4.928
5.093
5.257
5. 421
5.585
5. 750
5. 914
6.078
6.242
6.407
0 14.785
0 14.949
0 15. 113
0 15.278
0 15.442
0 24. 641
0 24. 805
0 24. 970
0 25. 134
0 25. 298
0 34. 498
0 34. 662
0 34. 826
0 34. 990
0 35. 155
0 44. 354
0 44.518
0 44. 683
0 44. 847
0 45. Oil
0 45. 176
0 45. 340
0 45. 504
0 45. 668
0 45. 833
0 54. 211
0 54. 375
0 54. 539
0 54. 703
0 54. 868
-^-
4.067
4.231
4.396
4. 560
4.724
1 13.924
1 14.088
1 14.252
1 14.416
1 14.581
1 14.745
1 14.909
1 15.073
1 15.238
1 15.402
30
31
32
33
34
35
36
37
38
39
.082
.085
.088
.090
.093
.096
.099
.101
.104
.107
0 15.606
0 15. 770
0 15.935
0 16.099
0 16. 263
0 25.463
0 25. 627
0 25. 791
0 25. 955
0 26. 120
0 26. 284
0 26. 448
0 26. 612
0 26. 777
0 26.941
0 35. 319
0 35. 483
0 35. 648
0 35. 812
0 35. 976
0 55. 032
0 55. 196
0 55. 361
0 55. 525
0 55. 689
4.888
5.053
5.217
5.381
5.546
40
41
42
43
44
0
0
0
0
0
6.571
6.735
6.900
7.064
7.228
0 16.427
0 16. 592
0 16. 756
0 16.920
0 17. 085
0 36. 140
0 36. 305
0 36.469
0 36. 633
0 36. 798
0 45. 997
0 46. 161
0 46. 325
0 46. 490
0 46. 654
0 55. 853
0 56. 018
0 56. 182
0 56. 346
0 56. 510
5.710
5.874
6.038
6. 203
6.367
1 15.566
1 15.731
1 1.5.895
1 16.059
1 16.223
40
41
42
43
44
.110
.112
.115
.118
.120
45
46
47
48
49
0
0
0
0
0
7.392
7.557
7.721
7.885
8.049
0 17.249
0 17.413
0 17. 577
0 17. 742
0 17.906
0 18.070
0 18. 234
0 18.399
0 18.563
0 18. 727
0 18. 892
0 19.056
0 19. 220
0 19. .384
0 19.549
0 27. 105
0 27. 270
0 27.434
0 27. 598
0 27. 762
0 36.962
0 37. 126
0 37. 290
0 37. 455
0 37. 619
0 46. 818
0 46. 983
0 47. 147
0 47. 311
0 47. 475
0 56. 675
0 56. 839
0 57. 003
0 57. 168
0 57. 332
0 57. 496
0 57. 660
0 57. 825
0 57. 989
0 58. 153
6.531
6.695
6.860
7.024
7.188
1 16.388
1 16.552
1 16.716
1 16.881
1 17.045
45
46
47
48
49
50
51
52
53
54
.123
.126
.129
.131
.134
.137
.140
.142
.145
.148
50
51
52
53
54
55
56
57
58
59
0
0
0
0
0
8.214
8.378
8.542
8.707
8.871
0 27. 927
0 28. 091
0 28. 255
0 28.420
0 28. 584
0 28. 748
0 28. 912
0 29.077
0 29. 241
0 29. 405
0 37. 783
0 37. 947
0 38. 112
0 .38. 276
0 38. 440
0 38. 605
0 38. 769
0 .38. 933
0 39. 097
0 39. 262
0 47. 640
0 47. 804
0 47. 968
0 48. 132
0 48. 297
0' 48. 461
0 48. 625
0 48. 790
0 48. 954
0 49. 118
7.353
7.517
7.681
7.845
8.010
1 17.209
1 17.373
1 17.538
1 17.702
1 17.866
0
0
0
0
0
9.035
9.199
9.364
9.528
9.692
0 58.317
0 58. 482
0 58. 646
0 58. 810
0 58.975
8.174
8.338
8.502
8.667
8. 831
1 18.0.30
1 18.195
1 18. 359
1 18.523
1 18.688
55
56
57
58
59
.151
.153
.156
.159
0.162
TABLE 9.
[Page 483
Mean Solar into Sidereal Time.
c
g
S
To be added to
a mean time interval.
8h
flh
lOh
lli>
12h
ISh
14h
15''
For seconds.!
m.
m. s.
m. 8.
m. s.
7/1. S.
m.
s.
m.
8.
m. s.
m. s.
s.
s.
0
1 18.852
1 28.708
1 38.565
1 48.421
1
58. 278
2
8.134
2 17.991
2 27. 847
1
1 19.016
1 28.873
1 38. 729
1 48.585
1
58. 442
2
8.298
2 18. 155
2 28.011
1
0.003
2
1 19.180
1 29.037
1 38.893
1 48.750
1
58. 606
2
8.463
2 18.319
2 28. 176
2
.005
3
1 19.345
1 29.201
1 39.058
1 48.914
1
58. 771
2
8.627
2 18.483
2 28.340
3
.008
4
5
1 19.509
1 19.673
1 29.365
1 29.530
1 39.222
1 39.386
1 49.078
1 49. 243
1
1
58. 935
59.099
2
2
8.791
8.956
2 18.648
2 18.812
2 28. 504
2 28. 668
4
5
.011
.014
()
1 19.837
1 29.694
1 39.550
1 49.407
1
59. 263
2
9.120
2 18.976
2 28. 833
6
.016
7
1 20.002
1 29.858
1 39.715
1 49.571
1
59. 428
2
9.284
2 19.141
2 28. 997
7
.019
8
1 20.166
1 30.022
1 39.879
1 49. 735
1
59. 592
2
9.448
2 19.305
2 29. 161
8
.022
9
1 20.330
1 30. 187
1 40.043
1 49.900
1
59. 756
2
9.613
2 19.469
2 29. 326
9
.025
10
1 20.495
1 30.351
1 40.207
1 50.064
1
59. 920
2
9.777
2 19.633
2 29. 490
10
.027
11
1 20.659
1 30.515
1 40.372
1 50. 228
2
0.085
2
9.941
2 19,798
2 29.654
11
.030
12
1 20.823
1 30.680
1 40.536
1 50. 393
2
0.249
2
10. 105
2 19.962
2 29. 818
12
.033
13
1 20.987
1 30.844
1 40. 700
1 50.557
2
0.413
2
10. 270
2 20. 126
2 29. 983
13
.036
14
1 21.152
1 31.008
1 40.865
1 41.029
1 50.721
1 50. 885
2
0.578
0.742
2
10. 434
2 20. 290
2 30. 147
14
. 038
15
1 21. 316
1 31.172
2
10. 598
2 20.455
2 30. 311
15
.041
16
1 21.480
1 31.337
1 41. 193
1 51.050
2
0.906
2 10.763
2 20. 619
2 30. 476
16
.044
17
1 21.644
1 31.501
1 41.357
1 51.214
2
1.070
2
10. 927
2 20. 783
2 30. 640
17
.047
18
1 21.809
1 31.665
1 41.522
1 51.378
2
1.235
2
11.091
2 20. 948
2 30. 804
18
.049
19
20
1 21.973
1 31. 829
1 31.994
1 41.686
1 51.542
2
1.399
2
11.255
2 21.112
2 30. 968
2 31. 133
19
20
.052
.055
1 22.137
1 41. 850
1 51. 707
2
1. 563
2
11. 420
2 21.276
21
1 22.302
1 32. 158
1 42.015
1 51.871
2
1.727
2
11.584
2 21. 440
2 31. 297
21
.057
22
1 22.466
1 32.322
1 42. 179
1 52.035
2
1.892
2
11. 748
2 21.605
2 31.461
22
.060
23
1 22.630
1 32.487
1 42.343
1 52.200
2
2.056
2
11.912
2 21. 769
2 31.625
23
.063
24
25
1 22. 794
1 22.959
1 32.651
1 42. 507
1 42.672
1 52. 364
2
2.220
2
12. 077
2 21. 933
2 31. 790
24
25
.066
1 32.815
1 52.528
2
2.385 ; 2
12. 241
2 22. 098
2 31.954
.068
2(5
1 23.123
1 32.979
1 42.836
1 52.692
2
2.549 2
12. 405
2 22. 262
2 32. 118
26
.071
27
1 23.287
1 33. 144
1 43.000
1 52.857
2
2. 713 2
12. 570
2 22. 426
2 32. 283
27
.074
28
1 23.451
1 33.308
1 43. 164
1 53.021
2
2.877 ' 2
12. 734
2 22.590
2 32. 447
28
.077
29
30
1 23.616
1 33.472
1 43.329
1 43.493
1 53. 185
2
3.042 , 2
12. 898
2 22. 755
2 32. 611
29
.079
1 23.780
1 33.637
1 53.349
2
3.206 1 2
13. 062
2 22. 919
2 32. 775
30
.082
31
1 23.944
1 33. 801
1 43.657
1 53.514
2
3.370 2
13. 227
2 23. 083
2 32.940
31
.085
32
1 24. 109
1 33.965
1 43.822
1 53.678 2
3.534 2
13. 391
2 23. 247
2 33. 104
32
.088
33
1 24.273
1 34. 129
1 43.986
1 53. 842 i 2
3.699 2
13. 555
2 23. 412
2 33. 268
33
.090
34
35
1 24.437
1 24.601
1 34. 294
1 34.458
1 44. 150
1 44. 314
1 54.007 ; 2
1 54. 171 ; 2
3.863 2
13. 720
2 23. 576
2 33.432
34
35
.093
4.027 2
13. 884
2 23. 740
2 33. 597
.096
36
1 24.766
1 34.622
1 44.479
1 54.335 2
4.192 2
14. 048
2 23. 905
2 33. 761
36
.099
37
1 24.930
1 34. 786
1 44.643 1 54.499 2
4.356 2
14.212
2 24.069
2 33. 925
37
.101
38
1 25.094
1 34.951
1 44.807
1 54.664
2
4.520
2
14. 377
2 24. 233
2 34.090
38
.104
39
40
1 25.259
1 35. 115
1 44. 971
1 54.828
2
4.684
2
14. 541
2 24. 397
2 34. 254
2 34.418
39
.107
1 25.423
1 35.279
1 45. 136
1 54. 992
2
4.849
2
14. 705
2 24. 562
40
.110
41
1 25. 587
1 35.444
1 45.300
1 55. 156
2
5.013
2
14. 869
2 24. 726
2 34. 582
41
.112
42
1 25. 751
1 35.608
1 45.464
1 55. 321
2
5.177 i 2
15. 034
2 24. 890
2 34. 747
42
.115
43
1 25.916
1 35. 772
1 45. 629
1 55. 485
2
5.342 ! 2
15. 198
2 25. 054
2 34.911
43
.118
44
45
1 26.080
1 26.244
1 35.936
1 36. 101
1 45. 793
1 45.957
1 55. 649
1 55. 814
2
2
5. 506 1 2 15. 362
5.670 2 15.527
2 25.219
2 25. 383
2 35. 075
2 35.239
44
.120
45
.123
46
1 26.408
1 36.265
1 46. 121
1 55.978
2
5. 834 2
15. 691
2 25. 547
2 35. 404
46
.126
47
1 26.573
1 36.429
1 46.286
1 56. 142
2
5. 999
2
15. 855
2 25. 712
2 35. 568
47
.129
48
1 26.737
1 36.593
1 46.450
1 56. 306
2
6.163
2
16. 019
2 25. 876
2 35. 732
48
.131
49
1 26.901
1 36. 758
1 36. 922
1 46.614
1 46. 778
1 56.471
2
6.327
2
16. 184
2 26. 040
2 35. 897
49
50
.134
50
1 27.066
1 56.6;^
2
6.491
2
16. 348
2 26. 204
2 36. 061
.137
51
1 27.230
1 37.086
1 46.943
1 56. 799
2
6.656
2
16.512
2 26. 369
2 36. 225
51
.140
52
1 27.394
1 37.251
1 47.107
1 56.964
2
6.820
2
16. 676
2 26. 533
2 36. 389
52
.142
53
1 27.558
1 37.415
1 47. 271
1 57. 128
2
6.984
2
16. 841
2 26. 697
2 36.554
53
.145
54
1 27. 723
1 37.579
1 47.436
1 57.292
2
7.149
2
2
17.005
17. 169
2 26. 861
2 27. 026
2 36. 718
54
.148
55
1 27.887
1 37. 743
1 47. 600
1 57.456
2
7.313
2 36. 882
55
.151
56
1 28. 051
1 37.908
1 47. 764
1 57.621
2
7.477
2
17. 334
2 27. 190
2 37. 047
56
.153
57
1 28.215 1 38.072
1 47.928
1 57. 785
2
7.641
2
17. 498
2 27. 354
2 37.211
57
.156
58
1 28.380 1 38.236
1 48.093
1 57. 949
2
7.806
2
17. 662
2 27.519
2 37. 375
58
.159
59
1 28.544 1 38.400
1 48.257
1 58. 113
2
7.970
o
17. 826
2 27.683
2 37.5.39
59
0.162
Page 484j
TABLE 0.
Mean Solar into Sidereal time.
c
ai
To be added to a mean time Interval.
leh
l**"
ISh
ISk
20'J
211.
in. s.
22h
ash
For seconds.
m.
m. s.
m. 8.
m.
s.
m. s.
TO. 8.
m. 8.
tn. 8.
8.
! 8.
0
2 37. 704
2 47. 560
2
57. 417
3 7.273
3 17. 129
3 26.986
3 36.842
3 46. 699
1
2 37. 868
2 4^. 724
2 57. 581
3 7. 437
3 17.294
3 27. 150
3 37.007
3 46. 863
1
i 0. 003
2
2 38.032
2 47. 889
2 57. 745
3 7.602
3 17.458
3 27.315
3 37. 171
3 47. 027
2
.005
3
2 38. 196
2 48. 053
2 57.909
3 7.766
3 17. 622
3 27. 479
3 37. 335
3 47. 192
3
.008
4
2 38. 361
2 48. 217
2 58. 074
3 7. 930
3 17. 787
3 27. 643
3 37. 500
3 47. 356
3 47.520
4
5
i .011
:oi4
5
2 38. 525
2 48. 381
2 58. 238
3 8.094
3 17.951
3 27.807
3 37. 664
6
2 38.689
2 48. 546
2 58. 402
3 8.259
3 18. 115
3 27.972
3 37. 828
3 47. 685
6
! .016
7
2 38. 854
2 48. 710
2 58. 566
3 8.423
3 18.279
3 28. 136
3 37.992
3 47. 849
7
.019
8
2 39. 018
2 48. 874
2 58. 731
3 8.587
3 18.444
3 28.300
3 38. 157
3 48.013
8
.022
9
2 39. 182
2 49. 039
2 58. 895
3 8.751
3 18.608
3 28.464
3 38. 321
3 48. 177
9
.025
10
2 39. 346
2 49. 203
2 59. 059
3 8.916
3 18. 772
3 28. 629
3 38. 485
3 48. 342
10
j .027
11
2 39.511
2 49. 367
2 59. 224
3 9.080
3 18.937
3 28. 793
3 38. 649
3 48. 506
11
! .030
12
2 39. 675
2 49. 531
2 59. 388
3 9.244
3 19. 101
3 28.957
3 38. 814
3 48. 670
12
! .033
13
2 39.839
2 49. 696
2 59. 552
3 9.409
3 19.265
3 29. 122
3 38. 978
3 48. 834
13
; .036
14
15
2 40.003
2 49. 860
2 59. 716
3 9.573
3 19.429
3 29. 286
3 39. 142
3 39. 307
3 48. 999
14
i .038
2 40. 168
2 50. 024
2
59. 881
3 9.737
3 19.594
3 29. 450
3 49. 163
15
.041
16
2 40. 332
2 50. 188
3
0.045
3 9.901
3 19. 758
3 29. 614
3 39.471
3 49. 327
W
.044
17
2 40. 496
2 50. 353
3
0.209
3 10.066
3 19.922
3 29. 779
3 39.635
3 49. 492
17
.047
18
2 40. 661
2 50. 517
3
0.373
3 10.230
3 20.086
3 29.943
3 39. 799
3 49. 6;56
18
.049
19
2 40. 825
2 50. 681
2 50. 846
3
0.538
3 10. 394
3 20.251
3 30. 107
3 30. 271
3 39. 964
3 40. 128
3 49.820
3 49. 984
19
.052
20
2 40. 989
3
0.702
3 10.559
3 20.415
20
. 055
21
2 41. 153
2 51.010
3
0.866
3 10.723
3 20. 579
3 30.436
3 40. 292
3 50. 149
21
: .057
22
2 41.318
2 51. 174
3
1.031
3 10.887
3 20. 744
3 30. 600
3 40. 456
3 50. 313
22
.060
23
2 41. 482
2 51. 338
3
1.195
3 11.051
3 20. 908
3 30. 764
3 40. 621
3 50. 477
23
.063
24
2 41. 646
2 51. 503
3
1.359
3 11.216
3 21.072
3 30. 929
3 40. 785
3 40.949
3 50. 642
3 50.806
24
25
.066
25
2 41.810
2 51. 667
3
1.523
3 11.380
3 21.236
3 31. 093
: .068
26
2 41.975
2 51. 831
3
1.688
3 11.544
3 21. 401
3 31.257
3 41.114
3 50. 970
26
.071
27
2 42. 139
2 51.995
3
1.852
3 11.708
3 21. 565
3 31.421
3 41.278
3 51.134
27
.074
28
2 42. 303
2 52. 160
3
2.016
3 11.873
3 21. 729
3 31. 586
3 41.442
3 51. 299
28
.077
29
2 42. 468
2 52. 324
3
2.181
3 12.037
3 21. 893
3 31. 750
3 41. 606
3 41.771
3 51.463
29
.079
30
2 42. 632
2 52.488
3
2.345
3 12.201
3 22.058
3 31.914
3 51.627
30
.082
31
2 42. 796
2 52. 653
3
2.509
3 12.366
3 22.222
3 32. 078
3 41.935
3 51. 791
31
.085
32
2 42. 960
2 52. 817
3
2.673
3 12.530
3 22.386
3 32.243
3 42. 099
3 51. 956
32
.088
33
2 43. 125
2 52. 981
3
2.838
3 12.694
3 22.551
3 32.407
3 42. 264
3 52. 120
33
.090
34
2 43. 289
2 53.145
3
3.002
3 12.858
3 22.715
3 32.571
3 42. 428
3 52. 284
34
.093
35
2 43.453
2 53.310
3
3.166
3 13.023
3 22. 879
3 32. 736
3 42. 592
3 52. 449
35
.096
36
2 43. 617
2 53. 474
3
3. 330
3 13. 187
3 23.043
3 32.900
3 42. 756
3 52. 613
36
.099
37
2 43. 782
2 53. 638
3
3.495
3 13.351
3 23.208
3 33.064
3 42. 921
3 52. 777
37
.101
38
2 43. 946
2 53. 803
3
3.659
3 13.515
3 23.372
3 33. 228
3 43. 085
3 52. 941
38
.104
39
40
2 44. 110
2 44. 275
2 53. 967
3
3.823
3 13.680
3 23. 536
3 33. 393
3 43. 249
3 53. 106
39
40
.107
.110
2 54. 131
3
3.988
3 13.844
3 23. 7UU
3 33.557
3 43. 413
3 53. 270
41
2 44. 439
2 54. 295
3
4.152
3 14.008
3 23. 865
3 33. 721
3 43.578
3 53.434
41
.112
42
2 44. 603
2 54. 460
3
4.316
3 14. 173
3 24. 029
3 33. 886
3 43. 742
3 53. 598
42
.115
43
2 44. 767
2 54. 624
3
4.480
3 14.337
3 24. 193
3 34. 050
3 43. 906
3 53. 763
43
.118
44
2 44. 932
2 54. 788
3
4.645
3 14.501
3 24. 358
3 34. 214
3 44. 071
3 53. 927
3 54. 091
44
45
.120
.123
45
2 45. 096
2 54. 952
3
4.809
3 14.665
3 24. 522
3 34. 378
3 44. 235
46
2 45. 260
2 55.117
3
4.973
3 14.830
3 24. 686
3 34. 543
3 44. 399
3 54. 256
46
.126
47
2 45. 425
2 55. 281
3
5.137
3 14.994
3 24. 850
3 34. 707
3 44. 563
3 54.420
47
.129
48
2 45. 589
2 55. 445
3
5. 302
3 15. 158
3 25. 015
3 34.871
3 44. 728
3 54. 584
48
. 131
49
2 45. 753
2 55. 610
3
5. 466
3 15.322
3 25. 179
3 35. 035
3 44. 892
3 54. 748
3 54.913
49
50
.134
.137
50
2 45'. 917
2 55. 774
3
5. 630
3 15.487
3 25. 343
3 35. 200
3 45. 056
51
2 46. 082
2 55. 938
3
5. 795
3 15.651
3 25. 508
3 35. 364
3 45. 220
3 55. 077
51
.140
52
2 46. 246
2 56. 102
3
5.959
3 15.815
3 25. 672
3 35. 528
3 45. 385
3 55. 241
52
.142
53
2 46. 410
2 56. 267
3
6.123
3 15.980
3 25. 836
3 35. 693
3 45.549
3 55. 405
53
.145
54
2 46. 574
2 56. 431
3
6.287
3 16: 144
3 26. 000
3 35. 857
3 45. 713
3 55. 570
54
55
.148
55
2 46. 739
2 56.595
3
6.452
3 16.308
3 26. 165
3 36. 021
3 45. 878
3 55. 734
. 151
56
2 46. 903
2 56. 759
3
6.616
3 16.472
3 26. 329
3 36. 185
3 46. 042
3 55. 898
56
.153
57
2 47. 067
2 56. 924
3
6.780
3 16.637
3 26.493
3 36. 350
3 46. 206
3 56. 063
57
.156
58
2 47. 232
2 57. 088
'J
6.944
3 16.801
3 26. 657
3 36. 514
3 46. 370
3 56. 227
58
.159
59
2 47. 396
2 57. 252
3
7.109
3 16.965
3 26.822
3 36. 678
3 46. 535
3 56. 391
59
0.162
^ 3
^ -i
2
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 486
«»
•ajBp
xoaddv
i;Z;
cdacP^oQPj'ccpjccp^GQTiJoQPH'aQl^oQPj'cQQ^aQiPciaQp^aJM
.r-irr'^t^-^aoc-iOi-^c^ascct^iricot^ig^c^c^i-i !o
■ajBp
■xoiddv
.^;2;
iOO»AOiOOiraO'^^H|Tj<r-(Tj<i-tTjt,-i'Vi-l-^i— I
5i O*0Q i-H:OCO^iCMr»OOi
^c^,_i^MQ-.#XiCr-t-Ucx'^oc^c^occosio
I^:D;DX'^f3SCOr-li-HCO
ost^xx^o-rc^c^-^O'-o
Oi'^X^^OX-^OSNiHrHCC
:£<MO^^*CiOOXiC'^'-o!iOXCCO?C^r-lOC^ai'«J''t^»C'dt^'<J<XeOOC^i-l
SiCOiOO-^O'^Ci-^O ■VOrl^O'^r-c^r-lOOrH l»i-iCOrHCCi-«CCC^C0C^
lOCOXTftCtOiCXCOOiC^i-H
~i';NOi-*»HQC<5X-^t^i£' iCr-"^X00Ot-<f-4OC0 XTT't^:0';OI— -^xcco
^f-^Ciecxic^coicxcoos
SiOOlOO»0 0"^0'^0|'*0'*J<0'^0'J<rHTfT-fCCr-H?5i--teO»-lCOrHCCrH
'NOOrHOseCXiOCDtOiCX
oc^a>'^x»0'0?cicX'^asc^Of-'(MOcox'^t— (o
SS2
■^OiCSi-iCJC^OecCit
r*r>-tDX»CO"^rHC^(N— (C^
xor^r^^XiC^-^o
locpa>r*xxr*g»500
CO^C^Mi-tCOO'^OSiC
ii2 COiC
Oi iC O "^ «-H CC 5
.-ICC.-" c<i
O iC to iC
(M CO <N eo w
CO ic CO lO eo
r*x X t>-
i-HCOr-lCC
CO iC (O i/^
OicCOtOi-i
i-icc(Nc»5m
CO iC CO lO o
c^t-rHi>oxa>c?xo!xrHt-c^cocmcco'fT»<
lOCOiCCOiCCOiCCOiCCOUOcOiC^iCCOi^COiOCO
gco'^iort'iQiO'^cp'g'to
^iCCOiOcOiC^OiOcOiCcO
kccoiccoi^coiccrutico
~^t>-iOcOiOcO»C»ftcp»Ct"
^lOcOvCcOiCCOiCCOiOCO
■^xcococooc^^i-HO i-(^oc^aic^xccx-^
iCCOvftCO^OCOiCCOiCCO lOCOiCCOiOCOiCsOiC^
OSi-HXC^t^C^COCO^Tf
lO CO i^ CO iC CO lO CO lO CO
»i^tct^icr-cpcocpcot>-
: ic o lO o ic o ic o »c o
aiCCOiC'^iCCOiCcOiCCO
iCX'^X'^^CO^C^O<Ni-<»-(.-t.-iC^OCOC^CO
iCCOii^COi^'COiCCOiCCOiCcOiCCOiCcOiCCOiOCO
>XcpXcpxt>-t^t-*t^X
»iOcOiOcOiCtOiCcO»CcO
gX>CXiCO?"^05 7pOCCrHCO'-iCSC^C^C^r-tcC
iCCOiCCOiOcOi^COiOcO iCCO»CCO»OcOiCCOOCO
lO CO iC
t^oxoiOixor-T
iir5cccoc^t>-f-ixoa>g>o
5 to iC CO ift CO >C c
? COiC COiOcO
lOCOiO
iC-^COCC
cOiC COiC
t^M X .— OS
,_, -rr »-i -^ .-I
CO iC COlO CO
lO CO iC
incocctCco-^t^-^x
Oi^X
iC cOiO
COii^COiCCOiCCOiCCO
iC T-H lO
iC COiO
i-H iS rH -^
CO iC CO iC
iC Oi CO X CO
;aii>o>tN-^t^Qor^xxi
fttOCOiO'>OiOCOtOCO»CCO
^xr»gicog>cootOO lOr^-^i-H-^c^qoMc^cc
f^cOiCCCiCCOiCCOiCCO »OCO»CCO^COiCcOiC^
CO COM
iC CO iC
CO iC CO if^
Tf< ^ lr^ Q lO
f-l iC r-. 25 T-l
CO Lt CO ir: CO
sssg
xoxoxosx
icO«OcO:OCOcOiCcOiCco'iCcOiCCOiCcOiCcOiOCO'iCCOiCCOi^<OiCcOiCCO
S2S
2 CO iC t^ Ut) :o
• OKOQOOOO
:oooooo
j ;o to o to to '-O
ooo I
lO to to to
> lO o i.-;
siotoio
CO iC CO iC CO
g.-< i^ .-I r* tH t^ c^ ^* CJ
iftCOiCcOiOcOi^COiOcO
CD C^ CO
i?5 .-" lit)
COCOCOiCCOiC'^iO-
i-iiC rHiC
CCiCCOiC
CO iC CO iC CO
:0000000c
acOCOCOCOCOCO^C
itOCO
SS8
CO CO CO
OOOOr-.
.-t0^25rH
CO CO CO CO CO
1-^lCrHiJf^r-^lOr^lCrH
COCOiCcDiOCOiCCOiOsO
XlMXMXCOXCOt^COt^CO
lO to iC c
; CO »C CO iC
.-1 iC ^ iC 1-1
CO iC CO iC CO
•gsg
i to to to
to to to
S2§2
to to to to
'MO--iO.HO-<Ot-i..<
Or-<Or
i-lrHT-l^.-l.-<Oi-(0'-l
Or-io.-^Ot-<o,-5^
to to to to to o to to to to
S28
to to to
to to to to
rt iCi-liC i-i
toic t0 40 to
.COr^CCf— fCOi-HCC.— (Ctlf— t
:ort o
' to to to
rH OrH
to to to
OrtOi-H
to to to to
Mi-ce^r-i?^
:SS3
^ CO coco
to to to
■*i-i5<.-i
Or-lOi-(
to CO to to
Tl&rt Ot-I
to to to to to
tototototototototoco
C<MC3INtIC-)C^M'-lC^'-"M
> to to to to
to to to to to
■«*<T-ICCi-IC0iHM'-(COi-tM^«r-tCO^CC^HCC»-HCCT-HC»5r^COrHCCr-lCC^C0»
(Or-HO
> to to to
i-.Oi-lO>-l
to CO to to CO
OrHO'-iOr-lOrHOr.l
CO to to to to CO CO to to to
Or-IO
to to to
T-HOr-lOr
to to to to t
fi r_ai6 (BPiaiPi zD fi w Oiw(Axf^mPixPix\oiaifi!K^'£c^:n!^w\Pi(aPit^('ixPiaiCiia-leiai
-^^
'-^-^
ic CO r* X OS o
Page 486]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
o
3
•^Z
•xojdav
^'A
¥»
•xojddv
5^
i-l«0?-^>0 tOt-OOOlO >-llMM'*>0 tor-
we^cslNe^ iNNe5<Noo Meorfobeo coco
pHCcP^osPclcoP^aiP^cc
ooTftoo-fooc^Qoeo
g"t~.HlOeOCOlOr-lt^»0 t; ^ "2 '^ S2 'ff 2 OC 00 r^
r^ '(J* iH ^ r-l -^ r-t -^ O lO O lO O lO O lO O lO W5 O
.^ lO O lO ?D iC to i^ «£> »c <o »c o »o o u^ o »o ;o -^ r»
tfospHCcO^ccOJc/iOiaJ
coiotooo-a<©i-ie^o>in
O>0OiSoOOOi.0O
05 oD eS aj OS aj oi aa 05 tfi 05 cc 05 to 05 of 05 oi 05 oi
tpr^-^O'HC^OliCCOCO CO^HO'^l^I^'^Qi-lCO
ift O »0 ^ U5 fH Tf rH -n* t-< -^ (N -^ C>l CO C^ CO CO CO CO
rHC^r-tCOi-HCCr-ITr'THTrO'VO'^O'VOiQOlO
u-«
. CO r* ic lO r* CO o>
ft ?5 CC i-H CC i-< 00 i-l CO rH -^ i-t -^ O "^ O Tf O ■«* O ''5'
(MCOC^COfHCOrHCOt-lCO
g'coo5;^'-<0(Nas-^i>co
lMC^(NCO(NCOi-HCOrHCO
COO>ir4r-(OCOGOlC^O
f-lCOrHTj^i-H-^O-^O-^
iHC0iHC0rH-<9<rH-^O'^
g'iCI>-^Oi!NQi-H(NasC0
C^C<lfMC^C4CO(N0Oi-HCO
XiOtDCgvOCOCOO-— <i— t
I— « cO r-t CO r—\ CO i-H ^ ^^ ^
S'aootoi>icaicooc^c^ ocoai»or*50(Doo^oi
C<I (M CN (>» iM iM "N CO IN CO - • -" "" "* "' "
(MCOi-HCOr-tCOrHCOrHCO
T»'i-l^'<S>00t^tD©COCO
■*r-C*i-iCO.-ICOC5cOO
■^O-^O-^i-HCOr-ICOiH
) CO t^ icin CO c^i o o CO
SopCJOOCOGCiOtOI^
C0O>i-IC^O5'*COtO'*»
u0e0l0C0i0OiCC0"^<0
t^tO-*30lMQQCO0piC
ocooo>otoi~3iai'3i-i
COfH.-HiM^^'QOtOtoao
lOcOOtOiOOtOCOiCtO
■*Qe4(MO-^00!0!000
I00l00i0t0-^CO"^«0
«INC^lNIMlM!NC-4O<e0
^»CC0iC?0iCO»C?0i050
S.-ieo<
CO (M C
>■* O»«OO0t~5O00
■CO<NeOC<l(NC4<NINOC^
rf*iOOiOCO»C«OiOCOiOCO
gC0C^C<IC0THiOO«0 0>t^
COC<COlMCOe^C0<MlNC4
.^iCtOiO«D»CCOiCCOiCO
ifNcoo-^oiot^t-tooi-^OMCoiHeooim
iNCO(Neoc^eorHeOTHCO
r1COi-l'«'i-('«<rH'.J<0
c^cMCJcocM»(Meo?ico
T-tCOr-ICOr-tCOrH-^rH^
iO?OiCCOiO«0050tO^
COODl^OlOO-^C^COCOMKJ'-l'OOlt^COOStOO
C^(MCmMCICOC^MC^COfaeOINCOrHCOiHCOr-l-<l<
iOOiCOiCCO»0^iCCO!iOOiC«OiCO»0«0>C^
S*?OIN»OCO"^-^COlCC^tO
eoc^coc^icoo)cO(Ncoe4
,^ioeo>0!0>n«oiOtDoto
i-tt^OQ0050^t^O50.H
COlNCOC^OllNCJCOlNCO
gonr-<I:^r-i:OC4»CCO"^'^
S5c^co<Nco<Ncoc<icoe^
^iC<CiC«0lCCDiC:0»OC0
S'OOQOOJrHOOlNt— CO
■<5<(M^<NeO<NeO(NCOIN
g'eoo><N03C^Oi-ii-ioc^
giooO'^oo'^ocoase^o
»aoi^t^r^t^ooocoio<35
tootooit^oot^oooo
: S 1-1 Tfi r-l ■*
> lO CO iC ^ lO
1-4 -^ T-f -<J< i-H
«OiO«0»C ?o
COiCC^tDrHt^Q0DC»O>
CONCOCT CO c<i CO cmMC^
'^Tj'ioiO'j'coeot^iNoo
eoeJcONeoc^eoiNcoc^i
CO c^ CO ?a CO c<i
to in lO to
COC^CO<N
lOtOiOtO
iCCOT)<-*(Ni!Ji-ltOOOO
CJCOMCOC^ICOC^COI^CO
iCtOiOtOiOtOiCtOiCtO
30i-(t^C^tOCOtO-^COiO
UeOC^COIMCOlNCOC^lCO
lOtOiAtDiCtOiAtOtOtO
i-IO>OOCT>rHCOlNl^CO
COCJCOCOC^COC^COOCO
lOtOiOtOiOtOiOtOiOtO
"t t^-^ooeo
cocqcOiMco
lO to lA to lO
N CO CO CO CO
to lO to lO to
•<}< H •«(< IM Tj" C^ C
lO to iC to lO to 1
;■* [t^ic t~- tot
ireo-^oco-ie^c^oaco
SiCtOiOtOOtOiOtO
1 1^ IC t^ ■»** 00
I C^ CO C^ COS
I to if^ to 1/t) to
i-iCO<— l-rJ<QU5OSiC0QtO
l^ 00 1^ Oi to o>
'CMiOIMlOC^tOiHtOi-lt^
:idHio 1-tio
iiotoifl toic
1-t tC T-t lO rH
to in to lo to
Ol^ QCCOIOD
iC to iC to lO to
inOlOr-l
Tr <M ij" c^
lOtOiCtO
0>0> 00 (35
ijir-l^r-l
in to lO to
ic toio toin
a in to in to ic
in CO in CO to
i-llOrHini-H
to in to in to
»t~'^ t^-* to
: lO rH in .-H l75
• in to in to in
■^ to "^ to in
oin toin to
»05coo>coo»cooicocoeo
sinrHinfHin
fin to in to in
iHini-iini-H
to in to in to
eotooitocioc^t-r
\fi r^ ^ T^ ^fi T-i
in o in to in to
iniHinrH
in to in to
CO IN CO rH-*
<N tC (N ■<ji (N
to in to in to
JOt^Ot^rHtOrHinC^
in to in to in
e^ ■»)< IN -"ji 6i
to in to in to
5QCintOt~-*0>C^r-(
oinininininiOinino
into'*to'^to-^toTi<t~
OOt~tOO>-^r-IC3COO'^
o-^O'fOinoinoin
intointointointointo
. . J" ^ to 00 00 to Q Tjl T-l
rHTTO-^o-^oinoin
in to in to in to in to in to
iniNcoeoiNinot^gocc
ooo»t~i-iiniN'<i<'^(Nin
' CO rH "^ I— t ^ tH ^ rH ^
intointointointointo
<NtOi-l00O>O>00iHr~lN
<NeOC<COr-(CO>H'*r1T}<
intointointointointo
tO')<'<llinCOtOINOO.HO>
iNCOINCOe^COINeOlNCO
intointointointointo
oc^oocot-'^tominto
COCOiNCOiNCOC^COC5cO
intointointointointo
COO>iNO<-It-IOC-IC:»CO
COINCOCOCOCOCOCOCMCO
intointointointointo
i^r^tpocinooi<a>coQ
co<Neoc5eoc^coiNcoco
intointointointointo
i-f in o to oi to Gci
)COC4COI^
5 in to in to
inco'*-(<co-*coiniN
in to in
INt)<1N
to in to
•*»i(Nt)<S
inointo
«00©00Q
in rH in th in
iintointom
Oi Oi Oi Oi ^
rH TJi i-( T}< C^
to in to in to
toin in in in in
in rH in i—( in rH
in to in to in to
jgto-*tO
in to in to
■^t- cor- CO
in rH in rH in
in to in to in
00 CO 00 -* aj -"ji
in to in to in to
iCrHinrH
in to in to
JrHlNrH^JrHC^i-KNrHlNrHINrHCOi-ieO
:OrHOrHO
a to to to to to
rHOrHO
to to to to to
OrHOrHOrH
to to to to to to
rH CO O CO
OrnSrH
to to to to
.grHgrHg
^ CO CO CO CO CO
i-lOrHOrH
CO CO CO CO CO
COrHeOrHeCi-HCOi-ICO(N
OiHOrHOrH
CO CD CO CO CO CO
OrHOr-1
COCO COCO
t^ CO 00 C^ 00
t^iocpioco»ccpcococo
iCrHiOrHiCrHiOrHiOrH
iOCOOCO»CCOiOcOiOcO
to to to to to
38383
to to to to to
coiNcoc^cooicoe^coc^
O ?H S rt S
^ CO CO CO CO
rtOi-HOrH
CO CO CO CO CD
05yJa5a5o5a305t»Q5co05c»05oc05c»e5cco5codaae5vJ05coo5a303co
'T"
00 ^ ^^^ .- c^i CO -^ in
?5c^co cococococo
OOOOOrHt-rHt-C^ItO
in toin
c^-riN
to into
into in to
(NQ0C^0>rH05rHOOO
OrHin
in to in
inrH
to in to
ine<iS(N
in to in to
to to in
Jo I— ( in
in to in
toin to
to in to
in to in to
l-iJ'OJ-^C
S rH in rH t
jtoin tou
OrHO
to to to
iNgiN
to to to
to to to to
O5o5o5c»05c»05cc05a}
to i^ 05 Ol C3
M CO CO CO TT
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 487
12;
.^^
•xoaddy
•xojddv
-^ C>1 cc
(^aifiiaafiicapiaifiitn oj cc pj cc P4 cc pj co pj oq
g'MCOlN'^fil'i-l'i'r-llC
OiOOOOOiOOiOi— I
S't-i-HTfiCOOOtOiMC^tO
^ ^ t^ ^ t^ ^ t^ ^ t^ ^ t^
5 c<i ir4 o» C4 M CJ e
OiQOiCOiOiCOiOO
3<aQp4iX!pHixipiJ!Xipja}
pjasp:;c»QHaQpH!»McQ
•r th e<5 c^ M M M e<3 1-1 ■* i-i>oooino-*i-icoc^
coaocoGOcoxccxcccc;ccoo c«ra> c^ a» c^ os c-i ai
MOOCOCOCOOOCOXCOTO
rHT(IO^OinOlS>ftO
— <inicooo-i'c<ioooo
f-H'^OiOiCO'iT'i-IWr-l
or-ecrH05-^L':5airHcooi:^i-tc^:oi^»-Hcoioooos"^nr-iiooit^t^
eot^cooocooocococooo
MOOCOOOCOOOWQOCOOO
■<JI rl M tH « i-l «
» lO r- CO m o c^ I
rfi •<ji t^ -^ t~ •* t~ -
ItHCOi-l
r»O5C3t^>OiC00C^-HO»M
>-li-IOOiO-^OOi-H^I^«5
«>tOMOlOMtOtOCOO
01INC^O)C^eOrHMr-ITr
50C^C^C^<NMC>)COi-l05
M»Hciir-ICOlNC4c5ciN
sss
iC O-^ O "^O-
,^-^t~T»lt~T)lt~^t
C^(Na>'S<Ol^MOOCO
■^r-IC0i-l«lr-ICOC^M<N
giS5iraioio»ooiC
ht^O^r-l-^T-tOOT-ICOi-H
>>0(NcocOrtico>r-
(NMOior-goiooc^co
lOOiOOfO-^r-ITl'i-l
SsooeooooiOMO
■*t~eOt~M00M00COO0
JOCOiOt^QC
<OiCiOiCiSC
■rf*r»T}<t^-<ti-*cot>oooo
iCt~o»eoo50>r^!DOco
i<o«i-teo.-Hc^c^oje<5
COQOMOOCOOOCOQOWOO
moor-ic^t-toiMQaoio
r-IOTi-l'^O'^OlOiniiS
COOOOiOCJOOOOCO
»-i (M rococo OS OS ccior*
~)C<3i-I«i-CMO-^Ot)<
r-o-^QOiNr-t^coi-i
NOJMOTC^ CO 1-IOT !-(■<}>
-iOi-it<i-^aot~500co
T O -Tf rH CO
CO 00 CO CO CO 00 ec
T-(eo<N
xcooo
SC<ltOt^02JiCQpOSCO
■<J<t~COt~COO0CO00CO00
GOlO ^ Q
©■^ois
OJiCtM
cot- CO
00 CO CO
eooiS
H I^ OJ C^ CO O) CO i-H ^ ^^
- £! ■
o-rou
Tfr--*
00 CO 1-1 p iQ t- 00
rH CO e^ « N e^ oS
t- Tj< |> ■* t^ ^ t~
coc^ostCiOosiH-^r-^os
t^OiUJi-tCOCO^H?
t- It t- ■* r~ -^ r-
g" ^ !-» 2 00 OO p --O
iH -r O -f o 55 o
SoS
— ■lOCO'TiOe^tOiHOOC
Si-ITf<rH-*i-C^i-C^<
;osoooi-ir~cou5'^»j<o
- — ^ — -"Jlr-IT)"
SOS o 00 1-t r* CO lo
iH •>»' 1-1 ■* 1-1 ^ T-l
!ii«t~eoooMpfHT
S (M CO c5 CO 6j ^ e^ '
Sc5SlNCO
t^iootoi^r^^os
iNCoSc
iC?o»o t
SsjcocOcO
j; lO to lO «0
C^NrHCOQ'^OQUJ
S* t^ OS to OS ki
C0lMeOC4C
^iC to iC to u
<r-IC2 0»
3 CO CO CO
5tOiO to
COiOi-H^OSOStOiH-
0U50 - - - ^ -
lO tOkO
. _ _ toiHifeo
lO >A iC lO O kO o
to T)< to Tt< t- -Tji t-
tOr-ICOCOOtOt-OS-^C^iHOI^CTi
•^i-|-*rH-*r-ICO<HCOMCOCJC^t^
c5coc
(NtOOSQOr^i-t-^COrHtO
- "Oil'i-lrJliH-^rH
t>. ^ t^ ■^ t>. ^ t>.
00 1-1 to
OiOO
iCtOiO
CO ^iflejt^QOS
to iC to IC to iC to
SoSc
(Nt^oos^i-n^eom-
iHrfrl
lOtOi/S
lO O tC O ^
to kC to lO to iC to
sss
intoio
l-3<tO
r-li*iH
lOtOO
lO IC t- CO OS rH p
ii< rt Tji i-( ■» iH Cn
to lA to lO to iC to
SOS p t- CO in >o
^ O iO p lC O
to ■<J< t» ■^ t~ ■^ t»
lOtOiO
■* to to s 00 53 p
o in to in to lO r»
C^^C^^C4'tT-(^iH^
lOtointointointoioto
1-ITjlrH
iintoio
OS C^ rH O N go -V
•^ rH in r^ lO P in
to in to in to in to
30sincOi-itooDpt(<co
Si-ieoe^eociiMeoojeo
incoM to
Tfr-cairH
OS OS to c
COrHrtC
inp'Vi-i
t>-co-^
to^oo
l>1^t^
inpinp
t^Tfint^c)
— mom
S to ■"too
mom
m torn to
sss?
mt^imt
r^totor^mos-^pc^rH
HOTC^eoc'icoc^^NiS"
mtomtomtomtomto
s^joototor^-mos
stomtomtomto
COpi-l(N
mtomto
omo
m torn
CQCCCCOOCQCOCCOOCOOO
_i tp CO ift ■^
'»»' !M "^ 61 '^ 5^
liO coo CO lO o
gS2S2
,c;m to mto
CO 00 CO
m 1-1 in
mtom
r-imi-l
torn to
g'Qomoom
m 1—1 m rH
.fl* m to m to
QO moo t
mtom t
oocor"COt>.T»<tommm
mtomtomtomtomto
r-ostooti-'coc^c^'*
(MCOIM-
m tom t
CO 3; cj in T^
CO CO CO
mtom
p 00 OS OS
CO CO CO CO CO C^ CO
tom tom tom to
Smos t^
mtomto
t~oom
m tom
Scorj
i-im
tomto
H in CO CO
:mtom
I- j^to
tom to
3 .H t^ (N to CO m a;
iCOCOCOCOCOCOCO
stomtomtomto
T« in CO toe
cococoeoc
m to m to L
5 CO e^ CO
^tomto
m to -^ to CO t^ CO 00 c^ OS
caosoioi-ioi-i.-ii-irt
mT-imc^m(NmMmc>i
mtomtomtomtomto
mSmc
m tom t
5 OS CO 00 t
>mtom to
TtOI-VCO
m tomo
poo>-<occ^r-co
CO CO CO
mtom
CO CO CO
tomto
mtomto
tomm
II Si-*
mtom
tomt~.
tomto
t^tot^tOI^t^tOt^tOt^
mrHm»— imi— <mi-^mr- 1
mtomtomtomtomto
X in 00 u^. 00 »« o>
\0'^^'£>
^^
*z
g g oj g ca
^ to to to to
gCO'NC
r-(Or
to to to t
IC^COOJCOOICOi-tCOi-tCO
jOi-lOi-lOrHOi-lOrt
itotototototototo to to
rH OJ CO -^ m to
-* -^r KS< ■* ■* I -T
05 02 a; 03 05 CO Pf 03 05 OQ
1-hCO^HOO— ^COi-H^i— (■"J*
Oi-l O
to to to
i-IOi-i
to to to
Oi-lOi-l
to to to to
1-1 •*P'*
Oi-iOi-l
to to to to
g3g
OtOtO
mpm
^-* O 1— I
to to to
05o3'o5oco5a}pjo305o3bjaQ05os05;cOiGCQ5o3
X OS P r- ^'l CO -"t l?f"^| t$^ (^ ^5 OS p^
^^m mi-'^mmmmmmmto
Page 488]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
Xi u.
^z
o T-i c^ ec
'xojdd V
iO<oi-*ooci Oi-tc^eo
li^ to I^ CO o
C^xQ^aiP^cGP^cctfcd,94%p^cctfcctic/ipHcdOiJccOi$cfi0cioc^vj^
S*C»«OOS(C5itpcyi«pai«P 04!03050X)<©CC«DCO«P
ootpao<£>oo'^op?©oo«p
QO^oo^aD'^aotpao^ootp
CiCCaiaOOJOOOiCOOiOO
aOqOX'OOQOOOODXXQOCCOC
jsQCCOaOQGOQQCOXOOSQOiQOaOa'-OiOs
00OG0Q00Q00O0Di-HQ0»-i
iCtOiOOiC^CiC^DiCO
GCC^OOC^CCC^XCOt^CCI^CC
^iC^iCCOiOCOiC^iCtO
iCCOiOOiC^dCtOiCtO
co^oot'-t^r*t^t^r*oocox
g^ai50asr*QOt^Gcoo
gt^QOOOQOOO^QOO
t^Or-r-l?Oi-f!CC^iOC^iCCO
O^OOOSOOOi-tOCM
iC^iCiOiOtOiJStD»C<y3
Or-iQ<Na>iMXCOOD'<1*
t^fNt^COCC'^iO'^iOiC'^'C
iC^iCtOificOiCOi^^OiCtO
TTi-ITf^i-C'S'rHTri-l-^i-H-Tfr
^iCCCiCtOiCtCi»0^«C^ ,iCcOiCtOiCcO»C«vC«D
•.DC£JCOl-*iOGO"^OOCCOaCOO
iCtO»C^iCCO»C?DiC'Oir20
»acoxr^r^t^xix?Das
SiOOiCOOOiOOiCO
fliOtOiCCOiCeOiO«OiO^
Sot^QOi-^QCoci^-ai^o
. icoiJ5oicoicoi?5i-i
^:OtOiO?OintOiCiOiOCO
OOiOOiOi-tiOrHi5r-l
^tO«0»C<iOiC<OiO'^iCtO
g<N'^CO'^"^C0iC<MtO
iC(OiO<dOCOi050iCcD
gT-igiOOOir-(cO(Mr*eO(OTt»iOiOCOtD(NI»i-iX
OOOi-liCrHtSrHiCrH
UOQCOGstCO'^^COMiM':
f-HiCQtoait-oooot^as
1— it^QODOiOoOOt^i— I
iOtOiC«OiCtOiCCOiOtO
SOOOlOJOOOt^rH^C^
co(NiccO'^'^oo>frc^!iOfHi-*
iCCO'^TfCC'^OiMt^i-taOOOi
tpi^OiOt^eoooc^Oit-i.— I
QC^Q0CCt>-^tO<OiCr^
ccxc^oO'-iasiMoO'V^u
Oi-lOi-*Of-(iCr-.iOT-l
iCtOiOtOiC«OiCOi/HO
oscooo»cr*<:oiOi^'^a>
iC(0iCt0iC(0iCOi.0?0
_ . _ CO coicr
iO:OiOOiO?OiCOiO«OiC',
^(0':0':00':0-^ii^'-OiCcO
SS2
O— 1^
CO oc in to to
to iC to iC to
iOt~--9iaOMOr-.HQCO
lOi-llCrHiCC^lCC^liSC^
iCtOiCtOiCtOiOtOlOtO
lOtC
r* toto^«•-
•* c^-^iN-
iO toiA to L
5MOIi-ir-lOMaCiCtOtOiCQOMS
SiOtokntOiOtOiCtOiCtOtOtOiftt
iCtOtOtOLCtOintOlCtO
lOtO
lO tOiC to
marl—'
^ CO ^ CO
UD tOiO to
OCOX'^tOtOiCopcOOiC^^
■^ coco CO CO CO CO CO CO coco -T
intOiOtOvCtOintOiOtOiCtO
Sg2
^ ^ :o
t-t»C
•sO'-DiC
00 c**^ coco
1-1 iC i-H i?5 i-H
CO iC CO iC CO
-pj"r*Mai— iT-*Oi-sxTt<
ic t-* cox
tC CO iC CO
XCCt^iCiCt^COXi-tOOC^
COCQC0C0C0C0eCCCCC*^CC-^
irscoirrcoiccoiCcoiccoiCico
dlBp
•xojddv
2-^'
^55
S to tOiTi
i-(id-iin.-i
to iC to lA to
T-.IC
lO to ic
rHift Ol
tOtC to
00?J tO"*
lOtOiC to
S8§
.MtOtO
00^t--i-liCCOCO'*
iCOiCr-tiOr- (iCi—l
iCtOintOiAtOiAto
c^too
ic toiC
toic to
tOrH-*eO
lOtoioto
5 CO t~ C4 OS
I ■'T fN -^ 04
; ic toio to
-^ CO CO CO
in to lO to
tO-^iCtOCOOOrHOsasrHt^CO
cocococococococooa^c^-*
lOtoictointointointoiCto
•VC^COOJ
in to in to
t^QiCIN
CO CO CO CO
in to lO to
eOTj<(Ntoooooco»toi-ii<co
COCOCOCOCOCOC^COfN-^lN*^
intointointoiotointointo
r in o
". lOto
in oui
intoic
.t>-intot~'«)'ooc^o>-<c^Oicot^intor--^ai!N'-i
J to in to
oin i-HinrH
to in to in to
> in to in to
COMCOC^
in to in to
■*00(NO
CO ?1 CO CO
in to in to
QC^OOrftOtO-^CCC^OOC^
COCOC-<COI^COC^CO(N'*C^'»
intointointointointointo
pixXxQiaicixoiai\ci!XiciiK(A^Xx!^wm^fiiixaiwXi^x<£mcDaixa^X!jiOia^oi^
"^^ ^ m ^, ^a
to l~ X
O ^^"^ 1-H
in to t^ X
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 489
a ^
s
BO
a
■c
o
»
(M
^
M
'6
•P
T1
cc
a
0
■*->
3
vi
u~t
^
O
O
^
n
t,
'.r3
*;z;
•ajBp
xojddv
?i
(M CJ CJ
C^I C-l iM CO
s ^
P^OSC^GOp^OQf^COpjX P4 X C^ OD plj (Xl 0^ TjO p^ CO p< X p^ CO p^ GQ Q^ CO P^ CC C^ CO Ct^ 00 OEh CC pE^ CO pg ^
^iCiCidOiCiCiOiCiCiC lOiOiO^Ci^UtiiOiOiCiC »0 iC »C- iC tC tO iC lO iCiC j»C lO »C iC i-C iC iC iC iC «c
S'«Otpi^cpcOt*iCt^iCX'iOQO-^GO-<*'OS'^OCOai
ccoiNOCMi-irH^^c^'orNoeoaiocoi'^cO'^
S"«pi^iOOi»aO"^o^OTr'-HccrHcoc^c^c^c^coi.-HcC'-^'^ooosiC'as^cO'-or^t-'t^»«o«'Xio>
TfH^'^.-H^f-ITPr-l-n^r-H -frH'^i-C^.-H^i-CtJ^rH iJOf-'Mi-HCCr-lfCrHCCr-t
:COiC»-''n".--C0C4C0C0
«c^coc^cccslccc^ccc<i
S'co:ocor-2^r*c^corHosooidoaoi-ir^Mr*co
■V^H'Tf<T-C«»"i-t'^r-('^rHhtT-ieOC^COC^CCC^COC^
COC^Ct5c^COC^CQCMCCW|CCC^CO?JCOCCC^«1^»CO
-^rt'^1-H^c^'^c^'^^^coc^coc^«^^coc^cOl^J^coe^cc?1ccc^cc«ccco54eoc<^otc^ccc^«
S'w^^^oc^^cooO'^r>-u5tDcoict^'^xccaik^Oi-^r-*Qc^aic<50Q3;t^iO?ct^w^ocMffic^
^c^"^c^"^c^coc5o5mcoc^o5c^co^^coc^ccc^IjCOcoccccmccc^ccc5ccc^w
S'^HCQO'*o>iOx«pr*t^
^C^COCM«C4CC5«55cC
ig '-• T? c^ ?? w rr! T?
^■^coic^?oooDOio>h-Q«D^-?'eoeO'n*?^«o
COCCeO«COCCiCCCo5lCOC^^(N^'M'<!fC4^C^^
'xojddv
WCOCCCOCvCCOOOOCOW
g*t>.WCDC5iOii^C05O(NGO
CCCOCOCiCsCOOTCCCCCC
SSCOCCCCCOCOCOPOCCCO^
S'lOt^MOOfMOQ^OiCO
CQ?Sco6lCCMCOMCO«iCOCC0O«c1cOC^COC^W 65C0C^-rCM'^C^-^tN*3*
»OtOiOtOiOX>iC*^iOO i0:DiCOiC?0iC?0iC'-0 iC:3iC?DiC^iCOift'-0
CCCCMC^COCCCOCCCCJC^CO?iMrJCOC5^C^'VC^'#C^'TfrH'^rHTf<^-^
lO ?0 iC ?OiC «
^ ^ lO to lO ^ iC to
'NCOi-lXasO>0Q^t>-(NiCW^iC5^tOi-<XOiOi
lO to tC <0 ift to lO ^ 1^2 O ^ tOtC ^ lO CO LC tOiO ^
Xi-ttOW-^-^WtOrHOO
iocoic<oir:?oictoin^
^OiO>OXritOMiOiCMtOMXOOSCii-Ht^CO
iCCOi^tOiCtOiOCDiCcOiCtOinftOiOtOiOtOiC*©
iCTMtOr-iX^QXfN
rHiAfHlSr-iiOOOOO
iotoictoiOtoicr*ior^
oac^r*co«OiO"^^c^QO ^^oiOi— 'XcctO'^'^to
?1 -^ M -^ Csj ^ C^ TP IN -^r C^ -^ C^ iC iH »C ri lO 1-t J5
lOtOiCtOiC^OiCtOiOtO lOtOiOtOiO^OiCtOiCtO
i^^<;o<OTt"t>-c^<5s.-i<-i
lO^LCtOiAtOiOtOtOtO
owr-'^iOtpMooi-HO
lOtOi/StOOtOiCtOiOt*
2S28SgSo3S
OOOOOOOOOrH
t^ i-t m t^ ec Q ^ M © 31
i-(U5.-iiCrHO^OOO
OOOOmO — K^i-H
g§S
coX'^oeoioxcOQ
OiC<:OiC^kOCOiOCO
tOiCtOiCtOiCtOiCtO
^COiO
i-t O MX*C to to
»0 C^ lO T-» lO r-^ iC
to lO to iC to iC to
-^XClOOCOcCiOtOt^
■ ^ CO -f Oi
iO?OiC
Sr* lO ic r* CO OS
r-t iC i-H iC r-i iC
to iC to lA to lC to
^Hi-H^COt^tOiftXC^O
fiOOOOOOOOrH
S3
> iC -^ t^ C^ Oi O 11
3 to iC to lO to iC t*
XTptOtpcOXi-t^-XCO
OOOOOOOr-tLf*,-!
S*iOu5COt^i-tO>Oi»Ht^CO
C^iAtOiOtOiAtOiCtOiOtO
iCOOOO
to vC to lO t'- iC t>-
'ftp'NOiOlT-th*'^'rtO
OOOOiCrtiC'i-HiC-l
iC eo lO =.
gaCOCOiCWMiOQOC
r^icu; X c^ o
SOO ^ -^ OC -^ iC o
r-l to ^ T ^ -rr a
^l^f t~
r^.H'?''.}'.— t^oGOiCcc
•* M ■* M C
■^ r* -^ t^ •"
= ■00
0D-«O — -MOiiC I'J^r^-^O^C^Osi
OOiOO
O iC t^ lO r-» ■
^ !>■ ^ t^ ^ t^ ^ t^
P4!»pjaipJGCQ^3SP4:c
-H IM CO -^ iC
iM M r) C^l CnI
C4 00 Ci; «j Pi en Cti GO ;i{ CO Cl4 0SPJ3QQicCCEHCOP£cC
.— (T^ CO -^ 15
CO CO CO CO CO
OHCceiasQJaJoiaiaJaj
to r^ oC' ff> o
CO CO CO CO T
Page 490]
^
N a
3 o
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
^'^
•xoiddv Q"^
p^cdaiccO^aQp^agpduD
pdaQpHOQpjaQpjastfcceiHCCpHail^aS^ceOicnpiScAQjaiojcoOHCCPdai
7
II
CO
o
O
bo
<ri
n
«
a
is
P
0
a)
3
Tt<
'So
■«1
0)
>
•73
m
3
C
-J r* i^ t* 1^ w r* t^ CO r^ oo
- I t
2 §.
; O ^ iC 5;] »o
g^i
lO^iCiCiCiCU^iOiOiC
kCtCiAiCiCtdCiOiOiA iCLOiCiCiCtOiOOiC^
S5S
<i0:DiC:0if^Oi0tDiCOU0OiC50iCC0i0Oi0O
OaOCOOGPrHI>.-(t^C^
CO i-H 00 ^H CO »~< 00 f-H OO rH
,^OOOiHO>rHOO'MQOeOGCCOt>-COt;r*^^"5^'^^5'-^3I'^S!2*^£2^£3^
g^^^r^eOi-HCOr-tCCiH55i-^COi-HCOrHCOi-tCOrHCOi-tOOTHCOi-ICOrHCOTH
05i-tCOrHCO»-H0OiH0Oi-t
g'lCO'^OCO^^C^C^C^CO T-ICOO'«t<5>iQOQ«DCCr*
ffS 5l W ?l CO IM CO 5^ CO C^ CO C5 CO C^ C^ C^ C^ iN C^ <N
5P(NiOcoi(5-^3;»ccoic
CO^HOOrHCOi-HCOi-^COrH
CO<-HCOM<NC4C^6lN!N
^,_4C;^^COr^COC^COfN,CO^^COC^C^01'MC<C^C5C'JCJ(NC^C^OIC^COC^CO
SwC^COfNCOC^C^CSc5c^C^C<IC^C^C^COC^COC^C0C^COC^CO.-HCOrHCOTH00i-HTpi-H'^
t-WOO-^QCOi-IC^JfN
!NC^(NC^C^COC^CONCO
i-f^o»oaocp?OGOica>
C^COC^COrHCOilCOiHCO
^c^5«?<c^coc^coc5co
•ffcocOTf^c^O'-tr^aiX
Mcocsicoc^co<NcOi-teo
ccoOf-Hiccoco-^c^co ot^cooeni-HTfcoMic
i-( TP 1-t -^ t-t -^J* I-H -^ I-H ■*}* rH Tf O"^ OlOOlO 0»0
^i>coo-^»oic-^oc^t*;f-(ooooaoi-Ht^coic-^
gC^C0C^COCslC0CSlC0CJC0tMS5(N-^rH'<»'rH'^rH"^
ftO^COC^loOC^TpCa-^rHTj*
rH^rHTPT-(*^i-H-9"rHlO i-(iCOiCOiCO^OO
cii-t'MOCOGO'^t^OiCt-;
Sc^'^tN'^rH'^'H-^T-lTj*
t* 00 o r- 00 ic o -^ »-H c^j M
f;,-H^i-H-^^HTri-HiCi— (iC
'^OC^t-Oa>g?»-lt^C0lidCC0I:>-i-40iQ0^(0C0
rH'^i-H-'TrHTrOiOOiCjOlOOOOlClOOlOO
S^t-TPkCI^WOiO(N
iCGOCOOrHC^Oi-'
O lO O O O O »-C <
lO O »C t^ iC t^ -^ I:
■^-^iHC^OQ-^lCt^COO
lOOiCrH-^rHTPi-H-^C^
rHTt*a>-.pi>ocicocooi»-t'g^aootosO'q*»-if-(ooix<©icaic^c^aiOX'ai
i-HOO»COiCOOOOjOOiOO>50»C>»-ii/it-H Ti«rH-t«i-(TrO*CO(MCO<N
-aiCi-HCOC^C^'«fOtC>COt* t>-0>tO*-«C0C0Q^C0l'*
,«©ococ^r-iioaooo>co
ifti-HtCi-Hi/ii-HTjirH-^C^
2 «
Or^OSOit^t-H^COCOtrt'i-Ht^OsaiOi-H-^'^F-HtDOiOi^'MCOvOOOO
i-Hu5i-HiOOiCOOOO
. . rH-^^
|OOOOiOOiCrHiOi-H
»0 I>iOt^'^t>'^t^"^l>"
•^c^coc^oococococ^co
:3i-HC0iOai00iQC^i-HtO
COCOCOCO?4COC5'VW'^
sssssssssss
!0C^«liOOC0I>.H-^iO|O00O01WOC0'-HC0i2
^ t^ rf t^ Tj< i> -^ t> •* i> M" r- ^ r» ^ t^ rf r- ■.>< t~
•ajwp
•xojddv
«z;
*2: BJxMcccs'uaaJccaSoiiQiaoaSMSJxaJccaia! aJaJaJxaSaiMcfiaSM
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 491
p a
•^^
•xojdd V
flj 02 C^' CO C4 CO p5 CG Ph' OQ
pHMP^copt^MpiHaip^QQpiHcdaHCOpt^cociix'CiicoaSaic^coP^cotf
i0TfOTl<O"»t<O'^O-^lO'^OC0OC0rHC0»-HMi--lC0iHC<5r-tfNC^C^C^WC^'r)
- C^ O CO O ■<** "
gQOO*-^_ _ _ _
C0-a<"^iM^Q»^Or-r-lif:i00C0»C0ir-O30G0O?0C^'^Tt*!N'^OG000O':D
StOiCTjT^CCaO.— lOa>■C^00C0'O>Ol0t^CC00r-'
■<5'lC•^lC•^^S"^Oc0 ,occocoocoocoocc
irjTpiO'^iOTriS'rrioeoiCicooccocoocooeo
gCO»-HC^O^Orf<a>iCI>!t^'--OQC'Tt* O«i-Hr-iC0O
'Tj'iO-^O'^iCCQiOCOi/SCOiOCOOCOOWiOCO
■■ r'-^'^*0"^iocoiccc;»ccotocctcccic*ooco
ss
t^(NXi'-»aiaiQocr)t^'co*^-^'^cpcot-»rHa>o
Tr-^Tj"»j<cc>5wiocoiCcoiocoi5«iCcciioeo
8Q0Cl(^COtO-^'«J*«OCOt*.-H
tDC^t^r-taOOiaiQOiHt^iC^:pOO'0'^CO':p(NI--i-t
20>O00r-<(0!N»O^'Tt<OC0
■^■^■^TP^"»?''rcoiCco
rH<:OC^iQCO'^iCCCtOC4
iOCOiCCOiCCCiCCCilScC
COiOCOiCCOiOCOScO
COiCCOOfjiOC^O(NO<N
iCcO'^Ml:^»-iXiO<
■♦co»oc^^t-ii>oooai
aia>ooQi-ir~c^t$coir5
■TCoiceoiccoiocOiCieo
OS 0004^00 OJt-CS to
Tf'^S'iSCOiOOOiCCCtCCO
;i-ta>iM00C^t*CCt>--^5O.iOiOiO"^«DC0t-CC00C^
'<f^»CC5«C<lt*r-(GOOOaOi
iCCOOCOiScOiOCOiOCOiOCM
lOCOOCOiQeOiOCOiOCOiOOO
fti-tOi!NaOWQCCOt-*fl>
ac^ocooiccoo'^oog'r*
iCOiOiCO-n'l^-TfOOeO'aOINOl^Q'-''— '0<-H0a
c^r*cctp'^>oiOT5<tpcct^co
iCCOiOCOiAcOiOCCtOCCiCOO
iCcciccoiCcoiocoiccoicoS
rHOC^JOeooscoog-^t^iftt^
iC^iC-^iOCOiOCOiCOOiOCO
(MOC00S"»**0>'^00iriC0,i0t^«Ot^':0Or*(0XiO
lO . _ .
,iOOiO»OidO»COidC
cc2ja>3jaicoQcooc^
T-t CS 1-1 r-( C^
lO ^ lO ^ »o
iC ^ iG lA 40
O CO O CO OS Tj< o>
■V u5 -^ lO CO iC CO
lO lO lO iC iC iC lO
coO-^OrfOaiCOs
5 00OQCO
5 i/5 iC ifS iC
lO i^' iC iC ^
iC iC lO iC L? t
g CO r-( CO rH
C^ W IM <M rH CO 1-1
^ iJCt "^ ift ^ u^ ^
ITS O iCiC iC lO iC
: n<ifi
Tf f-l IC
r-l iC QiO O
lO 'V O ^ J3 I
iC iO lO tO iC
> Q O Ol t^
5 O iC iC t^
Ci r* ao t^ c
.ooccoc r* oa
I Tj» -r TT '^ ''T
iiC iC i^ iCift
lO lC 11^ lAiC
• C^ iC CM »0 C^ »0 -H t-O 1-t 'O I-" *o Q r'-
-■■* — -— — ■-— — - - -^iC^^C^
S ift tC lO lO
3 ift lO O lO »C I
O (^ 15 I- 3S
CO 0» COQO OC
lO iC iC iC lO u
H -^ ^H -^ C^ TT» C^ CO
iC ^ tCiO tC ij
O lO lO »o iC
<r)0«0i-i
iC lO lO lO
lO U^ lO
-^CO'lO
tC iC lO
g!DCMOCM
■^ 1/2 TJ* IQ
lO 1^3 ifl »C »C
-CM (^ M r*
I* iC -^ »o T
^ ic o to lO
r-fi>i— ao— tX)»-iX':
lO »C iC iC iC
iC lO iC iC' »/5
Sd 01 01 01
■*r '^ "^ -^
iC lO »C lO iC
QOOOOrH
lO 4C lO
tOCO«OCO<£>COI^CO|.
lO irt lO
iC^ iC -V iC
• cor*cot^CMr^cMQOCM aoc^oo'NoO'-'0>r-io>i-i,oi
' iC ■**" »C Tp — ^ - - - -._..-..__.-„_
5 ITS iC iC iC
f< lO ^ iC ■^ iC
C iC u^ tC lO
lO ^ lO lO
iO lA lO ^
lO Ida
> t^ in
Tf .C t*
TJ< iC ^ iC I
iC U^ lO »C iC I
J tO lO iC ^
•n* 00^ x>^ QCv X cococo ca CO o»co ioi n CiCM a>
vC' iC »0 t/2 iC
i"^ lib ■Tj' ic
iC lO iC »c >a
iC ■^ 1/5 -^ iC
tf2 iC lO lO lO
lO iC iC lO »o
iTJ TT lO -^
iC iC lO lO
lO '^J^ iC
iC iC lO
•xoidd V
.^^
iiC lO
QOiOQOiOOOiCOOUJ OQi^GCiCOCOopiCXtO
iC lO lO lO iC
iCii^ iC
iC ^ iC ^ »0 TT* I
lO '^ lO T u
XiOXiCXift^X-^QO-^X
^ lO 'f lO f
iC lO lO »C i/i
iC "^ »C -^ lit
li^ lil lO i£^ iC
iO O lO lOiO
iC lO lO iC
■^ X rf
lO -V iC
; OS COS
5 50 0> '^ J> O
" iC "<J* irti ^ iC
3 lO iC lO O iC
^ ox cox
r ift ■^ ift TT
i lOiO iC iC
goo <©xo
^ iC Tf iC
lO lO lA lO ifi
00 to X CD X
■^ iC "S* ^ rr
lO iC iC iC i^
50 X to on '^
^ tC iO tO lO
X t^O X --o X
■^ *0 "^ -C "^
1/5 iC tC lO lO
CO X o xc
ifi ^ lO -^ u
lo tfi tft tfi \i
^ I
Oi-'CMCO-«3«,iOOl->-X04JO»-'CMCOTf iOcOI> 00 Ol "^"^
Page 492]
TABLE 10.
'Mean Time of Sun's Visible Rising and Setting.
S^
•xoaddv
«»
«
° 53 ?3 c5 IN S
dzfloixpiwfiixPizB
ecejecwccfioii-iTri-i
s s s s
tfcdp^xpjxtfxc^^
"-• ^ S3 3! "2
CQ CO CO OO CO
a^c^p(HCCPdGCpc^u3p<ccCc:a6D:H</3f<xa<GCQHX
lOOJSOiCiCOiOOtO O iC O -^ r-^ -^ 1-1 ^ ri CO
?Dift<Oio«o^t^'^i>^ t* ^ t^ -^ i> -^ i> -^ r* -^
S'<OC5QCOOQ«C'M-^'^04^0aiQO»H^CO^vC^!r*OiOr-.'N'^iOC«r*0>
c^c^c>5p-tcoi-tcci-^cOf-4 ,cci-(C0O'^O'<rO'VO :rj'ioioic»Cic»o*ciCi'^
S'.-ioDcor«'»c»cr-cooft^H'5?cci^iCict^cooii-HU-(ooeo«oco'^oowQOJ
c^,H^^I-^c^rH.'^4r-l(^^1-«coocoocoocoocoohr>OT^l0^lC■VlCic■^
^CDiO«OiC«Ci»ft«ClfttOiC |:0^C^lC^0^C«SlO^O4C kD'^«0'^0-^tD'n<':0'*f
■^O-^OTpOCOt-tCO
St^ir5Tf<Qcc^--aicoto
■^iO*^iC^rOCCOCO
cou^roiC'^riC'riO'vi^
,-,^,-,^^rHr-lrHC^r-iCSr-t(NOCSOC^OCOO
CCOCOiCCOiCCOiC'
STH^cooOTf^coiOQCco'aai-ii-HocoooiC50t02!
C^OCOOCOiCCOiO
cOiS
OCCOOQ'NOCiC'tOt^CO
ftOC^>-1rHr-lT-<i-.i-l,-H,-l.r-«rH,-lT-1^0iMOC^O
g«?^GCoaic30t-<r>-oiiO!CO"«rioco;oi-Hooa>ooo
Tf -^ ?0 C^ 00 O Q Oi
C^ O C^ O ?5 O M iC
COiO
^^tpcO»CtCCOOi-HOO<?S
'^lOOCOQOrHOOOC^':©
CO»CCOiJtiCOi/5"W'rf^
MiCCOiOCOiOCOiCCCiC
ficcc^Mr^ocsoioi'-
^50CO»C'^COtOO^I'*0
os^pr-c^^ccoTf'
SoiMOC^O?^OC^O.-i :Or-lr-<i-ir-iHi-<i-li-i
iNojooiNOCMOc^iceoic
OD&ejoc^ooiO(N
OIN 0.-I
OS OOrH
Or-r-
t^ n lo l-^-^
r-(i-l rH |i-l r-(
mCCtC-HOOOOSOD
C^01N0C^0C^0<N0
tOK5tOlO«liOtDiO«MO
SooO:Hi^c<itoe«5io-*M
OlMOCJOlNOC^OC^
(O lO ^ L
i^og?050oo .-( t~ N to eo ■* >o « <o 1-1
iCOiC CO iC ?0 iC CD lO CO iC «o i^
S4««Sc40MO(MO(M
.cfiClOCOiACO^COiOCOiC
t~coco afinm'^cocor-o'QOr-i
tCOiO COiO
mo
CO»C CO
iC co»o COiO
00>i-ll-~lMCD-*iO
CO^COiACOi/^cOiC
Sop<MQO»-HOsOQOSf-ian
HwiccoioroocJOM
^LCidciCkCOcoioco^
oSoo)
COiOCOlO
rot-'* core
OCM O
COiOCO
'(NOM oS
lO CO lO CO ire
OOC^Oli-IOOrHOO
OCMOC^i-lf4r^iH
cotrecoirecoiccoLO
St-TPt-coaoojovcqo-j
ireroireroireroirerooro
.^ireireireioicioicirecoire
8Or-i0iC^00«l-r»<l>. ire<OCDirei--9'90TO^fJ
coiccoirecoirecoocoire coirecoireco>recoirecoire
t— ooiosot— Mcpeo-^
i-ii-i-hC>mo^10<NO
coirecoiccoirecoirecotre
ire^COCJt-THOSOOQO
r-lrHi-lT-<rH,-lr-li-(<NS
CO ic CO .ire CO ire CO ire CO ire
c^r-roco-^ireco-^t— ro
coirecoirecDirecoirecoire
Oi-tf-HOfNosrooo-^t-
i-HOJi-lJirHi-HrtT-HMT-l
coirecoirecoirecoirecoire
Scococoiret-»ret— -^coco
ireroireccireroireroireco
^ireirevcireicireireireireio
o»rooe^©'-ii-iQ£io ccosTcocvrer-irecocoire
icirecoirecoirecoirecoiccoirecoirecoirecoirecoire
OCOiScCiScOtCCO
COiCCO'^a>'^OCOOC^Ii-ii-*OI'-*COOCOO>^OQ
iScO»CCOiCCOOCCOCOOCOOCOOCOOC^O?S
t'-'^aOCO^C^Of-lrHO
SCO CO
^ lO O
lO'n'iCCOiCCOiSCO
cc t-* r» r>- r- <© 00 «e cc ic oi-^o-^^co^coc^c^
lO CO iC CO iC CO iC CO iC CO iCCO oco oco o coocc
ocoocooeooiMOc^
COC^'^C^'«J<i-i»Cii-f
iCn'iOTpiCCOiCCOiCCOiCCOiScOiCOOiCCCOCO
8»CiHTj<C^"^CMC0C0C^
COOCOOCOOCOOCO
Sc^iCc^iOcO'^coTrcoco
i£i-rr — " ■ "
,^ iC 1/5
iC ^ iC ■^ lO -^
l-^CO'^C^'^C^»CCJiOt-tCpi-'^OI"«Ot^OSOOps
jiO'^UO'J'iC'^iO'^iO^ iC'^irt'^iOTOCOiCCO
if5 lOiOiC^iCidOiAkC iCiftiCiCtCOidOiOUi
[iCCOiCCOiCCOOCOOCO
CO O CO iC CO lO '^ lO •3' lO ^ '<*■ ^ CO »A CO ift CO lij c^
lO -^ iC ■^ kO ■^ lO ^i lO -^ iC ^ lO ^ lO T iC -^ iQ **
^ iC o
SOS rH a> r-l O 1-1 00
^ iC -^ iC*^ iC ^
i-iXi-HQO(NooiMooc^ooc^t^dr*cor-cot^coco
■xojdd V
SCI Q(M
iC lO iC
i/S iC lO Id
is ic i!5 ic
O* ■'J* Oi "^
0> ^ OS ^
lO iC id ^
gi-lQrHi-Hi-«r^.-t^i-t ^iH^i-Hi-HQi-HQfNO
iC i?ti lO lO iCiCiCiO O iC iC lOiC lO ift iC ut iCui
lO iQ iC "^ iO "^ ij3
iC iC iC »0 iCiC iC
^iCiC
00 <0 00 CO
•^ ic "^ iS
iC iC lO lO
00 to 00 «o
^ iC ^ lO
Q^!XiC^u^Oi<rJX':r^Oi^
2^
o w 6» S M S
00 «p 00 t* 00 t
oor*ooi^oot>-oot--oot>-
C iC iC lO »C »C iCi lOiCiC iC iCift tO iC »0 iCiO iC lO
&H95pt^C»Q^CX2p4c»tf GO pC^CGpjxPjCOpCHCOtfU^ Oh C» Qh GO C^h C/5 P4 CC P^ CC
OO OS
SCOOCOOCOQ
iC lO lC iC lO lC ^
oot^oot^t^i^r^t^t^r*
«£> r* oQ OS Q r-t eg c9 '^ uS"^ ^0 r*
wcJCiJico cococococo coco
•^
u^
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 493
x o I d d V
tftBpSwpjoopjtnBia!
sjuipjcnKaiQjcnpjGCi
Oi ZD fiiUl Pi ViOi'Xi fix a^ CC P4 en p4 I» (4 GO M r»
S*^«^r*OiO<o-^wr^os ^ «o »c c^ as oo co -^ t* o> ^j lO !>• o 5? -^ co o> co cc ©t^t^o-^coc<»o^«p
i-lMf-l?IC^C^C^(NC^»H COi-ICCi-ICOO-^O-^iC tCOiOiOO-VOCCi-tCO rlC^C^C^COr-C^OlOtS
c^ CO ■^ in to t~
lO ic »o 1/5 »c ic
iOO>Cli-c<1>r-CT<riM,fl?»IOC-l-r>-liCOOio
xci5Gccoaoc030Mooco'»«accooo«aoe<5a>c^
OCCOMi-HiNi-IHr-IC^
iCOOir^c^coooQO '^c^oor^cocoooooMfio
.-(l^^I-lI-l6^■-^l^^l-lMO«lOcOlC■^lO■*^lO■^
S'lOOOr-iCOMMOOt^
iOCOiOOSOMOS60(N
iC-^»COOiOCOiCCOOCO
fJiH<Mi-(MiHCOO MO hi* iO'q«>Oin'>5'U5T»<ClcOiOCCi-lI^C^i-l 041-1050
i«t^'*t-'*i>-*t~-*i~ect~cot~e<5t-eoooeoooe<3XMooei5aocOQOc<5
Ol'riN-^iOt^OtMO
OC^r-IC^rti-li-lr-imi-l
cooceoioo>iNc^«om
00400)004
gt-^-^^HOicr-oj'^oi
»50eOi-(Oli-(r-(04i-l
t^MOOCCOOeOOOMOOM
04 O CO O CO >i5 « ift ■* ■* ■* -Wi to CO O OS O 04 iH «
l> •* t~ ■* t~ CO C~ 05 t~ CO t^ 05 l~ 05 00 05 00 05 ao CO
a>t-H05ooi^^f-Ho»ciC
rti-IO)0 04 005 005u5
t~rl't^'>J<t^'<J(t^-.)lt-05
t^O)005CO«0:OCOg>0 04«OtD050»O>05 iCt—rH 04t*tOOI»-tr>"t^OI0150
i0 05O01O04O04O0)rHr-(rHr-lrHO05O0IO 05>O05lO'9'-<J<'*"T>C05
:0'^r^'»i<»^'^t^*^t^"^ |I>'i^t-»ra«t^'^t»'^l^^ t*O5t^O5t^O5t^O5t*O0
OO'OiOQOtpiOOjaQ
-.J'iC'^'^iO-^iiScOOOS
t^eor-o5r-o5i>coooo5
!SOt^01ir5T)<05t^r-ia!00
>-t'c9i^i-ipaoo5iC'!eMg5ooo5>otOi-(Ooo
5iC05iCC0O0)O0l|O0)Or-lr-lr-li-(i-l03O
S<O.-C00WOr-Oli(5iC05
CCiCCC'^-^"^^"^"^'^
t^^a>OD04<:p»C05t^O
^■^■^coir5co»r5o5iC05
gr-cofto-^oooeO'*
04C50400JrH.-ir-li-l
■^^000^05iO00OC0»O
oiooiiocciocc*-*-*
t^'.tt^COI^COt^COt^CO
iHr-l0»O<NO0jS05ift
t^'*t~'^i>-^r-o5t^eo
cOllO'fCO^THQQOiOt^
S05iOCO'C05iOCO'niTj"'<9>
S'0»0>Ot^01U5-1*'^^01
Ol4O«0iO05ifta5iC05iO
oiiO-foot~i-ias JO 04 to
•^"^•^•^■'J^'^M'COiOCO
tO^tO'^tO'^tO'^tOTj*
305t~OOt-05T)<t-.rH'Ot^»J"»'t~Or-ltOtOe3
OimCOO 04 004 004 -Hr-(r-lrHr1rH04 0 04 0
■^'*itO'*r-'*t>-'*t-'5"'r-'^t~'*t-'^t»'*t-"i'
0CQO0p04t0-^C0t^^
OT«0>tO'*05f-pOI^05-tt^i-lOt>-'*'*000
■^05>OCOiraCOK5eOOOJ004004rHr-lr-lrHr-Ci-l
o-*tO'^to-*tO'*r»'^t^'*t>-'*r-'^r-Tj<r»Ti<
;lOCOtOi-IQOO»OOOrH
wSeoS :oi
S0400400IIO
rfjtoiotoift-a-^to'^to-^
■^O05r*r-n3ao^.-tto
iCCOOCOU^CO-^"^-^
tDt)<tO'*tO'*tO-.J<0'*
.3"^tooiooa»i-it>-'^-*t>T-ioaoMioto>-iooo
T»'-4'»J'-^'*05ir505in05>(5 05O04O04O04rHi-(
o.s<;o-*tO'j'tO'^tO'^tO'*t^"rt-'Vf-'^r-->!(<
gO4t~05u'5iO-1<tOO400.H
010040040040010
^tOlCtOiOtOiCtO»OtOifl
Sooi-ioo^aocor^-ric
iHr-(04rH040040010
^tOtOtOiOtOlOtOiOtOtC
O>ai-jr»05tou9"jit^oi
04ir5CO»i5CC005»CCOii5
to-j'-js-^to-^to-^to-^
05 0r-IOOCOlOin0500i-l'rt00 05l(5t0 04a>5>04tO
io5ira-*'«'^-^'*'<>'-^'^|ioeoiC05iSo5ir504 0 04
i*^^t0^t0^t0^tO^'t0^t0^tO'T<t0^t*^
:o^r^oio>THO^c^^
040040040COiOCO>0
tOiCOiCtOiOtO-^tO-^
Tfi to to ■.f 00 Ol 00 04 t^
o5ioeoioeoio-3>0'*^
to^to-^to^o^to^
lCiCr»04Q004t>-i5'<J'
tO'^tO-^tO-n'tO^tO'^
ift»(5tD^0005a>i-tOO|040^C0r^iC^t03<00C0
erHi-lrHT-lr-(rti-(TH04i-(
.dtOLCtoiCtootoictoic
i^ooiooiSoiioiS
:0»ntOiC!0»00»CtOiO
!o>i-i'H©coaoi!itof-'^
M0 05 0COii5cOiC05iA
tOiOtOiCtO-^tO-^tO"^
3>04^0)o5r-to>caooj
to^to^to.s*to^to^
tfOlOS05»'*»'t^tOtOt^U5
,fl* to iC to iC to »C to iC '^ lO
00^0>0IO.-IJ4O05®
tOtCtOiCtOiCtOiCtOiO
S005004i-lrH04po50>
00)i-l04rH04>-l04i-(r-(
^tOir5tOiCtO>CtOi/5tOiC
■'j'ooicr^totoooicos'.^
tOi(5:OiOtOiOtOiCOir5
iOt~tOlS00-J<O3I4.HQ
010040040040050
tOiOtOiOtOiOtOiOtOiO
055C";tOt^-fa»O4O4p
o5iSo5"005ioe«5in-^iS
tO'*tO'»)<tO'T"0'<1"tO^
ooii-i.-1050'^gotot^
04 r-l04i-l 04^04 004 0
tolOtOlCtOU5tOtOtOtO
l--i(5O105i-IO4O5pi<50O
010040050050050
tOiOtOiCtOiiStOirttO'^
- 1- 1^ *"c gi ic <
- , >giic^-*
I004004004004
^tOiAtOiCtOLCtOiCtOlC
O05rH^01.H05O'*0>
i-(04i-IO4i-104i-l04r-li-H
tOtOtOiCtOiCtOlCtOtC
t^t^OOtOOstOOCO
rlrlrli-lr-lr-COlr-t
tOU5tO»OtO»CtO>(5
oioiccoi0^f^*oo»o
04r-C01i-l04 0 04 0 04 0
totntotctotctoictoio
a3'043<r-llOQtOOt001
S:OC00050C0005004
.C^tOiOtOLf5tOtCtOiOtOLC
SoogcoQO»r«a»tooio
O4001001004r-(04
tOiCtOiCtOiCtOiOtOiC
:005005J5050050»
;tOvatOiOtOi/5tOiCtOir5,tOiCtOlCeOiOtOiOtO»C
oi 05 cool
rt OliH 04
tOiOtOiO
IHO4I-I04
tOiO to iC
t^osoot*csto^ir50ico
oooa^x^r^oto
004 004 0 041-104
©lAtOiCtOiOtOiC
-HlC01-T05CO-»'J4tOi-l
r-(O4i-IOli-104i-104i-l04
tOkCtOiCtOiAtOiCtOiO
:»0-^iCCOli5 05ir5COiOCO
.■|C'^l5'*tp-9<tOT)'tOCO
«tniAiOiOLCL£5iOiCOiA
goo-HoOf-ir^oir^oito
COOCOOCOOCOOCO
to iC to vC to lO to lO to lO
'tom
ssss
ocftoco
§ooa>
o«o«oco©ecoe5
~ t* lO ■^ »0 "^ lO ■^ lO Tf<
•xojddy
aocooeoocoQccoco
- lO r^ "5 '^
r lo Tj< lit) ■^
5 iC lO iC lO
lO ■^ lO ^
©050COQCOQCOOCC
I0»0i0i0i0i00»0i0i0
iC lO iCi iC
tOGOtOQOtoccoostoqs
3 lO tO lO tC
O lO ^ lO
Pi CB C^ cc p4 03 p4 02 P:5 CO ' tf' oi P5 !» pi OQ Ph' cc pti cc c4 o^
Page 494]
TABLE 10.
Mean Time of Suit's Visible Rising and Setting.
^ -S
1^ w
.15 3
^^
•xojddv
xoiddy
5"^
^OQpjinadcQcdaOP^aQ
^ ■«< rt •g< rH -^ 1-1 -a" 1-1 ^ .H -31 r-l CO T-l eO 1-1 eC r-l CC r-l
SSi-HOrHOrHOr-lOi-l O 1-1 O i-( O r-l O ■-( O rt
pjaQPjtspjccQjcntf cQ pd co P4 % pj cc tf «: cj c» pj co pj aa oj oi PJ en pj co SIh co
$SOr-tOrHOt-IOT-»Ot-( Or-tOi— lOr^OfHOi— I
O-HOrlOrHOr-lOrH
?0 O <D *0 50 ^ ^ O ^ !0
S'lCcoinNioojioc^to'M
Or-IOi-lOrtOrHOi-l
©>-IOT-lOiHO.-40rH
CO ^ ^ CO >0 CO O to CO CO
OrHOiHOr-cOi-lOrt
COCOCOCOCOCOCOCOCOCO
S"cc-<j<t~Ti<r.-.jit^«ct^c<5,ooeoacc<occo)acc^a>oi
OrHOi-IOr-(OrHOi-lOi-IOrHOT-IOi-IOr-l
.tfCOCOCOCOCOcOCOcOCOCOcOCOCOCOCOCOCOCOcocO
Oi-IOi-IOr-IOi-HOrHOi-lOr-l,-lrti-li-lr-(iH
^COCOCOCOCOCOCOCOCOCO.COCOCOCOCOCOCOCOCOCO
.: 00 CO 30 ic 01 10 a> •<»< a» ■* o -.»< o « ^h m ih co i-m oj c^ c^ .-i « i-i co o ■* o
SOr-IOi-IO-HOr-IO.-l T-HtHr-lrtr-lrHrtT-lrHr-l •Hi-HrHi-li-li-li-li-lrHi-t
^COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO
Si-ieO»HC0^«THeCi-IC«i-HrorHM^«i-IMrHeCrf
.HOr-IO.-tOr-IOrHlc5i-(Oi-IO^Oi-IOrtOrt
COCOCOCOCOCOCOCOCOCCCOCOCOCOCOCOCOCOCOCOCOCO
rtOrtOrHOi-lOrHOTH
cocococococococococococo
CO C^ CO C^ CO t-l t^ r-l r^ r-l t^ r-( r* rH t^ O 1^ O t^ O t^ O
OrHOi-IOi-lOi-lOrH O 1-I O f-H O i-H O ■-I O tH O rH
COCOCOCOCOCOCOCOCOCO cocococococococococococo
Or.lOr-lSr-l©i-lO.HOTHOrHOi-(OrHi-lrHi-li-l
COCOCOCOCOCOCOCOCOCOCOCO CO COCOCOCOCOCOCOCOCO
Y-(0!-lrti-trHi-(rHTH,.Hi-(r-li-liHOr-lOr-tOi-'0
COCOCOCOCOCOCOCOCOCO CO CO CO CO CO CO CO CO CO CO CO CO
rH (N .-I >-l ^ 1-1 C^ •-I C^ O MOMOC5 0sC0»'^^-^cr0
1-1 i-H rH r-( rH 1-1 iH r-l i-H rH rH i-t >-l i-l rH O r-l O rH O rH O
CO CO CO cococococococo cocococococococococococo
~;xc0«iC00si0O>OO-*N-l'^'-'=^^"C^C^50^Wi-l'*r^-*OiCOiffiS COWCOOOt^aOt^l^OOt^QCCO
SOr-IOr-<0"-li-tt-li-li-li-lr-<rtrHi-lT-lT-lT-lrti-lii-li-li-lTHrHr-irHi-lr-.0 i-IOr-IOrHOi-IO.-(Oi-IO
^COCOCOCOCOCOCOCOCOCO CO cococococococococococococococococococococococococococococococo
■»J<OiCOSiOCC»COOCOOOCOt^
rtOiHOi-(Oi-IOrHOTHO
CO CO CO CO CO CO CO CO CO CO CO CO
g"oii^ocDo>o.Hic^-*c^-*c<i«iMMccc^-^i-ilin>-i>oocoocoo>t^gji^ooooQoa>t^aj«50cooin
^COCOCOCOCOCOCOCOCOCO cocococococococococococococococococococolcocococococococococococo
ss
05I^OCO-HCOi-liOO)iC|J^'*CO-*Tt<05-*CliCrH|COi-ICOOt^OX35CCX|Oi9COH^OCO.HvOC<liCN-
lOC^OlMOM O
^COCOCOCOCOCOCOCOCOCO cocococococococococolcocococococococococo'cocococococococococococo
;O00»-Ht~-HCO(NCOlNiO
^COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO
OTT)iT*<'^iOCOiCC-4CO-H
COCOCOCOCOCOCOCOCOCO cocococococococococococo
iOOOTHt^i-ICOC^COCOiCl'»3**rJ<Tj*cO»CC^cOC^t^i-IOOOaiOsascOOI^r-it^
4
COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO
OOOrHt^O)t^CCCO-^iO
^COCOCOCOCOCOCOCOCOCO
-JOOOtHl>-cNI>COcO-.l<iO
^COCOCOCOCOCOCOCOCOCO
c»OODrHt^C^COMiCTj«-.JH iCCOCOC^t^T-iODOaiOS
^COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO
[COCOCOCOCOCOCOCOCOCO
rHCpiM'Cm3<'*C0>OI^CO<N
cocococococococococococo
iC^iCCCcOC^t^^XO
CO CO COCDCOCOCOCOCOCO
iC^coMt^lNXrtOO
COCOCOCOCOCOCOCOCOCO
gOXr-lt^C^COCOtO-c)<-* COeOr-lNXi-l0500g
^ COCOCOCOCOCOCOCOCOCO CO COCOCOCOCOCOCOCOCO
oiopoi^x
SOI ^ X J< I^ C^ CO
OOJOOIOC^ o
:cococococococo>o
Oi^OXr-H^C-lCpCOlC
COCOCOCOCOCOCOCOCOCO
OXi-ll-»!NCpCCiO"*-J<
C^OCIOC-IOC^OMO
COCOCOCOCOCOCOCOCOCO
COCOCOCOCOCOCOCOCOCO
g'OXC^t^MCC^iOiC-*
^COCOCOCOCOCOCOCOCOCO
gOX'-icos^incOTj'Tjico
^COCOCOCOCOCOCOCOCOCO
l^r-ICO<NiCMOT-crC^
^COCOCOCOCOCOCOCOCOCO
COC^t^r-IXOSJiOlrHCC
iHr-li-l.-liH.H.-IO(NO
COCOCOCOCOCOCOCOCOCO
COm-^'»'>CCOCOClt^>-lXrH
COCOCOCOCOCOCOCOCOOCOCO
-»(< T)< lO CO CO C^ t- T
r^OCMOlMOC^OlNOC^liO
cocococococococococDcoic
lOMCOC^XiHOlQOCnT-HX
C02)t~i-l0>pO0Ji-<t~C^cp
c^oc^oc^ocoincoiocoiS
COCOCOCOCOCOCOlOCO^COlC
oj t^ eo CO -o" I© lO CO CO cj ao "H 01 p Q op T-H t~ CO CD ■* lO
c^oc<ioc^Of5[oc^o ?SoMoeouicoiOcoi25co3
COCOCOCOCOCOCOCOCOCO COCOCOCOCOlCCOiOCOlCCOlC
COC»l^i-IXOiOsX.-lt~
COCOCOCOCOCOCOCOCOCO
C0rHt^OXX05t^i-tCp
i-(rH,-lrHrHOtHOC^O
COCOCOCOCOCOCOCOCOCO
) c^ in ■« ■* ic CO
OICPC<MC-*COCOC^t^rtlciQCTiOXTHCOC.--, , .
S^OC^OMOC^OMO l5 iC CO vO CO ift CO iC ci 16 CO lO
COCOCOCOCOCOCOCOCOCO coiCCOiCCOiCCOlOCOiCCOiC
c^iccocoioricopxos
COCOCOCOCOCOCOCOCOtC
0>I^OCC{N>CCOCOiOC^cOQ
C^iCCOiCCOiCCOlCCOincOlS
COiCCOiOCOiCCOlCcOiCCOiO
c* X CO O lO »-* -^
S O .-I rH ,-1 r-l rt
^ CO CO CO CO CO CO
CO CO CO CO
:x t^05 CO o ^
> CO CO CO CO CO CO
-t~mo5-*oc^c^^eoos
SOi-IOrHrHrHi-lrHrHO
^COCOCOCOCOCOCOCOCOCO
■^XcOt^t^iCOi-fJ^OC^
-5.HO.-IOi-(OlMO
3COCOCOCOCOCOCOCO
^ CO CO CO CO CO CO
o^c^ X
CO CO CO CO
CO CO tC lO
CO CO CO CO
^ CO CO CO CO CO CO
OOr-l(5
CO CO CO CO
IN^COC^
CO CO CO CO
S* PXiH CpCOlC
000000
^ CO CO CO CO CO CO
0000
CO CO coco
giOOiTSoiOiO
• lO CO lO CO U3 10
Olt^rt CD
lO iC o ira
iCiOcOiO
pjccoSccpiccaScosJaJ
O O — • 7i :o "^
cocox «o>o
CO CO CO CO CO CO
lOi-i coosxr-
i-IOrHiCr-(iO
CO CO CO lC CO IC
C^COCO-HlOptQOOXt^
(MOC<OC^O^iSc5iC
COCOCOCOCOCOCOldCOlC
?»irtcoiocoiocoi0c0"*co-^
COiOCOlCcOiOCOiOcOuDCDiO
flr-ICOOSiOQCCOCOOlOlO OSCOrHMCOp'^XCOt^I^ip
f< o N ic c< io c^ lO ?i lO c^ lO CO lO CO ia CO ^ CO -^ CO T(<
COCOCOtCCOiCCOtOCOlO COLficOtCCOkCCOiCcOiCCOiC
^osfir^'fl'cocO'^t^n
COiCCOiOcOlOCOiCcOiO
pcDiH-5;cocoio^coo>
COlOCOiOCOiCcOiOCOiC
cr>rH005C^t^'*cgcDTfr^c^
e^>oco-«>cO'*co-*eo-*co-*
coiCCOiCcOiCcOiQcOiCcoiC
Xt^QcOe^'^COlNiOOl^X
SS'^eo'^cOTj'cO'^eo-^eoco
COinCOinCOiCCOlCCDUtlCOlC
) .^ CD CO 10 lO CO
5 1-1 in th 10 rt lO
s CD >c CO in CO in
coi-ixoox^coeo-* inc<)t»oo'o5'-i^-''S>ninco
1-1 in iH ■nl ?» ^ 6) ■* W* M ■>9< <N 9 (N CO CO CO CO CO CO CO
coincoincoincoincoin coincoincoincoincoincoin
CO in CO in
COQXOiO^-
OinO'^i-i-*
coin CO in CO in
Oh' 00 pd od tf OQ P< CO P<' c»
THincocoinjjr-oxcc
coin CO in coin coin CO in
P^GQpjUie^nPJGOpjCO
5fl-*-*lMcOOXXOCO
iMC06JC0(NC0lNC0f^CvlOT<N
coincoincoincoincoincoin
cd OQ pj cc p^ od Oh' »3 Pif OS p4 cc
m CO i~ X
l~ X era
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 495
^ a
M a
.^^
■xoiddy
HB3
13 ?3
C^ Cn| C^ C^I M
CdtKOJaJtfwPScortaJsSr/JBHwCrtaQPSaaPaaoWaJKoQrtaBrtaja^ai
M CO CO
s
•xojddv
ao5ort«5rHOi-IOi-iprHC5T-lOTHOT--(O!-iprHOrH0i-lOi--lC5i-HOr-lOT-lOi-HOrHO.--l
P4cCCd3aP4aQ3HKP<GQ
Sg2SSSS§2§g
OOOOOOOOOO OOOOOOOOr-tO
OtOOtD^tOOOtOO
(OO^OO^DtOOtOO
fti— lO'-tO'-'OrHOrHO [t-HOi— lOi— tOi— lOi— (O
rHOrHOi-tOrHOr-lO
i-HOi-tO^O^Oi-HO
SrH Ot-tOrHOi-HOr-tO i-lOrHOrlOi-lOi-lO
5:,-lOr-(Or-lO.-lO'-(0
rHOi-lOrHOrHOrHO
iH0rHOr-lOrHOi-(O
T-tOrHOT-HOi-iOrHOiHOiHOrHOr-lOi-lO
C<l COM M coerce iHTt4^!iOOiCO tOOlCDGCt^t^
MlO(M»CiCM>5cCiScOiC
?5iCC<iCC4iCeoiC)covo
CCiCCOiCCCiCCOiCCOiC
> t^ OS GO 1^1 Oi 00 5
CCiScCiCCOiOCCiCWiO
iCiM'^^«OQr*O10DQ0
cciO«»cccii5eo'^cC'^
» »c c^ :o C^ l^ f
)GOO|0>030QCi-lt*T^':pC^iO
QC 1— 1 1* T^ 'X' C^ I
iS JO tO CO »5 CO I
coi''^eo»cc^<Oi-HiN.o
.COiCCCiOCOiOCOiOCCiC
ooa>oiQCor*f-i?£>iMtio
S'i>r-taco QOOl Oioooi> 1-1 1>- w ?p cc iO "^ '<*' »^ CO
WOC^OC^iCCNiScOtC COiCCCiScOiCCCiOCOiC
OfNr-i-HQQQOiOsOt^
OOiCCOiOCOilCCO'^'^*^
r-( to C^ »0 CC -^iC PO CO i-H
S'csQOair-l00iMt-C0:0l'^iJ?::iCi-^c0C0r*C^GCT-i
<M25cOiCCOiC5COtOCOiC|CO'~CCOiCCOiCCOiCCOiC
^(OtOi^OiO'^^^iC^ifl tOi/50iC'OiO«OiC^iO
OiOOO»rHt^C<»?OT}<iC
?OiC'^iC«OiO«OiOtOi/5
S*oooi-*i^M:pcoio»C'^hPccr*wcoi-<osOQao
COiCCOi^COiOCOiOCOiCCOiCCOiCCOiCCOiQ^'^
^tOiC«OifltDiCOiC?0»^'Uo»/30*C<0»0^»i^cOiC
i-Hr*c^o-^iOiccot*c^
COiftCOiCCQiAcOiOCOiC
^tOiC^OiO^iCOift'lOiC
Qp-^o>QQa>i-Hr-co<o
COiCCOiC'^'^'^-^'V*'
^COiOCOiCCOiCCOiCCOiJo
^<OiOO»COiC?OiftCOiC
Q Oil-too Cji^O^JiCiCCO
COiOCOiCOiCeOiCOiC
J CO C^ 00 rH OS OS 1-H C
gcf5S?cci5iCi5iCC0'<*<'«j'
^tOi-HopoosQCf-tr*c^in
gCOiCCOiCCO'^'^'^'^^
.(OiCtOiCOiOeO^^iC
Wn'^cc^'-^oOOaOQC
'^•^■^■^^■^■'j'ccicco
coiCcoiO«Difitoic?oio
gt^OlOll^^'OC^^'^CC
CO^CO^^^^"^^^
ifti-ll^-QOOOOQOC^vO
■^"^'^^'^oSiOCOiCCC
cO»CtO»050^(OiCtOti5
^■^iCCOIr^C^ODpgCft
?oioeoic^io?oiO«oiO
t>-C^00r-lOSO4rH00C0«D
■^'^'^■^'^COiCOOiCCO
:0iC^iO?0iO^iC?0iC
iC'^<:OC^t>-r-IOSOOGQ
■rj«-^'<5<Tp'^'^-^-^i5cO
tOtOCOiCCOiOCOiCCOiC
OO^OiOSr-'QCC^eO'^'iC
Tf-^^coidcoiocoicco
i-tt^ec;o^-^«ocor-r-(
oeoiCcoiOcoiiScoioco
tOiftOiCtOvO^iC^ia
-^'*f(OCOt>-^OSOif-IOD
tOiC^iOcOiO«Oi/5C^»C
OSOSrH00C^«O^»5«DC0
^COiOCOiCCOiOCO^ftCO
i:OiC«OiO«OiCi«OiCOti:5
t>-^HOlOSrH00005OiC'^
;oiOtoict>-ior*»cr^iO
rHX'COlCiOCOCp.-iOOOS
iCCOiCCOiCCOiOCOiOC^
^O^iitlCOiOCOLn^iC
CCC0iOTHt»O>OS0Qi-(«O
iCCCiCC0iCf^iC?JOtM
«OiC?D»OcOiO«OU5r*iO
Soctjc^i'^coc^aoo
cc-^iCwr^o^r*rtiO
OWOC^OC^O*H.-tiH
SOOCOOiOr-'COCO'NiCO
cooDXt^QiCc^eocoi-i
TrM-^ccizScoioeoicco
tOUO«OiCCOiO«OiOOiC
S04t>-I>OSlOi-C^CCC^
?iOrHOr-l»Ht-liHi-l
SaiCCi^C^C^Q***OS«Ot^
C0^1*^^'^^C0^C0
^cOiC^iCtOiAOLAXiiO
t^inoico^H^cooiict^
■^SS-^coiccoicJ^icc^
COiC'OiC?C»0^iC^iO
SCO ^ ^ CO OS lO t*
C^ O 'M O 1-t O 1-t
cOift:DiOt*iCI>iCt*iO
S CO ^^CO'S'CO^OO^ CO
opfHpoic^r-'^iO'Cco
COiC«DiO?OiCtDiCtO»C
SS82g
t^-iOiCt^COC^OC^QO'^
T-*Or-tOi-l 1
lO I> »C I> »c
1-ii-lOrH
- .— .— . — O O 1—t O 1—1 O rH
t^ lO t» »o C* Ut) t^
■OrHOrHO
to lO t^ >c t*
Id f- TJI t~ -^
Sf-.-ll3SO».Ht^C0iCiOCC
g<N-<»<i>{I^HOOOOOOOtO
Tj'iH-^rH-^i-l'^OlOO
pHODtfajaSajSiHCcPScc aSaJtfasCSaJtfaQpScc
> t^ M ira lO c^ 00 c
OOOOO j
lO r-l ■* e^ -^
•* t^ -^ 1-- -*
SMOOO
O lO O iC
CCiC«OiO CO
TJI t>. ^ t^ ^
t^ (M •* Id i-H 00 C
anuctfoiWaJPiccB^aQWcftOSaJPHaJtfGcBJaQ
cc as o , ^- CI CO -7" ic '— 1^ 00 d o
Page 496]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
o3 to
*- a
0) CI
O II
5
^z
o 5
-^ cj eo
■xojddv S=»
pi^'xsiic'aiKisiaiiidx aixi:s^'cc3icca^u}p^ui pjcctfcctfos^cfitfai
^ PH & ^ & T-l
^ ^?c ^ too
SS2S2
to -.o o to o <o
.^ to to to to
S2S2S
.ci to to to to
sssss
,«• coo i^O ^
to to to to to to
to^ to « to w
rH O t-t O p^ O
to to to to to to
to to to to to to
I— < O 1— I O 1— t O rH
to to to to to to to to
Sot~o tot'-o
pH O I-. O >— ' O I-*
tototctototototo
totototototototo
rf*tO»CtOiOtOiCtOiCtOift
^tOiCtOiOtOlOtOiCtOiC tOiOtOiCtOiCtOiOtOO
0--.0r-.
to to to to
ooo©
to to to to
toMr»cci-»2J*£J*'-'
--<Or-lO.Hil.-t4>
to to to to to to to to
tOiCtOiAtOiCtOtA
rH!C— 'OT^M-:''*^-
rH O i-H O
to to to to
Oi-iOi-i
to '-O to to
I-* OS t^ ^
oooo
to to to to
CO ^p w 3?
to to to to
BncoiSHCcipjcQPJaQP^aQ
S3838
OrH OrH
to to to to t
r-mit^m t
o© oot
to to to to t
Tl<QiOOiC
to to to to to
>oo©oo
3 to to to to to
to to to to
r-«OrH
to to to
CO CO CO CO O
;sss8§
> to to to to t
oi r-i OS .-I <» c^ qo N t~ ec to
StOiCtO^tO^tOtO
^ to lO to lO lO to iQ r- ■* ^ <y> QO ci O' c^ o r-* <-! o
tOintOiCtOiCtOiCtOiCtOiOtOiCtO»OtOiOtO>C
totot~-toociC5R'^9;OT
tOiCtO^tOlAtOiCtOtO
gt-)r-M.-irmq<5o5C>
lOeoiCcoiiScoifteo'*
tOLOtOlCtOtCtOiCtO^
S'c^MMC^MrH-*0"5Qtoi3»r»ooaot~-a>too>iS
^tOLOtOiCtO^tOOtOiAtOiOtOiCtO^tOtAtOO
vcoQtot^t^toooinQ'^
tO^toUSCOiOtOiCtOiC
r-(e<5(NMeor-(2©too»
tOiOtoirsto&ctoiotoiA
«r-lU50lt-01COOOaitOrHlOC^<
S"toot^3»ooaoost-otOi-iiciM-«'coM5;. _ ^ ^ -
^tOiCtOiCtOiOtOlCtOiOltOiOtOiOtOiCtOiCtOiOtOif^tOiCtOiCtOiCtOiC
-ffcCiOt^tOtOt^ipOS^
totCtOtfttO^tOiCtOiC
rHCOe^rHCOOinOltOt;
■^ ^ ■^ ^ ^ Tf< ^« CC M* CO
toiAtoiatoicto^toio
r-t~o>toQ'*c^co-5'r-i
■^CO-.TCOtCCOiCCOOCO
tOiOtOLCtOiCtOiOtOiO
SMtoor»oooitOr-i'j<
eo>neoioc<ino4oc>i
tOiCtOiCtOi^tOiCl^iO
gs
t^-i-HcocmoeocoM'C^
CO^COOCOlOCOiOCOiC
I-n^^OCOCOr-IOOOOiOS
jtOiTScOvCCOiCcOif^COiO
iCTHl>OGOaiOr*rHO
^^^Tf*^00'9'CO»O CO
cOiOCOii^cOiCCOiCCOiO
5 r* (N CO CO '«!t -
;Gooa>oiQr-(McDcoio
rTpTT-^CCiiOCCiOOOUOCC
;coiCcOiOcoir5cOiCcO»C
. ,. "if^CCCOrH
COiCCOiT^COiAcCOCO
COiCCOiCcOiCcOiCcOiO
iCCCcOf-taOOOiOQ^CO
!iCCCiCCCkS55iC>c50C^
COiOCOiOcOiOCOifit^ift
COiOcO
CCiQCC
if^COO
COiCcOiO
iOCO»C
CO tC CO
ic t* »c t* id> »c
eoinincor*pHQso*fHco
s'i^t-cOiOiC'^coc^arrH
;iOcoiCi«iCco»5coiceo
*COiCCOiOcOiOCO»CCOiC
:iceoiccoioccoc3oc^
»coocoiccoior*ict>ic
05ffii-ir*cocoiC"^t^c^
cceoiC
i-lrHr-l
iC COGO-H
■^M'tOr-lOJOli-ltP'^CO
rHrH.-Hr-i,-lOC^OC<0
.iotocogOr-<©asc^t^
OIN oc5
■.J'r)<tOHO>©rHt~-'.r"
(MOINO
lOSO^rHOOCOtO't'^t
3 o © 00 mo in ■* t^,i-H
rfStoiot~iOt^ict^ioi^iojt-int^mt>inr»iot
(M©c^©c5o?S©eom
.-(00COmtOCJO»Ol(N
C^©C^©IMO
t* lO i> lO r* 4/3
HiceoS
r»rHOoo?2'2t~^©*' ■
(NOCOiftCOiO
icr* ■^ r* ■^
coio-v*
-^lOt^r-HrHOO'l'-^OpO
C0iOC0»O'«iJ*-^TT*'.t'-^TI<
S*eotoin"rr»c<i030r-ioocoto>n'*t~i-H©mjio
OMOC-IOC^OC^i-(r-l|iHrHrHi-HrHrHe^©CMO
65o (N ©COiS COiCCOiO -^ -f -^ "V -^ "^ lO CO lO CO
S"t^MO»©i-i«cotomcot~.-i©g>(Mtoioe2cc^
©C^©(Nrtr-li-lrHr-(rH|r-li-(f3 0(N0C^©Sl©
r-IOO'}'l5r-IM©OC-*lO
eoiocoineoiorr^'^''*'
g©t~INiC-»"COf-i-<0»»
C^ltOTj'COt^rHOCCeOlC
C^OOJ©01©CCiScOift
to<NO>opcomto.-(©oo ^■*o£C::^ — i;
S'<S'cotOr-iooccrHtocoeo torHa>coc^iniCiNoso>
r-lr-i-ii-lr-lO'MOlN© C^OIMu5cOlftCOlOCOl»c
.cj t~ m t» lO r- in t^ in t~ lO t» in r~ ■* r- '«' t~ ■.i' t- ^
g'wxostpi-Hco-^ot^QQ © in CO c^ to OS OS in CO c^
r-IOr-lOC^ONOHa M S CO in CO •* CO -.J" ■<<« '5'
,ci t^ in t^ in t^ in t^ in 1^ ^ t^ -.r t^ -^ t* -^ t^ -^ t^ -^
SSS?3S
inooocinTHMkf<osr-to©iN-^Sao^
cmnff<incoincOTj>eOTi'Tr'.»"rjicO'VC
rf;t~inr»int~T)<t~-.}<t-T)<t~T}<r-.-^t-Tj<t»'fl<r-"
S'l^l— ininOOC-)rHO>r)<tOt^lNrHOS-«'inoO?»C^OO
i^incginMioco'*coti'eo-*TfcO'.jicO'«»'coinc<
S'^r-ir»oo©incoc^t~o»|oin'.j"caopaoc^tj'to©
MinM-j'cO'^cO'a'eoeohi'corrco^tNintNinw
t-r^-Ht-.incoocjiin'*
■.^"■*incoinco©iN©(M
J OS CO in 00 © CO in
(inmcaaogociTjto©
. ^.^Tj*-^ coin coin CO
r-Htoin^-otoini-tr-fin
OC^O<NrHrH— IrtM©
ao'^aO'*oo-*oD-^oO'.»'
tooocsin^rHoor^NJ^
coiiScoincoinNoe^
t»'.i't~Tj<r-'*r»'«s<ootr
i-HrHinr»^CO^OSOS^
ineoinc^inc^©r-(0.-H
r»Ti<t^T)<t~T)'ooT)<oO''j<
tCTC©osininos©inin
l?5cM©r-l©.-l©rHr-lO
t-.'^ooi'00'.caO'J'oO'.j'
8inint-i©tpinr-*©in
i-l©T-lr-<Oi-l©IMin
00-^a0'^0C'*CC"*00CO
S*incOOO©r-(t^^COQOO rHtOinC^IOSODCO-I^GC©
iN-<j>iM^cocccocococo ■*c^-!)<M-*rHini-iirt.-H
.^ t* -^ r* 'f r^ -^ t* -.^ c^ -^ t^ -t^ t^ -.J. t^ 1* r^ -1^ i^ -^
Sintocoioooos^-*
0©©r-lini-IT}i(MTI<
■CC^OO-TOOCOOOCOOOCO
t^t>-NMt^r~-couosin
Oi-Hi-irHrHoe<ioc<in
oOTj.oO'J'oo-^oOTrooco
■^oooscoint^r-irqooin
iH©i-H©c5incoinco-*
oo-^ao^ooeooocoooeo
OOStO'*C^t-OSi-ltp'^
iMiniMinco'^co'^^co
oocooocooocooocoooeo
tOOSC'ICOOStOtOOS-W'rH
(M'.j'cO'^coco-Tj'c^inc^
«coaocooocooocoooco
ot~t^pT>icoiMinr^to
C0COC0M-*O»inr-(©©
oocoaocooocooocooseo
H9j
SrHin-.j'c^oocir-iininMccaoMi'toOrHtoini-!
c^cO{NeO!MMeoc^cos^cor-iTi<r-c'*rHin©ino
Stcini-^-HOtooN-t"
inoinrH-^r^^c^eo
'oocooocooocooocoooeo
xoiadV
pjccp^coa^tnpjaiaico
-H C^ CO
-^^r
t£5 r* ao OS ©
ost~to©'^coiMinr-ito
c<oieoc^-*riin©©in
OOCOOOCOOOCOOOCOOSOJ
p^coeticoQjcoptfcapeicc tfcde^oopiHaQtf qop^Scq
in I lo in
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 497
<N bib
c^ cc -^
•xo jdd V
p4cop3«ip5c>3D:iccp4uQlP:Jc»(^"aQP!JcGpicdaiccP^^
D^xajxPdaDpHaQp^GQOJ^
^ic^icOiCiCidocoii:: --oicxnCOiccoiOfSic !Ouocoicco»coicoic oicoictoooic^icoio
lO O lO hO lO lO k^ lO lC U5 us in O lO O O O lC O lO
lOvCOiCOiCOiSo-^jO'^'O'^O'^rlTj'rH'^
COasiOQP«DtP3DiCa>05'-H(M
^H ^ rH CO rH P3 rH CO rH CO rH CO
sss
-COOO'^OeOi^HC^C^P'^OlvOQO^OCOt^iC
> ^ O ^ ^ ^ irH ^r^^rHCOi— ICOr^COr^ CO
iCLACOLOOiC^^OiO<:Ot£:}';OLOCOiCCOiCOiO|^iCCOiA^iCCDiA^^COtO
tf'IMirsi-icooi^oiQOGcast^oco^iOij'^coco
S0HC00^t^G0«0^»0OC0»-<C^C0«-''^OiO0Q<©t*
•vOTfO'rro'^O-^r-iTfi-c'rr^'^t-HTri-^cOr-teo
S.-iiCQ^o»t^r*QO«o gi o o "^ iM CO CO c^ ■'J* o lO a>
lOOiOOTrO-^O^ O "^ r-* -^ r-( -^ fH -^ i-l -^ rH CO
:o to oo OiO c;oi0^lo to tc to lO ^ lO :o lC co lo co lO
:oiocotOtctoovacooUou5eoLr3cou7coiocoii:>coio
g*iCC0?$^'^i-tt*OC004
o> ao Q G0 1-* r* 5^ !;o CO ic co ^ 3" co lO c^ o i-< t> '-'
lO U3 O lO O O O ^ O ^ O lO O iC O lO O lC O UD
OiCCOiOCOiOOiOtOirS -^iO:OiO«OiC?OiCCOiC
gSoSoioSiooSo
SSdicoiooS&So
iC^O>OOtOO^OLO
lOictoio^ifitoutitoic
ioS8ooiOoSi>iO
lOOSSoOOiOOOO
SooooooSoio
o&oSoooooo
gsssssssss
c5^0t»0^oioO>C
C0G0-3*GC3"t*iCO!0«P
gX©l>OeOr-liftC^^COCO
ooo»o>OQO^-lr*c^coc^^>o
8COt^(NGOC^QSiHOQ001
I00t00i00i0r-l>0t-l-^
ssssssssssss
COiOtOiOcO^COiC^LCUSiOcOiCeOiCOiCOiOtOLC
oico»coi3oiSOin oioo>Soi5o»ooic oui
-jao5px»o<3ivoa>'*fQ^
SSiSOiOOiOOiOOOO
SCOf-ICOrH^^^'^'-t
000000010010 OiO OiOOiOOiOOiCOiO
?OtOOtDOi;D?0»0''OiO ,:0>0^iO:Oi050iOtOvOtOiO
i-*0it^3>'POsPOi0O>0
eiOOiOOOOOOOO
^iO^tOtO^^COCOOO
S8S8B8SSSSS
»tf CO O ^ ^ O ^ ^ ?0 ^O CO
OOOOOOOOOO
50C0^^^OC0C0^O
COCOCOt^^^^f-iiO--
oooiso&oooo
-0<:o:otOcOtO':0^^0
iSSS
So o oi.r* oa r* 00
O O lO O lOO lO
?0«O«0»0c0iO(O»O
,-nac^i:oc^iO^iOC0iO
ooooooiiooo
COt050t050^^^0?0
S'QXi-'QOi-HGO^-fh-tHI^-
oooooooooo
i^50CO!050COOtO?0^^
gggggggggg
•xojddv Q'^
ggggggggggg
ooooooooo
OOOOOOOOOO
SSc
i^i^^fHto^r-i-i
>oooooooo
JCOOCOCOOO'^OCO
cotpco>0'g'iO"a''^'g"5'
OOOOOOOOOO
•OtOtO'XtO-OtOtOO^
iCrj'iO'^iO'^iOCO
coxcot^-*'r*-^-0't"'^
OOOOOOOOOO
•^(O^OtCtC^O^tttOCO
^(;oo;o<:otocotococoo
c^j^MOico^cooscoas
OOOOOOOOOO
COOCO^O^^^^^
COCiCOXCOQOTt'XrJ'X
OOOOOOOOOO
OCO^CO«050?OtO'OCO
^"CO^COOCOOCOOCOO
SOi-lOi-tOrHOrHOrH
bC ^t0050?OtOtOOOCO
coocoocoocoocoocoocoocoo-^o-^o
Or-lOrHOi-lOrHOr-t
tDtO(OCOO^?00?D<0
Or^Oi-HOrHOf-lOr-l
•.OtOOOXi':0^0^?D«0
^cO^CO^O^COtOCO^O
3«-ICOi-ICOf-tCOi-tcpi-l
^Or-tOrHOrHOrH
to^o^oooo^oto
COf-HCOi-HCOi— ICO»HCOi-H
Oi-HOi-tOrHOrlOr-t
^tOO^?OOtDO?OCO
C^CQplJGOC^CCpC^CCp^GQ
O rH C^ CO '^
pC^GGajCCp^G0p<Q0tfCO
lO f^O t* X Oi
Sgggggg
tO?0^50?0?OCOO
5 »0 ^ tO lO »0 »0 lO »C
soooooooo
5tO^?050*^50050
3S3S
oooooooo
^o-^o
ssssssss
* CO rH CO *"* CO rH CO rH CO 1-^
iOi-(OrHOrHOrtOi-l
Bi oc OJ 02 W oc p^ t» pj cfi p^ as rt oQ P5 02 pi5 aj p3 cc PS M
O 1-1 M CO
in O 1^
"9r-s-
22489—03-
-32
Page 498]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
C3 »
s a a
3 s
•xojdd V
l^i
aaQDSaspicoai'XeiaaaSaDPfitKrtcooSaQrtaQa^ccaScfipitKDSasaSaJaJMjaicoojaQaJccsijtn
0'*corHtoooo»irari<N
cmoic-^r^c^osoi-
S'os-js^inmcc-^^tooiiosc^i-ioeocoini-ii^oi
OiCOiCOiSO-^rH-
•x> a> ■«' -J cj M o
xC ^ ^ O tC O ^
r-ICOr-(
lOOiOiCtOiCOiOOO
«?4«HCCi-IKlr1C0i-liC0i-IT)ii-l-.}<&'^O'<J'O
Oi-i'.-i.-imiotot^oo-^
^OiCOiOx/5>CiC»OiO
MC^COC^MC^MiHeOi-liC5i-<COi-l'*i-l'^i-ITi<0
^COLntCLC^CiC^LCOiC tQiC<:O^^LO<£^COLC OiCOiOCOL/^tOtOeOiC
-H'^i-HCCi-ICOi-IMCqcO
gco'<f<j<coicc4;OT-ir»OQOoao»ooot~.-itocqin
.HTJIr1TJIr-f<S>.-C*i-ITJ',-l«l>-lS5lNM<NCO!NCO
«f4C0!NeOrHeO-HC0i-l
l^r~0>«00-*MM'*r-(
Ctf^^iA^iC^tAcOiO
(»■*■* CO to C^I>--H00O5
C^lCO(NCO(MeOC^CCC^C^
i-l'<JirH"3irtT}<i-IC<5lNCO;C^COC^MlNe<5c^COCJ«
tOLC:OOtOiCtOiO:CiO|OLO^LCt£LO;CtCOiC
OiaOr-H^C^'-DCC^lOM
C4IMmC^CCC<COlN«(N
:0»0«0i0:Di0tCiCt0i/i
CJC<0?ScC?J«C0OIMC^
tDiC«OiOtOifttO»CtOiC
gi-lOpMCOMt^MtO'^'''
^:OiC?DiCtOiOtOi(t!tO»C
■O lO «5 T)< t~ M 00 e<l 00 -H OS O O 0» r-l 00 (N t^ CO to
rHTl<rtT}<i-l'^iH-<)<i-l-«< rl'VOJCOC^lCOI^COC^CO
toiAtoototCtoiototC toirstouotciAto^toin
I'^ujiC'^tocor-c^ooi-i
^Mcocico^^coc^cocaco
'tOiCtOiOtOiCtOiCtOiC
ftrHl«r-(
^tOiC to
i-H S i-l -^ i-i ■<)<
tC to O to iC to iC
SrHlCrH
.«; toicto
C'l .-I M .-I rt ?1 O
iCiH lO »H iC T— I lO
lO to iC to iC to iC
ii^iototcint^^J
5»CtOiOtO»OtOiO
OOeOOiCOOKNOfH^O'C^OlCOODil't^iCtOtOiC
— ■■ C-) CO I^ CO M CO J5 CO C^ CO
tOLOtOiCtOiCtOUt)tOiC
50i^osicoo»or^jtptpt^tpr*iCXTt<o»co]ocorHC^r:;.T55^ococft
>io toio tomtoio
Ic^i-^in-^c^-^StcNco
toictoictou^toiOtoic
SS188
»^ ;0 iC !:o
1— ( lO 1-H iC tH lO I
iC to lO ^ vi!5 'O iC
■^o>icos»ooo?ooor^r*
ssss
r*a5r>-os!so-o |OiCi-iiCr-f--rj«
lO O lO O tC rH iC
lO ^ lO ';o ic o tc
?o iC «o iC
"©10(0
'M Tf C^ -i* i-H lO »-l
lO rH iC 'H lO 1^ »C
lO to >c to »c to iC
QOtOGOiCOiiCO'^'— ICO
rH'^r-|-^i-H-«J'?iT)<!MTj*
tOiCtOiCtOiCtOiCOiO
toooost^ost^cooot*
i-HiOrHTfi-H-^rH-Vi-C'S'
tO^tOiflCOiCtOiCtOiC
Sooo
^ to to to
to to to to lO to iC
gS2
tOvC to
QOOt^or^f-ir-i-(toc^
iC-HiO
to lC to lO
tOiC to
to C^ iC CO iC CO -^
lO rH »0 r-H »0 rH i;^
lO to iC to iC '^ vC
■^"^^COiCCCiOC^tOC^
tOiOtOiOtOiCtO^CtOiO
S8S8
^' to to to
Mt^cjr^r-foo.-^ '^»-*3D
ooi)00oo
to to to to to to to
ooo
to to to
8S8
to to to
S8S8
to to to to
Oi« 1-1
a> O 30 r-l QC 1-1 QO
tO »-t id— I lO »-< iC
1(5 to iC to »0 to iC
S8SS
<^ to to to
m m in to 3< i~ -»
to to to to to to -s
ss
i^cor^coc^cot^co
>ooo
; to to to
oooo
to to to to
ooo
to to to
ggggggg
to to to to to to to
lOt^iCC^iCt^iCt^iO
Soco
.cjtotco
8 iC to iC to to to to to
oooooooo
totototototototototoior-ict^ic
^ '->ooooooooo
to to to to to to t
, to to to to to to to to to to
r-ir*c^r^c^i^oitocot
rHiOi-l
to to to
IC Trt tO r-4 IC rH lO
lO to lO to lO to iC
OO-H
to to to
— i0t-(0000
O.HOi-iOi-(0
to to to to to to to
OOO
to to to
xoidd V
^M
1^
SS8S
«; to to to
Cs ^ Oi '^ C5 ^ CS
OO OOOOO
to to to to to to to
sss
to to to
ooo
to to to
383
to to to to
OS^^iOOiiC^iOOiiOC
SOOOO I
> to to to to to to to
St^ -^ r* Tj« i^ -^
OOOOOO
to to to to to to to
yoo^ oo»cooic 00
>ooooooo
> to to to to to to to
C0^00^COrH';Oi-'COr^lcO»-fCO^HC0»-*C0f-tCOC^ CO^COC^COC4CO!MCOC^icOC^COr42^C^2JC^C4C^
a Ort o
^ to to to
) rt 0.-1
1 -o tO'tO
Oi-lOrl
to to to to
O^O'
to to to t
S5;::;Srto;^
to to to to to to to
P5aia;cc3iccPi3ccW73
o "S^'^^^'^'i"
fim(i<n(i^(imA^m'£(i^t^<£(A^<Amm'Xi(^!£tiaiKm;idi
-S--K-
s xr
TABLE 10.
Mean Time of Sun's Visible Kising and Setting.
[Page 499
•xoiddy
■H M M
tf t» c4 oj p4 M pi cc e? oj
a; cc pi CO W «3 05 tK tf tn (13 cc On aj P5 co pj aJ 03 aj
MC^Trr-f^i-H'*i-iiCO»000»COiQ'-'^rHCOC^CO«C^'^t-t'^i-HiOO
CCC^COC^Cd-H-^f-H'^i-HiOOiOOOi^OiCr-t'^rHCOC^CCC^tNCCT-i'^f-l
t>'^I>'^l^-^t^-^t^'^t^'^t^'^XCOXCCX«3OCOXtOXC^C30COCOCO
SO'»'O'^r-l'»'iH'*i-ie0
S'WQiC0Ct>*«OOSCC(Ni— I
t-l C^ C<5
lO lO iC
s
iC iO O
C<c/5CehC/30[hCCP:hGCPe^o:3
xcooocoooccoocooac^
-raioc-X!i-i'MiCOiOsic 'C0r-ii-*or)'?-»i^t^^iiM t^«ocC'-«a>"^<;oxcO'-i
t^'^l>'^l>-^t>'^l>-'^'l^'^l>'^I>'^C^COGCCo|xCOCOCOXCC»CC0DCO
t>-Ttft:^Ti«i:^Tf<t^Tt<t^'^ ,t-.Tj«I>Tt«i>''^I>'^l>'^ W^C^COXCOaOCOOOCO
* 00 CO iCi-l i-» L
C^M-NC^CTlC^COr-tCCrH
'*<3>oo-g«ccosGO-^'^oo
t>.Tj*C^Tft^COt->-CC00CC
Sosr-^DOcocoOiCt^ xi -^ c^ ^ lO tt g;
S'OiTT'-'C^COOiOXX^ Q'^C^i-HiOOiXOOCClcOO*X>t^CT>'^CCr-t!;Or*
to OS X r^ O Tt* CO C^ ifi Oi X «D t-^ "9* "^ ^^ t^ X O ^ ^ ^H !>• t^ ^h cCiC O Cs lO
iTSimCiCOOOiCO'^O'^^-^T-i-^rH cocoes C^CCC^C^COCIWC^CCi-i
OOfH'-J'r-i'^OlQOiOlO
coc^co^icoi-i'^i-iTpo
-^i(;i:OiCtOiOOid<:OiO !(0'^t^*^t^'^l>''^t>-'* t>-'<J«t*'^t^"^t-»'^l>-'^
^ !;0 lA ^ in ^ lO CO lC <:0 kO O lA e& iC ^ iC O iC CO lO
^<Oii5:OiCOiOCOiO«OUt
OX'Mt^COiCiC'^t^fN
!;OiCOiCcCiCOiO«OiC
^»QO--HOSC^t^■»**tOlClQ^OCOXC^OS01-HOiC^t^'^OlO'^l:^C^OSOr-tCOMy?'53;
gCOCC0:i?4CCC^CC'NCO!NCOC^COC^ICOC*^'»»<i-»"^i-l '^ri'^T-l'«7<r-t'^rHU30|»nOiOOiOOOiOOiC
^coiC50iOOiC«oio«ciickoiccoio<oic<oiC?o»o coic^oioo^c^icoio j?ointOif550icr*'^r*"^
C|5'a'iC^XQQQ0^iCUCC^XP«-ir^-^Tj'i>rH
iooioo55o25iooiooico25t-(TrT-i'^i-tTr
oio«oiCOicoiC(Oio cO'^i>'*r*'^i*'^t*-^
c^«(^^co5^cccccocococ«5c5coc^coc^coc^coc4'^cs■^c^'^rH"^rH'^1H|^
^(OiOtOiC500^iCitOin «OiC?D»C?OiOcOtC(Oif2 Uo i/5tOu^tDin?DiOOicUDifttDi0^in<OiOt04C
S"rfQOicr*':o<©r-u5X^
<NCOC^C0C^CC'M«WC0
P>COOW«-lrHfiOO-^OS
*jCOCCCOCCCCCOCOCOiM
;o^cou^^u:>:oicoiC
iCt*O<DXiC0iWi-<C^Wp'^Xt0r*XiCQC0
:oiCo^coincOtCcoiO{OiOeoiiT)^LC^Lro^LC
o5 CO C^ CCM CO C*i CC C^ CO CO CO CO CO CO CO CO CO CO 6S
i^O iC to iC ?0 lO "dC i:© iC to iC to iC CO u:; O »0 CO iC
r-r*cciCOrrcM(Ncoo
COe4COC^'9<C^"<J'C^'VC^
COiOCOiCCO^tOiCtOiO
NcococO'^'NTj'r-i4COtoostr*xxr*Oito^Hicc^"^coc^'^'-<tDpr-oQ
c^'T'M^c^^cs'^c^-^c^co^iSSc^coficococOiCoeocococococowcoc^
tOiCtOiCtO^rStOiCtOiC itO iCtOiCtOiCtOintOOiCOiOtOiCtOiOtOiCCOiO
^tOi-it>-f-Ht>-QXQXOiClXaiXpr^'-<t^»HtO
^tOLCtOiCtO^tOU^tOiO.COtCcOtCtOiAtOtCCOiO
C^iOCO'^-^COiCCOCOC^
S*COiC'«J'iA-^'<*<-^'t'iC'^'iCC0COCOtC'NI'*C^r*f-* XCDOSQOSOiOO^'-lX
i-HIO^iC«-^iCi-IiOt-Ii6 ^HiOi-"ir5r-l40'-(iCi-ilC i-tiCrtlOi-H-'t'C^'^C^I"^
^ CO O CO O tOtC CO iC to iC to iC CO iC CO O CO iC to tO to lO to iC O ^ to iC tOtO
<s^HPf^O'-iOi^HO>C^Oi!c^X?<XCOXCOr^COco
tei-HOi— lOi-(iCrHiOf-tiC It-HiC^HiJOi-HiOi-HiCi-tiO
»^COtOtOtOCOiOtO»CtO^ COiCtOii^COiCcOiCtOiO
■^tOTfCOiCtOiCiCtOiO
tOiCtOiCtOiCtOifttOiO
-;x2«x^gpcoxcoxco
(.^COtOCOCOCOCOtOtOtOtO
xcoqsco^co^co^c^o^o^o^^o^'H^
OOOOOOOOOOi— 'Oi-'O'-iO'-hO'-hO
tototocotototocotocotocotococototototoco
5**icxLCXicxioxoxoxiCx»ox>cxir)Xi^X'oxy?xtDao^x toxtpxtot^^r^tot;-
Soooooooooo 0000000000 0000000000 0000000000
■^tOOtOCOCOcOtOCOtOcO ^OtOCDCOCOcOCOtOCOJtOCOtOCOtOiOtOcOCOtO|OtOtOcDtOtOCOtOtOCO
•a}Bp
•xojddv
Or-lOiHOrH&r-lOr-l
rHi-lrHrHt-IQlNOC^O»
.-OrtOr-lOi-lOr-liO
Oi-IC>r-lOi-(Oi-IO.-l
! , ........
« cB 03 03 oj cc oi ai 05 (» i 03 02 ci oQ ej 00 Oh' aJ aj CO ; oj ai 0; 03 ci CO oJ tc oi CO
f-iCOi-'CO^HeOr-ITj'rHTjl i-HTfQ-^O-^OiCOiO
Or-lO>-HO-^0-HO«0«Oi-lOr-lOr-0'-'
O -H OJ «
5^ -^tp^tpS iC»bift»cS SiOioiOeo
Page 600]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
J
S
o
&<
f,
45
ti
00
S
a
03
^
Ti
P
o
o
3
9
P
Tl
3
i"
3
5 a
Oi-ic^w^ io«t^ooo> Oi-fnco-* i««5i-ooai
: o J d d 1
'xojdd V
^^
ftiai03MC!^«ia?aiai'/J
0^x'9Jx2^^a4c»2^a5pHcc^xP^ajC4cc^c»
c^xSE^xfiSMQ^coC^yJoix
:'^iaiOiOiOiCi«>C«JiO lOJSiriiCtCiCiOiftiOiO OtOi«iOiC>0"3»QiCiO iOiC?2>ClCift04t5u5iOiO»C
aiftiCiOiCiCidCiOiCiO lOiCJiOiOiCiOiCiOiCiO uOiOiCtOidOiOiCiftiC iC^»ftiftiC»CiOutiiC»f5iCiC
; i35 iC »c 3 lO i«
» lif »0 lO lO i'^ lO
» ^^ 0> W Ol C^ OS
: ifl ic lO lo »c iC
; lO iC lO »CiC iC
iCtOiOift kOiOiO^iCiOiCiQiOiO liOiC^»?l»«iOiOiOi/i;ift iCi«»QiC»CidOiOiC»OtOiO
: C^ Q 00 Q CO o
e lO CO O ^ l£2 to
'^0'^oiijo»oos^Oioa>--ooo-^ccr*r*Gor^GO?pootolaoooi';oasioai>coiftQ'^
»0 O »C O kO 0»0»0»C»CiCiCiOiC lOOiOiCvOiOiOiCiOiO |»C iOiOiC!>0>0»CiOOiOOiC
iCtOi0^iC^idOiOiCiOiO»0»0 V5iO»OidCiCiOiO»CiO iOiOiCiOiOidOtCOiOtOiC
• »0 1^ lO O i« o
lOOiOOUCOiOiCLOiOiCiOiOiO iCiOiOiOiCiOiC*COiQ
iCOiC^OiOcOiOiOiOiOiOiCidC >CiCiOiCiCiCi»C>iC50ift
OicoicoifboiiS^iicoiib
tOiOtOi^OiOCOiOtOiC^iC
iiccoic^coM
; 40 O iC O >« O
» lO CO tC CD iC CO
OiCO kCOiCOiOiOiCiCidC OiOOiCOiCOiQOiCiO'OOiOOiCOvftOiOOiO
ii550»C^»CtOin«0^iC^iCiOiO ?OiCCOiC«OiCOiO:0»cUoiO«Oi0^inO»0«OiC<OiC
s^
; ?o "g* IX) sc r- M
: lO O lC OO O
; iT- o to 50 lO to
t>- (N 35 '-'
lOOiCO
iooi00oooico55
lO^OiOCO^OO^tC^iO
«;t^if5r*TfGio«QOcoasc^
giOOmOiOOLOOiOO
-£ii050iCtDiO:OiCO»C^
-;t^iCQO-3*as^aicooco
StOOiSOiCOiOOOO
-iiceoiosoiAcoiCOOco
oooooi>ooic
?0'iO(OC050«00':OOiC
OOOOOOOOOvO
C0':0«0C0C0'OOOc0iC
"^acc^i^coh*coco-*5ol'g«»oiCioo-Tr'»'COi>?or^(N
&iOOiCOiOO»COiO'0»CO>COiCOiOOiCOiO
C0i0t0iC<OO'0iC?0i0,':0iC<0»0«0iC«0in<0»C«0iC
wxTtt>-Tfr^icOipohP'f^t^>0'Xi"^oDcc(^c^O'r)
Oi.cou:>oiooi?5o»ooiooiooi6oinoici-iic
?OiO«0»COiCcOiOOiC«0»0«OiC<0»COiC50»ncOiC
SXi^t^Cpt^b^'^Ot^iC
iCOiCOiCOiCiOtO
oioo»c?oiO':oir5!Oin
g*X?pOl»CQiCQ^'-<C0
iSou^OOOOOOO
^iCOtO^CO^^OtOCO
oi>oi>oooooin
OCOOtO^^OO^OiC
-JOO^OfOtOO^OtOtOtO
Soot^r'-GOt^^co^iO
iOOiCO»COiCO>C
OiOtOiCcOiCOiC^iO
tOiOOiOtOiCtOiCCOiO^OiO
r-HiOrHii5i-H»OrH4jOi-HtC^-*iC
io»0!OiOtoic^»coio«Oir;
~ — — — — - ^iCOuOOtOi— tiftrHlOr-tlOi—^irai— liOrHiCi-HlOi—t^
:otoococo;o:ocotOiO
:Oooooooooo
i^o^ooto^ootoocoo
oooi>oooooic
tOiriSOiOtOOtOiC^OiC Oi-O^iO^^tOiCCOiC^OiC
eoooooooooo
^50:00^t0'^50^^<0
iCCCOiMt^t-tCCOOsCi
ooooooooouo
iO:OtOOO!:OOOcOiO
OGCi-Ht^iMtOCOiC'^Tt' iOCCOC^GO'-ia>QO<?lr--CC
rliOi— 'lOrHlOrHiSrHiO rHiOi-HOi-HOi-tiCC^'^lM^
to vO ^ »0 O vO to 1/5 I© iC O iC «0 ift O iC O »C «0 lO O lO
S* ^ a> c^i 00 CO r^ ■:** ^ If: iC
oooooooooo
^tocooco^co^^^oco
oooooooooo
^^tootoooco^oto
Scoi^'^ioD'-H^ooas
OO&OOOOf-iiC
tOO^O'lOOtD'OOOiC
i-(oO!Nr^cO'y3iC»oO'fh*coaoc^ai005i'>iaccor*
!0»C^mOU^«0iCtDiC 'COiC^iCOiCtOiC^iOtOO
r^coxc^^t-tOQC^o
OOOOOOiHOr-iiC
COeO«0?0«0«0^?0'-OiC
«i*!MOCCCO'^t^iC'©cpiC
$:0i-(00000000
^CO«OOtOX>0';OtOCO«0
COTff^COO"— 'i-HOCOOi
OOOOrHOiHOrHiC
OCO^OO'^OOtOiC
coQO'^i^tccoso**'t^co c^MOT-^.-40ic^a0'^r^ic*o
CO»OOiOCOt0^i0^iC ;?OO^iOOvO:OiOOtCO>C
'^0D»0t-«0»0G0'^0lC0Oi-<?1QC0aC'^t-':0:0t^»C
?OiO«OiCOiOtOiO:0»okoiOOi/iCOiOOiO^»C^»0
■I O ■* Oi iC Xi O :
^^ :o to
OOOOOOO
to to to CO to CO to
S'^OCOi-Hi-HC^Q-^OS
Or-tO—lOi-tOr-llC
UotOtOtOtOtOtOtCtOiC
tCGCtotocciCOscooirjIc^Qcoaiior-totoooioascc
tOiOtOiOtDiOtO»i^tOiC ,tOiOtOiOtOiCtOiCtO»r5tOiC
»i^o-:l*a?i^qot£>teG£ju5iq>5?o<N'r^r-tcoo^oo
itototototototototoo
:iti-(0
* to to to
OOOOOOO
to to to to to to to
ior^wioaj-^oc^iMrH
r-tiCr-tiOr-liCC^iCi'MiC
tOlCtOiCtOiCtOiTJtOiC
gSSS
f' CO CO CO
o> o t^ t^ CO go ^
oooooSo
CO CO CO CO CO CO CO
fHOi— tOt-<0»— (iC»— liO
COCOCOCOCOCOCOiCCOiO
t^-COOC^OOTrHi-ICOO
COiOCOlOCOlOCO^CCOiCi
sgs§
^COCOCO
GO »c r^ ^ iC GO "^
ooooooo
CO CO CO CO CO CO CO
OOrH
CO CO CO
— I C^ OS ^ GO lO CO
O rH to r-t iC •— * »0
CO CO to CD O CO IC
moiiOoocococcioo>co.-icq
COtCCOiOCOLOCOtCCOiCCOtC
COLOCOtOCOtCCOlCCOLnCOtO
CO lC CO >0 CO to CO to CO to CO to CO to CO to CO tO CO to CO tO
SooS
^cococo
t^*^ CO CO - - -.
ooooooo
CO CO CO CO CO CO CO
lO t- CO 0> iH rt
ioOrt
:COCOCO
CO CO tO CO to CO to
r~coo»iNp©c^«'*co CO to t^ M g> rH .-I o ec GO to CO
■-HtOr-iiorii/sc^'j'c^'V ijTfffqTjifjTrco-^coaSoiSm
COtOCOtOCOtOCOtOCOtO COtOCOtOCOtOCOtOCOtOCOtO
S'OGOrH
©oo
^- CO CO CO
gg3gg§g
to to to to to to to
S8S
CO CO CO
lO to iC to iC to ift
gsss
S^^ CO CO rH -^ OS
OOOOOiO
CO to CO to to CO ^
§ioS
CO toco
coo-*-^ r)«0
tO r-t tO r-< tO f— I tO
tO CO to CO tO CO tO
p^QQMcQpi^aaQjaQajco pijaopiJcApjoBp^aop^oD adxp^xajoopfcfip^co
COi-HOOOOOOflcOCC-^ lOC^t^OOJOO—'l^COiOiQCO
COtOCOtOCOtOCOtOCOtO cOiOCOtOCOtOCOtOCOtOCOtO
ioo»r-t~ootoococ^c^i'?'OcooOGCcoQtCJe^'*o
CO to CO to CO lO CO lO CO to CO to CO to CO to CO tO CO tO CO to
OHCcp^oopjQQp^cnp^ccMai
a o
& .2
OQ el
0 S
1 3
5 r
^
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 501
•xojdd V
^^
r^
C^ Cvj CJ
IN C^ M C^ CO
CO '^ la <© i-^ Qi
CO CO 00 CO CO o
PJOQP^XP^CIQQJ^^CIQ
QHXpijxp^coQ^coc^GCpi^xpiHaQPi^oDQi^cQp^x QjcQp^asp^GCP<ccp:^7^
g*C0iCC0iCc0iOC0»O^»C
1— (tCrH;0.-^:pi-ft^— lO
rHCDr-('Or-ILQT-liCi-*lO f-HlCKNiCi'NlCOlu
lO lO iC lO iC iQ tC iC iCiC lO lO lO ^ iCiC C^ lO iC lO
lO lO iC kO lO vC iC lO »d^ lO iC iC iC iC lO lO iC lO lO
'^■«*'^-^iC'«5*0'q"iCCOiOCO^CO;pC050CO(DCO
t^ ^ I"* ^ t^ CO (^ CO t^ CO
>Q0^G0"r!*OS'^(J>C0QCO
i^-}(,HCOC^CO^C^?^CSl
gCOQC^Q'MrHCqr-IW
QOCOCOCOOOC^OO'MOiNOSTHOrHQi-lOf-iOO
OiOOiCOiOOiOOiO
COOi-^Oi-^Oi-3'OOiCCO
COC^COrHCOi-f^fH-^Q
-^COCOCOC<l^(M^i-*lOrH
OOi-l'^M'^COCOCO'N
goa>osi340>oooooot^
i-i<oc^O(N»ceoin'^'^
OOtO^^tCtOiO^U^
"xo add V
S*^^rHOC^0>C005C0G0
a> '^ QO »o op «o c*
iC o ic «o vC <o iC
i-tooc^opc^t^coo-^<p]iCiCi02J^cor^coooc^
tOiO'^iCtOiCtOiCtOiC
i-H-^t'.-c^^^iMCOC^CO
^t^iCt^iCtO^iCt^iC
tO^Ot^iOOO-^OiCOOCO
Q0^05C0OC^Ot-lT-tO
C^OiC000'^r>-iO(D<©iO
C^CO!NCOC^COC^0OiMCO
C^'<fC^'**'CS'*WCOC^CO
!X)i-^r*?CQOiQOi"^Qco
CMC0C^C0C^ICO(NCOeOCO
sgiCOi^ooiN^r^ootpoxo
lO CO lO ic ic ;o ic
OSiCp'^^COMC^COtH
:OiC«OiCCOiC«OiCtOiC
<N^05COMCOCMCO?^CO
;gt*OOGOr*Oa«OOiOi-H^I<NCOCO!M-^^iCO'Ogi
a eOiC CO U
COiCCOiO«OiO«OiOCOiO
l>QQQ0r^Q*.O^iOC^CO
c^coc^cococococococo
.(OU5COiCCOiOCOiO«OiC
0»C— I'^S^COCOf-H^O
cocococococOcococOco
tOiCtO»C«OiCcOincOiC
coc<ii2r-*coot^oQait*
COCOCOCOCOCOCOCnCOC^
;OiCOtCcOtC<;OiCCOiC
»pOOi-Hr>;C^<OC^'^Tf*Cp!vpC<l«5rHl
a CO lA CO t
* IN "* C^ -^ CS Tf ^
3 ic «o m CO lO CO ic
i-icO!N»r5co3;>ococO'-'
cocococococOcocococo
COiCCOvCCOiCcOiCCOiC
it^QOipOt>-C^COCO'^
]COCOCOC^'<»'CStJ<N'^N
COiCCOiOCOiCCOiCcOiO
a COiC CO
CO "^ iCiQ CO t^ IN
Tj* (N --J* <N -^ C^ -^
lA COlCCO^ CO^
a'<«*<cOiOi«cOCOOOiNOiO
:o4^c^ — ■■ -■ - -- -
« CO lC CO
2co'^r*coosc^pO'NOi
:in^(Ntpc^'^cO'^coco
aCOlOCOlCCOlO^^COLC
)»-l OiOQCirHt
S CO CO CO CO CO
5 CO ITS CO lO «0 iCi
5 CO CO cO
SiOcOiC
cot^^jioco-^
CO CO CO CO CO CO
CO»CCOiC COiO
sOOCOOiNi-HOCOO-^t^
:*^-^eo-^cO'^c'5cococo
• COlOcOlCcOiCcOlO^^
»OWNOCOO>iCt*t>a
• CO^CO^COCOCOCOOOCO
aCOtOCOvOCOlOCOiOCOiA
CQ CC CC
CC CO CO CO CC CO
cococococococcco
ooi-it^eo«c-^-*ocot^-^
CO CO CO
toicto
.-I 00 CO to
toiotDin
tda<:DiCcOLCOiCO^
lOiCtOCOOOC^OOi-HOO
ko»OtOiO«DiC;Oi^(0»0
tOiOCO
OJCOt-
to ic to in
ooc^<50iN05'<ri^tc4C
•»f<CSSC<linr-(iCi-li5r-(
tOiOtOiOtOLOtOifitCiC
to t^iO
CO CO CO
lO tOiO
oocoOi-HC^g
CO CO ^ CO ^ CO
tOiO t0 4C to iC
1 1-1 r-l CO » in 00
5 ■.ji CO ■* OJ "# ?1
; to in to ir;> to in
>e^Qts>inr»t>-toos'.ji
:co^cocococococococo
itointointoiotointoin
« CO -^ CO
5 in to in
■.I* a> to t^ t-* in
■* CM -9" ?J ■■»' cJi
to in to in to in
s t>-t~-in
> in to in
to in coin
CMO'^OOtOtOCC'^OCM
inCMiOrlinrHinrHSi-l
toictointointoint^in
to to op
to in to
in to in
c-Jr-i-5io>
inNinrH
to in to in
iCOiccoicr^ict^iot^tc
OSC0.-li-HCOOa»CQ0r-CO
COiCCOtCcOiOCOiAcOiC
o>*rr-ii-tcoaicpt>-GO"3<
iCi-(OrHOOOOOO
COiCt^iCI>iCI>iCI.^iC
iCOCOCOCOCOCOCOcO^CO
IcOiOCOiOCOiOCOiCCOift
)in-J3in
to to 00 •>»< o c<
■<>• CM ■«" CM 35 CM
to in to in to in
COiCcOiCcOiCCOiCt>-iC
lO O CO c^ p
1/2 1^ lO r» ic
jiCcOr-iCOiCOp^iNp
-cocococococo^co'^c^
aCOiCCOiCCOiCcOlCCO^
»f*^OQMPOC^OD^CO
:COCOCOCO"*COTfC^'^<N
IcO^COiCCOiOCOiCCOiC
« r-.cO*C
«C^'* IN
5 1/5 CO iC
Gc CO p i-H e^j OS
CO iC CO »0 CO iC
-^I>.cOu^04C0i— ii-rcO^
lAi— (iCrHiCrHOT-<PP
coiccoiccoior^ici^ic
gS2
t~ini^
.-J CO ^in to
OrHlC THl?5
lO r- ■.»< t^ Tji
> in to in
SOCMOC^tO
CMinrHinrH
to in to in to lO
t^-^o»CMf-<oacot^tpin
inr-iini-ioooooo
tointoint^int^int^in
oo
c-in
-Hoeo
1— I O »-l
i>int^
r^ to-^ oi CM
in r-H in I— ' in
TT t- Tf l- ■<»<
»t**-(a>a>»-it^coininco
:cceocofjTt<cM-*(N'*CM,
Jtointointointointoin
l-CMTTrH
5 in to in
>-H to CO ■'J' in CM
to in to in to in
Soot^-coininc^ooQ
-hOOOOOOOO
toint^int^ini>int^in
ot^cointocM^Oij^to
f-linr-l
in« tji fM ■
^ l^ ^ t^ TJI
"tOOQOOtOO-^CMCM'Tj'O
:COCMeOCM-^CM-*CMTj<CM
itointointointointoin
toooooint5cOMr-(ino>
^T-H'^T— tin.— iici— (tno
tointointointointoin
i^toO'<>cMr-iino>r~tp
inoooooomoin
tcini>'ini>.int»'.jit>-^
|0 -^ CO ^ to
U-HinT-iini-i
|t>. Tji r» rji t-
00 05 in pi CM
■* — TfCM -91
■.}* t^ Tji r* -^
91 I
tfcQrtccpiHCCpaccffJccOHCoeJaQDJodKoDpHCO
tfcoPJaQP^cntfuipHCCP^oaPJastfaQpjcoCdcQ
CMNcMCMCQ CMCM^flCO
Page 502]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
S
CO
o
1
•xojddv
•xojddv
^^
5S
5
in to t-
«!»pl5M«OptfCO(J5M
St^ t^ t^ r^ r^ t^ t^ QO r* 00 r* cc r* go t^ ao t^ cc so ao
TI" iC ■<)' IC -^ >0 -"t "3 tC iO -^ >C -^ is Tf> iS TP is -^ i3
^»CiOlC»C»OlOiO»OidCiO»OiCiOif5iOiniC»CiC
S 3
lO o
dHaQpHSOpjcQpjcfifriJaQ
pcJagPnOQpcJcopdccpjaQ
iOiO»OiOiOiCidCift»fl
^»
l> 00 a Q
lO lO »0 CD
e^ccp^ccf:cjcof:^ci!}p^cG
iC iC »C lO *C iC lO lO iQ iC lO lO iC iC iC lO »C »C lO »5i
Ma»0*GOCCGOCCt^-3«t^
O-^O-rr OtI^O-"?*©^ rH 'Tf i-i tJ« rH tP rH '^ rH Tf*
i-HCOT-twSrHCOi-lCOiHW
-OiCcOiCOiOCOin<^iO
(N C^ CCiM ■<*« 1-^ -^ O »C Ol 1:0 go t^ CC 00 1^ 00 CO OitO
to »0 «0 lO ?D iC CO iC O iC :0 iC !0 iC CD iC CO lO CO lO
COiOcOiOCOiC-COiCCOiC
t^ccoooOiJit^aicoOic i-H"»tccc«5Tfc^ir5t-<cOQ
r-toSi-HCCrHCOi— ICCMCOC^CCCJCOC^CCC^COC^CO
CDiOCOiCCOiOCOiOcOid pOiCcOiOcO»OCD»CCOiC
- Oicor^
SiCcOKO
OS CO 1-H lO C^ 00
CDiCCOiC COiC
C^i^CO-^-^CCiftiMCOi-H
CDiCcOiCCDiOcOiOCOiC
GO<MOl.-IOOrHGOC^t^
cOiCc
a CO CO CO c^ CO cs
; CD iC CD if5 CO iC
CO Oi '^ r^ lit) CD i-"- iC
COC4COCNCO<N
'O iC CD lO CO lO
r^OOiOiOGOf-'I-^tNiO
C^COC^tNCOfNCO-MCOiM
^DiCcOiOCDiiOcOiCcOiO
sc^coc^
51OC01C
t^ iH 00 OS O t-
CO C^ CO f-l -^ tH
COiC COiC COiO
COC^ COC^C0!NCO?5
COiCCOiCcOiOcOiC
asc^i-iocooi'<**r*cDir:'
COC^'^C^Tj'i-l-^r-l-^r-1
COiOcOtCcOiCCOiCCOtC
^olco
icoc5
3CDiC
CDiCCOiCCOiCcOiC
i>-co a>
COiCCD
i-HiOfHiCrH
liT CD iC CO iC
gcooot^r^aicoo"^-Hco
COC^COC^CO(N'^(N'^<M
^cOi^cOiCcOiCcOiCCOiO
CO^i:
COiCC
) CO 00 GO t>« O lO
I ^ i-( -^ iH L(5 rl
S CO lO CD lO CO iC
goiO(N'«tcoc^iCi-icoai
^COiOCOiCCDvCCDiCcOiC
XOOOCOrH-^COlMiOO
COiCcOiOcOiCcOu^^iiO
COrH 10
iCi-HiO
COiC CD
OiCOOO
iOCDiCI>iO
i-iOicot^-'^iLCcocoaor-t
ooco01-<(^^ol^I•>.
5iO cOiO
lC O »C O vS o
CDiO CO iC CDiC
iOGCt^iCasC0<Mi-H-«I<c
SOiCO
5iC COLO
ir: OOOOiS
CO iCl^ lO t^ Tj*
3000
• iC i> »o
O iC i-H iC I— ( lO
I> -^ l>- -7< I> Tj<
t-ooot.cD'M^'^c^r-ai
COiOI>
s CD C^ -^
vCtH X OOi-HlO
rH iC iH rf !N 'Sf
I> -^ l--"^ t^ 'fj^
;iCrJcO'-Hao
COiCcO
OiQ 00i-t CD
t-H lO »— I lO I— I
iC CD iC CD lO
i-tCDiCO'^iCC^t-^OOiOO'-HC
liCrHiCOOO OOOOOiOr-itOi-HiC
^ CO lO i^ ic t^ lO i^ ic c^ -^ t^ -^ i> Ti<
cOt— iaoaii-*r^-^-hi^.— (OoocoiccorHcsOO
OOOiOr-nOi-HiCi— l»CC^-^C^Tj'C^)Tj<«5C0
»c c^ -^
C^l ■^ 00 ^
r* "^ i-^ Tt r* rt<
1-tOOcO
lO iH lO
':oiOco
cO-^"^CDC^
lO CD »0 COiO
;cocDiC-*t-(MaiOr-foc
?:iOr-(
.j^COiO
iCrHlC
CDiOCO
a 00 CO
■^ ITS r-t
^COiO
§-g<t~tO-3i
0000
10 1^ lO r* >o
^OOOOOOOOrHO i-ILSi-liOrtiCOJlSOJTr
^ t^ »c t> lO i> 10 1^ lO t^ 10 r^ -^ t^ -^ t^ Tj< r* tH t>- Tj4
» 00 0000 i-tiCi-HiOr-llCT-liOC^T)!
< 1-1 00 •* -»" 00 Q
< f~ ■* t~ TJ> 1^ -^
COcgvO'^OOOOffiCOt^ OT('00^^00-#inoO(M
O O O O i-H 10 I-H lO i-HiOr
f lO (M Tf (M Tf C^ Tf
• --T* t^ -^ t^ -^ t^ -^
iHOaiCOOOT-HC^t^t^CO
ooe^i-HOcot~'j5-*aic^ci05ioooocOT-taiiO'0
JCslfN CO
OrfrHOOm
■* IN lO C^ lO i-(
t^ ''t t* -^ t^ -^
■OOOOrHOfHiCrHlC
3 t^OO'i'rt Ol
:rHOrH5rHOrHlAe^in
O>-<J'C<I.-liO00CC"Q>-t(M
003<i-IOiQt~00C0I^O
t^-*i>-^t~-^t^-(<t^-.^
r-i Of-t 00
t^ -ni « ■^ oo -91
^r '■^-' -A^ ^T »— ^ »— ' uj i"* u»* fj
T}HCTit^:pOC0CCCst^:0
JC^'^0000i-'MMrtOt£i
iiC00C~inOC0MC5t0t~O>-*lN,-(iOW0l'<J<C0O
:r-llCr-l>OC^iOC^iSC^-*f<-*COTPCOC<JCOCO'9IC<5
t^^oo-^
rt< o> 00 -^ 00 Ci oc
)r-liCT-(
CO -^ 00 -^00 w
iH r:* i^ cc CO a>
r-< O rt lO C^ rf
00 ■* 00 00 00 00
JeOT(<OOOiM-.OI:^000
>Oi-iiomnN'*cO'ji
5-^OOOOOOCOOOCOOOOO
; 00 CO .-I -H ■* 00 t^ lO Q IN COQOt~iOOrH3<OOM'*
: r-( in <N 10 (N ■V C^ -"J" CO -^ CO 00 CO CO -^ 00 ■* IN TJ< (N
' t~ -* t~ ■»!< t- ■^ t- Tjl t~ Tf t~ TJH l> rt< t~ -SI I> ■* I> Tj<
S*C<10iiC50Q0C0i-HO'^=0 QOCOiHOiiCiOOirHCOt^
(N-^fNTj^cN-^CO-^OOOO O0CO'^C<l'<^CN-^C>linTH
^ t> -^ t^ -^ t- Tj< i> Tji t- T)< t^ "^ t^ -"^ r>. "a< t- ij< t- -^
HOOOrHiHCO^rtr
10 Clio
-*<00t)I
OOrHO
00-* 00-^
OOOOC^OOt^COlNOOOOCO
lOi-HOOOOr-liBiHlC
t^-a<00'*«'-^ODCOOOCO
;tocoaoO'Ht^Tjicoooo ■HomtNoiooco-^oco
-INTt<(NTj<COCOCOCOO0CO --rC^-^fN-^rHinrHiOT-t
» t^ -^ I> -"l^ t^ -^ t^ rH I> Tt t>. '•^ I> •«*< t^ TjH |> -"^ t^ T}<
rioa>ootOi-i(Nioosooio
jINCOCJCOCOCOOOiNeOlN
P^ccPhcqPhcoP^coPJco
sss
SCOlO c
i-H lO r
I -^ ooco c
iNiN«500Q-*'^roOliO
QHQQPjCQI^OQpljUipHOQ
'Ti'
•»»• "^ iC
00-* 00
10 ■* Oi O ■* ^3 00
in rH -T C^ •^ IN CO
CO 00 CO 00 CO 00 CO
!iC<NO
HiniNio
3000000
ooeoic t^ciQ
O) "J* CO CO ■^00
00 CO 00 CO 00 CO
c5^m'
1 1^ -T< -^ 1-^ C^ 0>
' 00 CO -^ (N in rH
1 00 00 00 CO 00 00
>t^t^OTf<coc<inrttp
5COCOeOT)>(Ninr-lOO
)ooooccoococococnc<5
Sr-tp-^t^oinoo-^ai
sco^c^Tj^^^LOooin
iOOOOCOOOCOODCOOSC^
Oi5t»p4=op!3a6c4(»Wc»picotfa3pi;ooa3a3pia>
rt IN C3 ■^ tQ ^S '"" OS "^
ininininin inuoinin
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 503
o a
•xoaddy
P5 aj 03 CO « 73 rt cfj rt CO
Wco'McoCKHCBPiccMccPSMtfcoPiGdrtccOHCC
:iCOiooiao-*OTjio
n
coocoocoocoocco
d:h cd piH CO a; cc jii aJ si X* Cij x'
C^?1C5cCC^CQN0trHCCi-IC0
;ooo
;oaDOaoigcot>-r-iiCC^
iC CC iC CC »d
>OG0C5giC5Ot;THO_<N
iC CCiC CO iC
TttCCCO'^'N^prHt^asCO
coiC«»AcoiScCiOc^i3
OQOOiO t^
iC O lO OiO
1— I ?0 CO "^ Tf W ?D
to iC O iC O lO CO
Ou^ CO iC O iC O
-MiCi— i^pOOOOsOiI^OCOC^
O i-H O f-l ,-1 ,-( rl
CO lO CO iC CO vC CO
3010000I^'-'CO(N
-CC^CCiCWiOCOiO
»poc
CO-^COiCCOiOCOiC
COiOOOiCCOioCOiOCOiC
lOCOf-'tCOiAC^CO
coiccoiAcoiCcoiS
OiQOQOOil^OCO^^iOCO
lOiOiCidCcDiCcOiOcO
SQooiaaccQi-«>^coc^
irjiCiCidOcoiccoiOco
;OQ0 OiCl CO Ol
; '^ Tj* CO Tf4 CO Tf
» lO lO ^ lO o »c
t^QcO^
COOCOiC
iC lO iC ifl
iCC^iCCO-^TfCOiC
COiOCOiCCOiCCOiO
'MCO
COiS
COiCCOi
: ga 05 GO o t^ .-H
J lO iCiC CO O CO
■^'^COiOi-t
lOCOiC COiC
CO O t^ Ol ^ 00 o
O C^ O i-( O rH r-t
CO ir5 CO lO CO li^ CO
ic CO -^ -3" c^
iC CDi/3 CO iC
0(NO(N Oi-H O
CO ift CO uC CO IC CO
cOC^iOCO'^'tCOiC'McO.— tl
lO CO iC CO o
O C^ O C^J O CM o
CO lit; CO ic :o i/t CO
sOOD
O i^ »C LC
ooor-i-i
COiO COiC
\ft ifi \^ lO
CO CM CO CO iC -^ -^ ift
COiOCOiCCOiOCOiC
COiSoOiCCOiCCMiCC^O
lOiOiCiOiCiCiOiCiOCO
t^»-'COCMiCCOTj<-5*cO»CC^lcO
r-j o c-i o C'J ^^ '^ f^ '^ f"^ '^^ '^
iC CO iC CO iC
OCM O CM OCMO
CO iC' CO lO CO >C CO
:-<^'*f<TT"Tp-^iCcoiocoiC
f- CM rococo
COiCCOiOCO
COiCCOiO
iC irt iC lO
:c*»o
t»o»c
Tj< i?5 -^ lO '
;C^Q
CMQC-li-lrH.-l.-ICM
IcOCOCMt^CMXr-CiQO
jcoiCcOiCcoiScoiC. coo
'lO iQiCiCiCidTSiOiCCO
?i ^ GO- rH t-
. I O CM O C^I
lO CO Iff cOiC
CI CO CO »C tJ* lO iC
O C-l O CM O Cl O
CO lO CO lO CO lO CO
5 CC t~- CO I- -^ CO iC
Scoin
iff tff iC
'-fcocoi^cococMOir^ai
COiffCOiffCOiffCOiffCOO
iffiffiffiOiffiffiffiffiffiff
OOQ^ OS
COOCOOCM
Iff CO >ff CO Iff
O OC CI t>- CO t^ -^
O CM O Ct O CI O
CO iff CO Iff CO Iff CO
71 CO 00 CO 00
CO iff CO iff CO
iff Iff Iff Ifflff
S CO iff
Iff Iff iff
CO Iff
cocoiffr^-t'^-cooccoaa
COiffCOiffCOiffCOiffCOiff
ifflfflfflfflfflfflfflfflfflff
I01CJO»-*^^0.— I^CJCICO
CO Iff CO
iff Iff iff CO iff
OCOO CI OCMO
CO Iff CO iff CO iff CO
Tf S«iff CO
iff iff CO Iff iff
Oicoo^'^oQ'^r^iff
iff Iff
iff o5 Iff
I"- CO CO CO CO 1-- Iff 30 -^ 00
iCOiffCOiffCOiffCOiffCOiff
Ifflfflfflfflfflfflfflfflfflff
^ Oi CO d CI
CO iff CO iff CO
iff ■ Iff lO Iff Iff
SCJ rH -H ^ ,-. CM
CO O CO Occ o
CO iff CO Iff CO Iff CO
•xojddy
aCO rH ^
: TPiff '
j^ CM^ C^CM
>* iff rr Iff ■«1« Iff
D iff Iff iff iff iff
«— < CO O CO o
"^ Iff -^ Iff ■^
iff iff iff iff iff
Iff CO iff
Iff Iff Iff
CQiri
Iff Iff
t>-co»^r»cot-.cooo
CO Iff CO iff CO iff COiff
Ifflfflfflfflfflfflfflff
Iff QOiff Oi -^
CO Iff CO iff CO
Iff iff iff Iff iff
OS -r o CO Q CO r-.
Iff CO O CO O CO o
iff iff CO iff CO iff CO
I-^lff '
" CI CO CM CO CO
>* Iff ■ TT Iff -^ Iff
; iff iff Iff Iff Iff
CM CO CI -^ 1—1
^Iff Tf iff Tf
iff Iff iff iff iff
-l^rHlff
Iff Iff
Oco
TT iff
Iff Iff
aicoost>aot^oooo
COiffCOiffCOiffCOiff
ifflfflfflfflfflfflfflff
sSco
OiCOOicoCicOQiffC
Iff CO Iff CO <
iff Iff Iff Iff Iff Iff iff Iff Iff. c
^CM'^CM'TfCM'^CO''
5 -^ iff -^
S iff iff Iff
iff -^ iff
iff iff Iff Iff Iff
coco CO -^ CM
■^ Iff Tt^ Iff TJ<
Iff Iff Iff Iff Iff
•^ CI Iff
Iff -^ Iff
rH CO O CO O t^ O I-
TflffTflffTTlffM'lff'
Ifflfflfflfflfflfflfflff
Oir^Oi* 00
CO iff CO iff CO
iff iff iff iff iff
SSS;
Jiff CO
: -n" Iff
Iff 25 Iff
Iff iff iff
CO Iff ■^ iff ■^
iff Tf Iff Tflff
Iff Iff Iff Iff Iff
■«(Ji Iff ■^ iff Tt*
iff iff iff iff iff
'^
--5
Iff Iff
■V iff -^
iff Iff iff
COC - - .
Iff Tj< Iff Tf Iff j
iff iff Iff Iff Iff ■
iffcoiffeoiff cococicocMcocMi--cMt^:r-(t-r-tooo
— „ -I ... J .... .^ ^ .. -I ... .- - .^ JJ-J ^ ^^ ^
Iff Iff Iff Iff Iff
X OOO
iff -riff
0 05001
■^ iff flff
Iff Iff Iff Iff
;co^
ITf Iff
-ifflff
co-rcO'^cO'^co'^
■^iffrt<iffTj«iffTf«iff
ifflfflfflfflfflfflfflff
iff -^ Iff -^ Iff
Ttl Iff TJ< Iff ■^
iff iff iff iff iff
Iff Iff iff L
rf CO
■^Iff
'iff Iff
-r CO"*
•^ Iff T
iff iff iff
cpcocococp|COt^cor*cit^CMi^CM
iff-^iff'jpiffTriff'tiffTj'iff'^irj'^
ifflfflfflfflff jlfflfflfflfflfflfflfflfflff
SCMOO
'??' Iff
Iff Iff Iff
• iffr*ifft-»ifft^ifft^iff
-iffTriffTfiffTjHiff-rPiff
Jlfflfflfflfflfflfflfflfflff
JXiffOOiffOOiffOOiffOOiff
:Tpiff'*iffTj<iffTj«iffT5fiff
[ifflfflfflfflfflfflfflfflfflff
O Iff CO iff . CO
-TJi iff TJ< Iff Tf
iff iff Iff Iff Iff
iff CO iff
Iff ■* Iff
Iff Iff iff
** iff ■* Iff ■tt
iff iff iff iff iff
Sl^lff
■^Iff
t^ CD
■^Iff
Iff Iff
i Iff Iff
05 CO Oi CO Oi CO Oi CO
TfllffrriffTj^lffTf^lff
Ifflfflfflfflfflfflfflff
pi^aipc^czipiHadp^iXpcjcc
^^'-
CM CO Tt
oa CO 00 CD 00
Tji Iff Tf< Iff ■^
iff Iff Iff Iff Iff
COOOCD
Iff '«*«Lff
iff Iff Iff
XCO
Tt^lff
Iff Iff
CO CO CO
Tjtlff TJ*
Iff Iff Iff
CO Iff CO Iff CD
Iff Tl« iff Tf Iff
iff iff iff iff iff
t^coi~^cot--cot>»cot^cp
^Iff'^lff'^lff'^lff-^lff
Ifflfflfflfflfflfflfflfflfflff
00 CO 00
■^ Iff TJ<
iff Iff Iff
CO 00 CD 00 CO
Iff •* iff 'Tiff
iff Iff Iff Iff iff
ifft^-ifft^ifft-ifft-'Tr^-
■< iff -* Iff
: Iff Iff. Iff
-•r iff "^f iff
Lff Iff Iff Iff
CO CO CO CO CO
Tf Iff '^ Iff f
Iff Iff iff Iff Iff
CO CO CO
iff ■^ Iff
Iff lO Iff
CO CO CO CO
-J* iff -T iff
iff iff iff iff
X CD
■rr Iff Tj« Iff Tj<
Iff iff Iff Iff Iff
GO CO X CD X CO
— ^ iff ■^ Iff
Iff Iff iff
X CD X CO
-riff n- Iff
Iff Iff Iff iff
;si:6pit^pi:£Qico^^\^:Qp^!^ci^^^oi:^\pi^^'^pi':^^f^^z6(^r^
"3S vs t* 00 ^^"^
O r- CM
'^5r^r
Iff CO t^ X OS o
Page 504]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
i §
V so
01 O
5 I
O^ II
0) OQ
T
S £
" a
3 55
.^=^
•xojadv
■xojddv
S5
§ ?
CO CO CO CO
C:i:^PCt^^:nC^a^:^z6iO^:c0^^^a!iO^^Xa^m!£p^rnP^iXiPia^P^m
g*»Ci-HC0C0»HiO^t^t^Q
tHCOOCOOCOO-^O-^ O -^ iC tI< tC 35 lA ift 4C lO
Cc!coft5cc0^cQtfajPc5a5
0it^y5OC0C0Q<Ct>-
C0<— 'COC^OOCS "■ ~'
'^i>-^r*'-j*t^Tj<i>.'^t^
COC^ iM?l
oit^i>-o-^^ri3"Oit>.qsococoo'©r*a>'^M
tfiOTpO^O'^OCOOCO.-lCOrHCOi-HC^i-tC^IC^I
a;0030'N^-^3*--5ri3o'ooccr)?p'n*co-^i-ioo
^i-H«OC0OC0OC0OC0.O"^»C'^i0'<ri0^iC'^
Oi^tDCO'^^.-ICOOir-t
'»j»tO'V»0'V»0'^iCCOO
^DCOTf-^r-I^XC^iClO
COOOOOCOOC^i-IC^T-l
rHMOC-IOCOOCOOffO OC0iCC0»?5c0iC-^*O'*
Q^a0QCiCQCO«Q»O
»QO»COCOCOOOt^C>
COiCCOOCOOCOOC^O
^iH?5oc^owc5c^ocojo
»H»-(ascor*?Dioopc^Q
>cor-.iOioooc^ooco
KiCCOiTiCOiOCOOCOO
^^■^tOTfO-^t^-"
Si-tC^OCJOr)065oC^ OC^OoSiCCOiOCOiCCO
SScoiceO"^-^-^''?''^'^
(NGOOf-HOOCOiOiOCOOO
'^'^'^lOCOiCCOiOCOiO
SiMt^OOSQOOt^C^iO"^ CO iC W r>- Q 30 CO o r* c^
iQtCOSO^QOOlOt^W
locoiocoicco"^'^'^-^
iC'^COCOiHOOOQrHCOCO
'^'^TT'^'Tj^-vCOiOCOiC
SgCOiCT-HOOXiXCSt^fH
S£Tj-C0C0-^(M'X>Or-ai04l>O«pC^'-t"C0C0»Cr-i-Xi
^vCcdCtOiC^iCOiCtO iO^»CtOiC':0»COiC50
» as GO 00 OS
t^OOi-tirs CO
lO :0 lO CO lO ?D
t^T-liCCOCO-Tf^CDQX*
tncOiOCO^COiCCOiOCO
coo'^M-f'^i-tt^aiOi
SXCCOtC-HTfCOCOiC
C^iOCOiCCOiCCOiOCO
1— It^OsCll-^i— (iCCOCOiC
iCC0'<rcO'^-«*'«Ti'^'«^Tp
c^iO»-Ht^csQor^O'x>c^
OC^OC^iC(N»OCOt?5cO
iCCOiOCOiCCOrf'CO'^'^
iCcoco-^c^cpor^OiOs
iC?0»CtO»CtOiCcO^?D
lOCOiCCOOCOiCCOiOCO
TfT^-COiCr-ltOOaOCftOS
t^O«Pi-HiCCOCO'^C<l!C
CSiOC^iCCOiCCOiOCO
? OS Ol GC O t^ "H
> lO ?o iC ^ iC ^
COC^uOCO'^'^CO'X'C^t-*
i0(0iO(0iC«0iCC0iO':0
OOOOlOlCCi-Mt^MiOCO
: c^ oc<io
iC ^ iC to iC CO
OiiH00Cm>C0«O"^idO
iCCOiCtOiCCOiCtOiOtO
>'CiCiCiC"^^COt^<NQ0
:C^OC^OC^O(NOC^O
iictoictoictoiocoicto
iiCCOiCCOiCcOiLCCOiitjCO
THa>ooa>i-HQOc^i>.co
iCcOiCOiOOiOOiOcO
COtOCMt>.i-IXOai^i-*
i-tiHi-ti-li-trHr-lrHOC^
iCCCiCcO^COiAtOiOCO
tO"*j<ic»0'<!t<«ocor>.c^x
THrHi-l»-lrHrHr->«-1i-1i-l
iCtOiCOiO':OiO<;OiO«0
•<ficc^cOr-(aoaiasQOi-t
OC^OiNOOIiCC^iccO
iCCOifSCOiOCO-^CO-^CO
OOC^COCOtOiCCOCCiNt^
0<NO(NOCsiO[NOiM
lOCDiCCOiC^iOCOiCCO
i-'iHrH(M0(N0c50CS
iCCOiCCOiCCOiOtOiO^
'^r*coqowa>i-HOp'-i
OsC^GOCOt^-^COiOiCtO
rHrHi-lrHrHTHr-(i-(r-li-l
iCCOiCtOiCcDiCCOiOCO
'^t^COOOlNOS— lOOtH
r-()-(i-lrHi-lr-(i-l(NT-ICS
OCOiO^OlOCOiCCOiflCO
ICOOS^OO'^t^iO
*QCOfliCOOS^*^ ^.^-„^ .-_^ ^
jiTDtOiCXi'iCOiC^i-t'O i-C^iO:OiCcOiCOiOcD
3 T^ ^ CO OS
>c^T-i?qc^^coQcoO'«*' ai'^ai»ooQcpi>r*tDt>-
:COOCOOCOOCOOCOO C^OtMOC^OiMOC^O
^iC^iCtCiCcOiO'-Ot^tC iCtOiCCOiCcOiCtOiCcO
JjOJNi-I^C^OC^OSCO
iCeOiOcOiCOiOcOift-co
•OOOiCOlTf*OCOOCO^-l
lOCOiOcDiCcDiCCOiOtC
oOTfr^io?D^iCt^-^oo
i^OiOOiCtOiCCDiCCO
iC?OiCCDiCtOiCtOiCCO
»ift^-lTj<.— |-^<NCOC^COCO C^COfN-^r-''g<Q>COCO
:cooccocoocoocoo,coocoocoocoocoo
BiC(DiC:OiCcCiCOiCcOiCOiC:OiC:OiC!^iCCO
OicpOSt^OOCCt^QOcOOi
tOOiCi-H-t^CO(MCOCO
tCt0iC«0»CC0iOtOiC«O
jr^Q'-OQCOi-Hifii-liOCq.iC^'^C^-^COCOCOCO'^
:coocoocoocoocoO:Coocoocoocoocoo
JiCcDiO':OiCOif5cDi^50 lOOiOcOiOCOiCcOiCCO
ri -^ CI tc 1-1
cooeooco
iC CO iC O iC
COQcpOl^
owocoo
CDiC CO lA CO
Sr*aoGOooast^a>t^o
iCCOiOcOiC^OiCCOiOCO
*55aiaiOiCiQCOQQO»HQOrHt^i— (t^C^^OC<|yDM
:c*tOcoiCcoocoocoocoocoocoocoocoo
iiOiOiCvdCcO'CcOiftiCO iC cOiCcOiOcOOcOiOcO
COCOiCCOiQ
CO O CO O CO
irj CO iC CO iC
OCOOCOC5
CO »C COiC CO
•^■^"fJ^lOCOlCCOcOC^COrHt^^r*
" COOCOOCCOCOOCOO
lOcOiCcOiCCOiCCOiCcO
ii-H!Xn-HQ0»-l0a.-H0SOaS|O0". OQOiOOaQOi^-t
S-TftCTriiS-'fiO'^iCi'^iCj-^iO-^OCOOCOOCOO
*iOidCiO»COtCiCidOU3iCu0c0iCCOiCC0iCC0
coocoococ
lO COiC CO lO C
t^cccococc^iCTriCto
ccocoocoocoocoo
iCcDiCcDiCcOiCcOi^CO
j-^Qc-^GO'^aO'^X'COGOcooDcoasc^aiMasc^o
iCCOiC ?o iC
COiC cOiC CO
»co^*cot^co^*co^*col^^ct^lCGOlCQplCaclftap
lC LO iC iC lC
00 ^ qo ^ X'
lO '^ O ^ lO
iC lO tO iC lO
rH^HOr-IO-MCl^JOSCil
■^O'^O'^OCOOCOO
iCCOiCCOiCcOiOCOiC.^
-'*«OS'*OiTt<O>C0CSC0Oi
iOS^OC'COQOCOXCOOOCpCOCOCOt^ODl^OOr^GOt*
D t>- 00 1^ 00 1>- 00 r^ 00 1^ 00 r^ 00 1^ t^ t^ t-. r-- r^ f*
lC lO lO ^ lA
iC^ iC ^ »c
iC iC ^ lO iC
WcoPtHCoOiccPtHCcPtHCop^ai^tfc/itfa^SiccCtHaDD^cotfo^QScdCd
rt C^ CO
c^ 5^ ri cs
tr^ CO r- X 31 o ^th" (M CO Hf^'^'p
C4 C^rJC^JC^CO COCOCOCOCO
PcHCoPCHxP^ccP^GCPcHa^
CD^ l^ ^^"^ ^ O
CO CO CO CO Tf*
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 505
s i
.H e^ CO
5
^
00 Oi <5-^ N CO ■^ "CMC
•xojddy
s I
aixaiaici^oixxx qjccq^ccpihssOhccp^hoq
tf-fcoo*-Di^ocofaioc»rec^iO'^0'--'-'ic^o
iC lO lO o
rt aj OS cc 03 CO pi aj OS aj ra aj DJ MJ pi 02 c4 as as cc
■*i-<COC-<r4CJC^CO.-l-f O'TOiCiOO'^iHCOC-l
COODCOCOCOXCOJOCOOc'c030COOOC^Oir-40sC^01
c^?5iHSi-HCOrHeoo-*!o-*3-*iniO-*in-*ocooeortS>H4^?5r-icoocoo->j'iOirtTi'Ocoi-i
,^-^t^'^i^'^r*'^t^Tj*t^-^t^cot^cor^coi^coGCcooocooocooocooocooocoaDcoaowoonciriOi
^•^t>-^r*-^t^-^t^-^t^ -^i^-^t^cot^cct^cor*
■^iCCOOCOOMi-Ht^Ni-HC^OCOS-TiSiS-^iO
cot~coaocoocco«co«'co»coooc^aoo4aoc^oc
M 1-1 e^ >-< i-i 1-1 ^ c^ 1-H c^ oc5ocoocoincoio-*
.^ Tjl t>. ^ t~ ■^ t~ ^ I^ ■* t>. 'J' t^ ■>>• t^ ■* t~ CO t^ CO t~
rfS Tj" b- -.jf i>
-3ir5 3' __ _
<e^io^JOMOcoineo
■>j"^'<i<iOcoiScooc^o5i>-ir-iNo6j3coin'*
?5t>-coc-eot-coaoco«.coaoeoooeoaoe^ace<co
O'r^'^-^iCCOlOeOOplOC^r-lrHrHOeqOCO
cot*coi>coi>cor*cooocooDcooocOQOcoaocoao
S'QQoQcoiC'OC^wocs^iireiC'Nooosc^iOiONOiaocoeot^OJC^Tf^Oi— hjitoooe^j^gceof^c^
«o?ioc4oe^OrtrH !-n-i«T-(Oc^oc^oc4>cco>ocO'^-*-*Ti<eoiocoiBc^o6)Oi-ii-iC>c^i
^■<j"i>-^r~'^t^-^c»Tft~-T)<t>-'^t~Tj<t-'^i>'*r~cot-cot-cot~cor»eot~eot~coaccoQOeoooeooD
S*CO»OrH000QQ^COC^^
coiocoinfioMOOJO
peoiceoocoin5)iO<No
:tj<-^CO-^CO»CCOiCCOiO
SiOeocomor-ooostocj
•^■^-^•v^-^co-^coic
0»3a«5C^COiOOOit^Ca COtOO>OiC"*QOOOCON-i005CCOQO>'*'^OCr-l
i-(Or-irH>-lrHrtrtOO) O0)l0C0lOe0iBC0'*'»J<h»"5<C0mC0iCI^Or^r-l
T)< t^ ■* t^ ■* i> "^ t- ■* t^ Tj< t~ CO t~ CO r~ CO t~ CO t^ CO t» CO t^ CO t^ CO GO eo 00
■"j'S'T-itooO'^iccocqtOiOOOiOcortt^t^-^coiOlooocoiOocorJicc-i-i
<N O (N O 1-1 O rH i-H -^ rH O r-l O C^ O N iC CO lO CO ■!»< ■* ■* ■ni CO is CO lO i^ O
■^r*'^c^*^t^'^i>Tt<t^'^t^'^t^Ti«r*cot^cor^cot^cot^cot^cot^cox
OsOiCOi-ICO'^Ot^t^O
CJiOCJOC^OC^O
■*C0i-<t~t»pa''^O0Q
■«-^r-i^oooi-^Mcoic'oooi^'-c'*'*ot>.f-'jS'Sooo>'^'^o>o>'»eo
COlOCOlOC^iCC^OlNO C^Oi-ti-lr-frHi-tf-(OC^ OC^iOC^lCCO'^COTP'^
^co*^^£)-<j<tO'^t*'^t^ ■^t^-^t^'^r^-^t^'^t* ^t^cor^cot^cot^coc^
iCCOlCCO'^'^'^'^COlO
cot~coc~cot~cot~cot-
c?ooo5^^"^coc^icot^ oposepc^co-^^t^ocoihoc^coioogct^i-ico^ ox'-pC'4c^«C'i^»-'CO"3
STf<co-*-*-4'*Tii-^T)i'fl< S'^eoiocoiceoicc^iCMoncSc^Or-ir-irHi-i »-<t-ioc^oc^iCco»ftco
.^•^tO'^CO^tO'^^O'^^ Tf<CO'^'©"^'£''^^'^CoU3*t^*^t^'^l^"^t^'<J*t^ -^t^-^i^-^t^coi^cot^
S'oi»OC>t^oso>t^»-'iftcocoiOf-<t^a»ai?oc^Tti*t'l^«oo»05co2?^^S59£'^^^wic^os»£co^r^
iCCOiCCO-^CO'^^'^'VTf-^Tf-^CO'^COiCCOiO COiCfNUS'NOC^OC^Or-lf-ti-tr-tOfHOWOC^
S^CNiO^COiCClt^OOl
OCOlCCOtCCOiOCOiOCO
aoo»<N3'3;<Nt^ooa
S'i-l0>0»QCCC^t0C0i0iOC0tOrt00 05Or~C^>O3'
OM>oeo3eoiftco>ocO|iOcoinm'^'^')'-*^'s"
COlOCOiCCOiS«lCC^Opl«55SOr1r1i-lri.-ci-l
^^•^TTCOiCCO^COkO
r-<o>002iiC>2'-iac«t-i
C04C?IOC50PJOi-lr-(
Soc^oc^oc-ioco»ccoSco35o5»5winwiO'^i-^'rr^^'n<-^'n''n'-^u5jwir5S535coSc^oc^o
t^
0
1-1
'*■
IH
QD
S'OSC^OOCOt'-lft^SD'^t^CO^i— 'QQC^GC'^^^K^t^COOS^HrHOiCOt^lS
oe-)Ocsloc5oc^ONOoiOMoeoiScoiocoioco>ncoio-^'*'*'*'<j<
■*^Ti>-<i<^iOcoiAeoi/5
c?e00SC^O»-4^O'N0S*^Q0l0<0t0in00C00i^i-l QC^O>iJit>-OiCC^COO>iiHrHO>COt^iO»CODCOO
grHS-iriSi-ce^Ssqoc^oMoc^oe^iotNoco oeoiocoiocoincoineo i/5irii'-*ir-*ifv*S
S't^eoi^r^toociftWcoo
l-li-ii-lr-lr-(r1i-lrHi-l(M
f)i-<?4r-ICgi-li-li-li-li-l
•xojddv q""
S' to 1-1 lO -H lO IN ■»»< CO CO •«< ca ■«*" '^ lO 1-1 to p t~ o> 00
C^i-lfJi-dNr-lMi-ifJi-l i^i-lC^i-IIMi-lSi-li-li-i
^iC too tCiC tOiO tO^ to in to lC to iA to O to lO to
I^-HiHNO-U'OJiQt'O
i-ie^i-ie^-^cjoiNOc<
latOiCtOiCtOiCtOiOtO
?SofJOcoocooco
U3tOiCtO»Oto»OtoiCto
t^OOtOOiiCp^^COC^
rt^l-l1-.rt?4lHC^llH^^
iCtCiCtOiCtDLCtOiCtO
C4'^i-liQOtOOOI^l--a>
iCtOii^tOiC'-OiCtOtAtO
SiCtor-'^osci^Qeo
coiccoiftcom-rio-*
■^tO-OitO-TtO-JitO-litO
lin.QS'C^Mcoputact^
oeoocoocoocoicco
lOtOiCtOiCtOiCtO^tO
COOSt^PiOf-l'^C^COCO
rHi-li-l«i-CCMi-l6<i-l'M
lOtointoiatoiotoioto
ojiOi-itDmc-gpostp<5
lO to iC to'io to »c to iC to
S*i-iODOCOO>050500Qi-ir*^^t^C^tOC^iOCOiO-^
eOOCOS!NO!Ni-l?i— ik^i-KNi-KNi-iOJi-iC^i^
.^iCtOiStOiOtOiCtOiCtOiOtOiCtOtOtOiCtOiOtO
rJ-iOCOtOC^t^i-IOOpoO
iCtOiOtOiOtOifltOiCtO
aiQ>OT}'iO"5>tccot^coi^;jt^MoC'-gpogjQO
fteoocooeoocoocoo coocoocoocoOMi-i
^iCtOiCtOLStOiCtOiCtO OtOtCtOiCtOiCtOtOtO
3»oa>i-iocc^t^c^tceo
5Ni-(C^i-tC^^HC4i-t!N^
iCtOiStOiStO»J^tOi/ttO
i-l?iiHC^i-ICMi-loSi-l(N
lOtOlfttOiOtOiOtOiCtO
tO-^iCO'^tCCOt^I^OO
|C<i-iCJi-ie^i-i04^oii-i
ifitOiOtOiCtOiCtOiCtO
• qj CO OJ CO 30 eo 0
"t^iCtOiCtOtOtot
:5sScooSocOocoocoocooc%ocooco
,^iStOi/5tOiCtOiCtO»OtC iCtOiCtOiCtOiOtOiOtO
iCtOiSt^-^t^-^QpCOGO
COOCOOCOOCOOCOO
ictoictoiotoiotointo
CC O CQ ^H CQ i-H CQ ^^ CQ 1—*
lO^OCCOCOOlC^
ccoSSocoocoocco
QnScCP^CfiP^Xp^ODp^CO
0^ CA 0^ X pc^ (X (3Q X ^' CC
tDaO'Saoi:oqo«DOi?paa
aiHCJDO^CCp^OQQ^aD^^ClQ
a^xp5co:rfaipfHXQiJj2
iCiOiOiftiCiLQiftiiCtOO
Page 506]
^ a
.t^ ^
^
J3 B
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
•xojddy
Of-HCaCO"^ irttSI^OOOi Or^C^M-^ lO«Ot>-0DO^C^
peic»P<aQpic»0:4a:ip4aQ odcopiacaiaQP'i'Xtf oi tf cd P< od oi x OS cc d oo p^ccPE^aip^ccp^coa^JoQoicc
SO^SrH5--lO^Or-lO.->Or-lO.->OrHOr-lOrHO.-IOiHOrHOi-10r-cOrHC5-<Or-lO^Ort
-SineoiOMinMiCccioco niM^'W^'Mico^"-*' ^jTfjp-^^j-.fMTj.to-*
gO.-'Oi-'O'— •Ot-'O'— I Or- tOi— lOf— <0»-.0t-t|0i— lOrHOrHOi— iOr-1
0^0'-<OrHO.-Oi-iO--c
-^ ;o ;s o «o o o o ^ to o -o
O^OrHOi-lOrtOr-lOi-l
:OOtD^COtC^OtC^OCO
g3i-tO'— lOT-tOf-'Oi— t Oi-HOrHOi— tOr-tOi-lOrHOi-iOi-HOr-tOf— t
ec t^ eo i^ ru^ M 1^ ?j w CI 00
Oi-HOr-lO — OrHOi-lOm
t05CCO:00:0^:0?0:wO?0
ftOr^Oi-iO'-tOr^Or-tjOi-HOr-tOr^Ot-lOrH
gortO-'0-^Or-i0r-.5rHSr-lOT-lOr-<0rH
St^^r-Mt-wooccooi^ooMOi'-icii-ioi-'Ot-io
i-IOr-lO>HOrlO>-IOi-IO.-lO.-lO>-IOnOC^
^!0?00?OCOtO?OtO?0 l?0<0-OtO'-0 0':CCSO:0:OCO
Oi-(Oi-iOrHOSo55jOMOMO(NOOJOC10C^
^ O O O O ^ ^ O ^ ^ 5© ^ 5fl ^^ ^ C3 ;5 tc CO !0 O ^
Or-«©f-tOi-'Oi-tOi^
S O rH O r-( O tH O rt O 1-1 O i-H O ?5 O C^ O C^ O 6l
^ ?0 CO O to <:0 O ^ O ?S ^ ;0 to CO ^ CO O to O ?0 O
i-HOrHOr-^Oi-tOi-l
COOOOIOCOtOCO^CO tOCOO^OCOCOCOCOCOOiOCO
cooox'O^ioaaico-3'O
CDCOCOCO^COtOtOCOO
CO«00<OtOCO«OtDOO OCOCOCOCOtOOCOi^cOtCCO
^ocococococo'^oococo :oococococo:oocoo
COcOtOcO^OcOtOOCOO iCOOCOCOiOOiCOti^COiCO
CO C*5 ^ Tf C^ iC r-f CO Q O Q r^ asi-*30 00 t^ 31 t^O CO o
OCJ OC^ CXN OC^ O CJ O tMiC C^OC^iC (N»0 CCiC cc
1^ CO CO CO ^ CO CO CO CO CO CO CO >0 CO lO CO iC CO i« CO O CO
-aOoO^OOasOiCCOt^OCOfHC
I »C (M -^ CO CO ■*
^cocococococococococo'cocococococococococo
-iOCO^QCdOiOUOl'-O cOi— tcp?^*cco-^^coiO
^COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO
rJ-TfClif^f-iCOpl-QX a>XXail:^OCOi-iiO'-"CM
OCIOCMOC^OC^OC^ iO<NiC<MuOCO»OCOiCCOiOCO
CO CO CO CO CO'CO COCOCOCO iCCOlCCOiCcOiCcOOCOi^CO
OCOCOCOCOCOCOCOiOCO
fiO « O OSOl OiOO O t^ <— ' CO C^ CO CO iC -^ -^i »C CO CO
^ to CO CO CO ^ CO CO CD CO CO CO CO CO CO CO CO CO CO CO CO
p**oxooioiooo»-it-ri ■cpcoicco'^'^coicijco
g^;iHrti-(OCSIOC^OMjOCMOC10C^OC-JOC^
^COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO
XOt^OCOr-lil^C^'^CO'^"^
iCCOiCCOiCCOiCCOiOCOiOCO
iCCOiOCOK^COiCcOi^COiTicO
c^coi-tr*ox^^XO I'-i-icpiMicco-^'^cooc^co
OC4OiNO?SiCOliSc0 tOCOi5cO>OCOiCCOiCCOiCCO
cOcOCOCOCOCOiCcOvOCOOcOvCCOOCOiOCOiOCOiCCO
OC^Oc5»C(MiOcOiOCO
COCOCOCOtOcOiOCOiOCO
t^»H COC^lC
co'^'^coiC'McO'-ir^
iCCOiOCOiOCOiCCOiOCOiOCO
iCcO»CCOiOCOiOCOiCCO»i5CO
-;oxa>o»xpt>-'-H coiM ic co^ -rcoic^co^t- ;
p^ CO CO CO CO CO CO CO CO CO CO COCOCOCOCOCOCOCOCOCO
Sco-^-^cococ^t^i-^xoci
COiAcCiOCOiCCOiCCOiOCO
kocOtCCOiOcOiCCOtCCOiCcO
ptfCOCOCOCOcOcOcOCOtOCO
^COCOCOCOCOCOCOCOCOCO COCOCOCOCOCOCOCOCOCO
lOCO-^-^COCOC^t^rHX
COCOCOCOCOCOCOCOCOCO
SaiOSOXrHCOC^lCCC
C^iOCOiOCOiOCOiOCO
COCCiCcOiCcOOcOvOcO
■^Tj^coicc^t^i-'ocoiaixo
iCCO»OCOiCCOiCCO"^CC"rp-^
iCCOiOCOu^COiOCOiCCOiOCO
OiQXf-'t-C^iOCOTP-rf
iCCOiCCOiCCOOCOiCCO
lOCOiOCOiCcOiOcOi^CO
jxaioaxi-ico-M
S*Oxq50iXor*i-iiC(N
^COCOCOCOCOCOCOCOCOCO
'^'^C0>C»-<COQt^0S01
CO CO CO CO CO CO CO CO iC CO
IxOcOr-tlCtN'^TfCOiC
lOCOiScOiOCOiOCOiCCC
'lO CO »C CO tO CO ifi CO iC' CO
i-iCOQXXOiI:^OcO<M-^CO
iCCO»CcOiOcO»CCOiOcOiCCO
■cJaat~*xxr^cicorH-j<c^cO'tfNiCQcoo5Xr*oa
^cocococococococococolcocococococo»cico>cco
COOiCC^-fCOI^-ffHCO
ioco»ccciAoo»ocoicco
iOCOiCCO»CCOif^CO^CO
Oii^xoicooirtii— I'^cotN'^
"■ " "" " '■^ -^ -^ tP "^
COiC COlC CO
S" X CO 1^ t^-co Oi ■3' o CO n
^(OCOCOCOCOCOCOCCCDCO
rHCCp
0<N0
CO CO CO
■ri* Oi CO t>. t^ CO Oi
C^ U5 -M lO C^ »C C^
CO lO CO lO CO iC CO
■^OCOiMC^COQTjOlCO
lOCOiCcoocoiocoTrco
iCCOOCOiOCOiOCOiCCO
I^t>»COOi"^rHC^C^i-l'^a>
'^COtJ'CO'*'^'' " — — —
lO CO lO CO »0 CO t
rt* Tf ^ 00 '^
CO iC CO lO CO
S"t^lC^t^^XCOp^rH
^COCOCOCOCOCOCOCOCOCO
gcox
CO coo
'^ t>. CO lO t^ -^ Oi
C^ lO 1?^ iC OJ lO w
CO lO CO iC CO lO CO
!NQi-i(NClC0X^cOCO
lOcoioeO'^co-^co-^cc
lOCOiOCO^CCOiOcOiOCO
: iC X CC Ol 1— i rH O
CO GC Tf t>. CO
'^ CO'^CO'^
COiC CCiO CO
,ci<o<o
SiO CO 1^ rH 00 O O
I-H O fH O ■-! O C^
rf£COCO
C^cOi-tifiOicor-X
CO CO CO CO iC CO iC CO
X«-Ht*COiOiOCOcOC^X
lO COiC
C4 iC C^ iC C^ iO CM
CO iC CO lO CO lO CO
gOiOii-tr^-'McO'^'^cO
CMttCO-^CO'^CO'^^CO
iCcOiOcOiCCOlOCOiOcO
CM r^ 1-H Oi Oi t-J t^
■^ CO Tf CO CO -^ CO
lO CO iC CO iC CO iC
CMiO -^-^ CO
-fjt co-^ cO'^
COlO CO lO CO
cootT^'^^Q*^'^'^
ic cmS
C^ lO CM S C^ TJ^ CM
CO iC CO iC «0 lO CO
l^ X CO o ^
lOcOiOCOiCcOiCcOiCco
CMCOf-(iC'air^l"-X^O"^CMCM-»t
, CO CO CO «5 CO '^T* CO
lO CO >fl CO lO CO iC
■tH CO -^ ^"^
CD »0 CO iTi CO
^CDCO
xoir-^iCcocoTf
lOCOiCCOiCCOiCCO
CM COQ
lO rH lO
»r3 cDiC
t^ X Ol CD 1-1 iC CO
iH -^ r-l ^ C>» -^ CM
CO iC CO lO CO lO CD
lCOlflr-'t--OSXI>Ol5CM
|'^c5'<tCMCOCMCOC0COC0
'iCCOiCCOOcOiCCOiCcO
co-^ c^cooxco
CO CO CO CO CO CO CM
lO CO »C CD u^ CO lO
^iC CO
lOCOiOCOtOcOiOCD
CO—f'^C^C^IM'rHCOaiX
't't-1Tj«rH-^rH'^T-lC0r-<
lOCDiCCOtCCOlCCOtACD
t^oiio^cocoi-tiooir-
WilCOCMCOCMCOCMCMCM
iCCDiACOLCCOiOCOtCCO
OlCO^'T^ CO
CO CM'* CM ^
CO vO CD»C CO
r^ one 1-i CO CO r-i
CM CM <N CO CM CO CM
iC CO lO CO lO CO o
»fr oj 1-^ r* o>
CO rH CO ^-( CO
coo CO lO CO
QJ 00 P^ CO Clj CC P^' CC p^ OD !fi4 «} p4 C» QJ CQ 0:^ GG p^ OQ 1^
cS"^~^h" cm CO -^ ifl XD t^ x"* Oi p
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 507
a
s
C^ C< iM M
■aiBp
•xojddv
a
fimPilxOicDe^CBfilXl
(sjodaSajOSaQPSajP^co
Or-IOiHOr-lOrH Or-I O r-( O rH O rH O i-H O r^
PJGQOjoQP^aJP^cQP^cc
Oi.^OrHOi-iO.HOrH
-JM-fw-i'cofco-^c^-^ n-*cj'»<c^-^£j'*Tqic|cqiO>-Hio^iOT-iin.-iii5
jj 5S o O O O O O O O O o --0 o --o O O O O O 'O
■oo-oooooooo
S' til to C^ O 5S O 2) to rH O
OiHOi-IOr-lOr-IOr-l
.c^tootototoootototo
Oi-iOiHO-hS.-hS.-I
totototstootootoo
tOtOiCtOiOOiCtOOtO
0.-I0r-(0.-I0rt0i-I
^ otototototototototo
ga>ooo>oo>oo>.-i
tOtOtOtOtCOiOtOiCtO
iCtOiOtOiOtOiOtOiOtO
.cftotototototototo<>to
iCMSlNiOCSiiniNiOlM
iCtOiOtOiCtOiCOiOtO
t^-^-O'.i'touoiou^ioto
iCtOlCtOiOtOiOtOiOtO
WaJWasp^cotfaJOHCo
C9MMM?3C^UM01C<I
Oi-HOi— IOi-«0»— lOi— (
to to o to to to to to to to
.-H O ^ to © to O to o to
to to to to to to to to to to
asaiQooaoooooor^o
lOi-iSi-iinMuiciiac^
lOtOvCtOiOtOiCOiCtO
t^CCtOM
lOtOiOtO
iC to»o tOiO to
■n'tO'^r»
lO to in to
CO 00 C<I 00 C^ 00
iC tOiC tOiO to
S"OC0OCC0»C<30>-J"00'*
^COtOtOtOiOtOiOtOtCtO
SiCI-*>Ot^tOtOtOtOt>.
irstoiCiOiCtoiotoioto
iOc^io(Miraoiioc^iCco
lOtOiOtOiOtOiOtOiOtO
lO CCU3 CO
lO toio o
SCO
CO
ic to in to lO to
S'OilOCO»CQOtOt^tOl^t>-
inC>lSc^lSc^>0(NiOCM
^LQOiAtOlOtOiOtOOtO
S*coi^r^r*i^oQtooQicai
^>CtO»CtO»CtO»AtOirttO
Sl^-toOOCOO-^OJ-^O
^jiSc^ioiMiONinco
]iOtOiCtOiCtOiCtO>i5tO
lioo-'j'oco.-icie^c^co
I lO CO iC CO >C CO »C CO iC CO
jiCtOiAOiCtOiCtOLCtO
COOCOt-iMI^i-hCMOCO
lOMOCOincOOOOiCCO
i^tOiOtOiOtOiCtOutltO
CO ■'J' CO
vn tomo
GC iC t^ to t>" t-*
^ CO ".I* Co "^ CO
liD to >n to »o to
«"tco5to«?iOQin^'»'CJ
SOC^iScOiOCOiOCOiOCO
,«»iCtOiCtOiCtOiOtOirttO
COOJiMCOi-l-^QlOOtO
iCCOiOCO»CCOiOCOi^CO
lOtOiCtOOtOiCtOtOtO
-iiO^'«<C^'*COCOC0C^'^
giacoiocoiocoi-ocomco
^lOtOiCOiCtOiitltOiOto
fHifj«5too5t^ooooooo>
iocoii5eo-^co-*cO'.i<co
if^tOi^tOtCtOiCtOtCtO
'HCOi-i'^O'OCViQOOtO
incOiOCOl5CO-^CO'«**CO
iCtOiCtOiCtO'fitOiCtO
ait>-oof^t^90t^oitoo
^CO^CO^CO^CO^f^
lOtoiCtoir^tototoicto
t^oto.-iiijo)3jeoco3|
LctoiotoiotointoiAto
§iAcoSSSc<5ibOTiOco
.«»iCtOLCtOiOtO>OtOiOtO
gooo>o>goor-rHtO'M|iOco^:.r-^ioc3t5rHt^
CO ^ CO "^ "^ ^ ""S^ ^ ^ -" ~ " " —
lOOiOtOLOtOiAtOiCtO
t^ t- to 00 to oi ic o 3; rH
tJ'CO^^COtJ^CO'^^^^
lOtOiCtOlAtOOtOiCtO
lO.^^oicococ^-^i-'ijrs
lOtou^toiCtointoicto
e^ic^toQr*o^oooca>
__ . .-^lOC^tOtHt^QOOOOOll^OtOC^i-ICO
'^TI'^^lO'.J*-'^^'^.^* ^■^CO^COiOCOiOCOiO
LCOOtOtf^tOiOtOi^tOu^tOU^tOiAtOiCtOiCtO
jSC0i0C^t0r-lf»Oa00>05
fticco>oeoincoSco^co
.<»iCtOiOtOLCtOiCtOiCtO
incoSco'*cO'*^T>i'.)<
^lOOiOtOlOtOlfltOiOtO
OQQt^.HtOJJiOCO-*-!'
lAtOiOtOtCtOtftltOOtO
'»'-<5<-9<'*^'S<cO'j<MiSco>Oei5'Ocoioeoirtco>o
»CtOiGtOir5tO»r5tOlCtO»OtOiCtO»OtOlOtOiOeO
to oi lO CO ■.»" 3j CO to ?J t^ I o oc o? en
iftOiOtOiCOiOtOiOtO
_ 00Qt~<MiOCO-^iOC>)tOrt«5>aj00i-(
■*-.)> co-*MiScoiOcoiocoiOcoiccoiO?jireoio
ictoiotOiCto»i5tokato i»cto»ctoioto»otoiot*
S'00^0»QOO'-t|-*'MiOCO
,aj i^ to ic to i.c to »o to *£; to
■^■.J-COiO-Mt^OXasOilgOrH
iC50»^tOiOtO»CtO»OtO
;^ 00 O 1^ ^H to CO iC 2* CO iC
^i?3tOiCtO»CtOifttOii5tO
C^tOrJOOOaiOCi-Ht^Ol
^^•).^COTJ<COiCCOlC
lOOiCtOiOtOiCtOtOtO
-. . . - . . UJ CO •* iQ OJ to
C0iCC0»flC0iOC0»Sc0»O
OtOi^tOiCtOiCtOiCtO
gr-noc03j3;ojtorHi--.
.5*iOtO»CtOiCtOiCCOiOtO
occoior-i-itocO'^-.i!
•^■^coiocoiocoincoo
iCtOiOtOiCtOiOtOLCtO
COtOi-ir«QO>OOOtON
COiCCOiCMiCoSOC^O
tctoiotoutitotot^icr*
r-l0OO»Ol«O.-ltOCO'»'3l
lOtOii^tOiCt^i/^t^iOt*
0Qi-ltO«>->"2'C-ltO-^CO
S 31 CO to .-I
OCMOO
) i> in r- lO
CCOJOt^iH
t>-in t*ict^
•cjiotoiotoictointointo
QCi-itoc-ii/jcocoice^t^
coiocotneoiccoincoo
iotoLOtoLCto>nto>cto
Qcoooot^ojioeocoic
eoioc^oi^oojoe^o
iOo»ot^iot^iot^»nr»
r^coini-ttooooGocii^^H
55^^Tj<^.q«TT"cO^COiO
•cjictoictoictoictointo
coiccoiocoincoicc<i»n
lOtOiOtoictoiotoioto
t^i-*iCCOCO-^t-(tpOiOO
c^ocaooioc4 0i-io
lOi-tOrH
5 r~ lO t~ m
t-H in CO CO ic
t>- in i^ ic t^
• oinrjco
jt~-ini^in
■*i-nogao
r-inr-int-
S'<-itpasr>"t>-oito^H-.*<co
'»"^cO"»ico->j<OTincoin
rfjintointointoictointo
cO'j'OT'^coincoincoift
,<iintointointointointo
e^'^i-itooat^t^oitoi-^
coincoinfiine^mno
iC to in to in to in to in t^
osinoot^tooi'^r-ie^cj
Minc5ios^iniMo6io
intointointoint^inr*
teoc^iinQt~.oo»to.-i
int*int>-int*iOt*int^
■.fcOf-iinoat^r-Oiinji
■IrHi-lO
D t^in t^ in
in t^ in t^
O^ioOOtO^-l'THC^CC
MOi-lOrHOrH,-lr-lf-l
int*int»im--int^int»
o>int^ooinocje<
Oi-IO>HO
ic t^ in t-* in
c^ £> c4 o S
t-*in t>-in t^
2 I ««
•xoiddy
rfiin
XMOJi-l
^ CO ^ CO
toin oio
mwSSin
to in to in to
tOtO-»'COC^OO'N002''
in to in to in r* in t^ in t^
j-n^ooc^^^ocot^inin
>iHOi-HT-li-lTHOrHO
• int^int^int~"ioi> iin
r«.io t»in
CO i^ in in 00
c^in c^ in c^
CO
^in
to in to in
c^ to CO ■^ m
in<Nine>iin
to in to in to
c^i^ooiooi-itoco'^in
c^ine5inr-ioi-iorHo
lOtoictoinc^int^int^
ootoo-^
tomtom
e^iM-^ioto
mNinc^m
to m to m to
S?}^S^S
s tomtom
Stoo-*^
r^m rH m
tom tom to
i-lOrH
m r*m
.H O rH O rH O T-<
t^m t^m t*m t^
)Oi^c^inmo«»a>o
>cjmo)mc>»miM'Vco
^ T}< t~ .* t^
m t^-n* t^-^
xaotoQ-^c^i-i-a'Oto
i-HmrHOi-lOi-IOOO
mtomt~-mt^mt~mi>
23S8S
r«.Oift CO tM ic
000000
iOtOiCtOiCt^tOt>id:>-
mt^m
1-1 C^ •.Ji o> to t- o>
I— tOrnmi— tmr-i
t^ m t~ -^ r» -^ t^
-r-tC^-^Olt^tOOCOCO
jiMmiN-a"
e<ii"cO"3<co
-.r t^ ^ t^
00m
mt^^
omcooimoco
I— 1 m tH m 1—1 in rH
r- ■* t^ ■* i> li' t~
1-* 00 o m CO
(M coco coco
t^ ■^ t^ ^ l^
3*mi— icocOTHm^t>»t^o
rfS'm
torn torn
Tf<om
to m to m to
A^dixnfii^A^^'Ji
° S ?1 C<l «^
Sc^'Nt»<oco»a>in.-i
momommmino
mtomtomto-^to-^t^
co-fo
mom
O ^ O ^ i.^ ^ i-H
1^ ■* r~ ■^ t» ■^ t~
McKOJoQQ^aaajccKccpHKP^copjccPJccPdcc
to t^ 00 a> ^5^ ^ cS~c5 ■.»' m
c^fje^cico cocococoeo
> I^ to oco
(i-HCOlNCO
< l~. Tf t^ -.J"
.^ ■* I- ■* t~
»5coe3c»OHa3P:5cca3ai
Page 508]
J3 !
•^ s.
^ a
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
.iSaJ
cojdd
dv
MOQPJQQpliCQtfa^OHCC p; OS B< OQ PlJ CO tf Ui 04 OQ
-^ u5 ic to ^ l6 ic
Oscopjccpjccp^cntfccfficcKaiajcnpHcctfco
0<-tO<-iOi-iOr-lOrt
^-j.O'J'O^QUSOiO
Oi-iO>HC>>-l*i-(OrH
O t— t O rH lO rl lO F-^ »C I-H UO i.^ lO ^H IC rl in ?H lO f-i iO*-*iCtHiOi— »lOC4l«C^
^t0OC0;0»0Ou'3t0i0<0UCOiCeCiC?Di0O»C?0 iCtOiCOiCeO»OtO»0?0
lO?Oi050iC«OiC5CiC«0
S•^•,_lt~,Hto.-lOe^t©e^lnNlOeo■^elS^T^<•5l■^c5•<J<MlOlN'Ce^to•H;Orfr~Qcoo>a5ocg>«o
u5c^>oc<i5c^iftc^SN|ift6«Sc^ioc5icc^i««4CCjicc^oc^iOMioc^ioc^iftc5-*fi->r
^l/5«OiOOiCtO»COiC<C»0<OlO«OiC«0»0«Oi050iOO»0:Oi0^i0^iO<o'iCCOiC<0»050»00»i:;«D
^iC^»OtOiOOiCOiOCO i0^lC^t0^iOCDlOCOO«0»C^ifttOiCOiClCDiO«DiOtOiO'a»COiCO
eiON»c<NiCcoiocO'«rcc
^ CO ^ CC ^ 05 ^ CO '•1' CO i^ CO ^co^co^co^^
OtHca(NgOcot^'»j'iCiC
■^^CO'^J'CO^CO^CO^
iCCO>0«OiOtOi0^iO^
S"C3>-<J<00'}'QOlOI^t050t^imr~'»faCCOOSCJO<NrH|r-IINOCOQO'^r-lQtP5©
^ CO 'fl' CO "^ CO "*J* CO "^ CO 1^ CO "^ CO ^ CO ^^^1''<S' p^^'*?^CO ^ CO "*!* CO ^
^iCC0i0C0iCC0\CC&lCC0i0^i0t0i0C0iC^i0^Oc0i0^iCC0i0cdU5t0
C0'»'e0'<i'eoi5coio5jio
lO?DiC?0»0?DiC«Oir5^0
g'tO00lCC10'*3>C0OC^rH
•^CO'^CO"^CO'V^'^--y
.^iO^i0:0iC^»Ot0iOec
i-ic<©coo>^oou5r»o
^Tj^^^co^co^cO'^
I0^i0«0i0*^l0t0i0«0
®«ico>cooc^i-(i-ieo
M'<»<cO'^coi5eoiOcoio
iCeOiCtOiC<OiOCD»OCO
C^ii5MiOniO(Mif5j<0
g"COC^C^lMrtCOO'J<C»'^l»t^t^OOiQO»'*QCOCjl^COO'0 00!Or»ocm05
TfTj<'<}''<r'^'^'^"»1<CO'^jCO'^CO'^CO'^CO»OCOiC!COiOCO»CC^iSC<lioiN»0
^iC';OiCOiCOtC'OiC'£ii050iO(OiO«OiC^iC^lC«OiC(OiC«OiC50iC^
■^i-l(NCOO»OXt>-CO
X t>-CO OS
rHOi-lO
lOt'-iot^iOt^ioc^ict*
S'O^OOit^COOOt^OliOO -^fHCOCOiH^Q^OOt^ t^OJiOOCOC^C^I'g'O^pOCQOtCO'^C^I^H-^CStD
•^■^CO-^CO-n'CO'^COiC COiCCOiCCOlAcOirSC^iC C^iCT^OrJOC^OfMON-lOi-trrtT-tT-Hr^r-lOi-l
^i05Cio«oiceoic«ovc«o»ccoiotoic«»oo»cto»coiCt^ict^iCt^icr^ict^iOr*ici>ict^ict^
~" r-Q tc th ■* oi cocoes ico to oicot^oiio^'* CO M^jo-^p 0000 too-* C<1
SC04ScOi^CCiOCOlCCOiCCOlOC^iCC^iCnOC>10|T^OC^OfHOi-lr-tr-l^
^ictoicoictoiotoictoictoiotoictoict^ict^ict^ict^irsi^iftc^ict^
i-lrti-HrtOrHOCMOlN
ic r^ »m^ o t> ic t^ ic t^
g'e0'7'r^>c^t>.osooooo
eoineoicccioc^ioejo
^lOtoiocDirstoiotoict^
tOf-i-fcocoic^Htpoaoor*oioc^co-*r-itoasai'
coinc-i>cc^oe^ono c^oc^Oi-iOi-i^i-ii-i
^ lO to lO to »o i^ ic t^ ic t^ ic t^ lO t^ tc !> lO r* »o t*
:i-HCO-?<r-tt^OOOvCCJ
c^iooxocomc^coic
r-li-li-lrHOnOC^OO
iOt*iOt»iCt^iCt^»Ot*
S';o?ji0 3'comi-it>-oa>ocotDS^'<»<'fl<c^t~o»o>t-wiC'^Mtoo>g>t^c>)
(NiOCOiCCOiCCO-^'^
■>J>>lDO0Ct~MC0iCO01
»OCOiOCO-^'^"<J*-^rJ'-J"
S'SOtpi-(0005OTl^miOCOCO>OT-lt^O»0>t~C^'ai-*Mr~OS05tSCMCOii5QOO
C40CSOi-lO>Hrtr^rt|rHrH.-lt-lO.-lOCaOC^OCJi054i5cOiCCOiCM
^ict^»ot^»ot~-»ct*icr- |iot^>ot*ioi>»ot— lot*
iOt^'*t~-<Jit^'<»it^-*t
t-c^comoo2toeoc^t^
■*'J<'*"5"'<*'*CCiOCOiO
2»OOt^C^i(^'*CCtO*-*00
0»Ot0C^3'i0r-ct~0lO
oc^o6iocjoc^icco
to O CO iC Q 00 1^ rH ■<»< lO
lOcoiCcoiCco'^'^TjiTr
OOStOMC^tOCOt-HCOiC
■<)<-TCOiCCOiCO<OC-10
■^r^-^c^-s-i^-^oo-^oD
jiCCOCOiOi-'OOOSO^C^
jiCI>»Ot*iCt^iCt^iOt*
^i-^CJt^OlQtOMCOiC
i^CO-^M^^Tf-^-^fCOiC
cotoasOTf^ajoivc-^
COiSC^OC^OrHOrtiH
■»l't^'»(<00'^00'^CiOTj<00
OJOit^'M-^iOf-'OQOOrH
ICC^IOCOIOCOIOCO-^-^
■<I<-*-*TC0iCC0iAC02
to CO ^ t- -o C^ ^ t^ to CO
-rcCJ'GC'J'X-J'OO-^OO
-Jl^r-<lOCO(NlC3SOQt^'-l
SoMor5oc^iOc-i>oco
■^■^i-ltO«CJ>iOCO'MtO
lOCOiCCO'^CO'J'-^-^'V
co-^mScoiOc^ocJo
XOCOiCXO^iCt^^
t-i»-(r-(»-(OC^OC^iCCO
■>*i«-^00'*WM<00COO0
ft©M ©C^iO
i>r-OJ'^ !N
Seoioco
t^ -.J" t>- r)l r-
wxiC'-ioi'*O5 00iC>-;
■^CO^^^^CO^COiO
Minooos-^corotinTa
C0iC<NiCeMOrH©,-n-(
■9<t^tfl^Tj<a0-<J'Q0'9<0C
©i>-'rc^3it^cocot^©
i-iT-iOc^icc^iCco-^-r
■*0CT><«COaCCOOCC0 00
OS O iC CO C^ to Oa
TABLE 11.
[Page 509
For reducing the Time of the Moon's passage over the Meridian of Greenwich to the Time of its
pass- 1
age
over anv other Meridian. The numbers taken from this Table are to be added to the Time at 1
Greenwich in West Longitude,
subtracted in
East Longitude.
Longi-
tude.
Daily variation of the
moon's pa.ssing
the meridian.
Longi-
tude.
40"
42m
44m^
46m
48™
oO-» 52"
64m
66"
68"
60" 1
62" i
64"
66"
o
m.
m.
m.
m.
■m.
TO. TO.
TO.
TO.
TO.
TO.
TO. 1
TO.
TO.
o
0
0
0
0
0
0
0
0
0
0
0
0 !
0 :
0
0
0
5
1
1
1
1
1
1
1
1
1
1
1 1
1 1
1
1
5
10
1
1
1
1
1
1
1
1
2
2
2 1
2 ■■
2
2
10
15
2
2
2
3
2
2
2
2
2
2
2
3
3
3
15
20
2
2
2
2
3
3
3
3
3
3
3
3
4
4
20
25
3
3
3
3
3
3
4
4
4
4
4
4
4
5
25
30
3
3
4
4
4
4
4
4
5
5
5
5
5
5
30
35
4
4
4
4
5
5
5
5
5
6
6
6
6
6
35
40
4
5
5
5
5
6
6
6
6
6
7
7
7
7
40
45
5
5
5
6
6
6
6
7
7
7
7
8
8
8
45
50
6
6
6
6
7
7
7
7
8
8
8
9
9
9
50
55
6
6
7
7
7
8
8
8
9
9
9
9
10
10
55
60
7
7
7
8
8
8
9
9
9
10
10
10
11
11
60
65
7
8
8
8
9
9
9
10
10
10
11
11
12
12
65
70
8
8
9
9
9
10
10
10
11
11
12
12
12
13
70
75
8
9
9
10
10
10
11
11
12
12
12
13
13
14
75
80
9
9
10
10
11
11
12
12
12
13
13
14
14
15
80
85
9
10
10
11
11
12
12
13
13
14
14
15
15
16
85
90
10
10
11
11
12
12
13
13
14
14
15
15
16
16
90
95
11
11
12
12
13
13
14
14
15
15
16
16
17
17
95
100
11
12
12
13
13
14
14
15
16
16
17
17
18
18
100
105
12
12
13
13
14
15
15
16
16
17
17
18
19
19
105
110
12
13
13
14
15
15
16
16
17
18
18
19
20
20
110
115
13
13
14
15
15
16
17
17
18
19
19
20
20
21
115
120
13
14
15
15
16
17
17
18
19
19
20
21
21
22
120
125
14
15
15
16
17
17
18
19
19
20
21
22
22
23
125
130
14
15
16
17
17
18
19
19
20
21
22
22
23
24
130
135
15
16
16
17
18
19
19
20 i 21
22
22
23
24
25
135
140
16
16
17
18
19
19
20
21 1 22
23
23
24
25
26
140
145
16
17
18
19
19
20
21
22 ' 23
23
24
25
26
27
145
150
17
17
18
19
20
21
22
22 i 23
24
25
26
27
27
150
155
160
17
18
19
20
21
21
22
22
23 i 24
25
26
27
28
28
155
18
19
20
20
22
23
24 1 25
26
27
28
28
29
160
165
18
19
20
21
22
23
24
1 25 i 26
i 27
27
28
29
30
165
170
19
20
21
22
23
24
25
25 26
27
28
29
30
31
170
175
19
20
21
22
23
24
25
26 27
1 28
29
30
31
32
175
180
20
21
22
23
24
25 26
! 27 28
1 29
1
30
31
32
33
180
40m
42in
1 44".
1 46"-
4S">
1 60" 52"
64" I 66"
1 68"
60"
62"
64"
66"
Page 510] TABLE 12.
For finding the Variation of the Sun'e Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
1
2
3
4
5
6
7
8
9
10
Horary motion.
M.
1"
2"
8"
.4"
5"
6"
7"
8"
9"
10"
11"
12"
13"
14"
15"
16"
17"
18"
19"
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
0
0
0
0
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
0
0
0
0
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
7
7
7
7
7
0
0
0
-.
1
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
5
5
5
5
5.
5
5
5
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
8
8
8
8
0
0
0
2
2
2
2
2
2
2
3
3
3
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
5
5
6
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
8
9
9
9
9
0
0
2
2
I
2
2
3
3
3
3
3
3
4
4
4
4
4
t
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
9
9
9
9
9
9.
10
10
10
10
0
0
2
2
2
2
2
3
3
3
3
3
3
4
0
0
2
2
2
2
2
3
3
3
3
3
4
4
4
0
0
1
1
1
1
2
2
2
2
2
3
3
3
3
3
4
4
4
4
0
0
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
4
5
0
1
1
1
1
2
2
2
2
3
0
1
1
1
1
2
2
2
2
3
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
2
2
3
3
3
3
4
4
4
5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17 •
18
19
20
2
2
2
3
3
2
2
2
3
3
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
2
2
2
2
2
2
2
2
3
3
3
4
4
4
4
5
5
5
3
3
3
4
4
3
3
4
4
4
3
4
4
4
5
4
5
5
5
5
5
5
5
5
6
5
5
5
6
6
5
5
6
6
6
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
8
8
8
8
8
8
9
9
9
9
9
10
10
10
10
10
10
11
11
11
4
4
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
8
8
8
8
8
9
9
9
9
9
10
10
10
10
10
11
11
11
11
11
12
12
12
5
5
5
5
5
6
6
6
6
7
7
7
7
7
8
8
8
8
8
9
9
9
9
10
10
10
10
10
11
11
11
11
11
12
12
12
12
13
13
13
- 5
5
5
6
6
6
6
7
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
11
12
12
12
12
13
13
13
13
14
14
14
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
12
12
12
12
13
13
13
13
14
14
14
14
15
15
15
6
6
6
6
7
7
7
7-
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
12
12
6
6
7
7
7
6
7
7
7
8
7
7
7
8
8
21
22
23
24
25
26
27
28
29
30
26
27
28
29
30
0
0
0
0
7
8
8
8
9
8
8
8
9
9
8
9
9
9
10
31
32
33
34
35
9
9
9
10
10
10
10
11
11
11
9
10
10
10
11
10
10
10
11
11
31
32
33
34
35
36
37
38
39
40
11
11
11
12
12
11
12
12
12
13
36
37
38
39
40
41
42
43
44
45
41
42
43
44
45
•}
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
12
12
12
12
13
12
13
13
13
14
13
13
14
14
14
46
47
48
49-
50
51
52
53
54
55
56
57
58
59
60
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
12
13
13
13
13
14
14
14
14
15
15
15
15
16
16
13
13
14
14
14
14
14
14
15
15
15
15
15
16
16
16
16
17
17
17
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
14
15
15
15
16
16
16
16
17
17
15
16
16
16
17
17
17
17
18
18
18
18
18
19
19
TABLE 12. [Page 511
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
20"
21"
22"
23"
24"
25"
26"
27"
28"
29"
80"
81"
82"
88"
84"
85"
86"
1
2
3
4
5
0
1
1
1
2
2
3
3
3
0
1
1
1
2
2
2
3
3
4
0
1
1
1
2
2
3
3
3
4
0
1
1
2
2
2
3
3
3
4
0
1
1
2
2
2
3
3
4
4
0
1
1
2
2
3
3
3
4
4
0
1
1
2
2
3"
3
3
4
4
0
1
1
2
2
0
1
1
2
2
0
1
1
2
2
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
1
2
2
3
1
2
3
4
5
6
7
8
9
10
3
3
4
4
5
3
3
4
4
5
3
3
4
4
5
3
4
4
5
5
3
4
4
5
5
3
4
4
5
5
3
4
4
5
6
3
4
5
5
6
4
4
5
5
6
4
4
5
5
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
4
4
4
5
5
5
6
6
6
7
4
4
5
5
5
6
6
6
7
7
7
8
8
8
9
9
9
10
10
11
11
11
12
12
12
13
13
13
14
14
4
4
5
5
6
6
6
7
7
7
8
8
8
9
9
10
10
10
11
11
11
12
12
12
13
13
14
14
14
15
15
15
16
16
17
17
17
18
18
18
19
19
19
20
20
4
5
5
5
6
4
5
5
6
6
5
5
5
6
6
5
5
6
6
7
0
5
6
6
7
5
6
6
7
7
5
6
6
7
7
6
6
7
7
8
6
6
7
7
8
6
6
7
7
8
6
7
7
8
8
6
7
7
8
9
6
7
8
8
9
7
7
8
8
9
11
12
13
14
15
6
7
7
7
8
8
8
9
9
10
10
10
11
11
12
12
12
13
13
13
14
14
15
15
15
16
16
16
17
17
18
18
18
19
19
20
20
20
21
21
6
7
7
8
8
8
9
9
10
10
10
11
11
12
12
12
13
13
14
14
14
15
15
16
16
16
17
17
18
18
18
19
19
20
20
20
21
21
22
22
7
7
8
8
8
7
7
8
8
9
7
8
8
9
9
7
8
8
9
9
8
8
9
9
10
8
9
9
10
10
8
9
9
10
10
9
9
10
10
11
11
12
12
13
13
9
9
10
10
11
9
10
10
11
11
9
10
11
11
12
10
10
11
11
12
16
17
18
19
20
21
22
23
24
25
7
7
8
8
8
9
9
9
10
10
10
11
11
11
12
12
12
13
13
13
9
9
10
10
10
9
10
10
10
11
9
10
10
11
11
10
10
11
11
12
10
11
11
12
12
11
11
12
12
13
11
11
12
12
13
12
12
13
13
14
12
12
13
14
14
12
13
13
14
15
13
13
14
14
15
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
11
11
12
12
13
13
13
14
14
15
15
15
16
16
17
11
12
12
13
13
13
14
14
15
15
12
12
13
13
14
12
13
13
14
14
13
13
14
14
15
13
14
14
15
15
13
14
14
15
16
14
14
15
15
16
14
15
15
16
17
15
15
16
16
17
15
16
16
17
18
16
16
17
17
18
26
27
28
29
30
31
32
33
34
35
14
14
15
15
16
14
15
15
16
16
15
15
16
16
17
16
16
17
17
18
16
17
17
18
18
19
19
20
20
21
17
17
18
18
19
19
20
20
21
21
17
18
18
19
19
20
20
21
21
22
18
18
19
19
20
20
21
22
22
23
18
19
19
20
20
21
22
22
23
23
19
19
20
20
21
22
22
23
23
24
16
16
16
17
17
16
17
17
18
18
17
17
18
18
19
17
18
18
19
19
18
19
19
20
20
36
37
38
39
40
41
42
43
44
45
14
14
14
15
15
14
15
15
15
16
16
16
17
17
18
17
18
18
18
19
19
20
20
20
21
18
18
19
19
20
20
20
21
21
22
18
19
19
20
20
21
21
22
22
23
23
23
24
24
25
19
20
20
21
21
20
20
21
21
22
21 21
21 22
22 22
22 23
23 23
22
22
23
23
24
23
23
24
24
25
2Z
24
24
25
26
24
25
25
26
26
25
25
26
26
27
41
42
43
44
45
46
47
48
49
50
15
16
16
16
17
21
22
22
23
23
22
23
23
24
24
23
24
24
25
25
24
24
25
25
26
25
25
26
26
27
25
26
26
27
28
26
27
27
28
28
27
27
28
29
29
28
28
29
29
30
46
47
48
49
50
51
52
53
54
55
17
17
18
18
18
18
18
19
19
19
21
22
22
23
23
22
23
23
23
24
24
24
25
/25
26
25
25
26
26
27
26
26
27
27
28
26
27
27
28
28
27
28
28
29
29
28
29
29
30
30
29
29
30
31
31
30
30
31
32
32
31
31
32
32
33
51
52
53
54
55
56
57
58
59
60
19
19
19
20
20
20
20
20
21
21
21
21
21
22
22
21
22
22
23
23
22
23
23
24
24
23
24
24
25
25
24
25
25
26
26
25
26
26
27
27
26
27
27
28
28
27
28
28
29
29
28
29
29
30
30
29
29
30
30
31
30
30
31
31
32
31
31
32
32
33
32
32
33
33
34
33
33
34
34
35
34
34
35
35
36
56
57
58
59
60
Page 512] TABLE 12.
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
I
2
3
4
5
6
7
8
9
10
87"
88"
89"
1
1
2
3
3
40"
1
1
2
3
3
4
5
5
6
7
7
8
9
9
10
11
11
12
13
13
14
15
15
16
17
17
18
19
19
20
21
21
22
23
23
41"
42"
48"
44"
45"
46"
47"
48"
49"
50"
51"
52"
58"
1
2
3
4
5
1
1
2
2
3
1
1
2
3
3
1
1
2
3
3
1
1
2
3
4
1
1
2
3
4
1
1
2
3
4
1
2
2
3
4
1
2
2
3
4
1
2
2
3
4
1
2
2
3
4
1
2
2
3
4
1
2
3
3
4
1
2
3
3
4
1
2
3
3
4
1
2
3
4
4
6
7
8
9
10
4
4
5
6
6
7
7
8
9
9
4
4
5
6
6
7
8
8
9
10
10
11
11
12
13
13
14
15
15
16
16
17
18
18
19
20
20
21
22
22
23
23
24
25
25
26
27
27
28
29
29
30
30
31
32
32"
33
34
34
35
35
36
37
37
38
4
5
5
6
7
7
8
8
9
10
10
11
12
12
13
14
14
15
16
16
17
18
18
19
20
20
21
21
22
23
23
24
25
25
26
27
27
28
29
29
30
31
31
32
33
33
34
34
35
36
36
37
38
38
39
4
5
5
6
7
8
8
9
10
10
11
12
12
13
14
14
15
16
16
17
18
18
19
20
21
21
22
23
23
24
4
5
6
6
7
8
8
9
10
11
11
12
13
13
14
15
15
16
17
18
18
19
20
20
21
4
5
6
6
7
4
5
6
7
7
5
5
6
7
8
5
5
6
7
8
5
5
6
7
8
5
6
6
7
8
5
6
7
7
8
5
6
7
8
8
5
6
7
8
9
5
6
7
8
9
5
6
7
8
9
11
12
13
14
15
8
9
9
10
11
11
12
13
14
14
15
16
16
17
18
19
19
20
21
22
8
9
10
10
11
8
9
10
11
11
8
9
10
11
12
9
9
10
11
12
9
10
10
11
12
9
10
11
11
12
9
10
11
12
13
13
14
15
16
17
11
12
13
14
14
15
16
17
10
10
11
12
13
10
11
11
12
13
11
12
13
14
15
16
17
18
19
20
10
10
11
12
12
12
12
13
14
15
12
13
14
14
15
12
13
14
15
15
13
13
14
15
16
13
14
14
15
16
13
14
15
16
16
14
15
16
16
17
14
15
16
17
18
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
13
14
14
15
15
16
17
17
18
19
15
16
17
18
18
16
17
17
18
19
16
17
18
18
19
16
17
18
19
20
17
18'
18
19
20
17
18
19
20
20
18
18
19
20
21
18
19
20
20
21
18
19
20
21
22
19
19
20
21
22
21
22
23
24
25
19
20
21
21
22
20
20
21
22
23
20
21
21
22
23
20
21
22
23
24
21
22
22
23
24
21
22
23
24
25
22
23
23
24
25
22
23
24
25
26
23
23
24
25
26
23
24
25
26
27
26
27
28
29
30
31
32
33
34
35
19
20
20
21
22
22
22
23
24
25
22
23
24
24
25
23
23
24
25
26
23
24
25
26
26
24
25
25
26
27
24
25
26
27
27
25
26
26
27
28
29
30
30
31
32
25
26
27
28
29
26
27
28
28
29
30
31
32
33
33
26
27
28
29
30
31
31
32
33
34
27
28
29
29
30
27
28
29
30
31
32
33
34
34
35
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
22
23
23
24
25
25
26
27
27
28
'28
29
30
30
31
31
32
33
33
34
35'
35
36
36
37
24
25
25
26
27
27
28
29
29
30
31
31
32
33
33
34
35
35
36
37
37
38
39
39
40
25
25
26
27
27
28
29
29
30
31
31
32
33
33
34
25
26
27
27
28
26
27
27
28
29
26
27
28
29
29
27
28
29
29
30
28
28
29
30
31
28
29
30
31
31
29
30
31
32
33
31
32
33
34
35
36
37
38
39
40
29
29
30
31
32
32
33
34
34
35
29
30
31
32
32
33
34
34
35
36
30
31
32
32
33
31
32
32
33
34
31
32
33
34
35
32
33
34
34
35
36
37
38
38
39
33
34
34
35
36
33
34
35
36
37
34
35
36
37
38
35
36
37
37
38
39
40
41
42
43
36
36
37
38
39
40
41
42
42
43
36
37
38
39
40
41
42
42
43
44
41
42
43
44
45
46
47
48
49
50
34
34
35
36
37
35
35
36
37
38
35
36
37
38
38
37
38
38
39
40
38
38
39
40
41
38
39
40
41
42
35
36
36
37
38
"38
39
40
40
41
36
36
37
38
39
39
40
41
41
42
37
37
38
39
39
40
41
42
42
43
37
38
39
40
40
38
39
40
41
41
39
40
41
41
42
40
41
42
42
43
41
42
42
43
44
42
42
43
44
45
43
43
44
45
46
43
44
45
46
47
44
45
46
47
48
45
46
47
48
49
51
52
53
54
55
56
57
58
59
60
41
42
43
43
44
42
43
44
44
45
43
44
44
45
46
44
45
45
46
47
45
46
46
47
48
46
47
47
48
49
47
48
48
49
50
48
48
49
50
51
49
49
50
51
52
49
50
51
52
53
56
57
58
59
60
TABLE 12.
[Page 513
For finding the Variation of the Sun's Kight Ascension or Declination, or
of the
Equation of Time, in 1
any number of minutes of time, the
Horary Motion bemg given at the top of the page in seconds, |
and 'the number of minutes of time
in the side column.
Also for finding
the Variation of the 1
Moon's Declination or Right Ascension in
seconds of time.
the motion
in one minute being given 1
at the top, and the numbers in the side column being
taken for seconds
1
M.
Horary motion
M.
54"
66"
1
66"
1
1
5S"
1
69"
1
60"
61"
02"
6S"
64"
65"
66"
67"
68"
69"
70"
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
9
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
5
5
5
4
5
5
5
5
6
5
5
5
5
5
0
5
5
6
5
6
6
6
6
6
5
6
5
6
6
6
6
6
6
6
6
7
- 7
7
7
7
7
6
7
6
6 ! 7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
7
8
7
7
7
8
8
8
8
8
8
8
9
9
9
9
9
9
9
8
9
8
8
8
9
9
9
9
9
9
9
10
10
10
10
10
10
11
9
10
11
9
10
9
10
9
10
10
10
10
11
10
10
10
10
11
11
12
11
11
11
11
12
12
10
11
11
11
11
12
12
12
12
12
13
13
11
12
11 11
11
11
12
12
12
12
12
13
13
13
13
13
14
14
14
12
13
12
12
12
12
13
13
13
13
13
14
14
14
14
15
15
15
15
13
14
13
13
13
13
14
14
14
14
14
15
15
15
15
16
16
16
16
14
15
14
14
14
15
14
15
14
15
15
15
15
15
16
16
16
16
17
17
17
17
18
15
16
16
15
16
16
16
17
17
17
17
18
18
18
18
19
17
15
16
16
16
16
17
17
17
18
18
18
18
19
19
19
20
20
17
18
16
17
17
17
17
18
18
18
19
19
19
20
20
20
20
21
21
18
19
17
17
18
18
18
19
19
19
20
20
20
21
21
21
22
22
22
19
20
18
18
19
19
20
19
20
20
20
21
21
21
22
22
22
23
23
23
20
21
21
19
19
20
20
21
21
21
22
22
22
23
23
23
24
24
25
22
20
20
21
21
21
22
22
22
23
23
23
24
24
25
25
25
26
22
23
21
21
21
22
22
23 23
23
24
24
25
25
25
26
26
26
27
23
24
22
22
22
23
23
24
24
24
25
25
26
26
.26
27
27
28
28
24
25
23
23
23
24
23
24
24
25
24
25
25
25
25
26
26
27
27
28
28
29
28
29
29
30
29
25
26
26
26
26
27
27
28
28
29
30
26
27
24
25
25
26
26
27
27
27
28
28
29
29
30
30
31
31
32
27
28
25
26
26
27
27
28
28
28
29
29
30
30
31
31
32
32
33
28
29
26
27
27
28
28
29
29
29
30
30
31
31
32
32
33
33
34
29
30
31
27
28
28
28
28
29
29
29
29
30
30
30
30
31
31
31
32
32
33
33
33
34
34
35
35
30
32
32
33
34
34
35
35
36
36
31
32
29
29
30
30
31
31
32
33
33
34
34
35
35
36
36
37
37
32
33
30
30
31
31
32
32
33
34
34
35
35
36
36
37
37
38
39
33
34
31
31
32
32
33
33
34
35
35
36
36
37
37
38
39
39
40
34
35
36
32
32
32
33
33
34
33
34
M
35
34
35
35
36
36
37
36
37
37
37
38
39
39
40
39
40
41
40
41
41
42
35
38
38
40
36
37
33
34
35
35
36
36
37
38
38
39
39
40
41
41
42
43
43
37
38
34
35 I 35
36
37
37
38
39
39
40
41
41
42
42
43
44
44
38
39
35
36 i 36
37
38
38
39
40
40
41
42
42
43
44
44
45
46
39
40
36
37 37
38 I 38
38
39
39
40
39
40
40
41
41
42
41
42
42
43
43
44
45
45
46
46
47
47
48
40
41
41
37
43
44
44
45
46
42
38
39 1 39
40
41
41
42
43
43
44
45
46
46
47
48
48
49
42
43
39
39 40
41
42
42
43
44
44
45
46
47
47
48
49
49
50
43
44
40
40 1 41
42
43
43
44
45
45
46
47
48
48
49
-50
51
51
44
45
46
41
41
41
42
42
43
43
44
44
44
44
45
45
46
46
47
47
48
49
49
50
51
50
51
51
52
52
53
53
54
45
47
48
48
50
46
47
42
43
44
45
45
46
47
48
49
49
50
51
52
52
53
54
55
47
48
43
44
45
46
46
47
48
49
50
50
51
52
53
54
54
55
56
48
49
44
45
46
47
47
48
49
50
51
51
52
53
54
55
56
56
57
49
50
51
45
46
46
47
47
48
48
48
48
49
49
50
50
51
51
52
53
53
54
53
54
55
56
56
57
58
59
58
60
50
51
52
54
55
57
58
52
47
48
49
49
50
51
52
53
54
55
55
56
57
58
59
60
61
52
53
48
49
49
50
51
52
53
54
55
56
57
57
58
59
60
61
62
53
54
49
50
50
51
52
53
54
55
56
57
58
59
59
60
61
62
63
54
55
56
50
50
50
51
51
52
52
53
53
54
54
55
55
56
56
57
57
58
58
59
60
61
61
6'2
61
63
62
63
63
64
64
65
55
56
59
60
57
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
57
58
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
58
59
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
59
60
54
55
56
57 58
59
60
61
62
63
64
65
66
67
68
69
70
60
22489 -(18-
Page 514] TABLE 12.
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
71"
72"
1
2
4
5
6
7
8
10
11
12
13
14
16
17
18
78"
1
2
4
5
6
74"
76"
76"
77"
78"
79"
80"
81"
82"
88"
84"
85"
86"
87"
1
2
3
4
5
1
2
4
5
6
f
2
4
5
6
1
3
4
5
6
1
3
4
5
6
1
3
4
5
6
1
3
4
5
7
1
3
4
5
7
1
3
4
5
7
1
3
4
5
7
1
3
4
5
7
1
3
4
6
7
1
3
4
6
7
1
3
4
6
7
1
3
4
6
7
1
3
4
6
7
1
2
3
4
5
6
7
8
9
10
7
8
9
11
12
7
9
10
11
12
13
15
16
17
18
19
21
22
23
24
26
27
28
29
30
32
33
34
35
37
38
39
40
41
43
44
45
46
47
49
50
51
52
54
55
7
9
10
11
12
8
9
10
11
13
8
9
10
11
13
8
9
10
12
13
8
9
10
12
13
8
9
11
12
13
8
9
11
12
13
8
9
11
12
14
8
10
11
12
14
8
10
11
12
14
8
10
11
13
14
9
10
11
13
14
9
10
11
13
14
9
10
12
13
15
6
7
8
9
10
11
12
13
14
15
13
14
15
17
18
14
15
16
17
19
14
15
16
18
19
14
15
16
18
19
14
15
17
18
19
14
16
17
18
20
14
16
17
18
20
15
16
17
19
20
15
16
18
19
20
15
16
18
19
21
15
17
18
19
21
15
17
18
20
21
16
17
18
20
21
16
17
19
20
22
16
17
19
20
22
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
19
20
21
22
24
25
26
27
28
30
19
20
22
23
24
25
26
28
29
30
31
32
34
35
36
37
38
40
41
42
43
44
46
47
48
49
50
52
53
54
55
56
58
59
60
61
62
64
65
66
67
68
70
71
72
20
21
22
23
25
20
21
23
24
25
20
22
23
24
25
21
22
23
24
26
21
22
23
25
26
21
22
24
25
26
21
23
24
25
27
22
23
24
26
27
22
23
25
26
27
22
24
25
26
28
22
24
25
27
28
23
24
26
27
28
23
24
26
27
29
23
25
26
28
29
16
17
18
19
20
26
27
28
30
31
32
33
35
36
37
38
39
41
42
43
44
46
47
48
49
51
52
53
54
56
26
28
29
30
31
27
28
29
30
32
27
28
30
31
32
27
29
30
31
33
28
29
30
32
33
28
29
31
32
33
28
30
31
32
34
29
30
31
33
34
29
30
32
33
35
29
31
32
34
35
30
31
33
34
35
30
32
33
34
36
30
32
33
34
36
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
31
32
33
34
36
37
38
39
40
41
33
34
35
36
38
33
34
35
37
38
33 34
35 35
36 36
37 38
39 39
34
36
37
38
40
35
36
37
39
40
35
36
38
39
41
■36
37
38
40
41
36
37
39
40
42
36
38
39
41
42
37
38
40
41
43
37
39
40
42
43
38
39
41
42
44
26
27
28
29
30
39
40
41
43
44
45
46
48
49
^0
51
53
54
55
56
39
41
42
43
44
46
47
48
49
51
52
53
54
56
57
40
41
42
44
45
40
42
43
44
46
41
42
43
45
46
41
43
44
45
47
42
43
45
46
47
42
44
45
46
48
43
44
46
47
48
43
45
46
48
49
44
45
47
48
50
44
46
47
49
50
45
46
48
49
51
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
43
44
45
46
47
49
50
51
52
53
54
56
57
58
59
60
62
63
64
65
'66'
67
69
70
71
46
47
49
50
51
47
48
49
51
52
47
49
50
51
53
48
49
51
52
53
49
50
51
53
54
49
51
52
53
55
50
51
53
54
55
50
52
53
55
56
51
52
54
55
57
52
53
54
56
57
52
54
55
57
58
36
37
38
39
40
53
54
55
56
58
53
55
56
57
59
54
55
57
58
59
55
56
57
59
60
55
57
58
59
61
56
57
59
60
62
57
58
59
61
62
57
59
60
62
63
58
60
61
62
64
59
60
62
63
65
59
61
62
64
65
41
42
43
44
45
56
57
58
60
61
62
63
64
66
67
68
69
71
72
73
57
58
59
60
62
63
64
65
67
68
69
70
72
73
74
58
59
60
61
63
64
65
66
68
69
70
71
73
74
75
58
60
61
62
63
59
60
62
63
64
60
61
62
64
65
66
68
69
70
72
61
62
63
65
66
67
68
70
71
72
61
63
64
65
67
68
69
71
72
73
62
63
65
66
68
69
70
72
73
74
63
64
66
67
68
70
71
72
74
75
64
65
66
68
69
71
72
73
75
76
64
66
67
69
70
7l
73
74
76
77
65
67
68
69
71
66
67
69
70
72
67
68
70
71
73
46
47
48
49
50
51
52
53
54
55
65
66
67
68
70
65
67
68
69
71
72
74
75
77
78
73
75
76
77
79
74
75
77
78
80
56
57
58
59
60
71
72
73
75
76
72
73
74
76
77
73
74
75
77
78
74
75
76
78
79
75
76
77
79
80
76
77
78
80
81
77
78
79
81
82
77
79
80
82
83
78
80
81
83
84
79
81
82
84
85
80
82
83
85
86
81
83
84
86
87
56
57
58
59
60
TABLE 12. [Page 515
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
. and the number of minutes of time in the side cohmm. Also for finding the Variation of the
Moon's Declination or Right Ascension, in seconds of time, the motion in one minute being given
at the top and the numbers in the side column being taken for seconds.
M.
Horary motion. 1
M.
88"
89"
90"
91"
92"
98"
94"
95"
96" 1 97"
98"
99"
100"
101"
102"
103"
104"
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
1
3
4
6
7
9
10
12
13
15
16
18
19
21
22
23
25
26
28
29
31
32
34
35
37
1
3
4
6
7
9
10
12
13
15
16
18
19
21
22
24
25
27
28
30
31
33
34
36
37
39
40
42
43
45
2
3
5
6
8
9
11
12
14
15
17
18
20
21
23
24
26
27
29
30
32
33
35
36
38
39
41
42
44
45
2
3
5
6
8
9
11
12
14
15
17
18
20
21
23
24
26
27
29
30
32
33
35
36
38
2
3
5
6
8
9
11
12
14
15
17
18
20
21
23
25
26
28
29
31
32
34
35
37
38
2
3
5
6
8
9
11
12
14
16
17
19
20
22
23
2
3
5
6
8
2
3
5
6
8
2
3 i
5
6
8
2
3
5
6
8
2
3
5
7
8
2
3
5
7
8
2
3
5
7
8
2
3
5
7
8
2
3
5
7
9
2
3
5
7
9
10
12
14
15
17
2
3
5
7
9
1
2
3
4
5
6
7
8
9
10
9
11
13
14
16
17
19
20
22
24
10
11
13
14
16
10
11
13
14
16
10
11
13
15
16
10
11
13
15
16
10
12
13
15
17
10
12
13
15
17
10
12
13
15
17
10
12
14
15
17
10
12
14
16
17
17
19
21
22
24
18
19
21
22
24
18
19
2i
23
24
18
20
21
23
25
18
20
21
23
25
18
20
22
23
25
19
20
22
24
25
19
20
22
24
26
27
29
31
32
34
19
21
22
24
26
19
21
23
24
26
11
12
13
14
15
25
26
28
29
31
33
34
36
37
39
25
27
28
30
31
25
27
29
30
32
26
27
29
30
32
26
27
29
31
32
26
28
29
31
33
34
36
38
39
41
26
28
30
31
33
35
36
38
40
41
27
28
30
32
33
27
29
30
32
34
27
29
31
33
34
28
29
31
33
35
16
17
18
19
20
33
34
36
38
39
33
35
36
38
40
34
35
37
38
40
34
36
37
39
40
35
37
38
40
42
35
37
39
40
42
36
37
39
41
43
36
38
39
41
43
36
38
40
42
43
21
22
23
24
25
26
27
28
29
30
38
40
41
43
44
39
41
42
44
46
40
41
43
44
46
40
42
43
45
47
41
42
44
45
47
41
43
44
46
48
42
43
45
461
48
42
44
45
47
49
42
44
46
47
■ 49
43
45
46
48
50
43
45
47
48
50
44
45
47
49
51
44
46
48
49
51
45
46
48
50
52
45
47
49
50
52
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
45
47
48
50
51
53
54
56
57
59
46
47
49
50
52
53
55
56
58
59
47
48
50
51
53
54
56
57
59
60
47
49
50
52
53
55
56
58
59
61
48
49
51
52
54
48
50
51
53
54
49
50
52
53
55
49
51
52
54
55
50
51
53
54
56
50
52
53
55
57
51
52
54
56
57
51
53
54
56
58
52
53
55
57
58
52
54
56
57
59
53
54
56
58
60
53
55
57
58
60
54
55
57
59
61
31
32
33
34
35
55
57
58
60
61
56
57
59
60
62
56
58
60
61
63
57
59
60
62
63
58
59
61
62
64
58
60
61
63
65
59
60
62
64
65
59
61
63
64
66
60
62
63
65
67
61
62
64
66
67
61
63
65
66
68
62
64
65
67
69
62
64
66
68
69
36
37
38
39
40
41
42
43
44
45
60
62
63
65
66
61
62
64
65
67
68
70
71
73
74
62
63
65
66
68
69
71
72
74
75
62
64
65
67
68
70
71
73
74
76
63
64
66
67
69
71
72
74
75
77
T8~
80
81
83
84
86
87
89
90
92
64
65
67
68
70
64
66
67
69
71
65
67
68
70
71
66
67
69
70
72
66
68
70
71
73
67
69
70
72
74
68
69
71
73
74
68
70
72
73
75
69
71
72
74
76
70
71
73
75
77
70
72
74
76
77
71
73
75
76
78
41
42
43
44
45
46
47
48
49
50
67
69
70
72
73
71
73
74
76
78
79
81
82
84
85
87
88
90
91
93
72
74
75
77
78
80"
81
83
85
86
88
89
91
92
94
73
74
76
78
79
74
75
77
78
80
74
76
78
79
81
75
77
78
80
82
76
78
79
81
83
77
78
80
82
83
85
87
88
90
92
77
79
81
82
84
78
80
82
83
85
79
81
82
84
86
80
81
83
85
87
46
47
48
49
50
51
52
53
54
55
51
52
53
54
55
56
57
58
59
60
75
76
78
79
81
82
84
85
87
88
76
77
79
80
82
83
85
86
88
89
77
78
80
81
83
84
86
87
89
90
77
79
80
82
83
85
86
88
90
91
81
82
84
86
87
82
83
85
86
88
82
84
86
87
89
83
85
87
88
90
84
86
87
89
91
86
88
89
91
93
87
88
90
92
94
88
89
91
93
94
88
90
92
94
95
8J
90
92
93
95
90
91
93
94
96
91
92
94
95
97
91
93
95
96
98
92
94
96
97
99
93
95
97
98
100
94
96
98
99
101
95
97
99
100
102
96
98
100
101
103
97
99
101
102
104
56
57
58
59
60
Page 516] TABLE 12.
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
anH the number of minutes of time in tlie side column. Also for finding the Variatior of the
Moon's Declination or Right Ascension, in seconds of time, the motion in one minute being given
at the top and the numbers in the side column being taken for seconds.
M.
1
2
3
4
5
Horary motion.
M.
105"
106"
107"
108"
109" 1 110" f 111" 112"
113"
114"
115"
116"
117"
118"
2
4
5
7
9
2
4
5
7
9
2
4
5
7
9
• 2
4
5
7
9
2
4
5
7
9
2
4
6
7
9
2
4
6
7
9
2
4
6
7
9
2
4
6
8
9
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
11
12
14
16
18
11
12
14
16
18
11
12
14
16
18
11
13
14
16
18
11
13
15
16
18
11
13
15
17
18
11
13
15
17
19
11
13
15
17
19
11
13
15
17
19
11
13
15
17
19
12
13
15
17
19
12
14
15
17
19
12
14
16
18
20
12
14
16
18
20
6
7
8
9
10
19
21
23
25
26
19
21
23
25
27
20
21
23
25
27
20
22
23
25
27
20
22
24
25
27
20
22
24
26
28
20
22
24
26
28
21
22
24
26
28
21
23
24
26
28
21
23
25
27
29
21
23
25
27
29
21
23
25
27
29
21
23
25
27
29
22
24
26
28
30
n
12
13
14
15
16
17
18
19
20
28
30
32
33
35
28
30
32
34
35
29
30
32
34
36
29
31
32
34
36
29
31
33
35
36
29
31
33
35
37
30
31
33
35
37
30
32
34
35
37
30
32
34
36
38
30
32
34
36
38
31
33
35
36
38
31
33
35
37
39
31
33
35
37
39
31
33
35
37
39
16
17
18
19
20
21
22
23
24
25
37
39
40
42
44
37
39
41
42
44
37
39
41
43
45
38
40
41
43
45
38
40
42
44
45
39
40
42
44
46
39
41
43
44
46
39
41
43
45
47
40
41
43
45
47
40
42
44
46
48
40
42
44
46
48
41
43
44
46
48
41
43
45
47
49
41
43
45
47
49
21
22
23
24
25
26
27
28
29
30
46
47
49
51
53
46
48
49
51
53
46
48
50
52
54
47
49
50
52
54
47
49
51
53
55
48
50
51
53
55
48
50
52
54
56
49
50
52
54
56
49
51
53
55
57
49
51
53
55
57
50
52
54
56
58
50
52
54
56
58
51
53
55
57
59
51
53
55
57
59
26
27
28
29
30
31
32
33
34
35
31
32
33
34
35
54
56
58
60
61
63
65
67
68
70
55
57
58
60
62
55
57
59
61
62
56
58
59
61
63
56
58
60
62
64
57
59
61
62
64
57
59
61
63
65
58
60
62
63
65
58
60
62
64
66
59
61
63
65
67
59
61
63
65
67
60
62
64
66
68
60
62
64
66
68
61
63
65
67
69
36
37
38
39
40
64
65
67
69
71
64
66
68
70
71
65
67
68
70
72
74
76
77
79
81
65
67
69
71
73
66
68
70
72
73
67
68
70
72
74
67
69
71
73
75
68
70
72
73
75
68
70
72
74
76
69
71
73
75
77
70
72
73
75
77
70
72
74
76
78
71
73
75
77
79
36
37
38
39
40
41
42
43
44
45
72
74
75
77
79
72
74
76
78
80
73
75
77
78
80
74
76
78
80
82
75
77
79
81
83
76
78
80
81
83
77
78
80
82
84
77
79
81
83
85
78
80
82
84
86
79
81
82
84
86
79
81
83
85
87
80
82
84
86
88
81
83
85
87
89
41
42
43
44
45
46
47
48
49
50
81
82
84
86
88
81
83
85
87
88
82
84
86
87
89
83
85
86
88
90
84
85
87
89
91
84
86
88
90
92
85
87
89
91
93
86
88
90
91
93
87
89
90
92
94
87
89
91
93
95
88
90
92
94
96
89
91
93
95
97
90
92
94
96
98
90
92
94
96
98
46
47
48
49
50
51
52
53
54
55
89
91
93
95
96
98
100
102
103
105
90
92
94
95
97
99
101
102
104
106
91
93
95
96
98
92
94
95
97
99
93
94
96
98
100
94
95
97
99
101
94
96
98
100
102
95
97
99
101
103
96
98
100
102
104
97
99
101
103
105
98
100
102
104
105
99
101
102
104
106
99
101
103
105
107
100
102
104
106
108
51.
52
53
54
55
56
57
58
59
60
100
102
103
105
107
101
103
104
106
108
102
104
105
107
109
103
105
106
108
110
104
105
107
109
111
105
106
108
110
112
105
107
109
111
113
106
108
110
112
114
107
109
111
113
115
108
110
112
114
116
109
111
113
115
117
110
112
114
116
118
56
57
58
59
60
TABLE 12. [Page 517
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
119"
120"
121"
122"
123"
124"
126"
126"
127"
128"
129"
180"
131"
132"
1
2
3
4
5
6
7
8
9
10
2
4
6
8
10
12
14
16
18
20
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
11
2
4
6
8
11
2
4
6
9
11
2
4
6
9
11
2
4
7
9
11
2
4
7
9
11
2
4
7
9
11
1
2
3
4
5
6
7
8
9
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
12
14
16
18
21
12
14
17
19
21
13
15
17
19
21
13
15
17
19
21
13
15
17
19
21
13
15
17
19
21
13
15
17
19
22
13
15
17
20
22
13
15
17
20
22
13
15
18
20
22
11
12
13
14
15
22
24
26
28
30
22
24
26
28
30
22
24
26
28
30
22
24
26
28
31
33
35
37
39
41
43
45
47
49
51
23
25
27
29
31
23
25
27
29
31
23
25
27
29
31
23
25
27
29
32
23
25
28
30
32
23
26
28
30
32
24
26
28
30
32
24
26
28
30
33
24
26
28
31
33
24
26
29
31
33
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
61
63
65
67
69
32
34
36
38
40
42
44
46
48
50
32
34
36
38
40
42
44
46
48
50
33
35
37
39
41
43
45
47
49
51
33
35
37
39
41
33
35
38
40
42
34
36
38
40
42
34
36
38
40
42
34
36
38
41
43
34
37
39
41
43
35
37
39
41
43
35
37
39
41
44
35
37
40
42
44-
16
17
18
19
20
43
45
48
50
52
44
46
48
50
52
44
46
48
50
53
44
47
49
51
53
45
47
49
51
53
45
47
49
52
54
46
48
50
52
54
46
48
50
52
55
46
48
51
53
55
21
22
23
24
25
52
54
56
58
60
52
54
56
58
61
53
55
57
59
61
53
55
57
59
62
54
56
58
60
62
54
56
58
60
63
55
57
59
61
63
65
67
69
71
74
55
57
59
61
64
66
68
70
72
74
55
58
60
62
64
56
58
60
62
65
56
59
61
63
65
57
59
61
63
66
57
59
62
64
66
26
27
28
29
30
62
64
66
68
70
63
65
67
69
71
63
65
67
69
71
64
66
68
70
72
64
66
68
70
72
65
67
69
71
73
66
68
70
73
75
67
69
71
73
75
67
69
72
74
76
68
70
72
74
76
68
70
73
75
77
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
71
73
75
77
79
72
74
76
78
80
73
75
77
79
81
73
75
77
79
81
83
85
87
89
92
94"
96
98
100
102
104
106
108
110
112
74
76
78
80
82
84
86
88
90
92
94
96
98
100
103
105
107
109
111
113
74
76
79
81
83
85
87
89
91
93
75
77
79
81
83
76
78
80
82
84
76
78
80
83
85
77
79
81
83
85
u
80
82
84
86
78
80
82
85
87
79
81
83
85
87
79
81
84
86
88
36
37
38
39
40
81
83
85
87
89
82
84
86
88
90
83
85
87
89
91
85
88
90
92
94
86
88
90
92
95
87
89
91
93
95
87
90
92
94
96
88
90
92
95
97
89
91
93
95
98
90
92
94
96
98
90
92
95
97
99
101
103
106
108
110
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
91
93
95
97
99
101
103
105
107
109
92
94
96
98
100
93
95
97
99
101
95
97
99
101
103
96
98
100
102
104
97
99
101
103
105
97
99
102
104
106
98
100
102
105
107
99
101
103
105
108
100
102
104
106
108
100
103
105
107
109
46
47
48
49
50
102
104
106
108
110
103
105
107
109
111
105
107
110
112
114
106
108
110
113
115
107
109
111
113
116
108
110
112
114
116
109
111
113
115
117
110
112
114
116
118
111
113
115
117
119
111
114
116
118
120
112
114
117
119
121
51
52
53
54
55
56
57
58
59
60
56
57
58
59
60
111
113
115
117
119
112
114
116
118
120
113
115
117
119
121
114
116
118
120
122
115
117
119
121
123
116
118
120
122
124
117
119
121
123
125
118
120
122
124
126
119
121
123
125
127
119
122
124
126
128
120
123
125
127
129
121
124
126
128
130
122
124
127
129
131
123
125
128
130
132
Page 618] TABLE 12.
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion l)eing given at the top of the page in seconds,
and the number of minutes of time in the side cohimn. Also for findmg the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
188"
134"
2
4
7
9
11
185"
186"
4
187"
188"
189"
140"
141"
142"
148"
144"
145"
146"
1
2
3
4
5
2
4
7
9
11
2
5
7
9
11
2
5
7
9
11
2
5
7
9
11
2
5
7
9
12
2
5
7
9
12
2
5
7
9
12
2
5
7
9
12
2
5
7
9
12
2
5
7
10
12
2
5
7
10
12
2
5
7
10
12
2
5
7
10
12
1
2
3
4
5
6
7
8
9
10
13
16
18
20
22
13
16
18
20
22
14
16
18
20
23
14
16
18
20
23
14
16
18
21
23
14
16
18
21
23
14
16
19
21
23
14
16
19
21
23
14
16
19
21
24
14
17
19
21
24
14
17
19
21
24
14
17
19
22
24
15
17
19
22
24
15
17
19
22
24
6
7
8
9
10
11
12
13
14
15
24
27
29
31
33
25
27
29
31
34
25
27
29
32
34
25
27
29
32
34
25
27
30
32
34
25
28
30
32
35
25
28
30
32
35
26
28
30
33
35
26
28
31
33
35
26
28
31
33
36
26
29
31
33
36
26
29
31
34
36
27
29
31
34
36
27
29
32
34
37
11
12
13
14
15
16
17
18
19
20
35
38
40
42
44
36
38
40
42
45
36
38
41
43
45
36
39
41
43
45
37
39
41
43
46
37
39
41
44
46
37
39
42
44
46
37
40
42
44
47
38
40
42
45
47
38
40
43
45
47
38
41
43
45
48
38
41
43
46
48
39
41
44
46
48
39
41
44
46
49
16
17
18
19
20
21
22
23
24
25
47
49
51
53
55
47
49
51
54
56
47
50
52
54
56
48
50
52
54
57
48
50
53
55
57
48
51
53
55
58
49
51
53
56
58
49
51
54
56
58
49
52
54
56
59
50
52
54
57
59
. 50
52
55
57
60
50
53
55
58
60
51
53
56
58
60
51
54
56
58
61
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
26
27
28
29
30
58
60
62
64
67
58
60
63
65
67
59
61
63
65
68
59
61
63
66
68
59
62
64
66
69
60
62
64
67
69
60
63
65
67
70
61
63
65
68
70
61
63
66
68
71
62
64
66
69
71
62
64
67
69
72
62
65
67
70
72
63
65
68
70
73
63
66
68
71
73
31
32
33
34
35
69
71
73
75
78
69
71
74
76
78
70
72
74
77
79
70
73
75
77
79
71
73
75
78
80
71
74
76
78
81
72
74
76
79
81
72
75
77
79
82
73
75
78
80
82
73
76
78
80
83
74
76
79
81
83
74
77
79
82
84
75
77
80
82
85
75
78
80
83
85
36
37
38
39
40
80
82
84
86
89
80
83
85
87
89
81
83
86
88
90
82
84
86
88
91
82
84
87
89
91
83
85
87
90
92
83
86
88
90
93
84
86
89
91
93
85
87
89
92
94
85
88
90
92
95
86
88
91
93
95
86
89
91
94
96
87
89
92
94
97
88
90
92
95
97
36
37
38
39
40
41
42
43
44
45
91
93
95
98
100
92
94
96
98
101
92
95
97
99
101
93
95
97
100
102
94
96
98
100
103
94
97
99
101
104
95
97
100
102
104
96
98
100
103
105
96
99
101
103
106
97
99
102
104
107
98
100
102
105
107
98
101
103
106
108
99
102
104
106
109
100
102
105
107
110
41
42
43
44
45
46
47
48
49
50
102
104
106
109
111
103
105
107
109
112
104
106
108
110
113
104
107
109
111
113
105
107
110
112
114
106
108
110
113
115
107
109
111
114
116
107
110
112
114
117
108
110
113
115
118
109
111
114
116
118
110
112
114
117
119
110
113
115
118
120
111
114
116
118
121
112
114
117
119
122
46
47
48
49
50
51
52
53
54
55
113
115
117
120
122
114
116
118
121
123
115
117
119
122
124
116
118
120
122
125
116
119
121
123
126
117
120
122
124
127
118
120
123
125
127
119
121
124
126
128
120
122
125
127
129
121
123
125
128
130
122
124
126
129
131
122
125
127
130
132
123
126
128
131
133
124
127
129
131
134
51
52
53
54
55
56
57
58
59
60
56
57
58
59
60
124
126
129
131
133
125
127
130
132
134
126
128
131
133
135
127
129
131
134
136
128
130
132
135
137
129
131
133
136
138
130
132
134
137
139
131
133
135
138
140
132
134
136
139
141
133
135
137
140
142
133
136
138
141
143
134
137
139
142
144
135
138
140
143
145
136
139
141
144
146
TABLE 12. [Page 519
For finding the Variation of the Sun's Right Ascension, or Declination, or of the Equation of Time in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
147"
148"
149"
160"
161"
152"
153"
164"
166"
166"
157"
168"
169"
160"
1
2
3
4
5
6
7
8
9
10
2
5
7
10
12
2
5
7
10
12
2
5
7
10
12
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
11
13
3
5
8
11
13
3
5
8
11
13
1
2
3
4
5
15
17
20
22
25
15
17
20
22
25
15
17
20
22
25
15
18
20
23
25
15
18
20
23
25
15
18
20
23
25
15
18
20
23
26
15
18
21
23
26
16
18
21
23
26
16
18
21
23
26
16
18
21
24
26
16
18
21
24
26
16
19
21
24
27
16
19
21
24
27
6
7
8
9
10
11
12
13
14
15
11
12
13
14
15
27
29
32
34
37
27
30
32
35
37
27
30
32
35
37
28
30
33
35
38
28
30
33
35
38
28
30
33
35
38
28
31
33
36
38
28
31
33
36
39
28
31
34
36
39
29
31
34
36
39
29
31
34
37
39
29
32
34
37
40
29
32
34
37
40
29
32
35
37
40
16
17
18
19
20
39
42
44
47
49
39
42
44
47
49
40
42
45
47
50
40
43
45
48
50
40
43
45
48
50
41
43
46
48
51
41
43
46
48
51
41
44
46
49
51
41
44
47
49
52
42
44
47
49
52
42
44
47
50
52
42
45
47
50
53
42
45
48
50
53
43
45
48
51
53
16
17
18
19
20
21
22
23
24
25
51
54
56
59
61
52
54
57
59
62
52
55
57
60
62
53
55
58
60
63
53
55
58
60
63
53
56
58
61
63
54
56
59
61
64
54
56
59
62
64
54
57
59
62
65
55
57
60
62
65
55
58
60
63
65
55
58
61
63
66
56
58
61
64
66
56
59
61
64
67
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
26
27
28
29
30
64
66
69
71
74
64
67
69
72
74
65
67
70
72
75
65
68
70
73
75
65
68
70
73
76
66
68
71
73
76
79
81
84
86
89
66
69
71
74
77
67
69
72
74
77
67
70
72
75
78
68
70
73
75
78
68
71
73
76
79
68
71
74
76
79
69
72
74
77
80
69
72
75
77
80
31
32
33
34
35
76
78
81
83
86
76
79
81
84
86
77
79
82
84
87
78
80
83
85
88
78
81
83
86
88
79
82
84
87
89
80
82
85
87
90
80
83
85
88
90
81
83
86
88
91
81
84
86
89
92
82
84
87
90
92
82
85
87
90
93
83
85
88
91
93
36
37
38
39
40
88
91
93
96
98
89
91
94
96
99
89
92
94
97
99
90
93
95
98
100
91
93
96
98
101
91
94
96
99
101
92
94
97
99
102
92
95
98
100
103
93
96
98
101
103
94
96
99
101
104
94
97
99
102
105
95
97
100
103
105
95
98
101
103
106
96
99
101
104
107
36
37
38
39
40
1 41
42
43
44
45
41
42
43
44
45
100
103
105
108
110
101
104
106
109
111
102
104
107
109
112
103
105
108
110
113
115
118
120
123
125
128
130
133
135
138
103
106
108
111
113
104
106
109
111
114
105
107
110
112
115
105
108
110
113
116
106
109
111
114
116
107
109
112
114
117
107
110
113
115
118
108
111
113
116
119
109
111
114
117
119
109
112
115
117
120
46
47
48
49
50
51
52
53
54
55
113
115
118
120
123
113
116
118
121
123
114
117
119
122
124
127
129
132
134
137
116
118
121
123
126
117
119
122
124
127
117
120
122
125
128
118
121
123
126
128
119
121
124
127
129
120
122
125
127
130
120
123
126
128
131
121
124
126
129
132
122
125
127
130
133
123
125
128
131
133
46
47
48
49
50
51
52
53
54
55
125
127
130
132
135
126
128
131
133
136
128
131
133
136
138
129
132
134
137
139
130
133
135
138
140
131
133
136
139
141
132
134
137
140
142
133
135
138
140
143
133
136
139
141
144
134
137
140
142
145
135
138
140
143
146
136
139
141
144
147
56
57
58
59
60
137
140
142
145
147
138
141
143
146
148
139
142
144
147
149
140
143
145
148
150
141
143
146
148
151
142
144
147
149
152
143
145
148
150
153
144
146
149
151
154
145
147
150
152
155
146
148
151
153
156
147
149
152
154
157
147
150
153
155
158
148
151
154
156
159
149
152
155
157
160
56
57
58
59
60
Page 520]
TABLE 13.
For finding the Su
a's change of Right Ascension for any given number of hours. 1
Hourly
Number of hours
Hourly
tion.
1
2
3
4
5 6
7
8
0
10 j 11 1 12
tion.
8.
«.
s.
s.
B.
g. 8.
s.
c.
*.
«. 8. ! 8.
8.
8.50
8.5
17.0
25.5
34.0
42. b
51.0
59.5
68.0
76.5
85.0
93.5
102.0
8.50
8.55
8.6
17.1
25.7
34.2
42.8
51.3
59.9
68.4
77.0
85.5
94.1
102.6
8.55
8.60
8.6
17.2
.25. 8
34.4
43.0
51.6
60.2
68.8
77.4
86.0
94. 6
103.2
8.60
8.65
8.7
17.3
•26.0
34.6
43.3
51.9
60.6
69.2
77.9
86.5
95.2
103.8
8.65
8.70
8.7
8.8
17.4
1775
26.1
26:3"
34.8
35.0'
43.5
43. 8
52.2
52.5
60.9
61.3
69.6
70. 0
78.3
7"8.8
87.0
87.5
95.7
96.3
104.4
105. 0
8.70
8.75
8.75
8.80
8.8
17.6
26.4
35.2
44.0
52.8
61.6
70.4
79.2
88.0
96.8
105. 6
8.80
8.85
8.9
17.7
26.6
35.4
44.3
53.1
62.0
70.8
79.7
88.5
97.4
106.2
8.85
8.90
8.9
17.8
26.7
35.6
44.5
53.4
62.3
71.2
80.1
89.0
97.9
106.8
8.90
8.95
9.0
9.0
17.9
18.0
26.9
27.0
35.8
36.0
44.8
53.7
62.7
63.0
71.6
80.6
81.0
89.5
98.5
99.0"
107.4
8.95
9. 00
9.00
45.0
54.0
72.0
90.0
108.0
9.05
9.1
18.1
27.2
36.2
45.3
54.3
63.4
72.4
81.5
90.5
99.6
108.6
9.05
9.10
9.1
18.2
27.3
36.4
45.5
54.6
63.7
72.8
81.9
91.0
100.1
109.2
9.10
9.15
9.2
18.3
27.5
36.6
45.8
54.9
64.1
73.2
82.4
91.5
100.7
109.8
9.15
9.20
9.25
9.2
9.3
18.4
18.5
27.6
27.8
36.8
37.0
46.0
55.2
64.4
64.8
73.6
82.8
83.3
92.0
101.2
101.8
110.4
111.0
9.20
9:25
46.3
55.5
74.0
92.5
9.30
9.3
18.6
27.9
37.2
46.5
.55.8
65.1
74.4
83.7
93.0
102.3
111.6
9.30
9.35
9.4
18.7
28.1
37.4
46.8
56.1
65.5
74.8
84.2
93.5
102.9
112.2
9.35
9.40
9.4
18.8
28.2
37.6
47.0
56.4
65.8
75.2
84.6
94.0
103.4
112.8
9.40
9.45
9.5
18.9
19.0
28.4
37.8
47.3
47.5
56.7
57.0
66.2
75.6
85.1
94.5
104.0
104. 5
113.4
9.45
9.50
9.5
28.5
38.0
66.5
76.0
85.5
95.0
114.0
9.50
9.55
9.6
19.1
28.7
38.2
47.8
57.3
66.9
76.4
86.0
95.5
105.1
114.6
9.55
9.60
9.6
19.2
28.8
38.4
48.0
57.6
67.2
76.8
86.4
96.0
105.6
115.2
9.60
9.65
9.7
19.3
29.0
38.6
48.3
57.9
67.6
77.2
86.9
96.5
106.2
115. 8
9.65
9.70
9.7
19.4
29.1
29.3
38.8
39.0
48.5
58.2
58.5
67.9
77.6
87.-3
87.8
97.0
106.7
116.4
9.70
9.75
9.8
19.5
48.8
68.3
78.0
97.5
107.3
117.0
9.75
9.80
9.8
19.6
29.4
39.2
49.0
58.8
68.6
78.4
88.2
98.0
107.8
117.6
9.80
9.85
9.9
19.7
29.6
.39.4
49.3
59.1
69.0
78.8
88.7
98.5
108.4
118.2
9.85
9.90
9.9
19.8
29.7
39.6
49.5
59.4
69.3
79.2
89.1
99.0
108.9
118.8
9.90
9.95
10.0
19.9
20.0
29.9
39.8
49.8
50.0
59.7
60.0
69.7
70.0
79.6
80.0
89.6
90.0"
99.5
109.5
119.4
9.95
10.00
10.0
30.0
40.0
100.0
110.0
120.0
10.00
10.05
10.1
20.1
30.2
40.2
50.3
60.3
70.4
80.4
90.5
100.5
110.6
120.6
10. 05
10.10
10.1
20.2
30.3
40.4
50.5
60.6
70.7
80.8
90.9
101.0
111.1
121.2
10.10
10.15
10.2
20.3
30.5
40.6
50.8
60.9
71.1
81.2
91.4
101.5
111.7
121.8
10. 15
10.20
10.2
10.3
20.4
30.6
40.8
41.0
51.0
61.2
71.4
81.6
91.8
92. 3
102.0
102.5
112.2
122.4
10.20
10.25
20.5
30.8
51.3
61.5
71.8
82.0
112.8
123.0
10. 25
10.30
10.3
20.6
30.9
41.2
51.5
61.8
72.1
82.4
92.7
103.0
113.3
123.6
10.30
10.35
10.4
20.7
31.1
41.4
51.8
62.1
72.5
82.8
93.2
103.5
113.9
124.2
10. 35
10.40
10.4
20.8
31.2
41.6
52.0
62.4
72.8
83.2
93.6
104.0
114.4
124.8
10.40
10.45
10.5
20.9
31.4
41.8
52.3
52.5
62.7
6.3.0
73.2
73.5
83.6
94.1
94.5
104.5
105. 0'
115.0
115.5
125.4
126.0
10. 45
10.50
10.5
21.0
31.5
42.0
84.0
10.50
10. 55
10.6
21.1
31.7
42.2
52.8
63.3
73.9
84.4
95.0
105.5
116.1
126.6
10. 55
10.60
10.6
21.2
31.8
42.4
53.0
63.6
74.2
84.8
95.4
106.0
116.6
127.2
10.60
10.65
10.7
21.3
32.0
42.6
53.3
63.9
74.6
85.2
95.9
106.5
117.2
127.8
10. 65
10.70
10.7
21.4
32.1
32.3
42.8
43.0
5.3.5
53.8
64.2
74.9
85.6
86.0
96.3
96.8
107.0
107.5
117.7
118.3
128.4
129.0
10.70
10.75
1Q.8
21.5
64.5
75.3
10.75
10.80
10.8
21.6
32.4
43.2
54.0
64.8
75.6
86.4
97.2
108.0
118.8
129.6
10.80
10. 85
10.9
21.7
32.6
43.4
54.3
65.1
76.0
86.8
97.7
108.5
119.4
130.2
10.85
10.90
10.9
21.8
32.7
43.6
54.5
65.4
76.3
87.2
98.1
109.0
119.9
130.8
10.90
10.95
11.0
21.9
22.0
32.9
43.8
44.0
54.8
55.0
65.7
66.0"
76.7
77.0
87.6
88.0
98.6
109.5
110.0
120. 5
121.0
131.4
10. 95
11.00
11.00
11.0
33.0
99.0
132.0
11.05
11.1
22.1
33.2
44.2
55.3
66.3
77.4
88.4
99.5
110.5
121.6
132.6
11.05
11.10
11.1
22.2
.33.3
44.4
55. 5
66.6
77. 7
88.8
99.9
111.0
122. 1
133.2
11.10
11.15
11.2
22.3
33.5
44.6
55.8
66.9
78.1
89.2
100.4
111.5
122.7
133.8
11.15
11.20
11.2
11.3
22.4
33.6
33.8
44.8
45.0
56.0
56.3
67.2
67.5
78.4
89.6
100.8
101.3
112.0
112.5
123.2
123.8
134.4
11.20
11.25
22.5
78.8
90.0
135.0
11.25
11.30
11.3
22.6
33.9
45.2
56.5
67.8
79.1
90.4
101.7
113. 0
124.3
135.6
11.30
11.35
11.4
22.7
34.1
45.4
56.8
68.1
79.5
90.8
102.2
113.5
124.9
136.2
11.35
11.40
11.4
22.8
.34.2
45.6
57.0
68.4
79.8
91.2
102. 6
114.0
125.4
136.8
11.40
11.45
11.5
22.9
34.4
45.8
57.3
68.7
80.2
91.6
103.1
114.5
126.0
137.4
11.45
TABLE 13. [Page 521
For finding the Sun's change of Right Ascension for any given number of hours.
Hourly
varia-
tion.
Number of hours.
Hourly
varia-
tion.
13
14
15
16 1 17
18
19
20
21
s.
22
23
24
s.
s.
s.
s.
.«. s.
*.
s.
s.
s.
s,
s.
s.
8.50
110.5
119.0
127.5
136.0
144.5
153.0
161.5
170.0
178.5
187.0
195.5
204.0
8.50
8.55
111.2
119.7
128. 3
136.8
145.4
153. 9
162.5
171.0
179.6
188.1
196.7
205.2
8.55
8.60
111.8
120.4
129.0
137. 6
146.2
154.8
163.4
172.0
180.6
189.2
197.8
206.4
8.60
8.65
112.5
121.1
129.8
138.4
147.1
155. 7
164.4
173.0
181.7
190.3
199.0
207.6
8.65
8.70
113.1
121.8
122.5
130.5
131.3
139.2
147.9
156.6
157.5
165.3
166.3
174.0
175.0
182.7
183. 8
191.4
192. 5^
200.1
201.3
208.8
8.70
8.75
8.75
113.8
140.0
148.8
210.0
8.80
114.4
123. 2
132. 0
140.8
149.6
158. 4
167.2
176.0
184.8
193. 6
202.4
211.2
8.80
8.85
115.1
123.9
132.8
141.6
150.5
159.3
168.2
177.0
185.9
194.7
203.6
212.4
8.85
8.90
115. 7
124.6
133.5
142.4
151.3
160.2
169.1
178.0
186.9
195.8
204.7
213.6
8.90
8.95
9.00
116.4
117.0
125. 3
134.3
135. 0
143.2
144.0
152.2
153.0
161.1
162.0
170.1
171.0
179.0
188.0
196.9
205. 9
214.8
8.95
126.0
180.0
189.0
198. 0
207.0
216.0
9.00
9.05
117.7
126.7
135.8
144.8
153.9
162. 9
172.0
181.0
190.1
199.1
208.2
217.2
9.05
9.10
118.3
127.4
136.5
145.6
154.7
163. 8
172.9
182.0
191.1
200.2
209.3
218.4
9.10
9.15
119.0
128.1
137.3
146.4
155.6
164.7
173.9
183.0
192.2
201. 3
210.5
219.6
9.15
9.20
119.6
120.3
128.8
138.0
147.2
148.0
156.4
157. 3
165.6
166.5
174.8
175.8
184.0
185.0
193.2
194. 3
202.4
203.5
211.6
220.8
9.20
9.25
129.5
138. 8
212.8
222.0
9.25
9.30
120.9
130. 2
139.5
148.8
158.1
167.4
176.7
186.0
195. 3
204.6
213.9
223.2
9.30
9. 35
121.6
130.9
140.3
149. 6
159. 0
168.3
177.7
187.0
196.4
205.7
215.1
224.4
9.35
9.40
122.2
131.6
141.0
150. 4
159.8
169.2
178.6
188.0
197.4
206.8
216.2
225.6
9.40
9. 45
9.50
122.9
132.3
133.0
141.8
151.2
160.7
161.5
170.1
171.0
179.6
180.5
189.0
190.0
198.5
199.5
207.9
209.0
217.4
226.8
9.45
123.5
142.5
152.0
218. 5
228.0
9.50
9.55
124.2
133.7
143.3
152. 8
162.4
171.9
181.5
191.0
200.6
210.1
219.7
229.2
9.55
9.60
124.8
134.4
144.0
153.6
163.2
172.8
182.4
192.0
201.6
211.2
220.8
230.4
9.60
9.65
125. 5
135.1
144.8
154.4
164.1
173.7
183.4
193.0
202.7
212.3
222.0
231.6
9.65
9.70
126.1
135.8
136.5
145.5
146.3
155.2
156.0
164.9
165.8
174.6
175.5
184.3
185.3
194.0
203.7
204.8
213.4
223.1
232.8
9.70
9.75
126.8
195.0
214.5
224.3
-234.0
9.75
9.80
127.4
137.2
147.0
156.8
166.6
176.4
186.2
196.0
205.8
215.6
225.4
235. 2
9.80
9.85
128.1
137.9
147.8
157.6
167.5
177.3
187.2
197.0
206.9
216.7
226.6
236.4
9.85
9.90
128.7
138.6
148.5
158. 4
168.3
178.2
188.1
198.0
207.9
217.8
227.7
237.6
9.90
9.95
129.4
139.3
140.0
149.3
150.0
159.2
160.0
169.2
170.0
179.1
189.1
199.0
200.0
209.0
210.0
218.9
220.0
228.9
230. 0
238.8
9.95
10.00
130.0
180.0
190.0
240.0
10.00
10.05
130.7
140.7
150.8
160.8
170.9
180.9
191.0
201.0
211.1
221.1
231.2
241.2
10.05
10.10
131.3
141.4
151.5
161.6
171.7
181.8
191.9
202.0
212.1
222.2
232.3
242.4
10.10
10. 15
132.0
142.1
152.3
162.4
172.6
182.7
192.9
203.0
213.2
223.3
233.5
243.6
10.15
10.20
132.6
142.8
153.0
163.2
173. 4
174.3
183.6
184.5
193.8
194.8
204.0
205.0
214.2
215.3
224.4
225.5
234.6
235. 8
244.8
10.20
10.25
133.3
143.5
153. 8
164.0
246.0
10.25
10.30
133.9
144.2
154.5
164.8
175.1
185.4
195.7
206.0
216.3
226.6
236.9
247.2
10.30
10. 35
134.6
144.9
155. 3
165.6
176.0
186.3
196.7
207.0
217.4
227.7
238.1
248.4
10.35
10.40
135.2
145.6
156.0
166.4
176. 8
187.2
197.6
208.0
218.4
228.8
239.2
249.6
10.40
10.45
10.50
135.9
136.5
146.3
147.0
156.8
167.2
177.7
-178.5
188.1
198.6
199.5
209.0
210.0
219.5
229.9
231.0
240.4
250. 8
252.0
10.45
157. 5
168.0
189.0
220.5
241.5
10.50
10.55
137. 2
147.7
158. 3
168.8
179.4
189.9
200.5
211.0
221.6
232. 1
242.7
253.2
10.55
10.60
137.8
148.4
159.0
169.6
180.2
190.8
201.4
212.0
222.6
233.2
243.8
254.4
10.60
10.65
138.5
149.1
159.8
170.4
181.1
191.7
202.4
213.0
223. 7
234. 3
245.0
255.6
10. 65
10.70
139.1
149.8
150.5
160.5
171.2
181.9
182.8
192.6
193.5
203.3
204.3
214.0
224.7
235.4
236.5
246.1
247.3
256.8
10.70
10.75
139. 8
161.3
172.0
215.0
225.8
258.0
10.75
10.80
140.4
151.2
162.0
172.8
183.6
194.4
205.2
216.0
226.8
237.6
248.4
259.2
10.80
10.85
141.1
151.9
162.8
173.6
184.5
195.3
206.2
217.0
227.9
238.7
249.6
260.4
10.85
10.90
141.7
152.6
163. 5
174.4
185.3
196.2
207.1
218.0
228.9
239.8
250.7
261.6
10.90
10. 95
142.4
153.3
164.3
165.0
175.2
186.2
197.1
198.0
208.1
209.0
219.0
230.0
240.9
242. 0
251.9
253. 0
262.8
10.95
11.00
143.0
154.0
176.0
187.0
220.0
231.0
264.0
11.00
11.05
143.7
154.7
165. 8
176.8
187.9
198.9
210.0
221.0
232.1
243.1
254.2
265.2
11.05
11.10
144.3
155. 4
166.5
177.6
188.7
199.8
210.9
222.0
233. 1
244.2
255. 3
266.4
11.10
11.15
145.0
156.1
167. 3
178.4
189.6
200.7
211.9
223.0
234.2
245.3
256. 5
267.6
11.15
11.20
145.6
146.3
156.8
157.5
168.0
179.2
180.0
190.4
201.6
212.8
224.0
235.2
246.4
247.5
257.6
258.8
268.8
270.0
11.20
11.25
168.8
191. 3
202.5
213.8
225.0
236.3
11.25
11.30
146.9
158.2
169.5
180.8
192.1
203.4
214.7
226.0
237.3
248.6
259.9
271.2
11.30
11.35
147.6
158.9
170.3
181.6
193.0
204.3
215.7
227.0
238.4
249.7
261.1
272.4
11.35
11.40
148.2
159.6
171.0
182.4
193. 8
205. 2
216.6
228.0
239.4
250.8
262.2
273. 6
11.40
11.45
148. 9
160. 3
171. 8
183. 2
194.7
206.1
217.6
229.0
240.5
251.9
263.4
274.8
11.45
Page 522]
TABLES 14, 15, 16.
TABLE 14.
Dip of the Sea
Horizon.
Height of Dip of the
the Eye. Horizon
Feet.
0 59
2
1 23
3
1 42
4
1 58
5
2 11
6
2 24
7
2 36
8
2 46
9
2 56
10
3 06
11
3 15
12
3 24
13
3 32
14
3 40
15
3 48
16
3 55
17
4 02
18
4 09
19
4 16
20
4 23
21
4 29
22
4 36
23
4 42
24
4 48
25
4 54
26
5 00
27
5 06
28
5 11
29
5 17
30
5 22
31
5 27
32
5 33
33
5 38
34
5 43
35
5 48
36
5 53
37
5 58
38
6 02
39
6 07
40
1 6 12
45
6 36
50
6 56
55
7 16
60
7 35
65
7 54
70
8 12
75
8 29
80
8 46
85
9 02
90
9 18
95
9 33
100
; 9 48
Dlst. of
Land in
Sea Miles.
TABLE 15.
Dip of the Sea at different Distances from the Observer.
u
n
2
2J
3
H
4
5
10
11
6
4
3
23
12
Height of the Eye above the Sea in Feet.
80 I
15
34
17
12
20
45
23
15
12
10
8
26
57
28
19
15
12
10
85
34
23
17
14
12
40
27
20
16
14
11
6
40
91
45
30
23
19
16
12
10
Note to Table 15. — The numbers of this Table below the black lines
are the same as are given in Table 14, the visible horizon corresponding
to those heights not being so far distant as the land.
TABLE 16.
The Sun's Parallax
in Altitude.
Altitude.
Parallax.
o
//
0
9
10
9
20
8
30
8
40
7
50
6
55
5
60
4
65
4
70
3
75
2
80
2
85
1
90
0
TABLE 17.
Parallax in Altitude of a Planet.
[Page 523
•apmmv
0 COOO»opeO«005(MiCOO^^I:^0!M'*'©000<M-#COOCO
§
"p.
o
1
g
o
K
89
C0C0COCOC^)(NC-4CqCq(MC^r-H,-(r-i^,-(r-ir-l
1
St
(M(M(M(>5!N(Ml>)i-H,-H,-l,-(^T-lT-lr-IT-l
t^i^meo<Mi-(0050oi>-io-<*icoc<)i-ioioci-i-^iC'+<coc<irHO
(MiMiMC^MC^iM!— Ii— I^T-iT-iT-Ht-li-i
at
ioiococ^oo50ot^coio-*ecc<)T-H005coi:^<»iO'*eoooc^'-io
(N(M(M(M(Mi— li— It— It— iT-ll— 11— IrHi— IT-H
Tt<-*coT-iOocooi^coio-*coiMT-io5ooi:^i^<nm'tcocciMT-(0
<N(M(MS<IC^T-lT-lT-lr-lT-lT-lT-(r-ir-l
CCCC<MO0500t:-CDiC-*C0C<li-IO0500t^i»e0iC^C0(MC<I^O
lMlM<M(Mt-II-ll-(T-lT-lT-lT-lT-<,-lT-l
1.
S4
MMi— lOSOOt— COiO-*-*CO(Mi-IOOiOOt^COiCiO'*<COS^<MT-lO
lM(M(MT-(T-lr-(T-(T-lt-ll-lT-ll-l7-lT-l
at
T— It— IOaOt^i:DiCiC-*COiMT— lOOSOOt^cOCOiO'f'^CCMi— (rHO
(M(M(MT-^T-(^T-iT-ii-ir-(T-lr-(t-l
1
OO05t^i:0iCiCi-^C0(Mi-(i-IO05Q0I^C0C0»0'*0tCC(MT— It— lO
1^
OiO50Oi©cDiC'tccc<ie<)i— ioo5aot^coi:o»ciC'+icoso<MT-iT-(0
ooQOt^<:D»c**tcso<MT-iooa>aot^cocoic*'*< ec CO (M i-l r-l o
6
FN
t^t^«OvO'*CCC<)(MT-lOOOiaOt^t^COiCiC't<-t<C»:>0^(MT-lt-lO
(£)CDiC-*C0(M<MT-IOO0500C0t--C0lOlC'*-*e0e0C<l(Mi-(T— lO
lOiO'*ieO<NT-lt-i000505aDl^t^<:DiCiO-*-+ieOCO(M(MT-iT-iO
'*i'*CC<Mr-iT-IOC050iC0 1^t:^<»iC»C-+i'>*eCC0SqMi— It— lOO
OOCOiMrHT— iOO050i00l--l>-^5DlO"*-*-*C0OT<M<MT— li-lOO
T— 1 tH T— ( T— I T— ( I— ( I— (
(MlMT-lOOOlOSOOOOt^t^i^COinnO-^-^WOOINlMlMT-li-HOO
f4
i-iT-iooa>oooooot^i^cDcoio»o-^rt<ec«eo<N<MC^T-ii-ioo
I— 1 T— 1 T— 1 T— 1
^
fN
000:05COOOt^t^t-CDi:DkOW>!t<Tt<eCeOeO(N(N(MT-lT-irHOO
!>
050500a0t^l>-t>'iX>^C0i0»b'^'*'^C0e«5(MC<liNC<li-(T-irHOO
§D
QOoooot^t-i»co«OkC!ioiO'*-<t-<*eceoc<i(N<NiMT-i^^T-40o
t^
l^I:^t^iXi:0i0i0iC»n-<*<'*<'tiCCC0e0IM(N(M(NT-lT-iT-li-(OOO
«
cococDioicio-^-^-^TfeceocceoiMfNiNiNT-iT-iT-ii-iT-iooo
i
iciOiO'*Tj<rjH-.^eceoeoeoecc<ic<i<M(MiMrHi-i^T-iT-(r-ooo
^
■*Tj<rt<CCCOeOCO«CeC<NlMiM(N(M(MT-l,-lT-lT-lT-i.-(T-IOOOO
^
eOeCeCCOC^lMCqiMCNtNCOS^T-ii-iTHT-lT-iT-ir-iT-iT-iOOOOO
91
(N(N(M<M<N(NT-lT-lT-lT-HT-i^r-H,-H,-l,-.T-lT-iOOOOOOOO
^
T-lT-lT-lT-lT-lT-lT-lT-lT^T-ll-lT-lOOOOOOOOOOOOOO
•apmniv
o OOOOiOOCO":Cai(MiCOOt-iTt<tr^OC<l-rf<cOOOOMrt<?CicOO
Page 524] TABLES 18, 19.
TABLE 18.
Augmentation of the Moon's Semidiameter.
TABLE 19,
Augmentation of the Moon's
Horizontal Parallax.
CO
SS •
<
J)'s Semidiameter.
o ob
OJ >
S^ o
o
0
2
4
6
8
J) 's Hor. Parallax.
W
• !»'
16'
17'
1
80"
0"
80"
0"
80"
0"
53'
57' 81' 1
1
o
0
2
4
6
8
//
0.1
0.6
1.0
1.5
2.0
//
0.1
0.6
1.1
1.6
2.1
0.1
0.7
1.2
1.7
2.3
//
0.1
0.7
1.3
1.9
2.4
II
0.2
0.8
1.4
2.0
2.6
II
0.2
0.8
1.5
2.1
2.7
II
0.0
0.0
0.1
0.1
0.2
//
0.0
0,0
0.1
0.1
0.2
II
0,0
0.0
0.1
0.1
0.2
10
12
14
16
18
2.4
2.9
3.4
3.8
4.3
2.6
3.1
3.6
4.1
4.6
2.8
3.3
3.9
4.4
4.9
3.0
3.6
4.1
4.7
5.2
3.2
3.8
4.4
5.0
5,6
3.4
4.0
4.7
5.3
5.9
10
12
14
16
18
0.3
0.5
0.6
0.8
1.0
0.3
0.5
0.7
0.9
1.1
0.4
0.5
0.7
0.9
1.1
20
22
24
26
28
4.7
5.2
5.6
6.0
6.5
5.1
5.5
6.0
6.5
6.9
5.4
5.9
6.4
6.9
7.4
5.8
6.3
6.8
7.4
7.9
6.1
6.7
7.3
7.8
8.4
6.5
7.1
7. 7
8.3
8.9
20
22
24
26
28
1.2
1.5
1.7
2.0
2.3
1.3
L6
1.9
2.2
2.5
1.4
1.7
2.0
2.3
2.6
30
32
34
36
38
6.9
7.3
7.7
8.1
8.4
7.3
7.8
8.2
8.6
9.0
7.9
8.3
8.8
9.2
9.7
8.4
8.9
9.4
9.8
10.3
8.9
9.4
10.0
10.5
10.9
9.5
10.0
10.6
11.1
11.6
30
32
34
36
38
2.6
2.9
3.3
3.6
4.0
2.8
3.1
3.5
3.9
4.3
3.0
3.4
3.8
4.1
4.6
40
42
44
46
48
8.8
9.2
9.5
9.8
10.2
9.4
9.8
10.2
10.5
10.9
10.1
10.5
10.9
11.3
11.6
10.7
11.2
11.6
12.0
12.4
11.4
11.9
12.3
12.8
13.2
12.1
12.6
13.1
13.6
14.0
40
42
44
46
48
4.3
4.7
5.0
5.4
5.8
4.6
5.0
5.4
5.8
6.2
5.0
5.4
5.8
6.2
6.6
50
52
54
56
58
10.5
10.8
11.1
11.3
11.6
11.2
11.5
11.8
12.1
12.4
12.0
12.3
12.7
13.0
13.3
12.8
13.1
13.5
13.8
14.1
13.6
14.0
14.4
14.7
15.1
14.4
14.9
15.3
15.6
16.0
50
52
54
56
58
6.1
6.5
6.8
7.2
7.5
6.6
7.0
7.4
7.7
8.1
7.1
7.5
7.9
8.3
8.6
60
62
64
66
68
11.8
12.1
12.3
12.5
12.7
12.7
12.9
13.2
13.4
13.6
13.5
13.8
14.1
14.3
14.5
14.4
14.7
15.0
15.2
15.5
15.4
15.7
16.0
16.2
16.5
16.3
16.6
16.9
17.2
17.5
60
62
64
66
68
7.8
8.1
8.4
8.7
9.0
8.4
8.8
9.1
9.4
9,7
9.0
9.4
9.7
10.0
10.3
70
72
74
76
78
12.9
13.0
13.1
13.3
13.4
13.8
13.9
14.1
14.2
14.3
14.7
14.9
15.0
15.2
15.3
15.7
15.9
16.0
16.2
16.3
16.7
16.9
17.1
17.2
17.4
17.7
17.9
18.1
18.3
18.4
70
72
74
76
78
9.2
9.5
9.7
9.8
10.0
9,9
10.2
10.4
10.6
10.8
10.6
10.9
11.1
11.3
11.5
80
82
84
86
88
13.5
13.5
13.6
13.6
13.7
14.4
14.5
14.6
14.6
14.6
15.4
15.5
15.6
15.6
15.6
16.4
16.5
16.6
16.6
16.7
17.5
17.6
17.6
17.7
17.7
18.6
18.7
18.7
18.8
18.8
80
82
84
86
88
10.1
10.3
10.3
10.4
10.4
10.9
11.0
11.1
11.2
11.2
11.7
11.8
11.9
12.0
12.0
90
13.7
14.6
15.6
16.7
17.7
18.8
90
10.5
11.3
12.0
TABLE 20A.
[Page 525 |
Mean Refraction.
[Barometer, 30 inches. Fahrenheit's Thermometer,
50°.J
Apparent
Mean Re-
Apparent
Mean Re-
Apparent
Mean Re-
Apparent
Mean Re-
Apparent
Altitude.
Mean Re-
Altitude.
fraction.
Altitude.
fraction.
Altitude.
fraction.
Altitude.
fraction.
fraction.
o /
'
o /
9 30
5 35. 1
o /
15 00
3 34.1
o /
25 00
2 4.4
42 00
1 04.7
0 00
36 29. 4
35
5 32.4
10
3 31.7
10
2 3.4
20
1 03.9
1 00
24 53. 6
40
5 29. 6
20
3 29.4
20
2 2.5
40
1 03.2
2 00
18 25. 5
45
5 27.0
30
3 27.1
30
2 1.6
43 00
1 02.4
3 00
14 25. 1
50
5 24.3
40
3 24.8
40
2 0.7
20
1 01.7
4 00
11 44.4
55
5 21.7
50
3 22.6
50
1 59.8
40
1 01.0
5 00
9 52.0
10 00
5 19.2
16 00
3 20.5
26 00
1 58.9
44 00
1 00.3
06
9 44.0
05
5 16.7
10
3 18.4
10
1 58.1
20
0 59. 6
10
9 36.2
10
5 14.2
20
3 16.3
20
1 57.2
40
0 58.9
15
9 28.6
15
5 11.7
30
3 14.2
30
1 56.4
45 00
0 58.2
20
9 21.2
20
5 9.3
40
3 12.2
40
1 55.5
20
0 57.6
25
9 14.0
25
5 6.9
50
3 10.3
50
1 54.7
40
0 56.9
5 30
9 7.0
10 30
5 4.6
17 00
3 8.3
27 00
1 53.9
46 00
0 56.2
35
9 0.1
35
5 2.3
10
3 6.4
10
1 53.1
20
0 66.6
40
8 53.4
40
5 0.0
20
3 4.6
20
1 52.3
40
0 55.0
45
8 46.8
45
4 57.8
30
3 2.8
30
1 61.5
47 00
0 54.3
50
8 40.4
50
4 55.6
40
3 1.0
40
1 50.7
20
0 53.7
55
8 34.2
55
4 53.4
50
2 59.2
50
1 50.0
40
0 53.1
6 00
8 28.0
11 00
4 51.2
18 00
2 57.5
28 00
1 49.2
48 00
0 62.5
05
8 22.1
05
4 49.1
10
2 55.8
20
1 47.7
49 00
0 50.6
10
8 16.2
10
4 47.0
20
2 54.1
40
1 46.2
50 00
0 48.9
15
8 10.5
15
4 44.9
30
2 52.4
29 00
1 44.8
51 00
0 47.2
20
8 4.8
20
4 42.9
40
2 50.8
20
1 43.4
52 00
0 46.5
25
7 59.3
25
4 40.9
50
2 49.2
40
1 42.0
53 00
0 43.9
6 30
7 53.9
11 30
4 38.9
19 00
2 47.7
30 00
1 40.6
54 00
0 42.3
35
7 48.7
35
4 36.9
10
2 46.1
20
1 39.3
66 00
0 40.8
40
7 43.5
40
4 35.0
20
2 44.6
40
1 38.0
56 00
0 39.3
45
7 38.4
45
4 33. 1
30
2 43.1
31 00
1 36.7
57 00
0 37.8
■ 50
7 33.5
50
4 31.2
40
2 41.6
20
1 35.5
68 00
0 36.4
55
7 28.6
55
4 29.4
50
2 40.2
40
1 34.2
59 00
0 35.0
7 00
7 23.8
12 00
4 27.5
20 00
2 38.8
32 00
1 33.0
60 00
0 33.6
05
7 19.2
05
4 25. 7
10
2 37.4
20
1 31.8
61 00
0 32.3
10
7 14.6
10
4 23.9
20
2 36.0
40
1 30.7
62 00
0 31.0
15
7 10.1
15
4 22.2
30
2 34.6
33 00
1 29.5
63 00
0 29.7
20
7 5.7
20
4 20.4
40
2 33. 3
20
1 28.4
64 00
0 28. 4
25
7 1.4
25
4 18.7
50
2 32.0
40
1 27.3
65 00
0 27.2
7 30
6 57.1
12 30
4 17.0
21 00
2 30.7
34 00
1 26. 2
66 00
0 25.9
35
6 53. 0
35
4 15.3
10
2 29.4
20
1 25. 1
67 00
0 24.7
40
6 48.9
40
4 13.6
20
2 28.1
40
1 24.1
68 00
0 23.6
45
6 44.9
45
4 12.0
30
2 26.9
35 00
1 23.1
69 00
0 22.4
50
6 41.0
50
4 10.4
40
2 25.7
20
1 22.0
70 00
0 21.2
55
6 37.1
55
4 8.8
50
2 24.5
2 23.3
40
36 00
1 21.0
1 20.1
71 00
72 00
0 20.1
0 18.9
8 00
6 33.3
13 00
4 7.2
22 00
05
6 29.6
05
4 5.6
10
2 22.1
20
1 19.1
73 00
0 17.8
10
6 25.9
10
4 4.1
20
2 20.9
40
1 18.2
74 00
0 16.7
15
6 22.3
15
4 2.6
30
2 19.8
37 00
1 17.2
75 00
0 16.6
20
6 18.8
20
4 1.0
40
2 18.7
20
1 16.3
76 00
0 14.6
25
6 15.3
25
3 59.6
50
2 17.5
40
1 15.4
77 00
0 13.5
8 30
6 11.9
13 30
3 58.1
23 00
2 16.4
38 00
1 14.5
78 00
0 12.4
35
6 8.5
35
3 56.6
10
2 15.4
20
1 13.6
79 00
0 11.3
40
6 5.2
40
3 55. 2
20
2 14.3
40
1 12.7
80 00
0 10.3
45
6 2.0
45
3 53.7
30
2 13.3
39 00
1 11.9
81 00
0 9.2
50
5 58.8
50
3 52.3
40
2 12.2
20
1 11.0
82 00
0 8.2
55
5 55.7
55
3 50.9
50
2 11.2
40
1 10.2
83 00
84 00
0 7.2
0 6.1
9 00
5 52.6
14 00
3 49.5
24 00
2 10.2
40 00
1 9.4
05
5 49.6
10
3 46. 8
10
2 9.2
20
1 8.6
85 00
0 5.1
10
5 46.6
20
3 44.2
20
2 8.2
40
1 7.8
86 00
0 4.1
15
5 43.6
30
3 41.6
30
2 7.2
41 00
1 7.0
87 00
0 3.1
20
5 40.7
40
3 39.0
40
2 6.2
20
1 6.2
88 00
0 2.0
25
5 37.9
50
3 36. 5
50
2 5.3
40
1 5.4
89 00
0 1.0
9 30
5 35.1
15 00
3 34.1
25 00
2 4.4
42 00
1 4. 7
90 00
0 0.0
Page 526]
TABLE 20B.
Correction of the Sun's Apparent Altitude for Refraction and Parallax.
[Barometer, 30 inches. Fahrenheit's Thermometer,
50°.]
Apparent
Altitude.
Mean Re-
fraction and
Parallax 0.
Apparent
Altitude.
Mean Re-
fraction and
Parallax 0.
Apparent
Altitude.
Mean Re-
fraction and
Parallax ©.
Apparent
Altitude.
Mean Re-
fraction and
Parallax ©.
Apparent
Altitude.
Mean Re-
fraction and
Parallax 0.
o /
/ //
O /
' II
o /
/ //
o /
1 II
0 1
' II
9 30
5 26
15 00
3 25
25 00
1 56
42 00
0 58
0 00
36 20
35
5 23
10
3 24
10
1 55
20
0 57
1 00
24 45'
40
5 21
20
3 21
20
1 55
40
0 56
2 00
18 17
45
5 18
30
3 19
30
1 54
43 00
0 55
3 00
14 16
50
5 15
40
3 17
40
1 53
20
0 55
4 00
11 35
55
5 13
50
3 15
50
1 52
40
0 54
5 00
9 43
10 00
5 10
16 00
3 13
26 00
1 51
44 00
0 53
05
9 35
05
5 8
10
3 10
10
1 50
20
0 53
10
9 27
10
5 5
20
3 8
20
1 49
40
0 52
15
9 20
15
5 3
30
3 6
80
1 48
45 00
0 52
20
9 12
20
5 0
40
3 4
40
1 48
20
0 52
25
9 5
25
4 58
50
3 2
50
1 47
40
0 51
5 30
8 58
10 30
4 56
17 00
3 0
27 00
1 46
46 00
0 50
35
8 51
35
4 53
10
2 58
10
1 45
20
0 50
40
8 44
40
4 51
20
2 57
20
1 44
40
0 49
45
8 38
45
4 49
30
2 55
30
1 44
47 00
0 48
50
8 31
50
4 47
40
2 53
40
1 43
20
0 48
55
8 25
55
4 44
50
2 51
50
1 42
40
0 47
6 00
8 19
11 00
4 42
18 00
2 50
28 00
1 41
48 00
0 47
05
8 13
05
4 40
10
2 48
20
1 40
49 00
0 45
10
8 7
10
4 38
20
2 46
40
1 38
50 00
0 43
15
8 2
15
4 36
30
2 44
29 00
1 37
51 00
0 41
20
7 56
20
4 34
40
2 43
20
1 35
52 00
0 40
25
7 50
25
4 32
50
2 41
40
1 34
53 00
0 39
6 30
7 45
11 30
4 30
19 00
2 40
30 00
1 33
54 00
0 37
35
7 40
35
4 28
10
2 38
20
1 31
55 00
0 36
40
7 35
40
4 26
20
2 37
40
1 30
56 00
0 34
45
7 29
45
4 24
30
2 35
31 00
1 29
57 00
0 33
50
7 25
50
4 22
40
2 34
20
1 28
58 00
0 32
55
7 20
55
4 20
50
2 32
40
1 26
59 00
0 31
7 00
7 15
12 00
4 19
20 00
2 31
32 00
1 25
60 00
0 30
05
7 10
05
4 17
10
2 29
20
1 24
61 00
0 28
10
7 6
10
4 15
20
2 28
40
1 23
62 00
0 27
15
7 1
15
4 13
30
2 27
33 00
1 22
63 00
0 26
20
6 57
20
4 11
40
2 25
20
1 20
64 00
0 24
25
6 52
25
4 10
50
2 24
40
1 19
65 00
0 23
7 30
6 48
12 30
4 8
21 00
2 23
34 00
1 18
66 00
0 22
35
6 44
35
4 6
10
2 21
20
1 17
67 00
0 21
40
6 40
40
4 5
20
2 20
40
1 16
68 00
0 21
45
6 36
45
4 3
30
2 19
35 00
1 15
69 00
0 19
50
6 32
50
4 1
40
2 18
20
1 15
70 00
0 18
55
6 28
55
4 0
50
2 17
40
1 14
71 00
0 17
8 00
6 24
13 00
3 58
22 00
2 15
36 00
1 13
72 00
0 16
05
6 21
05
3 57
10
2 14
20
1 12
73 00
0 16
10
6 17
10
3 55
20
2 13
40
1 11
74 00
0 15
15
6 13
15
3 54
30
2 12
37 00
1 10
75 00
0 14
20
6 10
20
3 52
40
2 11
20
1 9
76 00
0 13
25
6 6
25
3 51
50
2 10
40
1 8
77 00
78 00
0 12
0 10
8 30
6 3
13 30
3 49
• 23 00
2 8
38 00
1 8
35
6 0
35
3 48
10
2 7
20
1 7
79 00
0 9
40
5 56
40
3 46
20
2 6
40
1 6
80 00
0 8
45
5 53
45
3 45
30
2 5
39 00
1 5
81 00
0 7
50
5 50
50
3 43
40
2 4
20
1 4
82 00
0 6
55
5 47
55
3 42
50
2 3
40
1 3
83 00
0 6
9 00
5 44
14 00
3 41
24 00
2 2
40 00
1 2
84 00
0 5
05
5 41
10
3 38
10
2 1
20
1 2
85 00
0 4
10
5 38
20
3 35
20
2 0
40
1 1
86 00
0 3
15
5 35
30
3 33
30
1 59
41 00
1 0
87 00
0 2
20
5 32
40
3 30
40
1 58
20
0 59
88 00
0 2
25
5 29
50
3 28
50
1 57
40
0 58
89 00
0 1
9 30
5 26
15 00
3 25
25 00
1 56
42 00
0 58
90 00
0 0
TABLE 21. [Page 527 1
Correction of the Mean Refraction for the Height of the Barometer.
Barom.
Mean refraction.
Barom.
Add.
0
1 1
'
2
8' j
A
' 1 6'
6'
1'
8' 1 9' |l0'
Subtract.
0"
80" j 0"
80"
0"
80"
0" 80"
0"
80" 0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
II
If 1 "
„
„
„
„
II
II
„
„
„
„
„
n
//
//
II
II
;;
27.50
0
2
5
7
10
12
15
17
20
23
25
28
30
33
35
38
40
43
45
48
51
27.55
0
2
5
7
10
12
15
17
20
22
25
27
30
32
35
37
40
42
45
47
50
27.60
0
2
5
7
10
12
14
17
19
22
24
27
29
31
34
36
39
41
44
46
49
27.65
0
2
5
7
9
12
14
16
19
21
24
26
28
31
33
36
38
40
43
45
48
27.70
0
0
2
2
5
4
7
7
9
9
11
11
14
16
18
21
23
25
28
30
32
35
37
39
42
44
47
27.75
13
16
18
20
23
25
27
29
32
34
36
39 41
43
46
27.80
0
2
4
7
9
11
13
15
18
20
22
24
27
29
31
33
35
38 40
42
45
27.85
0
2
4
6
9
11
13
15
17
19
22
24
26
28
30
32
35
37 39
41
44
27.90
0
2
4
6
8
10
13
15
17
19
21
23
25
27
30
32
34
36 38
40
43
27.95
28. 00
0
0
2 4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
21
20
23
22
25
24
27
26
29
28
31
30
33
32
35 37
34 j36
39
42
2
4
38
41
28.05
0
2
4
6
8
10
12
14
16
18
20
22
24
25
27
29
31
33
35
37
39
28.10
0
2
4
6
8
9
11
13
15
17
19
21
23
25
27
29
31
33
34
36
38
28.15
0
2
4
6
7
9
11
13
15
17
19
20
22
24
26
28
30
32
34
36
37
28.20
0
2
4
5
7
9
11
13
14
16
18
20
22
24
25
27
29
31
33
35
36
28.25
0
2
3
5
7
9
10
12
14
16
18
19
21
23
25
26
28
30
32
34 35
28.30
0
2
3
5
7
8
10
12
14
15
17
19
21
22
24
26
27
29
31
33 34
28.35
0
2
3
5
7
8
10
12
13
15
17
18
20
22
23
25
27
28
30
32 33
28.40
0
2
3
5
6
8
10
11
13
14
16
18
19
21
23
24
26
27
29
31 32
28.45
0
0
2
3
3
5
4
6
6
8
7
9
9
11
10
12
12
14
14
16
15
17
17
19
18
20
20
22
21
23
23
25
24
27
26
28
27
30 31
29 30
28.50
31.50
28.55
0
3
4
6
7
9
10
12
13
15
16
17
19
20
22
23
25
26
28129
31.45
28.60
0
3
4
6
7
8
10
11
13
14
15
17
18
20
21
23
24
25
27128
31.40
28.65
0
3
4
5
7
8
9
11
12
14
15
16
18
19
20
22
23
25
26|27
31.35
28.70
0
3
4
5
6
8
9
10
12
13
14
16
17
18
20 121
22
24
25126
31.30
28.75
0
2
4
5
6
7
9
10
11
13
14
15
16
18
19
20
21
23
24
25
31.25
28.80
0
2
4
5
6
7
8
10
11
12
13
14
16
17
18
19
21
22
23
24
31.20
28. 85
0
2
3
5
6
7
8
9
10
12
13
14
15
16
17
19
20
21
22
23
31.15
28.90
0
2
3
4
5
7
8
9
10
11
12
13
14
16
17
18
19
20
21
22
31.10
28.95
0
2
3
4
5
6
7
8
9
9
11
10
12
11
13
14
15
16
17
18
19
20
21
31.05
29.00
0
2
3
4
5
6
7
8
12
13
14
15
16
17
18
19
20
31.00
29.05
0
2
3
4
5
6
7
8
9
10
11
11
12
13
14
15
16
17
18
19
30.95
29.10
0
2
3
4
4
5
6
7
8
9
10
11
12
13
14
15
15
16
17
18
30.90
29.15
0
2
3
3
4
5
6
7
8
9
9
10
11
12
13
14
15
15
16
17
30.85
29.20
0
2
2
3
4
5
6
6
7
8
9
10
10
11
12
13
14
15
15
16
30.80
29.25
0
2
3
4
4
5
6
7
8
8
9
10
11
11
12
13
14
14
15
30.75
29.30
0
2
3
3
4
5
6
6
7
8
8
9
10
11
11
12
13
13
14
30.70
29.35
0
2
3
3
4
5
5
6
7
7
8
9
9
10
10
11
12
13
13
30.65
29.40
0
2
2
3
4
4
5
5
6
7
7
8
8
9
10
10
11
12
12
30.60
29.45
29.50
0
0
0
-Y
2
2
2
3
3
4
4
5
6
6
7
7
8
8
9
9
10
11
11
30.55
2
3
3
4
5
5
6
6
7
7
8
8
9
9
10
10
30.50
29.55
0
0
2
2
3
3
4
4
5
5
5
6
6
7
7
8
8
9
9
30. 45
29.60
0
0
2
2
2
3
3
4
4
4
5
5
6
6
6
7
7
8
8
30.40
29.65
0
0
2
2
2
3
3
4
4
4
5
5
5
6
6
6
7
7
30.35
29.70
0
0
1
2
2
2
3
3
3
4
4
4
5
5
5
5
6
6
30.30
29.75
0
0
0
1
1
2
2
2
3
3
3
3
4
4
4
4
5
5
5
30.25
29.80
0
0
0
1
1
1
2
2
2
2
2
3
3
3
3
3
4
4
4
30.20
29.85
0
0
0
0
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
30.15
29.90
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
30.10
29.95
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
30.05
30.00
0
0
0
0
0
0
0
0
0
0
0 ; 0 0
U
0
0
30.00
Subtract.
0"
30"
0"
80"
0"
80" 0"
80"
0"
80" 0" 83" 0" 80" 1 C" 80" 0" | 80"
0" 1 80"
0"
A^d.
0'
1'
2' 1 8'
4' 5' C 1 V \ 8'
9'
10'
^lean refraction.
Page 528J
TABLE ^.
Correct
ion
of tl
e Mean Refraction for the Height of the Thermometer.
Mean refraction.
Ther.
Ther.
Add.
o
0'
I'
1/
"'
4'
5' 1
8' ; 7' 8'
9'
10'
Add.
0"
80"
II
0"
II
80"
II
0"
80"
II
0"
80"
II
0"
II
80"
II
0"
80"
II
0'
II
80"
0"
80" j 0"
80"
II
0"
II
80"
0"
II II
II
II
o
—10
0
4
8
12
16
20
24
28
33
37
41
46
50
55 60
65 ! 70
75
80
85 90
-10
— 8
0
4
8
•2
15
19
23
27
31
36
40
44
48
53 :58
62 \ 67
72
n
82 , 87
- 8
— 6
0
4
7
11
15
19
22
26
30
34
38
42
47
51 55
60 64
69
74
79 84
— 6
— 4
0
4
7
11
14
18
22
25
29
33
37
41
45
49
53
57 i 62
66
71
76 80
— 4
— 2
0
3
3
_7_
7
10
lb
14
13
17
16
21
20"
24
23
28
27
31
30
35
34
39
37
43
41
47
45
51
49
55
53
59
57
64 I 68
61 65
72 77
69 74
— 2
0
0
0
2
0
3
6
9
12
16
19
22
25
29
32
36
39
43
47
50
54
58
62
66 i 70
2
4
0
3
6
9
12
15
18
21
24
28
31
34
37
41
44
48
52
55
59
63 ' 67
4
6
0
3
6
8
11
14
17
20
23
26
29
32
36
39
42
46
49
53
56
60 i 64
6
8
10
0
0
3
3
5
5
8
8
11
10
14
13
16
15
19
18
22
21
25
24
28
26
31
29
34
32
37
35
40
38
43
41
47
44
50
48
54
51
57
54
61
58
8
10
11
0
2
5
7
10
13
15
18
20
23
26
28
31
34
37
40
43
46
49
53
56
11
12
0
2
5
7
10
12
15
17
20
22
25
28
30
33
36
39
42
45
48
51
54
12
13
0
2
5
7
9
12
14
17
19
22
24
27
30
32
35
38
41
44
47
50
53
13
14
15
0
0
2
2
5
4
7
7
9
9
11
11
14
13
16
16
19
18
21
20
24
23
26
25
29
28
31
30
34
33
37
36
40
38
42
41
45
44
48
47
51
50
14
15
16
0
2
4
6
9
11
13
15
18
20
22
25
27
29
32
35
37
40
43
45
48
16
17
0
2
4
6
8
10
13
15
17
19
21
24
26
29
31
33
36
39
41
44
47
17
18
0
2
4
6
8
10
12
14
16
19
21
23
25
28
30
32
35
37
40
43
45
18
19
20
0
0
2
2
4
4
6
6
8
8
10
9
12
11
14
13
16
15
18
17
20
19
22
22
24
24
27
26
29
28
31
30
34
33
36
35
39
37
41
40
44
42
19
20
21
0
2
4
5
7
9
11
13
15
17
19
21
23
25
27
29
31
34
36
38
41
21
22
0
2
3
5
7
9
11
12
14
16
18
20
22
24
26
28
30
32
35
37
39
22
23
0
2
3
5
7
8
10
12
14
15
17
19
21
23
25
27
29
31
33
36
38
23
24
0
2
3
5
6
8
10
11
13
15
17
18
20
22
24
26
28
30
32
34
36
24
25
0
2
3
5
6
8
9
11
13
14
16
18
19
21
23
25
27
29
31
33
35
25
26
0
3
4
6
7
9
11
12
14
15
17
19
20
22
24
26
28
29
31
33
26
27
0
3
4
6
7
9
10
12
13
15
16
18
19
21
23
25
26
28
30
32
27
28
0
3
4
5
7
8
10
11
12
14
15
17
19
20
22
23
25
27
29
30
28
29
30
0
0
3
2
4
4
5
5
6
6
8
7
9
9
11
10
12
11
13
13
15
14
16
15
18
17
19
18
21
20
22
21
24
23
26
24
27
29
29
26
28
30
31
0
2
3
5
6
7
8
9
11
12
13
15
16
17
19
20
22
23
25
26
31
32
0
2
3
4
6
7
8
9
10
11
13
14
15
16
18
19
20
22
23
25
32
33
0
2
3
4
5
6
7
8
10
11
12
13
14
15
17
18
19
21
22
23
33
34
0
2
3
4
5
6
7
8
9
10
11
12
13
14
16
17
18
19
21
22
34
35
0
2
3
4
5
6
6
7
8
9
10
11
13
14
15
16
17
18
19
20
35
36
0
2
3
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
36
37
0
2
2
3
4
5
6
6
7
8
9
10
11
12
13
14
15
16
17
18
37
38
0
2
3
4
4
5
6
7
7
8
9
10
11
12
13
13
14
15
16
38
39
0
2
3
3
4
5
5
6
7
8
8
8
9
8
10
9
11
10
11
10
12
11
13
12
14
13
15
13
39
40
40
0
2
2
3
4
4
5
6
6
7
41
0
2
2
3
3
4
4
5
6
6
7
7
8
9
9
10
11
11
12
41
42
0
0
2
2
3
3
4
4
5
5
6
7
7
8
8
9
S
10
11
42
43
0
0
2
2
3
3
3
4
4
5
5
6
6
7
7
8
8
9
9
43
44
0
0
^
1
2
2
3
3
3
4
4
4
5
5
6
6
7
7
8
8
44
45
0
0
1
1
2
2
2
3
3
3
4
4
4
5
5
6
6
6
t
45
46
0
0
0
1
1
1
2
2
2
2
2
3
3
4
4
4
4
5
5
5
46
47
0
0
0
1
1
1
1
1
2
2
2
2
2
3
3
3
3
4
4
4
47
48
0
0
0
0
0
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
3
48
49
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
49
50
50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80" i 0"
Add.
i
Add.
c
V
1'
2'
3'
4'
5' 1
V 7' 8'
9' 10'
Ther.
Ther.
Mean refraction.
TABLE 22. [Page 529
Correction of the Mean Refraction for the Height of the Thermometer.
Ther.
Subt.
Mean refraction.
Ther.
Subt.
0'
V
2'
8'
4'
6'
6'
7'
8'
9'
10'
0"
80"
0"
30"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
II
0
1
2
3
4
5
6
6
7
8
9
10
11
12
13
0"
II
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
80"
II
0
1
2
3
4
5
6
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0"
80"
0"
o
50
51
52
53
54
55
56
57
58
59
II
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
II
0
0
0
0
0
0
0
0
0
2
2
II
0
0
0
0
0_
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
II
0
0
0
2
2
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
4
5
5
5
II
0
0
0
1
1
1
1
2
2
2
2
3
3
3
3
3
4
4
4
4
5
5
5
5
5
6
6
6
6
6
II
0
0
1
1
1
1
2
2
2
3
3
3
3
4
4
4
5
5
5
5
6
6
6
7
7
7
7
8
8
8
II
0
0
1
1
1
2
2
2
3
3
3
\
5
5
II
0
0
1
1
2
2
2
3
3
4
4
4
5
5
6
II
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
7
8
8
9
9
10
10
11
11
11
12
12
13
13
II
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
//
0
1
1
2
2
3
4
4
5
5
6
7
7
8
8
9
9
10
11
11
12
12
13
13
14
14
15
16
16
17
II
0
1
1
2
3
3
4
5
5
6
7
7
8
8
9
10
10
11
11
12
12
13
14
14
15
16
16
17
18
18
II
0
1
1
2
3
4
4
5
6
6
7
8
9
9
10
11
11
12
13
13
14
15
16
16
17
18
18
19
20
20
II
0
1
2
2
3
4
5
6
6
7
8
9
9
10
11
12
12
13
14
15
16
16
17
18
18
19
20
21
21
22
II
0
1
2
2
3
4
5
6
7
8
9
9
10
11
12
13
14
14
15
16
17
18
18
19
20
21
22
22
23
24
"
0
1
2
3
5
6
7
8
9
10
11
12
14
15
16
17
18
19
20
21
22
23
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
II
0
1
2
4
5
6
7
8
10
11
12
13
15
16
17
18
19
20
22
23
24
25
26
27
28
29
31
32
33
34
35
36
37
38
39
40
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
II
0
1
3
4
5
o
50
51
52
53
54
6
8
9
10
12
13
14
15
17
18
19
20
22
23
24
25
27
28
29
30
31
32
34
35
36
37
38
40
41
42
55
56
57
58
59
60
61
62
63
64
60
61
62
63
64
65
66
67
68
69
5 6
6 6
6i 7
6: 7
7i 8
14 |15
15 il6
16 117
16 !18
17 |l9
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
7
7
8
8
8
8
9
9
9
10
8
8
9
9
10
10
10
11
11
11
18
19
20
21
22
20
20
21
22
23
70
71
72
73
74
22 124
23 |25
24 126
25 127
26 28
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
7
8
8
8
.8
7
7
7
7
8
8
8
8
8
9
9
9
9
9
10
10
10
10
10
11
11
8
9
9
9
9
10
10
10
10
11
11
11
11
12
12
12
12
13
13
13
13
10
10
11
11
11
12
12
12
13
13
13
14
14
14
14
15
15
15
16
16
12
12
13
13
13
14
14
14
15
15
16
16
16
17
17
17
18
18
18
19
14
14
14
15
15
16
16
17
17
17
18
18
19
19
19
20
20
21
21
21
22
15
16
16
17
17
18
18
19
19
20
20
21
21
22
22
22
23
23
24
24
25
17
18
18
19
19
20
20
21
21
22
23
23
24
24
25
25
26
26
27
27
28
19
20
20
21
21
22
23
23
24
24
25
25
26
27
27
28
28
29
29
30
31
21
21
22
23
23
24
25
25
26
27
"27
28
29
29
m_
30
31
32
32
33
34
23
24
24
25
26
26
27
28
28
29
30
31
31
32
33
33
34
35
35
36
37
25
26
26
27
28
29
29
30
31
32
32
33
34
35
35
36
37
38
38
39
40
27 29
28 130
28 131
29 i31
30 32
31
32
33
34
35
36
37
38
38
39
40
41
42
43
44
45
46
47
48
49
50
80
81
82
83
84
31
32
32
33
34
35
36
37
37
38
39
40
41
41
42
43
33
34
35
36
37
38
39
39
40
41
42
43
44
44
45
46
43
44
45
46
48
49
50
51
52
53
54
55
56
58
59
60
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
95
96
97
98
99
100
16 19
100
Subt.
Then
0"
80"
0"
80"
0"
80"
0" 1 80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
Subt.
Ther.
0'
1'
2'
8'
4'
5'
6'
V
8'
9'
10'
Mean refraction.
22489—03-
-34
Page 530]
TABLES 23, 24.
TABLE 23.
Correction of the Moon's Altitude for parallax and re-
fraction corresponding to a mean
value of the hori-
zontal parallax, 57^ ?>W.
Moon's
alt.
Corr.
Moon's
alt.
Corr.
Moon's
alt.
Corr.
Moon's p
alt. C°'^'^-
» o
,
o
,
0
,
o
,
10
51
31
48
51
35
71
18
11
52
32
47
52
35
72
17
12
52
33
47
53
34
73
17
13
52
34
46
54
33
74
16
14
52
35
46
55
32
75
15
15
52
36
45
56
32
76
14
16
52
37
45
57
31
77
13
17
52
38
44
58
30
78
12
18
52
39
44
59
29
79
11
19
52
40
43
60
28
80
10
20
51
21
51
41 42
61
27
81
9
22
51
42 42
62
26
82
8
23
51
43 41
63
26
83
7
24
50
44
40
64
25
84
6
25
50
45
40
65
24
85
5
26
50
46
39
66
23
86
4
27
49
47
38
67
22
87
3
28
49
48
38
68
21
88
2
29
49
49
37
69
20
89
1
30
48
50
36
70
19
90
0
TABLE 24.
Correct]
on of tV
[B£
le Mooi
irometer
I's Apparent Altitude
30 inches.— Fahrenheit's 1
or Par
rhermon
allax and Refr
aeter, 50°.]
action.
Moon's
app. alt.
Horizontal parallax.
§
Correction for seconds of
parallax.— Add.
Corr. for
minutes
of alt.
54'
55'
56'
57'
58'
59'
60'
61'
0"
2"
4"
6"
8"
o r
,
//
/ II
' //
/ //
' II
/ II
1 II
/ //
//
II
II
II
II
„
5 0
43 56
44 56
45 56
46 56
47 56
48 55
49 55
50 55
0
0
2
4
6
8
10
44
11
45 11
46 11
47 11
48 11
49 10
50 10
51 10
10
10
12
14
16
18
20
25
25
25
25
25
24
24
24
20
20
22
24
26
28
30
89
39
38
38
38
38
37
37
30
30
32
34
86
38
40
52
51
51
51
51
51
51
51
40
40
42
44
46
48
50
45
4
46 3
47 3
48 3
49 3
50 3
51 3
52 3
52 13
50
0
50 1 52
0 2
54
4
56
6
58
8
6 0
45
15 46 15
47 14
48 14
49 14
50 13
51 13
10
26 1 26
25
25
25
25
25
25
10
10 12
14
16
18
20
36 36
36
35
35
34
34
34
20
20 22
24
26
28
30
46 1 46
45
45
45
44
44
44
30
30: 32
34
36
38
40
55
55
55
54
54
54
53
53
40
40 1 42
44
46
48
50
7 0
46
46
4
12
47 3
48 3
49 3
50 3
50 12
51 2
51 11
52 1
53 1
50
50
0
52
2
54
4
56
6
58
8
47 12
48 12
49 12
52 11
53 10
0
10
21
20
20
20
19
18
18
18
10
10
12
14
16
18
20
29
28
28
27
27
26
25
25
20
20
22
24
26
28
30
36
36
35
35
34
34
34
33
30
30 32
34
36
38
40
43
42
42
41
41
40
40
40
40
40 42
44
46
48
50
50
49
48
48
48
47
46
46
50
50 52
54
56
58
Add.
8 0
46
56 47 56
48 55
49 54
50 54
51 54
52 53
53 53
0
01 2
4
6
8
V \"
10
47
2 48 2
49 1
50 0
51 0
59
59
58
10
10 12
14
16
18
2 1
20
8' 7
7
6
6
52 5
53 4
54 4
20
20 ' 22
24
26
28
8 2
30
13 13
12
11
11
10
10
9
30
30 i 32
34
36
38
4 2
40
19 18
17
17
16! 16
15
• 14
40
40
42
44
46
48
5 3
50
9 0
24
23
22
49 26
22
50 26
21 20
19
53 24
19
50
0
50
0
52
2
54
4
56
6
58
8
6 4
7 4
47
28
48 27
51 25
52 24
54 23
10
33
32
31
30
30
29
28
27
10
10
12
14
16
18
8 5
20
37
36
35
34
34
33
32
32
20
20
22
24
26
28
9 5
30
41
41
40
39
38
37
37
36
30
30
32
34
36
38
40
45
44
43
43
42
41
40
39
40
40
42
44
46
48
50
49
48
47
46
46
45
44
44
50
49
51
53
55
57
TABLE 24. [Page 531 1
Correction of the Moon'tj Apparent Altitude for Parallax and Refraction. 1
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.] 1
Moon's
Horizontal parallax.
Correction for seconds of
parallax. — Add.
Corr.
for
app. alt.
minutes
of alt.
54'
56'
66'
67'
58'
59'
60'
61'
0"
2"
4"
6"
8"
O '
' //
/ //
/ //
' //
/ //
/ //
/ //
/ II
II
//
II
II
II
,/
Add.
10 0
47 53
48 52
49 51
50 50 51 50
52 48
53 48
54 47
0
0
2
4
6
8
V ^'
10
56
55
54
53 52
51
50
50
10
10
12
14
16
18
2 1
20
59
58
57
56 55
55
54
53
20
20
22
24
26
28
3 1
30
48 2
49 1
50 0
59 58
57
56
55
30
29
31
33
35
37
4 1
40
5
4
2
51 2 52 1
53 0
59
58
40
39
41
43
45
47
5 2
50
11 0
7
48 10
6
5
4 4
2
54 1
55 0
50
0
49
0
51
2
53
4
55
6
57
8
6 2
7 2
49 9
50 8
51 7 52 7
53 5
54 4
55 3
10
12
11
10
9 j 9
7
6
5
10
10
12
14
16
18
8 2
20
15
14
12
12 ! 11
9
8
7
20
20
22
24
26
28
9 3
30
17
16
14
13 13
11
10
9
30
29
31
33
35
37
40
19
18
17
15
15
13
12
11
40
39
41
43
45
47
50
21
20
49 21
18
17
17
52 17
15
14
13
50
0
49
0
51
2
53
4
55
6"
57
8
12 0
48 22
50 19
51 18
53 17
54 15
55 14
10
24
23
21
20
19
18
16
15
10
10
12
14
16
18
20
26
25
23
22
21
20
18
17
20
20
22
24
25
27
30
27
26
24
23
22
20
19
18
30
29
31
33
35
37
40
28
27
25
24
23
21
20
19
40
39
41
43
45
47
50
29
28
26
50 27
25
24
22
21
20
50
49
0
51
2
53
4
55
6
57
8
1 0
13 0
48 30
49 29
51 26
52 25
53 23
54 22
55 20
0
10
31
30
28
27
26
24
22
21
10
10
12
14
16
18
2 0
20
32
31
29
27
26
24
23
21
20
19
21
23
25
27
3 0
30
33
32
30
28
27
25
23
22
30
29
31
33
35
37
4 0
40
34
32
30
29
28
26
24
22
40
39
41
43
45
47
5 0
50
35
33
31
30
28
26
25
23
50
0
49
0
51
2
53
4
55
6
57
8
6 0
7 0
14 0
48 35
49 33
50 31
51 30
52 28
53 26
54 25
55 23
10
35
34
32
30
28
26
25
23
10
10
12
14
16
18
8 0
20
36
34
32
30
29
27
25
24
20
19
21
23
25
27
9 0
30
36
34
32
30
29
27
25
23
30
29
31
33
35
37
40
36
34
32
30
29
27
25
23
40
39
41
43
45
47
50
15 0
36
34
32
30
29
27
25
54 25
23
55 23
50
0
49
0
51
2
53
4
55
6
57
8
48 36
49 35
50 33
51 31
52 29
53 27
10
36
35
32
30
28
26
24
22
10
10
12
14
16
18
20
36
35
32
30
28
26
24
22
20
19
21
23
25
27
30
36
34
31
29
28
25
23
21
30
29
31
38
35
37
40
36
34
31
29
27
25
23
21
40
39
41
43
45
47
50
35
48 35
33
30
28
26
24
21
19
50
49
0
51
2
53
4
55
6
57
8
16 0
49 32
50 29
51 27
52 25
53 23
54 20
55 18
0
10
34
32
29
27
25
23
20
18
10
10
12
13
15
17
20
34
32
29
27
25
22
20
17
20
19
21
23
25
27
30
33
31
28
26
24
21
19
16
30
29
31
33
35
36
40
33
31
28
25
23
21
18
16
40
38
40
42
44
46
50
32
30
27
24
22
20
17
15
50
0
48
0
50
2
52
4
54
6
56
8
Sub.
17 0
48 31
49 29
50 26
51 23
52 21
53 18
54 16
55 13
10
30
28
25
22
20
17
14
12
10
10
12
13
15
17
2 0
20
28
26
23
20
18
15
12
10
20
19
21
23
25
27
3 0
30
27
25
22
19
17
14
11
9
30
29
31
33
34
36
4 0
40
26
24
21
18
16
13
10
7
40
38
40
42
44
46
5 1
50
26
48 24
23
20
17
15
52 13
12
53 10
9
6
50
48
0
50
2
52
4
53
6
55
8
6 1
7 1
18 0
49 21
50 18
51 15
54 7
55 4
0
10
23
20
17
14
12
9
6
3
10
10
11
13
15
17
8 1
20
22
19
16
13
11
8
5
2
20
19
21
23
25
27
9 1
30
21
18
15
12
10
6
3
0
30
29
30
32
34
36
40
20
17
14
10
8
4
1
54 58
40
38
40
42
44
46
50
19 0
18
15
12
9
51 7
6
52 4
2
53 59
56
50
48
0
50
2
51
4
53
6
55
8
48 16
49 13
50 10
53 0
53 57
54 55
0
10
15
12
8
5
2
52 59
55
53
10
10
11
13
15
17
20
13
10
6
3
0
57
53
51
20
19
21
23
25
27
30
12
8
5
2
51 58
55
51
49
30
29
30
32
34
36
40
10
6
3
0
56
53
49
47
40
38
40
42
44
46
50
9
5
2
50 58
55
51
48
45
50
48
50
51
53
55
Page 532] TABLE 21.
1
Correction of the Moon's Apparent Altitude for Parallax and Refraction. |
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
1
Moon's
Horizontal parallax.
"f d
Correction for seconds of
. parallax.— Add.
Corr.
for
app. alt.
C c
1^
minutes
of alt.
Sub
64'
66'
56'
57'
58'
69'
60'
61'
0"
II
2"
II
4"
II
6"
II
8"
o /
1 II
1 11^
/ II
/ //
/ II
/ //
/ //
' II
II
20 0
48 6
49 3
49 59
50 56
51 52
52 49
53 45
54 42
0
0
2
4
6
8
V ^'
10
5
2
58
55
51
47
43
40
10
9
11
13
15
17
2 0
20
3
0
56
52
49
45
41
37
20
19
21
23
24
26
3 1
30
1
48 58
53
50
46
42
38
35
30
28
30
32
34
36
4 1
40
59
56
52
48
44
40.
36
33
40
38
39
41
43
45
5 1
50
57
47 55
54
50
46
42
51 39
38
34
53 31
30
50
47
0
49
2
51
4
53
6
54
7
6 1
7 1
21 0
48 51
49 47
50 43
52 35
54 28
0
10
53
49
45
41
37
33
29
26
10
9
11
13
15
17
8 1
20
51
47
43
39
35
31
27
23
20
19
21
22
24
26
9 2
30
48
44
40
36
32
28
24
20
30
28
30
32
34
35
40
46
42
38
33
29
25
21
17
40
37
39
41
43
45
50
43
39
35
31
27
22
18
14
50
47
49
50
52
54
22 0
47 42
48 37
49 33
50 29
51 25
52 20
53 16
54 11
0
0
2
4
6
7
10
40
35
30
26
22
17
13
8
10
9
11
13
15
17
20
37
32 I 27
23
19
14
10
5
20
19
20
22
24
26
30
34
30 i 25
20
16
11
7
3
30
28
30
31
33
35
40
32
27 22
18
13
9
4
0
40
37
39
41
43
45
50
29
25 , 20
48 22 ! 49 17
15
11
6
52 3
1
53 57
50
46
0
48
2
50
4
52
6
54
7
23 0
47 27
50 13
51 8
52 58
53 54
0
10
25
20 1 15
10
5
0
55
51
10
9
11
13
15
17
20
22
17
12
7
2
51 57
52
48
20
18
20
22
24
26
30
19
14
9
4
0
54
49
45
30
28
29
31
33
35
40
16
11
6
1
50 57
51
46
42
40
37
39
40
42
44
50
13
8
3
49 0
49 58
49 55
54
50 50
48
43
38
50
0
46
0
48
2
50
4
51
5
53
7
1 0
24 0
47 10
48 5
51 45
52 40
53 35
10
8
3
48 57
52
47
42
37
32
10
9
11
13
15
16
2 1
20
5
0
54
49
44
39
33
28
20
18
20
22
24
26
3 1
30
2
47 57
51
46
41
35
30
24
30
27
29
30
32
34
4 1
40
46 59
54
48
43
38
32
27
21
40
36
38
40
42
44
5 2
50
25 0
56
51
47 48
45
40
49 37
35
50 31
29
51 26
23
52 20
18
50
46
0
47
2
49
4
51
5
53
7
6 2
7 2
46 58
48 42
53 14
0
10
50
45
39
33
28
22
16
10
10
9
11
13
14
16
8 2
20
46
41
35
29
24
18
12
6
20
18
20
22
24
25
9 3
30
43
38
32
26
20
14
8
3
30
27
29
31
33
34
40
40
34
28
23
17
11
5
52 59
40
36
38
40
42
43
50
37
46 34
31 i 25
19
49 16
14
7
1
56
50
45
47
49
51
52
26 0
47 28
48 22
50 10
51 4
51 58
52 52
0
0
2
4
5
7
10
31
25
19
13
7
1
54
48
10
9
11
13
14
16
20
27
21
15
9
3
50 57
50
44
20
18
20
22
23
25
30
24
18
12
6
49 59
53
46
40
30
27
29
31
32
34
40
20
14
8
,2
55
49
42
36
40
36
38
39
41
43
50
17
11
47 7
4
48 58
51
49 48
45
38
32
52"28
50
0
45
0
47
2
48
4
50
5
52
7
1 0
27 0
46 14
48 1
48 54
50 41
51 35
10
11
4
47 58
51
44
37
31
24
10
9
11
12
14
16
2 1
20
7
1
54
r 47
40
33
27
20
20
18
20
21
23
25
3 1
30
3
46 57
50
43
36
29
23
16
30
27
28
30
32
34
4 1
40
45 59
53
46
39
32
25
19
12
40
36
37
39
41
43
5 2
50
56
45 53"
49
46 46
42
47 38
35
48 31
28
21
15
8
50
44
46
48
50
52
6 2
7 3
28 0
49 24
50 17
51 11
52 4
0
0
2
4
5
7
10
49
42
34
27
20
13
6
5159
10
9
11
12
14
16
8 3
20
45
38
30
23
16
9
2
55
20
18
19
21
23
25
9 3
30
41
34
26
19
12
5
50 57
50
30
26
28
30
32
33
40
37
30 23
15
8
1
54
46
40
35
37
39
41
42
50
34
26
46 22
19
47 15
11
4
49 0
49 57
49 53
49
42
50
44
46
2
48
4
49
5
51
7
29 0
45 30
48 7
50 45
5138
0
0
10
26
18
11
3
48 56
49
40
34
10
9
10
12
14
16
20
22
14
7
47 59
52
44
36
29
20
17
19
21
23
24
30
18
10
2
55
47
39
31
24
30
26
28
30
31
33
40
14
6
46 58
51
43
35
27
20
40
35
37
38
40
42
50
11
3
55
47
39
31
23
15
50
44
45
47
49
51
TABLE 24.
[Page 533 1
Correction of the Moon
's Apparent Altitude for Parallax and Refraction. 1
[Barometer
30 inches
.—Fahrenheit's Thermometer 50°.] 1
Moon's
Horizontal parallax
-5^
Correction for seconds of
paraillax.— Add.
Corr.
for
app. alt.
is
minutes
of alt.
54'
66'
56'
57'
58'
69'
60'
61'
0"
2"
4"
II
6"
II
8"
o /
/ //
/ II
/ //
/ //
/ //
/ //
/ II
/ //
„
//
II
II
Sub.
30 0
45 6
45 57
46 50
47 42
48 34
49 26
50 18
51 10
0
0
2
3
5
7
V 0''
10
2
54
46
38
30
22
13
6
10
9
10
12
14
16
2 1
20
44 58
50
42
34
26
18
9
1
20
17
19
21
23
24
3 1
30
54
46
37
29
21
13
4
50 56
30
26
28
29
31
33
4 2
40
50
42
33
25
17
8
0
52
40
35
36
38
40
42
5 2
50
31 0
45
44 41
38
29
21
12
4
49 55
47
50 42
50
0
43
0
45
2
47
3
49
5
50
7
6 3
7 3
45 33
46 24
47 16
48 7
48 59
49 50
10
37
29
20
12
2
54
45
37
10
9
10
12
14
15
8 4
20
33
24
15
7
47 58
49
40
32
20
17
19
21
22
24
9 4
30
28
20
11
2
54
45
36
27
30
26
27
29
31
32
40
24
16
7
46 58
49
40
31
22
40
34
36
38
39
41
50
20
. 11
2
53
44
35
26
49 22
17
50 13
50
0
43
0
44
2
46
3
48
5
50
7
32 0
44 15
45 7
45 58
46 49
47 40
48 31
10
11
3
53
44
35
26
17
8
10
8
10
12
14
15
20
7
44 58
48
39
30
21
11
2
20
17
19
20
22
24
30
3
53
44
34
25
16
6
49 57
30
25
27
29
30
32
40
43 58
48
39
29
20
11
1
52
40
34
35
37
39
41
50
54
44
34
24
15
6
48 56
47
50
42
0
44
2
46
3
47
5
49
7
1 0
33 0
43 48
44 39
45 29
46 19
47 10
48 0
48 50
49 41
0
10
44
34
25
15
5
47 55
45
36
10
8
10
12
13
15
2 1
20
40
30
20
10
0
50
40
31
20
17
18
20
22
23
3 1
30
35
25
15
5
46 55
45
35
25
30
25
27
28
30
32
4 2
40
30
20
10
0
50
40
30
20
40
33
35
37
38
40
5 2
50
34 0
25
15
5
45 55
45
35
24
14
50
42
43
45
47
48
6 3
7 3
43 21
44 11
45 0
45 50
46 40
47 30
48 19
49 9
0
0
2
3
5
7
10
16
6
44 55
45
34
24
14
3
10
8
10
12
13
15
8 4
20
11
1
50
40
29
19
9
48 58
20
17
18
20
21
23
9 4
30
6
43 56
45
35
24
13
3
52
30
25
26
28
30
31
40
1
51
40
30
19
8
47 58
47
40
33
35
36
38
40
50
42 56
46
35
24
14
3
46 58
52
42
50
0
41
0
43
2
44
3
46
5
48
7
35 0
42 52
43 41
44 30
45 19
46 9
47 47
48 36
10
47
36
25
14
3
52
41
30
10
8
10
11
13
15
20
42
31
20
9
45 58
47
• 36
25
20
16
18
20
21
23
30
37
26
15
3
52
41
30
19
30
24
26
28
29
31
40
32
21
10
44 58
47
36
25
14
40
33
34
36
38
39
50
27
16
4
53
42
30
46 25
19
8
48 2
50
0
41
0
42
2
44
3
46
5
47
6
36 0
42 22
43 11
43 59
44 48
45 37
47 14
10
17
5
54
42
31
19
8
47 56
10
8
10
11
13
14
1 1
20
12
0
48
37
25
14
2
50
20
16
18
19
21
23
2 1
30
7
42 55
43
31
20
8
46 56
44
30
24
26
27
29
31
3 2
40
1
50
38
26
14
2
50
39
40
32
34
35
37
39
4 2
50
41 56
44
32
20
8
45 56
45 51
44
33
50
40
0
42
2
43
3
45
5
47
6
5 3
6 3
37 0
41 51
42 39
43 27
44 15
45 3
46 39
47 27
0
10
46
34
21
9
44 57
45
33
21
10
8
10
11
13
14
7 4
20
41
29
16
4
52
40
27
15
20
16
17
19
21
22
8 4
30
35
23
11
43 58
46
34
21
9
30
24
25
27
29
30
9 5
40
30
18
5
53
40
28
15
3
40
32
33
35
37
38
50
25
41 19
12
42 59
47
34
44 29
22
45 16
9
46 3
46 57
46 51
50
0
40
0
41
2
43
3
45
5
46
6
38 0
42 7
42 54
43 41
10
14
2
49
36
23
10
45 57
45
10
8
9
11
13
14
20
8
41 56
43
30
17
4
51
38
20
16
17
19
20
22
30
3
51
38
24
12
44 58
45
32
30
23
25
27
28
30
40
40 58
45
32
18
6
52
39
26
40
31
33
35
36
38
50
52
39
26
42 20
13
43 7
0
43 54
46
44 40
33
20
50
39
0
41
2
42
3
44
5
46
6
39 0
40 47
41 33
45 27
46 13
0
10
42
28
15
1
48
34
21
7
10
8
9
11
12
14
1 1
20
36
23
9
42 55
42
28
15
1
20
15
17
19
20
22
2 1
30
30
17
3
49
36
22
8
45 54
30
23
25
26
28
29
3 2
40
25
11
41 57
43
30
16
2
48
40
31
32
34
36
37
4 2
50
19
5
51
37
23
9
44 55
42
50
39
40
42
43
45
5 3
Page 534]
TABLE 24.
1
Correction of the Moon's Apparent Altitude for Parallax and Eefraction. |
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
-
Correction for .seconds of
parallax. — Add.
Corr.
for
minutes
of alt.
54'
56'
56'
57'
58'
59'
60'
61'
0"
//
2"
II
4"
II
6"
II
8"
II
0 /
/ //
1 II
/ //
1 II
/ //
/ II
' II
/ II
Sub.
40 0
40 14
41 9
41 46
42 32
43 18
44 4
44 60
45 36
0
0
2
3
6
6
6' W
10
8
40 54
39
26
11
43 57
43
29
10
8
9
11
12
14
7 4
20
2
48
33
19
6
50
36
22
20
15
17
18
20
21
8 5
30
39 66
42
28
13
42 59
44
30
16
30
23
24
26
27
29
9 6
40
50
36
22
7,
53
38
24
9
40
30
32
34
35
37
50
45
30
16
1
47
32
18
44 11
3
60
38
0
40
2
41
3
43
5
44
6
41 0
39 39
40 24
41 10
41 55
42 41
43 26
44 56
0
10
33
18
4
49
34
19
4
49
10
8
9
11
12
14
20
27
12
40 58
43
28
13
43 58
43
20
16
17
18
20
21
30
21
6
51
36
22
7
51
37
30
23
24
26
27
29
40
16
0
45
30
16
0
46
30
40
30
32
33
35
36
50
10
39 54
39
24
9
42 63
38
43 31
23
50
38
0
39
1
41
3
42
4
44
6
42 0
39 4
39 48
40 33
41 17
42 2
42 47
44 16
0
10
38 58
42
27
11
41 66
41
25
10
10
7
9
10
12
13
1 1
20
52
36
21
6
60
34
18
3
20
16
16
18
19
21
2 1
30
46
30
14
40 68
43
27
11
43 56
30
22
24
25
27
28
3 2
40
40
24
8
52
36
21
6
49
40
30
31
33
34
36
4 2
50
34
18
2
46
30
14
42 68
42
50
37
0
38
1
40
3
41
4
43
6
5 3
6 4
43 0
38 28
39 12
39 56
40 40
41 24
42 8
42 52
43 36
0
10
22
6
50
34
18
1
45
29
10
7
9
10
12
13
7 4
20
16
38 59
43
27
11
41 64
38
22
20
15
16
18
19
20
8 5
30
10
53
37
20
5
48
31
15
30
22
23
25
26
28
9 6
40
4
47
30
14
40 58
41
24
8
•40
29
31
32
34
36
50
37 57
37 51
41
38 35
24
7
51
34
17
42 10
1
50
0
37
0
38
1
39
3
41
4
42
6
44 0
39 18
40 1
40 44
41 27
42 54
10
45
28
11
39 54
37
20
3
46
10
7
9
10
11
13
20
38
21
4
47
30
13
41 56
39
20
14
16
17
19
20
30
32
15
38 58
41
24
7
49
32
30
21
23
24
26
27
40
26
9
51
34
17
0
42
25
40
29
30
31
33 34
50
20
2
44
27
10
40 63
35
41 28
18
42 11
60
0"
36
0
37
1
39
3
40 i 41
1 1
45 0
37 14
37 56
38 38
39 21
40 3
40 46
4
6
10
7
49
31
14
39 66
39
21
3
10
7
8
10
11
13
2 1
20
0
43
25
7
49
32
14
41 56
20
14
15
17
18
20
3 2
30
36 54
37
18
1
43
26
7
49
30
21
23
24
25
27
4 3
40
48
30
11
38 64
36
18
0
42
40
28
30
31
32
34
5 3
50
4(5 0
41
23
4
47
29
11
40 52
34
50
35
0
37
1
38
3
39
4
41
6
6 4
7 5
36 35
37 17
37 58
38 40
39 22
40 4
40 45
41 27
0
10
29
10
51
33
16
39 67
38
20
10
7
8
10
11
12
8 6
20
22
3
44
26
8
49
31
12
20
14
15
17
18
19
9 6
30
16
36 57
38
20
1
42
24
6
30
21
22
23
25
26
40
9
50
32
13
38 54
36
17
40 58
40
28
29
30
32
33
50
47 0
2
35 56
43
36 37
25
37 18
6
47
28
9
50
50
35
36
1
37
3
39
4
40
6
37 59
38 40
39 21
40 2
40 43
0
0
10
49
30
11
52
34
14
39 66
36
10
7
8
10
11
12
20
42
23
4
45
26
6
47
28
20
14
15
16
18
19
30
36
17
36 57
38
19
38 69
40
21
30
20
22
23
24
26
40
30
10
50
31
12
62
32
13
40
27
29
30
31
33
50
23
35 16
3
35 56
43
36 36
24
5
46
26
39 17
5
39 58
60
0
34
0
35
1
37
3
38
4
39
5
1 1
48 0
37 17
37 57
38 37
10
10
50
30
10
50
30
10
60
10
7
8
9
11
12
2 1
20
3
43
23
2
43
22
2
42
20
13
15
16
17
19
3 2
30
34 56
36
16
36 55
35
15
38 66
34
30
20
21
23
24
26
4 3
40
49
29
9
48
28
8
48
27
40
27
28
29
31
32
5 3
50
49 0
42
34 35
22
35 15
1
41
21
0
40
19
50
0
33
0
35
1
36
3
37 39
6 4
7 6
35 64
36 34
37 13
37 53
38 32
39 11
4
5
10
29
8
47
27
6
46
25
4
10
7
8
9
10
12
8 5
20
22
1
40
20
36 59
38
17
38 56
20
13
14
16
17
18
9 6
30
15
34 54
33
12
51
30
9
48
30
20
21
22
23
25
40
8
47
26
6
44
23
2
41
40
26
27
29
30
31
50
1
40
19
35 58
36
15
37 54
33
50
33
34
35
36
38
TABLE 24.
[Page 635
Correction of the Moon's Apparent Altitude
for Parallax and Refraction. 1
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
o 2
Correction for seconds of
parallax.— Add.
Corr.
for
minutes
of alt.
54'
55'
56'
57'
68'
59'
60'
61'
0"
2"
4"
6"
8"
o »
' //
' It
' //
' II
/ II
' II
' //
' //
II
//
II
II
II
II
50 0
33 54
34 33
35 11
35 50
36 29
37 8
37 46
38 25
0
0
1
3
4
5
10
47
26
4
43
21
0
38
17
10
6
8
9
10
12
20
40
19
34 57
36
14
36 53
31
9
20
13
14
15
17
18
30
33
11
49
28
6
45
23
1
30
19
20
22
23
24
40
26
4
42
20
35 58
37
15
37 53
40
26
27
28
29
31
50
19
33 57
35
34 28
13
51
29
7
45
50
0
32
0
33
1
35
3
36
4
37
5
Sub.
51 0
33 12
33 50
35 6
35 44
36 22
36 59
37 37
10
5
43
21
34 58
36
14
51
29
10
6
8
9
10
11
2 1
20
32 58
36
13
50
28
6
43
21
20
13
14
15
16
18
3 2
30
51
29
6
43
21
35 58
36
13
30
19
20
21
23
24
4 3
40
44
22
33 59
36
14
50
28
5
40
25
26
28
29
30
5 4
50
37
14
51
33 44
28
6
34 58
42
20
36 12
36 57
36 49
50
0
31
0
33
1
34
2
35
4
36
5
6 4
7 5
52 0
32 30
33 7
34 21
35 35
10
23
0
36
13
50
27
4
41
10
6
7
9
10
11
8 6
20
15
32 52
29
6
43
19
35 56
33
20
12
13
15
16
17
9 6
30
8
45
21
33 58
35
11
48
24
30
18
20
21
22
23
40
1
38
14
50
27
3
40
16
40
24
26
27
28
29
50
31 54
31 47
31
7
43
19
34 11
34 55
32
8
50
31
32
1
33
2
34
4
35
5
53 0
32 23
32 59
33 35
34 47
35 24
36 0
0
0
10
39
15
51
27
3
39
15
35 51
10
6
7
8
10
11
20
32
8
44
20
33 56
31
7
43
20
12
13
14
16
17
30
25
0
36
12
48
23
34 59
35
30
18
19
20
22
23
40
17
31 53
28
4
40
15
51
27
40
24
25
26
28
29
50
10
46
31 38
21
32 57
32
7
43
34 35
19
50
0
30
0
31
1
32
2
34
4
35
5
54 0
31 3
32 13
32 49
33 24
33 59
35 10
10
30 55
30
5
41
16
51
26
1
10
6
7
8
9
11
20
48
22
31 57
33
8
43
18
34 53
20
12
13
14
15
16
30
40
15
49
25
0
35
10
45
30
18
19
20
21
22
40
33
8
42
17
32 52
27
1
37
40
23
25
26
27
28
50
26
0
35
9
44
19
33 53
33 45
28
34 19
50
0
29
0
30
1
32
2
33
3
34
5
55 0
30 18
30 52
31 27
32 1
32 36
33 10
10
10
45
19
31 53
28
2
36
11
10
6
7
8
9
10
20
3
38
12
46
20
32 54
28
3
20
11
13
14
15
16
30
29 55
30
4
38
12
46
20
33 54
30
17
18
19
20
22
40
48 .
22
30 56
30
4
37
11
45
40
23
24
25
26
27
50
56 0
40
14
48
30 40
22
31 14
31 55
29
3
32 55
37
50
28
30
1
31
2
32
3
33
4
29 33
30 7
31 47
32 21
33 28
0
0
10
25
29 59
32
6
39
13
46
20
10
6
7
8
9
10
20
18
51
24
30 58
31
4
37
11
20
11
12
13
14
16
30
10
43
16
50
23
31 56
29
2
30
17
18
19
20
21
1 1
40
3
36
9
42
15
48
21
32 54
40
22
23
24
25
27
2 2
50
28 55
28
1
34»
7
40
12
45
50
28
0
29
1
30
2
31
3
32
4
3 2
4 3
57 0
28 47
29 20
29 53
30 25
30 58
31 31
32 3
32 36
0
10
39
12
45
17
50
22
31 55
27
10
5
6
7
9
10
5 4
20
32
5
37
9
42
14
47
19
20
11
12
13
14
15
6 5
30
24
28 57
29
1
33
6
38
10
30
16
17
18
19
21
7 5
40
17
49
21
29 53
25
30 57
29
1
40
22
23
24
25
26
8 6
50
58 0
9
41
13
45
17
49
21
3152
50
27
0
28
1
29
2
30
3
31
4
9 7
28 1
28 33
29 5
29 37
30 9
30 41
31 12
3144
0
10
27 53
25
28 57
28
0
32
4
35
10
5
6
7
8
9
20
45
17
49
• 20
29 52
23
30 55
26
20
10
12
13
14
15
30
38
9
41
12
44
15
46
17
30
16
17
18
19
20
40
30
1
33
4
35
6
38
9
40
21
22
23
24
25
50
22
27 14
27 53
27 45
24
28 55
27
29 58
29 49
29
30 20
0
50
26
0
27
1
28
2
29
3
30
4
59 0
28 16
28 47
29 18
30 51
0
10
6
37
7
38
9
40
11
42
10
5
6
7
8
9
20
26 58
29
27 59
30
1
31
2
33
20
10
11
12
13
14
30
51
21
51
22
28 53
23
29 54
24
30
15
16
17
18
19
40
43
13
43
14
44
14
45
15
40
20
21
22
23
24
50
35
5
35
5
36
6
36
A
50
25
26
27
29
30
Page 536]
TABLE 24.
Dorrection of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
§2
Correction for seconds of
parallax.— Add.
Corr.
for
minutes
64'
55'
56'
57'
58'
59'
60'
61'
IS
0"
2"
II
4"
II
6"
II
8"
II
of alt.
o /
/ It
/ //
' II
' II
/ //
' //
' II
' II
II
//
60 0
26 26
26 67
*^7 27
27 57
28 27
28 57
29 27
29 67
0
0
1
2
3
4
10
19
49
19
49
19
49
18
48
10
6
6
7
8
9
20
11
41
11
40
10
40
9
39
20
10
11
12
13
14
30
3
32
2
31
1
31
0
30
30
16
16
17
18
19
40
25 55
24
26 63
23
27 63
22
28 61
21
40
20
21
22
23
24
50
47
16
46
14
44
13
42
12
50
26
0
26
1
27
2
28
3
29
4
61 0
25 39
26 8
26 37
27 6
27 36
28 5
28 34
29 3
0
10
31
0
29
26 58
27
27 56
26
28 54
10
5
6
7
8
9
20
23
26 62
20
49
18
47
16
45
20
10
11
12
12
13
30
16
43
12
40
10
38
7
35
30
14
16
16
17
18
40
7
36
4
32
1
29
27 58
26
40
19
20
21
22
23
50
24 59
27
25 65
24
26 62
20
49
17
50
0
24
0
25
1
26
2
27
3
28
4
62 0
24 50
25 19
25 47
26 15
26 43
27 11
27 40
28 8
10
42
10
38
6
34
2
30
27 68
10
5
6
6
7
8
20
34
2
29
25 57
25
26 53
21
49
20
9
10
11
12
12
30
26
24 54
21
49
17
45
12
40
30
14
15
16
17
18
40
18
46
13
41
8
36
3
31
40
19
19
20
21
22
50
10
37
4
32
25 59
27
26 54
21
50
23
24
26
26
27
63 0
24 2
24 29
24 56
26 23
25 51
26 18
26 45
27 12
0
0
1
2
3
4
10
23 54
21
48
15
42
9
36
3
10
4
5
6
7
8
20
46
13
39
6
33
0
27
26 64
20
9
10
11
12
13
30
37
4
31
24 68
24
25 51
18
45
30
13
14
15
16
17
40
29
23 55
22
49
15
42
8
35
40
18
19
20
21
22
50
20
47
13
40
6
33
25 59
26
50
22
0
23
1
24
2
26
3
26
3
64 0
23 12
23 39
24 6
24 32
24 58
26 24
25 50
26 17
0
10
4
31
23 67
23
49
16
41
8
10
4
6
6
7
8
20
22 56
22
48
14
40
6
32
26 58
20
9
10
10
11
12
30
47
13
39
5
31
24 57
22
48
30
13
14
16
16
16
40
39
5
30
23 56
22
48
13
39
40
17
18
19
20
21
50
31
22 67
22
48
13
39
4
24 55
30
25 21
60
0
22
0
23
1
23
2
24
2
25
3
Sub.
65 0
22 23
22 48
23 13
23 39
24 4
24 30
10
14
40
5
30
23 56
20
46
11
10
4
6
6
7
7
V V
20
6
31
22 56
21
46
11
36
1
20
8
9
10
11
12
2 2
30
21 58
23
48
13
37
2
27
24 52
30
13
13
14
16
16
3 3
40
49
14
39
4
28
23 63
18
43
40
17
18
18
19
20
4 4
50
41
6
30
22 55
19
44
8
33
60
0
21
0
22
1
23
2
23
2
24
3
5 5
6 5
66 0
21 32
21 57
22 21
22 46
23 10
23 35
23 59
24 23
10
24
48
12
37
1
25
49
14
10
4
6
6
7
7
7 6
20
15
39
3
28
22 52
16
40
4
20
8
9
10
11
11
8 7
30
7
31
21 55
19
43
6
31
23 55
30
12
13
14
15
16
9 8
40
20 59
22
46
10
34
22 67
21
45
40
16
17
18
19
20
50
50
20 41
14
21 5
37
1
25
22 15
48
22 39
12
23 2
36
50
20
0
21
1
22
2
23
2
24
3
67 0
21 28
21 52
23 26
0
10
33
20 56
19
43
6
29
22 52
16
10
4
5
5
6
7
20
25
48
11
34
21 57
20
43
7
20
8
8
9
10
11
30
16
39
2
25
48
11
34
22 57
30
12
12
13
14
15
40
8
30
20 63
16
39
2
24
47
40
16
16
17
18
18
50
19 59
21
44
7
20 68
30
21 21
21 52
15
37
50
19
0
20
1
21
1
22
2
22
3
68 0
19 50
20 13
20 36
21 43
22 6
22 28
0
10
42
4
27
49
12
34
21 66
19
10
4
4
5
6
7
20
33
19 56
18
40
2
24
47
9
20
7
8
9
9
10
30
25
47
9
31
20 53
16
37
21 59
30
11
12
13
13
14
40
16
38
0
22
44
5
27
49
40
16
16
16
17
18
50
7
29
19 21
19 51
19 42
13
20 4
34
20 25
20 56
17
21 8
39
21 30
60
0
18
0
19
1
20
1
21
2
21
3
69 0
18 59
20 47
10
50
12
33
19 65
16
37
20 59
20
10
4
4
5
6
6
20
42
3
24
45
7
28
49
10
20
7
8
8
9
10
30
33
18 64
15
36
19 57
18
39
0
30
11
11
12
13
13
40
24
45
6
27
48
9
29
20 50
40
14
16
16
16
17
50
16
37
18 67
18
39
0
20
41
50
18
18
19
20
20
TABLE 24.
[Page 537 1
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
Horizontal parallax.
Correction for seconds of
parallax.— Add.
Corr.
for
app. alt.
minutes
of alt.
64'
55'
56'
57'
58'
59'
60'
61'
0"
2"
4"
6"
8"
o /
1 II
/ II
' H
/ //
' II
/ //
/ II
/ //
II
//
II
//
II
II
70 0
18 7
18 28
18 48
19 9
19 30
19 50
20 11
20 31
0
0
1
1
2
3
10
17 58
19
39
0
20
41
1
21
10
3
4
5
5
6
20
50
10
30
18 50
11
31
19 51
11
20
7
7
8
9
9
30
41
1
21
41
1
21
41
1
30
10
11
11
12
13
40
32
17 53
12
32
18 52
12
32
19 52
40
13
14
15
15
16
50
24
44
17 35
3
23
18 14
43
3
18 53
22
42
50
17
0
17
1
18
1
19
2
19
3
71 0
17 15
17 54
18 34
19 12
19 32
0
10
6
26
45
5
24
43
3
22
10
3
4
4
5
6
20
16 57
17
36
17 55
14
33
18 53
12
20
6
7
8
8
9
30
48
8
27
46
5
24
43
2
30
10
10
11
12
12
40
40
16 59
18
37
17 56
15
34
18 52
40
13
13
14
15
15
50
31
50
9
28
47
17 37
5
24
42
50
16
0
17
1
17
1
18
2
19
2
72 0
16 22
16 41
17 0
17 18
17 55
18 14
18 32
0
10
13
32
16 50
9
27
46
4
22
10
3
4
4
5
5
20
5
23
41
16 59
18
36
17 54
12
20
6
7
7
8
8
30
15 57
14
32
50
9
27
45
3
30
9
10
10
11
11
40
48
5
23
41
16 59
17
35
17 53
40
12
13
13
14
14
50
39
15 56
14
32
16 22
50
16 40
7
25
43
17 33
50
0
15
0
16
1
16
1
17
2
18
2
73 0
15 30
15 47
16 5
16 58
17 15
10
21
38
15 56
13
30
48
5
23
10
3
3
4
5
5
20
12
29
47
4
21
39
16 56
13
20
6
6
7
7
8
30
3
20
37
15 55
12
29
46
3
30
9
9
10
10
11
40
14 54
11
28
45
2
19
36
16 53
40
11
12
13
13
14
50
45
2
14 53
19
35
15 52
15 42
9
26
42
50
14
15
15
16
2
17
2
Sub.
74 0
14 36
15 9
15 26
15 59
16 16
16 32
0
0
1
1
10
28
44
0
17
33
49
6
22
10
3
3
4
4
5
Y 1//
20
19
35
14 51
8
24
40
15 56
12
20
0
6
6
7
8
2 2
30
10
26
42
14 58
14
30
46
2
30
8
9
9
10
11
3 3
40
1
17
33
49
5
20
36
15 52
40
11
11
12
12
13
4 4
50
75 0
13 52
8
23
39
14 55
10
26
42
50
13
14
1
14
1
15
16
5 5
6 6
13.43
13 59
14 14
14 29
14 45
15 1
15 16
15 32
0
0
2
2
10
34
50
5
20
36
14 52
7
22
10
3
3
4
4
5
7 7
20
25
41
13 56
11
27
42
14 57
12
20
5
6
6
7
7
8 8
30
16
32
46
1
17
32
47
2
30
8
8
9
9
10
9 9
40
7
22
37
13 52
7
22
37
14 51
40
10
11
11
12
12
50
12 58
13
28
42
13 57
13 47
12
27
41
50
13
0
13
0
14
1
14
1
15
2
76 0
12 49
13 4
13 18
13 33
14 2
14 17
14 31
0
10
41
12 55
9
24
38
13 53
7
21
10
2
3
3
4
4
20
32
46
0
14
28
43
13 57
11
20
5
5
6
6
7
30
23
37
12 51
5
19
33
47
1
30
7
8
8
8
9
40
14
27
41
12 55
9
23
36
13 50
40
9
10
10
11
11
50
5
18
32
45
12 59
13
26
40
50
12
12
13
13
14
77 0
11 56
12 9
12 22
12 36
12 49
13 3
13 16
13 30
0
0
0
1
1
2
10
47
0
13
27
40
12 53
7
20
10
2
3
3
4
4
20
38
11 51
4
17
30
43
12 57
10
20
4
5
5
6
6
30
29
42
11 55
8
21
33
47
0
30
7
7
7
8
8
40
19
32
45
11 58
11
23
36
12 49
40
9
9
9
10
10
50
10
23
35
48
1
13
12 4
26
12 16
39
50
11
0
11
0
12
1
12
1
13
2
78 0
11 1
11 14
11 26
11 39
11 52
12 29
0
10
10 52
5
17
30
42
11 54
6
19
10
2
2
3
3
4
20
43
10 55
8
20
32
44
11 56
8
20
4
4
5
5
6
30
34
46
10 58
10
22
34
46
11 58
30
6
6
7
7
8
40
25
37
48
0
12
24
36
48
40
8
8
9
9
10
50
79 0
16
28
39
10 51
3
15
26
38
50
10
0
10
0
11
1
11
1
12
1
10 7
10 19
10 30
10 42
10 53
11 5
11 16
11 28
0
10
9 58
9
21
32
43
10 55
6
17
10
2
2
3
3
3
20
49
0
11
22
33
44
10 56
7
20
4
4
4
5
5
30
40
9 50
1
12
23
34
45
10 56
30
6
6
6
7
7
40
31
41
9 52
3
13
24
35
46
40
7
8
8
8
9
50
22
32
43
9 54
4
15
25
36
50
9
10
10
10
11
Page 538]
TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer
30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
•a .2
5g
Correction for seconds of
parallax.— Add.
Corr.
for
minutes
54'
55'
66'
57'
58'
69'
60'
61'
■ji "^
0"
2"
4"
6"
8"
of alt.
o /
' n
' "•!
' II
/ //
/ //
/ //
/ //
/ //
II
II
II
II
II
II
80 0
9 13
9 23
9 34
9 44
9 55
10 5
10 15
10 26
0
0
0
1
1
1
10
3
14
24
34
45
9 55
5
15
10
2
2
2
3
3
20
8 54
4
14
24
35
45
9 55
5
20
3
4
4
4
5
30
45
8 55
5
15
25
35
45
9 54
30
5
5
6
6
6
40
36
46
8 55
5
15
25
35
44
40
/
7
7
8
8
50
27
37
46
8 37
8 56
6
15
25
9 14
34
50
8
0
9
0
9
1
9
1
10
1
81 0
8 18
8 27
8 46
8 56
9 5
9 24
0
10
9
18
27
36
46
8 55
4
13
10
1
2
2
2
3
20
7 59
8
17
26
36
45
8 54
3
20
3
3
4
4
4
30
50
7 59
8
17
26
35
44
8 52
30
4
5
5
5
6
40
41
50
7 59
8
17
25
34
42
40
6
6
6
7
7
50
32
41
49
7 58
7
15
24
8 13
32
50
0
7
0
8
0
8
1
8
1
9
1
82 0
7 23
7 31
7 40
7 48
7 57
8 5
8 22
10
14
22
30
38
47
7 55
3
11
10
1
2
2
2
2
20
4
12
20
28
37
45
7 52
0
20
3
3
3
3
4
30
6 55
3
11
19
27
35
42
7 50
30
4
4
5
5
5
40
46
6 54
2
10
17
25
32
40
40
5
6
6
6
6
50
37
45
6 52
0
6 50
1
15
7 5
22
7 12
30
50
7
7
0
7
0
7
1
8
1
Sub.
83 0
6 28
6 35
6 43
6 57
7 20
0
0
10
19
26
33
40
47
6 54
2
9
10
1
1
2
2
2
V V
20
9
16
23
30
37
44
6 51
6 58
20
2
3
3
3
3
2 2
30
0
1
13
20
27
34
41
48
.30
3
4
4
4
4
3 3
40
5 51
5 58
4
11
18
24
31
38
40
5
5
5
5
6
4 4
50
42
49
5 39
5 55
1
8
14
21
27
50
6
6
6
0
6
1
7
1
5 5
6 6
84 0
5 33
5 45
5 52
5 58
6 4
6 10
6 17
0
0
0
10
23
30
36
42
48
5 54
0
6
10
1
1
1
2
2
7 7
20
14
20
26
32
38
44
5 50
5 55
20
2
2
2
3
3
8 8
30
5
10
16
22
28
34
39
45
30
3
3
3
3
4
9 9
40
4 56
1
1
13
18
24
29
35
40
4
4
4
4
5
50
85 0
47
4 52
4 58
4 48
3
4 53
8
14
19
25
50
5
0
5
0
5
0
5
0
6
1
4 37
4 43
4 58
5 4
5 9
5 14
0
10
28
33
38
43
48
4 53
4 58
3
10
1
1
1
1
1
20
18
24
28
33
38
43
48
4 53
20
2
2
2
2
2
30
9
14
19
23
28
33
38
43
30
2
3
3
3
3
40
0
5
10
14
19
23
28
33
40
3
3
4
4
4
50
86 0
3 51
3 56
0
5
9
3 59
13
18
22
50
4
0
4
0
4
0
5
0
5
1
3 42
3 46
3 50
3 55
4 3
4 7
4 11
0
10
33
37
41
45
49
3 53
3 57
1
10
1
1
1
1
1
20
23
27
31
35
39
43
46
3 50
20
1
1
2
2
2
30
14
18
21
25
29
33
36
40
30
2
2
2
2
2
40
5
9
12
16
19
23
26
30
40
3
3
3
3
3
50
2 56
2 59
3
2 53
6
9
13
16
19
50
0
3
0
3
0
3
0
4
0
4
0
87 0
2 47
2 50
2 56
2 59
3 2
3 5
3 9
10
37
40
43
46
49
2 52
2 55
2 58
10
0
1
1
1
1
20
28
31
33
36
39
42
45
47
20
1
1
1
1
1
30
19
21
24
26
29
32
34
37
30
1
1
2
2
2
40
10
12
15
17
19
22
24
27
40
2
2
2
2
2
50
1
3
5
7
9
12
14
16
50
2
2
0
2
0
3
0
3
0
88 0
1 51
1 53
1 55
1 57
1 59
2 2
2 4
2 6
0
0
10
42
43
45
47
49
1 51
1 53
1 55
10
0
0
0
0
0
20
32
34
36
38
39
41
43
44
20
1
1
1
1
1
30
23
25
26
28
29
31
32
34
30
1
1
1
1
]
40
14
15
16
19
20
21
22
24
40
1
1
1
1
1
50
5
6
7
9
10
11
12
13
1 3
50
0"
1
0
1
0
1
0
2
0
2
0
89 0
0 56
0 57
0 58
0 59
1 0
1 1
1 2
10
46
47
48
49
0 50
0 51
0 51
0 52
10
0
0
0
0
0
20
37
37
38
39
40
40
41
42
20
0
0
0
0
0
30
28
28
28
29
30
30
31
31
30
0
0
0
0
0
40
19
19
19
19
20
20
21
21
40
0
0
0
0
0
50
9
10
■ 10
10
10
10
10
10
50
1
1
1
1
1
TABLE 25
[Page 539
Table showing the variation of the altitude of an object arising from a change of 100 seconds in the |
declination.
Unmarked quantities in the Table are positive. It the change move the body toward 1
the elevated pole, apply the correction
L to the altitude with the signs m the Table; otherwise, |
change the
signs.
a
o
"S
a
1
Q
o
o
o
0
Latitude of same name as declination.
Latitude of different name from declination.
<
d
.2
%
c
1
70°
60°
60°
40°
80°
20°
10°
0°
0
10°
20°
30°
40°
50°
60°
70°
94
87
76
64
50
34
17
17
It
34
50
64
76
II
87
94
o
0
o
10
95
88
78
65
51
35
18
0
18
35
51
65
78
88
95
10
?.o
100
92
82
68
53
36
18
0
18
36
53
68
82
92
100
20
30
100
88
74
57
39
20
0
20
39
57
74
88
100
30
0
40
100
84 i 65
45
22
0
22
45
65
84
100
40
0
fSO
100
78
53
27
0
27
53
78
100
50
60
100
68
35
0
35
68
100
60
70
50
100
34
51
17
0
51
100
70
0
0
94
87
77
64
0
17
34
50
64
77
87
94
10
95
87
77
65
50
34
17
- 1
18
35
51
66
78
88
96
10
20
99
91
81
67
52
35
17
- 1
19
37
54
69
83
93
101
20
30
107
98
87
73
56
38
18
- 2
22
41
59
76
90
102
30
?,
40
111
98
82
63
42
20
- 2
25
47
68
86
102
40
2
50
116
97
74
50
24
- 3
30
57
81
103
50
60
124
95
64
30
- 5
40
73
103
60
70
139
92
43
- 8
59
108
64
70
0
94
87
77
64
50
34
17
0
17 34
50
77
87
94
0
10
94
87
77
64
50
34
16
— 1
19 36
52
67
79
89
97
10
20
98
90
79
66
51
34
16
- 3
21
39
56
71
84
95
103
20
; 30
105
96
85
70
54
36
16
- 4
24'
44
62
78
93
104
30
4 40
107
94
78
59
39
17
- 6
29
51
71
90
106
40
4
50
111
92
70
45
19
- 8
35
62
86
109
50
60
117
88
56
23
-12
47
81
112
60
70
127
81
32
-19
0
70
119
70
0
94
87
77
65
50
34
17
17
34
50
65
77
87
94
0
10
94
87
76
64
49
33
16
- 2
20
37
53
67
80
90
98
10
20
97
89
78
65
50
33
15
- 4
22
40
57
73
86
96
104
20 1 1
30
103
94
83
69
52
34
14
- 6
26
46
64
81
95
107
30 1 1
6
40
105
92
76
57
36
14
- 9
32
54
74
93
109
40
6
50
107
88
66
41
15
-13
40
66
91
113
50
60
111
82
51
17
-18
53
87
119
60
70
0
95
65
118
72
22
18
-29
80
129
70
87
77
50
35
0
18
35
50
65
, 77
87
95
0
10
94
86
76
63
49
33
15
- 3
20
38
54
68
81
91
99
10
20
96
88
77
64
49
32
14
- 5
24
40
59
74
87
98
106
20 1
30
101
93
81
67
50
32
12
- 8
28
48
66
83
97
109
30
8
40
102
89
73
54
33
11
-12
35
57
78
97
113
40
8
50
104
84
62
37
11
-17
44
70
95
118
50
60
105
77
45
11
-24
59
93
125
60
70
»
109
62
13
-39
90
140
70
0
95
88
78
6^
51
35
18
0
18
35
51
65
78
88
95
0
10
94
86
75
63
48
32
15
- 3
21
38
55
69
82
92
100
10
20
95
87
76
63
48
31
12
- 6
25
43
60
76
89
100
20 1 1
30
100
91
80
65
49
30
10
-10
30
50
69
86
100
30
10
40
100
87
70
51
31
8
-15
38
60
81
100
40
10
50
100
81
58
33
6
-21
48
75
100
50
60
100
71'
39
5
-31
66
100
60
70
100
53
3
-48
100
70
0
96
89
78
66
51
35
18
0
18
35
51
66
78
89
96
0
10
94
86
76
63
48
32
14
— 4
22
39
56
70
83
94
101
10
20
94
86
76
62
47
29
11
- 8
27
45
62
78
91
102
20
30
99
90
78
64
47
28
8
-12
33
53
71
88
103
30
12
40
108
98
84
68
49
28
5
-18
41
63
85
104
40
12
50
112
97
77
54
29
2
-25
53
80
105
50
60
120
95
65
33
-1
-37
72
107
60
1
a
70
134
91
44
-6
-58
110
70
1
B
6
70°
60°
60°
40°
80°
20°
10°
0°
10°
20°
80°
40°
50°
60°
70°
0)
3
I
latitude of same name as 6
eclinat
tion.
Latitude of different name from declination.
O <
<
Q
Page 640] TABLE 25.
Table showing the variation of the altitude of an object arising from a change of 100 seconds in the
declination. Unmarked quantities in the Table are positive. If the change move the body toward
the elevated pole, apply the correction to the altitude with the signs m the Table; otherwise,
change the signs.
Declination.
Altitude.
Latitude of same name as declination.
Latitude of different name from declination.
<
c
1
70°
60°
^o
40°
80°
20°
10°
0°
10°
20°
80°
40°
60°
60°
70°
0
14
o
0
10
20
30
40
50
60
70
//
97
94
94
97
106
n
89
86
86
89
96
109
II
79
76
75
77
82
93
115
II
66
63
61
62
66
73
89
125
II
52
48
46
45
46
50
60
82
II
35
31
27
26
25
25
27
35
II
18
14
10
6
2
- 2
- 7
-16
II
0
- 4
- 9
- 14
- 21
- 30
- 43
- 69
II
18
23
28
35
44
58
79
121
II
35
40
45
55
67
85
114
//
52
57
64
74
88
110
II
66
72
80
91
107
II
79
85
93
106
II
89
95
104
II
97
103
o
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
o
14
16
18
20
22
24
26
1
OS
c
16
0
10
20
30
40
50
60
70
98
94
94
96
104
90
86
85
87
94
106
80
76
74
75
80
90
110
67
63
61
61
63
70
84
117
52
48
45
44
44
47
54
73
53
48
44
42
41
43
49
64
36
31
27
25
22
21
21
25
18
13
9
4
0
- 6
-14
-26
0
- 5
- 10
- 17
- 24
- 34
- 50
- 79
18
23
30
37
48
62
86
132
36
41
48
58
70
90
121
52
58
66
77
92
115
67
73
82
94
111
80
86
95
109
90
97
106
98
104
18
20
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
99
95
93
95
102
100
95
93
94
100
91
87
85
86
92
103
81
76
74
74
78
87
105
68
63
60
59
61
66
79
108
36
31
26
23
20
17
16
16
36
31
25
21
17
13
10
6
18
13
8
■ 2
- 3
-10
-20
-36
0
- 6
- 12
- 19
- 27
- 39
- 56
- 89
18
24
31
40
51
67
93
143
36
42
50
60
74
95
128
53
59
68
79-
96
121
68
74
84
97
116
81
88
98
112
91
98
109
99
106
0
10
20
30
40
50
60
70
92
87
85
85
90
100
82
76
74
73
76
83
100
68
63
60
58
59
63
74
100
53
48
43
40
39
39
43
56
18
12
6
0
- 6
-15
-26
-46
0
- 6
- 13
- 21
- 31
- 43
- 63
-100
18
25
33
42
55
72
100
36
43
52
63
78
100
53
60
70
82
100
68
76
86
100
82
89
100
92
100
100
0
10
20
30
40
50
60
70
22
0
10
20
30
40
50
60
70
96
93
94
98
110
93
88
85
85
88
97
117
83
77
73
72
74
80
95
131
69
63
59
57
57
60
68
92
•54
48
43
39
36
36
38
47
37
30
25
19
14
9
4
- 3
19
12
5
- 2
- 9
-19
-33
-56
0
^ 7
- 15
- 23
- 34
- 48
- 70
-111
19
26
35
45
58
77
107
37
45
54
66
82
106
54
62
72
86
104.
69
78
88
103
83
91
103
93
102
101
0
10
20
30
40
50
60
70
24
0
10
20
30
40
50
60
70
97
93
93
97
107
95
88
85
84
86
93
112
84
77
73
71
72
77
91
123
70
64
59
56
54
56
64
83
55
48
42
38
34
.32
32
38
37
30
24
18
12
5
- 2
-13
19
11
4
- 4
-12
-23
-39
-67
0
- 8
- 16
- 26
- 37
- 53
- 77
-122
19
27
36
48
62
83
115
37
46
56
69
86
111
55
63
74
89
109
70
79
91
107
84
93
105
95
104
103
0
10
20
30
40
50
60
70
0"
10
20
30
40
50
60
70
26
0
10
20
30
40
50
60
70
98
95
93
96
105
96
89
85
83
85
92
108
85
78
73
70
70
74
86
115
72
64
59
54
52
53
58
75
56
48
41
36
32
28
27
29
38
30
23
16
9
1
- 8
-23
19
11
3
- 6
-16
-28
-46
-78
0
- 9
- 18
- 28
- 41
- 58
- 84
-134
19
28
38
50
66
88
123
38
47
58
72
91
117
56
65
77
92
114
72
81
94
111
85
95
108
96
106
105
©
c
"3
OJ
1
<
70°
60°
50°
40°
80°
20°
10°
0°
10°
20°
80°
40°
50°
60°
70°
6
Latitude of same name as declination.
L
atitud
eof d
iflerent name from declination.
TABLE 26.
[Page 641
Variation of Altitude in one minute from meridian
passage
Declination of the
same name a.s the latitude;
npper transit; reduction additive.
Lati-
tude.
0°
Lati-
tude.
1°
.2°
3°
40
5°
6°
70
8°
9°
10°
11°
o
II
II
II
II
//
II
II
//
II
II
II
II
0
0
28.1
22.4
18.7
16.0
14.0
12.4
11.1
10.1
0
1
28.0
22.4
18.6
16.0
13.9
12.4
11.1
1
2
28.0
22.3
18.6
15.9
13.9
12.3
2
3
27.9
22.3
18.5
15.8
13.8
3
4
5
28.1
22. 4^
27.8
22.2
18.5
15.8
4
28.0
27.7
22.1
18.4
5
6
18.7
22.4
28.0
27.6
22.0
6
7
16.0
18.6
22.3
27.9
27.4
7
8
14.0
16.0
18.6
22.3
27.8
8
9
12.4
11.1
13.9
12. 4
15.9
18.5
22.2
18.5
27.7
22.1
9
10
10
13.9
15.8
27.6
11
10.1
11.1
12.3
13.8
15.8
18.4
22.0
27.4
11
12
9.2
10.1
11.1
12.3
13.8
15.7
18.3
21.9
27.3
12
13
8,5
9.2
10.0
11.0
12.2'
13.7
15.6
18.2
21.7
27.1
13
14
15
7.9
8.5
9.2
10.0
10.9
12.1
10.9
13.6
12.1
15.5
18.0
21.6
26.9
14
15
7.3
7.8
8.4
9.1
9.9
13.5
15.4
17.9
21.4
26.7
16
6.8
7.3
7.8
8.4
9.1
9.8
10.8
12.0
13.4
15.3
17.8
21.3
16
17
6.4
6.8
7.2
7.8
8.3
9.0
9.8
10.7
11.9
13.3
15.2
17.6
17
18
6.0
6.4
6.8
7.2
7. 7
8.3
8.9
9.7
10.6
11.8
13.2
15.0
18
19
5.7
6.0
6.3
6.7
6.3
7.2
7.6
8.2
8.9
9.6
10.6
9.5
11.7
13.1
19
20
20
5.4
5.7
6.0
6.7
7.1
7.6
8.1
8.8
10.5
11.6
21
5.1
5.4
5.6
5.9
6.3
6.6
7.0
7.5
8.1
8.7
9.5
10.4
21
22
4.9
5.1
5.3
5.6
5.9
6.2
6.6
7.0
7.5
8.0
8.6
9.4
22
23
4.6
4.8
5.0
5.3
5.5
5.8
6.1
6.5
6.9
7.4
7.9
8.5
23
24
4.4
4.6
4.8
5.0
5.2
5.5
5.8
6.1
6.4
6.8
7.3
7.8
24
25
25
4.2
4.4
4.6
4.7
5.0
5.2
5.4
5.7
6.0
6.4
6.8
7.2
26
4.0
4.2
4.3
4.5
4.7
4.9
5.1
5.4
5.7
6.0
6.3
6.7
26
27
3.9
4.0
4.1
4.3
4.5
4.7
4.9
5.1
5.3
5.6
5.9
6.2
27
28
3.7
3.8
4.0
4.1
4.3
4.4
4.6
4.8
5.0
5.3
5.5
5.8
28
29
3.5
3.7
3.8
3.9
4.1
4.2
4,4
4.6
4.7
5.0
5.2
5.5
5.1
29
30
80
3.4
3.5
3.6
3.7
3.9
4.0
4.2
4.3
4.5
4.7
4.9
31
3.3
3.4
3.5
3.6
3.7
3.8
4.0
4.1
4.3
4.4
4.6
4.8
31
32
3.1
3.2
3.3
3.4
3.5
3.7
3.8
3.9
4.1
4.2
4.4
4.6
32
33
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.9
4.0
4.2
4.3
33
34
2.9
3.0
3.1
3.2
3.2
3.3
3.4
3.6
3.7
3.8
3.9
4.1
34
35
2.8
2.9
3.0
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.9
35
36
2.7
2.8
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
36
37
2.6
2.7
2.7
2.8
2.9
2.9
3.0
3.1
3.2
3.3
3.4
3.5
37
38
2.5
2.6
2.6
2.7
2.8
2.8
2.9
3.0
3.0
3.2
3.2
3.3
38
39
2.4
2.5
2.5
2.6
2.7
2.7
2.8
2.9
2.9
3.0
3.1
3.2
39
40
40
2.3
2.4
2.4
2.5
2.6
2.6
2.7
2.7
2.8
2.9
3.0
3.0
41
2.3
2.3
2.4
2.4
2.5
2.5
2.6
2.6
2.7
2.8
2.8
2.9
41
42
2.2
2.2
2.3
2.3
2.4
2.4
2.5
2.5
2.6
2.6
2.7
2.8
42
43
2.1
2.1
2.2
2.2
2.3
2.3
2.4
2.4
2.5
2.5
2.6
2.7
43
44
2.0
2.0
2.1
2.1
2.1
2.2
2.1
2.2
2.3
2.3
2.4
2.4
2.5
2.5
44
45
2.0
2.0
2.1
2.2
2.2
2.2
2.3
2.3
2.4
2.4
45
46
1.9
1.9
2.0
2.0
2.0
2.1
2.1
2.2
2.2
2.2
2.3
2.3
46
47
1.8
1.9
1.9
1.9
2.0
2.0
2.0
2.1
2.1
2.1
2.2
2.2
47
48
1.8
1.8
1.8
1.9
1.-9
1.9
2.0
2.0
2.0
2.1
2.1
2.1
48
49
50
1.7
1.6
1.7
1.8
1.8
1.8
1.8
1.9
1.8
1.9
1.9
2.0
1.9
2.0
2.1
49
1.7
1.7
1.7
1.8
1.8
1.8
1.9
1.9
2.0
50
51
1.6
1.6
1.6
1.7
1.7
1.7
1.7
1.8
1.8
1.8
1.9
1.9
51
52
1.5
1.6
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.8
1.8
1.8
52
53
1.5
1.5
1.5
1.5
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.7
53
54
1.4
1.4
1.5
1.5
1.5
1.5
1.5
1.5
1.6
1.6
1.6
1.6
1.7
54
55
1.4
1.4
1.4
1.4
1.5
1.5
1.5
1.5
1.6
1.6
1.6
55
56
1.3
1.3
1.4
1.4
1.4
1.4
1.4
1.4
1.5
1.5
1.5
1.5
56
57
1.3
1.3
1.3
1.3
1.3
1.4
1.4
1.4
1.4
1.4
1.4
1.5
57
58
1.2
1.2
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.4
1.4
1.4
58
59
1.2
1.2
1.2
1.2
1.2
1.3
1.3
1.3
1.3
1.3
1.3
1.3
59
60
1.1
1.1
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.3
1.3
60
0°
1°
2°
3°
4°
5°
6°
70
8°
90
10°
11°
De
elinatio
n of the
same name as the
latitude;
upper tra
nsit; red)
etion add
Itire.
Page 542J
TABL?:
26.
Variation of Altitude in one minute from meridian passage.
Lati-
tude.
Declination of the
same name as the latitude; upper transit
reduction addltlre.
Lati-
tude.
12°
18°
14°
15°
16°
17°
18°
19°
20°
21°
22°
28°
24°
c
0
9.2
8.5
7.9
II
7.3
6.8
6.4
II
6.0
5.7
II
5,4
II
5.1
4.9
II
4.6
4.4
0
0
1
10.1
9.2
8.5
7.8
7.3
6.8
6.4
6.0
5.7
5.4
5.1
4.8
4.6
1
2
11.1
10.0
«.2
8.4
7.8
7.2
6.8
6.3
6.0
5.6
5.3
5.0
4.8
9
3
12.3
11.0
10.0
9.1
8.4
7.8
7.2
6.7
6.3
5.9
5.6
5.3
5.0
3
4
13.8
15.7
12.2
13.7
10.9
9.9
9.1
8.3
7.7
7,2
6.7
6.3
5,9
5.5
5.2
4
5
12.1
10.9
9.8
9.0
8.3
7,6
7.1
6.6
6.2
5.8
5.5
5
6
18.3
15.6
13.6
12.1
10.8
9.8
8.9
8,2
7.6
7.0
6.6
6.1
5.8
6
/
21.9
18.2
15.5
13.5
12.0
10.7
9.7
8,9
8.1
7.5
7.0
6.5
6.1
7
8
27.3
21.7
18.0
15.4
13.4
11.9
10.6
9,6
8.8
8.1
7.5
6.9
6.4
8
9
27.1
21.6
17.9
15.3
13.3
11.8
10.6
9.5
8.7
8.0
7.4
6.8
9
10
10
26.9
21.4
17.8
15.2
13.2
11.7
10,5
9.5
8.6
7.9
7.3
11
26.7
21.3
17.6
15.0
13.1
11,6
10.4
9.4
8,5
7.8
11
12
26.5
21.1
17.5
14,9
13,0
11.5
10.3
9,3
8.4
12
13
26.2
20.9
17,3
14.8
12.8
11.3
10,1
9.2
13
14
26.0
20.7
17.1
14.6
12.7
11,2
10.0
14
15
25.7
20.4
16.9
14,4
12.5
11.1
15
16
26.5
25.4
20.2
16,7
14,3
12.4
16
17
21.1
26.2
25.1
20.0
16.5
14,1
17
18
17.5
20.9
26.0
24.8
19.7
16.3
18
19
14.9
17.3
20.7
25.7
24.5
19,5
19
20
13.0
14.8
17.1
20.4
25.4
24.2
20
21
11.5
12.8
14.6
16.9
20.2
25.1
21
22
10.3
11.3
12.7
14.4
16.7
20.0
24.8
22
23
9.3
10.1
11.2
12.5
14.3
16.5
19.7
24,5
23
24
8.4
9.2
10.0
9.0
11.1
12.4
14.1
16.3
19,5
24.2
24
25
7.7
8.3
9.9
10.9
12.2
13.9
16,1
19.2
23.8
25
26
7.1
7.6
8.2
8.9
9.8
10.8
12.1
13,7
15,9
18.9
23,5
26
27
6.6
7.0
7,5
8.1
8.8
9.6
10.6
11.9
13,5
15.6
18.6
23.1
27
28
6.2
6.5
7.0
7.4
8.0
8.7
9.5
10,5
11,7
13.3
15,4
18.3
22,7
28
29
5.7
6.1
6.4
6.9
7.3
7.9
8.6
9,4
10,3
11.5
13.1
15.1
12.8
18.0
29
30
5.4
5.7
6.0
6.4
6.8
7.2
7,8
8,4
9,2
10.1
11.3
14.9
30
31
5.1
5.3
6.6
5.9
6.3
6.7
7,1
7.7
8,3
9.0
10.0
11.1
12.6
31
32
4.8
5.0
5.2
5.5
5.8
6.2
6,5
7.0
7,5
8.1
8.9
9.8
10,9
32
33
4.5
4.7
4.9
5.1
5.4
5.7
6,1
6,4
6,9
7.4
8.0
8.7
9,6
33
34
4.3
4.4
4.6
4.8
5.1
5.3
5,6
5.9
6,3
6.8
7.3
7.8
8.6
34
35
4.0
4.2
4.4
4.5
4.7
5.0
5,2
5.5
5,8
6.2
6.6
7.1
7, 7
35
36
3.8
4.0
4.1
4.3
4.5
4.7
4.9
5.1
5,4
5.7
6.1
6.5
7.0
36
37
3.6
3.8
3.9
4.0
4.2
4.4
4,6
4.8
5.0
5.3
5.6
6.0
6,4
37
38
3.4'
3.6
3.7
3.8
4.0
4.1
4.3
4,5
4.7
4.9
5.2
5.5
5.8
38
39
3.3
3.4
3.5
3.6
3.8
3.9
4.0
4,2
4.4
4.6
4.8
5.1
5,4
39
40
3.1
3.2
3.3
3.4
3.6
3.7
3.8
4,0
4.1
4.3
4.5
4.7
5.0
40
41
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3,7
3.9
4.0
4.2
4.4
4.6
41
42
2.9
2.9
3.0
3.1
3.2
3.3
3.4
3,5
3.7
3.8
4.0
4.1
4.3
42
43
2.7
2.8
2.9
3.0
3.0
3.1
3.2
3,3
3.5
3.6
3.7
3.9
4.0
43
44
2.6
2.7
2.7
2.8
2.9
3.0
3,1
3,2
3.3
3.4
3.5
3.6
3.8
44
45
2.5
2.6
2.6
2.7
2.8
2,8
2,9
3.0
3.1
3,2
3.3
3.4
3,5
45
46
2.4
2.4
2.5
2.6
2.6
2.7
2,8
2.8
2.9
3,0
3.1
3.2
3.3
46
47
2.3
2.3
2.4
2.4
2.5
2.6
2.6
2.7
2.8
2,9
2.9
3.0
3.1
47
48
2.2
2.2
2.3
2.3
2.4
2.4
2.5
2,6
2.6
2,7
2.8
2.9
3.0
48
49
2.1
2.1
2.2
2.2
2.3
2.3
2.4
2.4
2.5
2.6
2.6
2.7
2.8
49
50
2.0
2.0
2.1
2.1
2.2
2.2
2.3
2.3
2.4
2,4
2.5
2.6
2.6
50
51
1.9
2.0
2.0
2.0
2.1
2.1
2.2
2.2
2.3
2,3
2.4
2.4
2.5
51
52
1.8
1.9
1.9
1.9
2.0
2.0
2.1
2.1
2.1
2.2
2.2
2.3
2:4
52
53
1.8
1.8
1.8
1.9
1.9
1.9
2,0
2.0
2.0
2.1
2.1
2.2
2.2
.53
54
1.7
1.7
1.7
1.8
1.8
1.8
1.9
1.9
1.9
2,0
2.0
2.1
2.1
2,0
54
55
55
1.6
1.6
1.7
1.7
1.7
1.8
1.8
1,8
1.9
1.9
1.9
2.0
56
1.5
1.6
1.6
1.6
1.6
1.7
1.7
1,7
1.8
1,8
1.8
1.9
1,9
56
57
1.5
1.5
1.5
1.5
1.6
1,6
1.6
1,6
1.7
1.7
1.7
1.8
1,8
57
58
1.4
1.4
1.5
1.5
1.5
1.5
1.5
1,6
1.6
1.6
1.6
1.7
1.7
58
59
1.4
1.4
1.4
1.4
1.4
1.5
1.5
1.5
1.5
1,5
1.6
1.6
1.6
59
60
1.3
1.3
1.3
1.3
1.4
1.4
1.4
1,4
1.4
1.5
1.5
1.5
1.5
60
12°
18°
14°
15°
16°
17°
18°
19°
20°
21°
22°
23°
24°
De<
jlinatior
I of the t
ame nai
ne as th
3 latitud
e; uppei
transit;
reducti
on addit
l¥e.
TABLE
26.
[Page 543
Variation of Altitude in one minute from meridian passage.
Declination of the
same name as the latitude; upper transit
reduction additive.
Lati-
tude.
Lati-
tude.
26°
26°
27°
28°
29°
30°
31°
32°
83°
34°
35°
36°
37°
o
0
4.2
4.0
3.9
3.7
3.5
3.4
3.3
3.1
3.0
2.9
2.8
2.7
2.6
o
0
1
4.4
4.2
4.0
3.8
3.7
3.5
3.4
3.2
3.1
3.0
2.9
2.8
2.7
1
2
4.6
4.3
4.1
4.0
3.8
3.6
3.5
3.3
3.2
3.1
3.0
2.8
2.7
2
3
4.7
4.5
4.3
4.1
3.9
3.7
3.6
3.4
3.3
3.2
3.0
2.9
2.8
3
4
5
5.0
4.7
4.5
4.3
4.1
3.9
3.7
3.5
3.4
3.3
3.1
3.0
3.1
2.9
4
5.2
4.9
4.7
4.4
4.2
4.0
3.8
3.7
3.5
3.3
3.2
3.0
5
6
5.4
6.1
4.9
4.6
4.4
4.2
4.0
3.8
3.6
3.5
3.3
3.2
3.0
6
7
5.7
5.4
5.1
4.8
4.6
4.3
4.1
3.9
3.7
3.6
3.4
3.3
3.1
7
8
6.0
5. 7
5.3
5.0
4.8
4.5
4.3
4.1
3.9
3.7
3.5
3.4
3.2
8
9
6.4
6.0
5.6
5.3
5.0
4.7
4.4
4.2
4.0
3.8
3.6
3.5
3.3
9
10
6.8
6.3
5.9
5.5
5.2
4.9
4.6
4.4
4.2
3.9
3.8
3.6
3.4
10
11
7.2
6.7
6.2
5.8
5.5
5.1
4.8
4.6
4.3
4.1
3.9
3.7
3.5
11
12
7.7
7.1
6.6
6.2
5.8
5.4
5.1
4.8
4.5
4.3
4.0
3.8
3.6
12
13
8.3
7.6
7.1
6.5
6.1
5.7
5.3
5.0
4.7
4.4
4.2
4.0
3.8
13
14
15
9.1
9. 9
8.2
7.6
7.0
6.4
6.0
5.6
5.2
4.9
4.6
4.4
4.1
3.9
4.0
14
8.9
8.1
7.4
6.9
6.4
5.9
5.5
5.2
4.8
4.5
4.3
15
16
10.9
9.8
8.8
8.0
7.3
6.8
6.3
5.8
5.4
5.1
4.8
4.5
4.2
16
17
12.2
10.8
9.6
8.7
7.9
7.2
6.7
6.2
5.7
5.3
5.0
4.7
4.4
17
18
13.9
12.1
10.6
9.5
8.6
7.8
7.1
6.6
6.1
5.6
5.2
4.9
4.6
18
19
16.1
13.7
11.9
10.5
9.4
8.4
7.7
7.0
6.4
6.0
5.5
5.1
4.8
19
20
19.2
15.9
13.5
11.7
10.3
9.2
8.3
7.5
6.9
6.3
5.8
5.4
5.0
20
21
23.8
18.9
15.6
13.3
11.5
10.2
9.1
8.2
7.4
6.8
6.2
5.7
5.3
21
22
23. 5
18.6
15.4
13.1
11.3
10.0
8.9
8.0
7.3
6.6
6.1
5.6
22
23
23.1
18.3
15.1
12.8
11.1
9.8
8.7
7.9
7.1
6.5
6.0
23
24
22.7
18.0
14.9
12.6
10.9
9.6
8.6
7.7
7.0
6.4
24
25
22.3
17.7
14.6
12.4
10.7
9.4
8.4
7.5
6.8
25
26
21.9
17.4
14.3
12.1
10.5
9.2
8.2
7.4
26
27
21.5
17.0
14.0
11.9
10.3
9.1
8.1
27
28
.
21.1
16.7
13.8
11.7
10.1
8.9
28
29
22.3
20.6
16.3
13.5
11.4
9.9
29
30
17.7
21.9
20.2
16.0
13.2
11.1
30
31
14.6
17.4
21.5
19.8
15.6
12.9
31
32
12.4
14.3
17.0
21.1
19.3
15.3
32
33
10.7
12.1
14.0
16.7
20.6
18.9
33
34
9.4
10.5
11.9
13.8
16.3
20.2
34
35
8.4
9.2
10.3
11.7
13.5
16.0
19.8
35
36
7.5
8.2
9.1
10.1
11.4
13.2
15.6
19.3
36
37
6.8
7.4
8.1
8.9
9.9
11.1
12.9
15.3
18.9
37
38
6.2
6.7
7.2
7.9
8.7
9.6
10.9
12.6
14.9
18.4
38
39
5.7
5.3
6.1
6.5
7.1
7.7
8.5
9.4
10.6
9.2
12.2
14.5
17.9
39
40
5.6
6.0
6.4
6.9
7.5
8.2
10.4
11.9
14.1
17.4
40
41
4.9
5.2
5.5
5.8
6.2
6.7
7.3
8.0
8.9
10.1
11.6
13.8
17.0
41
42
4.5
4.8
5.0
5.3
5.7
6.1
6.6
7.1
7.8
8.7
9.8
11.3
13.4
42
43
4.2
4.4
4.6
4.9
5.2
5.5
5.9
6.4
6.9
7.6
8.5
9.5
11.0
43
44
3.9
4.1
4.3
4.5
4.8
5.1
5.4
5.8
6.2
6.7
7.4
8.2
9.3
44
45
3.7
3.8
4.0
4.2
4.4
4.7
4.9
5.2
5.6
6.0
6.6
7.2
8.0
45
46
3.5
3.6
3.7
3.9
4.1
4.3
4.5
4.8
5.1
5.4
5.9
6.4
7.0
46
47
3.3
3.4
3.5
3.6
3.8
4.0
4.2
4.4
4.6
4.9
5.3
5.7
6.2
47
48
3.1
3.2
3.3
3.4
3.5-
3.7
3.9
4.0
4.3
4.5
4.8
5.1
5.5
48
49
50
2.9
3.0
3.1
3.2
3.3
3.4
3.6
3.7
3.9
4.1
4.4
4.6
5.0
49
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.5
3.6
3.8
4.0
4.2
4.5
50
51
2.6
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.4
3.5
3.7
3.9
4.1
51
52
2.4
2.5
2.6
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.4
3.6
3.7
52
53
2.3
2.3
2.4
2.5
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.3
3.4
53
54
2.2
2.2
2.3
2.3
2.4
2.5
2.5
2.6
2.7
2.8
2.9
3.0
3.2
54
55
2.0
2.1
2.1
2.2
2.3
2.3
2.4
2.4
2.5
2.6
2.7
2.8
2.9
55
56
1.9
2.0
2.0
2.1
2.1
2.2
2.2
2.3
2.4
2.4
2.5
2.6
2.7
56
57
1.8
1.9
1.9
2.0
2.0
2.0
2.1
2.2
2.2
2.3
2.3
2.4
2.5
57
58
1.7
1.8
1.8
1.8
1.9
1.9
2.0
2.0
2.1
2.1
2.2
2.3
2.3
58
59
1.6
1.7
1.7
1.7
1.8
1.8
1.9
1.9
1.9
2.0
2.0
2.1
2.2
59
60
1.6
1.6
1.6
1.6-
1.7
1.7
1.7
1.8
1.8
1.9
1.9
2.0
2.0
60
25°
26°
27°
28°
29°
80°
31°
32°
88°
34°
85°|
86°
87°
De
3linatlor
1 of the
same na
me as th
e latltuc
le; uppe
r transit
reduct
on addl
tlve.
Page 544
TABLE
26.
Variation of Altitude in one minute from meridian past^age.
Declination of the
same name a« the latitude; upper transit
reduction additive.
Lati-
tude.
Lati-
tude.
o
0
88°
89°
40°
41°
42°
48°
44°
46°
46°
47°
48°
49°
60°
o
0
2.5
2.4
2.3
2.3
2.2
2.1
2.0
It
2.0
1.9
1.8
1.8
II
1. 7
1.7
1
2.6
2.5
2.4
2.3
2.2
2.2
2.1
2.0
1.9
1.9
1.8
1.7
1.7
1
2
2.6
2.5
• 2.4
2.4
2.3
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
2
3
2.7
2.6
2.5
2.4
2.3
2.2
2.2
2.1
2.0
1.9
1.9
1.8
1.7
3
4
5
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
2.0
1.9
1.8
1.8
4
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.2
2.1
2.0
1.9
1.9
1.8
5
6
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
2.0
1.9
1.8
6
7
3.0
2.9
2.7
2.6
2.5
2.4
2.3
2.2
2.2
2.1
2.0
1.9
1.8
7
8
3.1
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1.9
8
9
3.2
3.0
2.9
2.8
2.7
2.5
2.4
2.3
2.2
2.2
2.1
2.0
1.9
9
10
3.3
3.1
3.0
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
10
11
3.4
3.2
3.1
2.9
2.8
2.7
2.6
2.4
2.3
2.2
2.1
2.1
2.0
11
12
3.5
3.3
3.1
3.0
2.9
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
12
13
3.6
3.4
3.2
3.1
2.9
2.8
2.7
2.6
2.4
2.3
2.2
2.1
2.0
13
14
3.7
3.5
3.3
3.2
3.0
2.9
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.1
14
15
15
3.8
3.6
3.4
3.3
3.1
3.0
2.8
2.7
2.6
2.4
2.3
2.2
16
4.0
3.8
3.6
3.4
3.2
3.0
2.9
2.8
2.6
2.5
2.4
2.3
2.2
16
17
4.1
3.9
3.7
3.5
3.3
3.1
3.0
2.8
2.7
2.6
2.4
2.3
2.2
17
18
4.3
4.1
3.8
3.6
3.4
3.2
3.1
2.9
2.8
2.6
2.5
2.4
2.3
18
19
4.5
4.2
4.0
3.7
3.5
3.3
3.2
3.0
2.8
2.7
2.6
2.4
2.3
19
20
20
4.7
4.4
4.1
3.9
3.7
3.5
3.3
3.1
2.9
2.8
2.6
2.5
2.4
21
4.9
4.6
4.3
4.0
3.8
3.6
3.4
3.2
3.0
2.9
2.7
2.6
2.4
21
22
5.2
4.8
4.5
4.2
4.0
3.7
3.5
3.3
3.1
2.9
2.8
2.6
2.5
22
23
5.5
5.1
4.7
4.4
4.1
3.9
3.6
3.4
3.2
3.0
2.9
2.7
2.6
23
24
25
5.8
5.4
5.0
4.6
4.3
4.0
3.8
3.5
3.3-
3.1
3.0
2.8
2.6
2.7
24
25
6.2
5.7
5.3
4.9
4.5
4.2
3.9
3.7
3.5
3.3
3.1
2.9
26
6.7
6.1
5.6
5.2
4.8
4.4
4.1
3.8
3.6
3.4
3.2
3.0
2.8
26
27
7.2
6.5
6.0
5.5
5.0
4.6
4.3
4.0
3.7
3.5
3.3
3.1
2.9
27
28
7.9
7.1
6.4
5.8
. 5.3
4.9
4.5
4.2
3.9
3.6
3.4
3.2
3.0
28
29
8.7
7.7
6.9
6.2
5.7
5.2
4.8
4.4
4.1
3.8
3.5
3.3
3.1
29
30
9.6
8.5
7.5
6.7
6.1
5.5
5.1
4.7
4.3
4.0
3.7
3.4
3.2
30
31
10.9
9.4
8.2
7.3
6.6
5.9
5.4
4.9
4.5
4.2
3.9
3.6
3.3
31
32
12.6
10.6
9.2
8.0
7.1
6.4
5.8
5.2
4.8
4.4
4.0
3.7
3.5
32
33
14.9
12.2
10.4
8.9
7.8
6.9
6.2
5.6
5.1
4.6
4.3
3.9
3.6
33
34
35
18.4
14.5
11.9
10.1
8.7
7.6
6.7
6.0
5.4
4.9
4.5
4.1
3.8
34
17.9
14.1
11.6
9.8
8.5
7.4
6.6
5.9
5.3
4.8
4.4
4.0
35
36
17.4
13.8
11.3
9.5
8.2
7.2
6.4
5.7
5.1
4.6
4.2
36
37
17.0
13.4
11.0
9.3
8.0
7.0
6.2
5.5
5.0
4.5
37
38
16.5
13.0
10.7
9.0
7.7
6.8
6.0
5.3
4.8
38
39
16.0
12.6
10.3
8.7
7.5
6.5
5.8
5.1
39
40
15.5
12.2
10.0
8.4
7.2
6.3
5.6
40
41
15.0
11.8
9.7
8.1
7.0
6.1
41
42
16.5
14.5
11.4
9.3
7.9
6.7
42
43
13.0
16.0
14.0
11.0
9.0
7.6
43
44
10.7
12.6
15.5
13.6
10.6
8.7
44
45
9.0
10.3
12.2
15.0
13.1
10.2
45
46
7.7
8.7
10.0
11.8
14.5
12.6
46
47
6.8
7.5
8.4
9.7
11.4
14.0
47
48
6.0
6.5
7.2
8.1
9.3
11.0
13.6
48
49
5.3
5.8
6.3
7.0
7.9
9.0
10.6
13.1
49
50
4.8
5.1
5.6
6.1
6.7
7.6
8.7
10.2
12.6
50
51
4.3
4.6
5.0
5.4
5.9
6.5
7.3
8.4
9.9
12.1
51
52
3.9
4.2
4.5
4.8
5.2
5.7
6.3
7.0
8.0
9.5
11.6
52
53
3.6
3.8
4.0
4.3
4.6
5.0
5.4
6.0
6.7
7. 7
9.1
11.1
53
54
55
3.3
3.5
3.7
3.9
3.5
4.1
3.7
4.4
4.8
5.2
5.8
6.5
7.4
8.7
7.1
10.6
54
55"
3.0
3.2
3.3
4.0
4.3
4.6
5.0
5.5
6.2
8.3
56
2.8
2.9
3.1
3.2
3.4
3.6
3.8
4.1
4.4
4.8
5.3
5.9
6.8
56
57
2.6
2.7
2.8
2.9
3.1
3.2
3.4
3.6
3.9
4.2
4.6
5.0
5.6
o/
58
2.4
2.5
2.6
2.7
2.8
2.9
3.1
3.3
3.5
3.7
4.0
4.4
4.8
58
59
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.0
3.1
3.3
3.6
3.8
4.2
59
60
2.1
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.0
3.2
3.4
3.6
60
38°
39°
40°
41°
42°
43°
44°
45°
46°
47°
48°
49°
50°
De
.'linatior
1 of the
«anie nai
Tie as th
e latitiid
c; uppei
transit
red net i
on addit
hi'.
TABLE
26.
[Page
545
Variation of Altitude in one minute from meridian passage.
Declination of the
same name as the latitude; upper transit
reduction additive.
Lati-
tude.
Lati-
tude.
51°
52°
oS°
54°
55°
56°
67°
58°
69°
60°
61°
62°
68°
n
II
II
II
II
II
II
II
II
II
II
II
II
0
0
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
1.0
0
1
1.6
1.6
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.0
1
2
1.6
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
2
3
L7
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
3
4
1.7
1.6
1.6
1.5
1.5
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
4
5
1.7
1.7
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.1
1.1
1.1
5
6
1.7
1.7
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
6
7
1.8
1.7
1.6
1.6
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
7
8
1,8
1.7
1.7
1.6
1.5
1.5
1.4
1.4
1.3
1.2
1.2
1.1
1.1
8
9
1.8
1.8
1.7
1.6
1.6
1.5
1.4
1.4
1.3
1.3
1.2
1.1
1.1
9
10
1.9
1.8
1.7
1.6
1.6
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
10
11
1.9
1.8
1.7
1.7
1.6
1.5
1.5
1.4
1.3
1.3
1.2
1.2
1.1
11
12
1.9
1.8
1.8
1.7
1.6
1.6
1.5
1.4
1.4
1.3
1.2
1.2
1.1
12
13
2.0
1.9
1.8
1.7
1.6
1.6
1.5
1.4
1.4
1.3
1.3
1.2
1.1
13
14
2.0
1.9
1.8
1.7
1.7
1.6
1.5
1.5
1.4
1.3
1.3
1.2
1.2
14
15
2.0
1.9
1.9
1.8
1.7
1.6
1.5
1.5
1.4
1.3
1.3
1.2
1.2
15
16
2.1
2.0
1.9
1.8
1.7
1.6
1.6
1.5
1.4
1.4
1.3
1.2
1.2
16
17
2.1
2.0
1.9
1.8
1.8
1.7
1.6
1.5
1.5
1.4
1.3
1.3
1.2
17
18
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.5
1.4
1.3
1.3
1.2
18
19
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.6
1.5
1.4
1.4
1.3
1.2
19
20
2.3
2.1
2.0
1.9
1.9
1.8
1.7
1.6
1.5
1.4
1.4
1.3
1.2
20
21
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.5
1.4
1.3
1.2
21
22
2.4
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.6
1.5
1.4
1.3
1.3
22
23
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.4
1.3
23
24
2.5
2.4
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.5
1.4
1.3
24
25
2.6
2.4
2.3
2.2
2.0
1.9
1.8
1.7
1.6
1.6
1.5
1.4
1.3
25
26
2.6
2.5
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
26
27
2.7
2.6
2.4
2.3
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.4
27
28
2.8
2.6
2.5
2.3
2.2
2.1
2.0
1.8
1.7
1.6
1.5
1.5
1.4
28
29
2.9
2.7
2.5
2.4
2.3
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
29
30
3.0
2.8
2.6
2.5
2.3
2.2
2.0
1.9
1.8
1.7
1.6
1.5
1.4
30
31
3.1
2.9
2.7
2.5
2.4
2.2
2.1
2.0
1.9
1.7
1.6
1.5
1.4
31
32
3.2
3.0
2.8
2.6
2.4
2.3
2.2
2.0
1.9
1.8
1.7
1.6
1.5
32
33
3.4
3.1
2.9
2.7
2.5
2.4
2.2
2.1
1.9
1.8
1.7
1.6
1.5
33
34
35
3.5
3.2
3.0
2.8
2.6
2.4
2.3
2.1
2.0
1.9
1.7
1.6
1.5
34
3.7
3.4
3.1
2.9
2.7
2.5
2.3
2.2
2.0
1.9
1.8
1.7
1.6
35
36
3.9
3.6
3.3
3.0
2.8
2.6
2.4
2.3
2.1
2.0
1.8
1.7
1.6
36
37
4.1
3.7
3.4
3.2
2.9
2.7
2.5
2.3
2.2
2.0
1.9
1.7
1.6
37
38
4.3
3.9
3.6
3.3
,3.0
2.8
2.6
2.4
2.2
2.1
1.9
1.8
1.7
38
39
40
4.6
4.2
3.8
3.5
'3.2
2.9
2.7
2.5
2.3
2.1
2.0
1.8
1.7
39
5.0
4.5
4.0
3.7
3.3
3.1
2.8
2.6
2.4
2.2
2.0
1.9
1.8
40
41
5.4
4.8
4.3
3.9
3.5
3.2
2.9
2.7
2.5
2.3
2.1
1.9
1.8
41
42
5.9
5.2
4.6
4.1
3.7
3.4
3.1
2.8
2.6
2.4
2.2
2.0
1.9
42
43
6.5
5.7
5.0
4.4
4.0
3.6
3.2
2.9
2.7
2.5
2.3
2.1
1.9
43
44
7.3
6.3
5.4
4.8
4.3
3.8
3.4
3.1
2.8
2.6
2.3
2.2
2.0
44
45
8.4
7.0
6.0
5.2
4.6
4.1
3.6
3.3
3.0
2.7
2.4
2.2
2.0
45
46
9.9
8.0
6.7
5.8
5.0
4.4
3.9
3.5
3.1
2.8
2.6
2.3
2.1
46
47
12.1
9.5
7.7
6.5
5.5
4.8
4.2
3.7
3.3
3.0
2.7
2.4
2.2
47
48
11.6
9.1
7.4
6.2
5.3
4.6
4.0
3.6
3.2
2.8
2.6
2.3
48
49
11.1
8.7
7.1
5.9
5.0
4.4
3.8
3.4
3.0
2.7
2.4
49
50
10.6
8.3
6.8
5.6
4.8
4.2
3.6
3.2
2.9
2.6
50
51
10.2
. 7.9
6.4
5.4
4.6
4.0
3.5
3.0
2.7
51
52
9.7
7.6
6.1
5.1
4.3
3.8
3.3
2.9
52
53
9.2
7.2
5.9
4.9
4.1
3.6
3.1
53
54
8.8
6.8
5.5
4.6
3.9
3.4
54
55
10.2
8.3
6.5
5.3
4.3
3.7
55
56
7.9
9.7
7.9
6.1
5.0
4.1
56
57
6.4
7.6
9.2
7.4
5.8
4.7
57
58
5.4
6.1
7.2
8.8
7.0
5.4
58
59
4.6
5.1
5.9
6.8
8.3
6.6
59
60
4.0
4.3
4.9
5.5
6.5
7.9
60
51°
52°
53°
54°
55°
56°
57°
58°
69°
60°
61°
62°
68°
De
^linatioi
1 of the
liame nai
ne as th
e latitat
e; uppe
r transit
reduct
on addll
Ive.
22480—03-
Page 546]
TABLE 26.
Variation of Altitude in one minute from meridian
passage
Lati-
tnde.
Declination of a different name from the latitude
; upper transit; reduction additive.
Lati-
tude.
0°
1°
go
8°
4°
5°
6°
70
8°
9°
10°
11°
o
II
//
II
II
//
II
II
II
II
II
II
II
0
0
28.1
22.4
18.7
16.0
14,0
12.4
11.1
10.1
0
1
28.1
22.4
18.7
16.0
14.0
12.4
11.2
10.1
9.3
1
2
22] 4
22.4
18.7
16.0
14.0
12.5
11.2
10.2
9.3
8.6
2
3
28.1
18.7
16.0
14.0
12.5
11.2
10.2
9.3
8.6
8.0
3
4
28.1
22.4
18.7
16.0
14.0
12.5
11.2
11.2
10.2
9.3
8.6
8.0
7.4
4
5
22.4
18.7
16.0
14.0
12.5
10.2
9.3
8.6
8.0
7.4
7.0
5
6
18.7
16.0
14.0
12.5
11.2
10.2
9.3
8.6
8.0
7.5
7.0
6.6
6
7
16.0
14.0
12.4
11.2
10.2
9.3
8.6
8.0
7.5
7.0
6.6
6.2
7
8
14.0
12.4
11.2
10.2
9.3
8.6
8.0
7.5
7.0
6.6
6.2
5.9
8
9
12.4
11.2
10.2
9.3
8.6
8.0
7.4
7.5
7.0
6.6
6.2
5.9
5.6
5.3
9
10
10
11.1
10.1
9.3
8.6
8.0
7.0
6.6
6.2
5.9
5.6
11
10.1
9.3
8.6
8.0
7.4
7.0
6.6
6.2
5.9
5.6
5.3
5.1
11
12
9.2
8.5
7.9
7.4
7.0
6.5
6.2
5.9
5.6
5.3
5.0
4.8
12
13
8.5
7.9
7.4
6.9
6.5
6.2
5.8
5.6
5.3
5.0
4.8
4.6
13
14
7.9
7.4
6.9
6.5
6.2
5.8
5.5
5.3
5.0
4.8
4.6
4.4
14
15
15
7.3
6.9
6.5
6.1
5.8
5.5
5.3
5.0
4.8
4.6
4.4
4.2
16
6.8
6.5
6.1
5.8
5.5
5.2
5.0
4.8
4.6
4.4
4.2
4.1
16
17
6.4
6.1
5.8
5.5
5. 2 5. 0
4.8
4.6
4.4
4.2
4.1
3.9
17
18
6.0
5.7
5.5
5.2
5. 0 4. 8
4.0
4.4
4.2
4.1
3.9
3.8
18
19
5.7
5.4
5.2
4.9
4.7
4.5
4.4
4.2
4.0
3.9
3.8
3.6
19
20
5.4
5.1
4.9
4.7
4.5
4.3
4.2
4.0
3.9
3.8
3.6
3.5
20
21
5.1
4.9
4.7
4.5
4.3
4.2
4.0
3.0
3.7
3.6
3.5
3.4
21
22
4.9
4.7
4.5
4.3
4.1
4.0
3.9
3.7
3.6
3.5
3.4
3.3
22
23
4.6
4.4
4.3
4.1
4.0
3.8
3.7
3.6
3.5
3.4
3.3
3.2
23
24
4.4
4.2
4.1
3.9
3.8
3.7
3.6
3.5
3.4
3.3
3.2
3.1
24
25
4.2
4.1
3.9
3.8
3.7
3.5
3.4
3.3
3.2
3.1
3.1
3.0
25
26
4.0
3.9
3.8
3.6
3.5
3.4
3.3
3.2
3.1
3.0
3.0
2.9
26
27
3.9
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.9
2.8
27
28
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.8
2.7
28
29
3.5
3.4
3.3
3.2
3.1
3.1
3.0
3.0
2.9
2.8
2.8
2.7
2.6
29
30
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.7
2.6
2.5
30
31
3.3
3.2
3.1
3.0
2.9
2.9
2.8
2.7
2.6
2.6
2.5
2.5
31
32
3.2
3.1
3.0
2.9
2.8
2.8
2.7
2.6
2.6
2.5
2.5
2.4
32
33
3.0
2.9
2.9
2.8
2.7
2.7
2.6
2.5
2.5
2.4
2.4
2.3
33
34
2.9
2.8
2.8
2.7
2.6
2.6
2.5
2.5
2.4
2.4
2.3
2.3
34
35
2.8
2.7
2.7
2.6
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
35
36
2.7
2.6
2.6
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.1
36
37
2.6
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.2
2.1
2.1
37
38
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.1
2.0
38
39
2.4
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.1
2.0
2.0
2.0
2.0
39
40
2.3
2.3
2.2
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
40
41
2.3
2.2
2.2
2.1
2.1
2.1
2.0
2.0
1.9
1.9
1.9
1.8
41
42
2.2
2.1
2.1
2.1
2.0
2.0
2.0
1.9
1.9
1.9
1.8
1.8
42
43
2.1
2.1
2.0
2.0
2.0
1.9
1.9
1.9
1.8
1.8
1.8
1.7
43
44
45
2.0
2.0
2.0
1.9
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.7
44
2.0
1.9
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.7
1.7
1.6
45
46
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.7
1.7
1.6
1.6
1.6
46
47
1.8
1.8
1.8
1.7
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.6
47
48
1.8
1.7
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.6
1.5
1.5
48
49
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.5
49
50
1.6
1.6
1.6
1.6
1.6
, 1.5
1.5
1.5
1.5
1.5
1.4
1.4
50
51
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
51
52
1.5
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.3
52
53
1.5
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.3
53
54
1.4
1.4
1.4
1.4
1.4
1.3
, 1.3
1.3
1.3
1.3
1.3
1.3
1.3
54
55
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
55
56
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
56
57
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
57
58
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
58
59
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
59
50
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.0
1 0
1.0
1.0
60
0°
1°
2°
3°
4°
5°
6°
70
8°
9°
10°
11°
Declir
lation 0:
a differ
ent name from th
s latitude
; upper tr
ansit; rer
luction a(
Iditire.
TABLE 26. [Page 547
Variation of Altitude in one minute from meridian passage.
Lati-
tude.
Declination of a different name from the latitude; upper transit; reduction additive.
Lati-
tude.
12°
13°
14°
15°
16°
17°
18°
19°
20° 21°
22°
23°
24°
o
0
1
2
3
4
9.2
8.5
7.9
7.4
7.0
8.5
7.9
7.4
6.9
6.5
II
7.9
7.4
•6.9
6.5
6.2
5.8
5.5
5.3
5.0
4.8
II
7.3
6.9
6.5
6.1
5.8
5.5
5.3
5.0
4.8
4.6
II
6.8
6.5
6.1
5.8
5.5
5.2
5.0
4.8
4.6
4.4
II
6.4
6.1
5.8
5.5
5.2
II
6.0
5.7
5.5
5.2
5.0
II
5.7
5.4
5.2
4.9
4.7
II
5.4
5.1
4.9
4.7
4.5
II
5.1
4.9
4.7
4.5
4.3
II
4.9
4.7
4.5
4.3
4.1
II
4.6
4.4
4.3
4.1
4.0
II
4.4
4.2
4.1
3.9
3.8
0
0
1
2
3
4
5
6
7
8
9
6.5
6.2
5.9
5.6
5.3
6.2
5.8
5.6
5.3
5.0
5.0
4.8
4.6
4.4
4.2
4.8
4.6
4.4
4.2
4.1
4.5
4.4
4.2
4.0
3.9
4.3
4.2
4.0
3.9
3.8
4.2
4.0
3.9
3.7
3.6
4.0
3.9
3.7
3.6
3.5
3.8
3.7
3.6
3.5
3.4
3.7
3.6
3.5
3.4
3.3
5
6
7
8
9
10
11
12
13
14
5.0
4.8
4.6
4.4
4.2
4.8
4.6
4.4
4.3
4.1
4.6
4.4
4.3
4.1
3.9
4.4
4.2
4.1
3.9
3.8
4.2
4.1
3.9
3.8
3.7
4.1
3.9
3.8
3.7
3.5
3.9
3.8
3.7
3.5
3.4
3.8
3.6
3.5
3.4
3.3
3.6
3.5
3.4
3.3
3.2
3.5
3.4
3.3
3.2
3.1
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
3.2
3.1
3.0
2.9
2.8
10
11
12
13
14
15
16
17
18
19
4.1
3.9
3.8
3.7
3.5
3.9
3.8
3.7
3.5
3.4
3.8
3.7
3.5
3.4
3.3
3.7
3.5
3.4
3.3
3.2
3.5
3.4
3.3
3.2
3.1
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
3.2
3.1
3.0
2.9
2.9
3.1
3.0
2.9
2.9
2.8
3.0
2.9
2.8
2.8
2.7
2.9
2.8
2.8
2.7
2.6
2.8
2.8
2.7
2.6
2.6
2.8
2.7
2.6
2.5
2.5
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
3.2
3.1
3.0
2.9
2,8
3.1
3.0
2.9
2.8
2.8
3.0
2.9
2.8
2.8
2.7
2.9
2.8
2.8
2.7
2.6
2.9
2.8
2.7
2.6
2.5
2.8
2.7
2.6
2.6
2.5
2.7
2.6
2.6
2.5
2.4
2.6
2.6
2.5
2.4
2.4
2.6
2.5
2.4
2.4
2.3
2.5
2.4
2.4
2.3
2.3
2.4
2.4
2.3
2.3
2.2
20
21
22
23
24
2.9
2.8
2.7
2.6
2.6
2.8
2.7
2.7
2.6
2.5
2.7
2.7
2.6
2.5
2.4
2.4
2.3
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
2.7
2.6
2.5
2.5
2.4
2.6
2.5
2.5
2.4
2.3
2.5
2.5
2.4
2.3
2.3
2.5
2.4
2.4
2.3
2.2
2.4
2.4
2.3
2.2
2.2
2.4
2.3
2.2
2.2
2.1
2.3
2.3
2.2
2.1
2.1
2.3
2.2
2.1
2.1
2.0
2.2
2.1
2.1
2.1
2.0
2.2
2.1
2.1
2.0
2.0
25
26
27
28
29
30
31
32
33
34
2.5
2.4
2.3
2.3
2.2
2.4
2.4
2.3
2.2
2.2
2.3
2.3
2.2
2.1
2.1
2.3
2.2
2.2
2.1
2.0
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
1.8
1.8
2.2
2.1
2.1
2.0
2.0
2.1
2.1
2.0
2.0
1.9
2.1
2.0
2.0
1.9
1.9
2.0
2.0
1.9
1.9
1.9
2.0
2.0
1.9
1.9
1.8
2.0
1.9
1.9
1.8
1.8
1.9
1.9
1.8
1.8
1.8
30
31
32
33
34
35
36
37
38
39
35
36
37
38
39
40
41
42
43
44
2.2
2.1
2.0
2.0
1.9
2.1
2.1
2.0
1.9
1.9
2.0
2.0
1.9
1.9
1.8
2.0
1.9
1.9
1.8
1.8
1.9
1.9
1.8
1.8
1.7
1.9
1.8
1.8
1.8
1.7
1.8
1.8
1.8
1,7
1.7
1.8
1.8
1.7
1.7
1.6
1.8
1.7
1.7
1.7
1.6
1.7
1.7
1.7
1.6
1.6
1.7
1.7
1.6
1.6
1.6
1.9
1.8
1.8
1.7
1.7
1.8
1.8
1.7
1.7
1.6
1.8
1.8
1.7
1.7
1.6
1.8
1.7
1.7
1.6
1.6
1.7
1.7
1.7
1.6
1.6
1.7
1.7
1.6
1.6
1.5
1.7
1.6
1.6
1.6
1.5
1.7
1.6
1.6
1.5
1.5
1.6
1.6
1.6
1.5
1.5
1.6
1.6
1.5
1.5
1.5
1.6
1.5
1.5
1.5
1.4
1.6
1.5
1.5
1.4
1.4
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
40
41
42
43
44
45
46
47
48
49
1.6
1.6
1.5
1.5
1.4
1.6
1.6
1.5
1.5
1.4
1.6
1.5
1.5
1.4
1.4
1.5
1.5
1.5
1.4
■ 1.4
1.5
1.5
1.4
1.4
1.4
1.5
1.5
1.4
1.4
1.3
1.5
1.4
1.4
1.4
1.3
1.5
1.4
1.4
1.4
1.3
1.4
1.4
1.4
1.3
1.3
1.4
1.4
1.3
1.3
1.3
1.4
1.4
1.3
1.3
1.3
1.4
1.3
1.3
1.3
1.2
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
1.4
1.4
1.3
1.3
1.2
1.4
1.3
1.3
1.3
1.2
1.4
1.3
1.3
1.3
1.2
1.3
1.3
1.3
1.2
1.2
1.3
1.3
1.3
1.2
1.2
1.3
1.3
1.3
1.2
1.2
1.3
1.3
1.2
1.2
1.2
1.3
1.2
1.2
1.2
1.1
1.3
1.2
1.2
1.2
1.1
1.3
1:2
1.2
1.2
1.1
1.2
1.2
1.2
1.1
1.1
1.2
1.2
1.1
1.1
1.1
1.2
1.2
1.1
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
50
51
52
53
54
55
56
57
58
59
60
1.2
1.2
1.1
1.1
1.1
1.0
1.2
1.1
1.1
1.1
1.0
1.0
13°
1.2
1.1
1.1
1.1
1.0
1.0
1.2
1.1
1.1
1.1
1.0
1.0
1.1
1.1
1.1
1.0
1.0
1.0
1.1
1.1
Ivl
1.0
1.0
1.0
1.1
1.1
1.1
1.0
1.0
1.0
1.1
1.1
1.0
1.0
1.0
0.9
1.1
1.1
1.0
1.0
1.0
0.9
1.1
1.1
1.0
1.0
1.0
0.9
1.1
1.0
1.0
1.0
1.0
0.9
1.1
1.0
1.0
1.0
0.9
0.9
12°
14°
16°
16°
17°
18°
19°
20°
21°
22°
23°
24°
Declination of a different name from the latitude: upper transit; reduction additive.
Page 548] TABLE 26.
Variation of Altitude in one minute from meridian passage.
Lati-
tude.
Declination of a different name from the latitude; upper transit; reduction addltlre. 1
Lati-
tude.
26°
26°
27°
28°
29°
80°
81°
820
88°
84°
85°
86°
87°
o
0
1
2
3
4
4.2
4.1
3.9
3.8
3.7
II
4.0
3.9
3.8
3.6
3.5
II
3.9
3.7
3.5
3.4
II
3.7
3.6
3.5
3.4
3.3
II
3.5
3.4
3.3
3.2
3.2
II
3.4
3.3
3.2
3.1
3.0
II
3.3
3.2
3.1
3.0
2.9
II
3.1
3.1
3.0
2.9
2.8
n
■ 3.0
2.9
2.9
2.8
2.7
II
2.9
2,8
2,8
2,7
2.6
II
2.8
2.7
2.7
2.6
2.6
II
2.7
2.6
2.6
2.5
2.5
II
2,6
2,6
2.5
2.4
2.4
o
0
1
2
3
4
5
6
7
8
9
5
6
7
8
9
3.6
3.4
3.3
3.2
3.1
3.4
3.3
3.2
3.1
3.0
3.3
3.2
3.1
3.0
2.9
3.2
3.1
3.0
2.9
2.9
3.1
3.0
2.9
2.8
2.8
3.0
2.9
2.8
2.7
2.7
2.9
2.8
2.7
2.7
2.6
2.8
2.7
2.6
2.6
2.5
2.7
2.6
2,5
2.5
2.4
2.6
2,5
2.6
2,4
2,4
2.5
2.4
2.4
2.3
2.3
2.4
2.4
2.3
2.3
2.2
2.3
2.3
2.2
2,2
2,2
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
3.1
3.0
2.9
2.8
2.7
3.0
2.9
2.8
2.7
2.7
2.9
2.8
2.7
2.7
2.6
2.8
2.7
2.6
2.6
2.5
2.7
2.6
2.6
2.5
2.4
2.6
2.5
2.5
2.4
2.4
2.5
2.5
2.4
2.4
2.3
2.5
2.4
2-. 3
2.3
2.3
2.4
2.3
2.3
2.2
2.2
2,3
2,3
2,2
2,2
2,1
2.2
2.2
2,2
2,1
2.1
2.2
2,1
2,1
2.1
2.0
2,1
2,1
2.0
2.0
2.0
10
11
12
13
14
2.7
2.6
2.5
2.5
2.4
2.6
2.5
2.5
2.4
2.4
2.5
2.5
2.4
2.4
2.3
2.5
2.4
2.3
2.3
2.2
2.4
2.3
2.3
2.2
2.2
2.3
2.3
2.2
2.2
2.1
2.3
2.2
2.2
2.1
2.1
2.2
2.2
2.1
2.1
2.0
2.1
2.1
2.1
2.0
2.0
2.1
2.0
2.0
2.0
1.9
2,0
2,0
2,0
1,9
1.9
2.0
1.9
1.9
1.9
1.8
1.9
1.9
1.9
1.8
1.8
15
16
17
18
19
2.4
2.3
2.3
2.2
2.2
2.3
2.3
2.2
2.2
2.1
2.3
2.2
2.2
2.1
2.1
2.2
2.1
2.1
2.1
2.0
2.1
2.1
2.1
2.0
2.0
2.1
2.0
2.0
2.0
1.9
2.0
2.0
2.0
1.9
1.9
2.0
2.0
1.9
1.9
1.8
1.9
1.9
1.9
1.8
1.8
1.9
1.9
1.8
1,8
.1,8
1.9
1.8
1.8
1.8
1.7
1,8
1,8
1,7
1,7
1.7
1.8
1.7
1.7
1.7
1.6
20
21
22
23
24
25
26
27
28
29
2.1
2.1
2.0
2.0
1.9
2.1
2.0
2.0
1.9
1.9
2.0
2.0
1.9
1.9
1.9
2.0
1.9
1.9
1.9
1.8
1.9
1.9
1.9
1.8
1.8
1.9
1.9
1.8
1.8
1.7
1.8
1.8
1.8
1.7
1.7
1.8
1.8
1.7
1.7
1.7
1.8
1.7
1.7
1.7
1.6
1.7
1.7
1.7
1.6
1.6
1,7
1.7
1.6
1.6
1,6
1.6
1.6
1,6
1,6
1,5
1.6
1.6
1.6
1.5
1.5
25
26
27
28
29
30
31
32
33
34
30
31
32
33
34
1.9
1.8
1.8
1.8
1.7
1.8
1.8
1.8
1.7
1.7
1.8
1.8
1.7
1.7
1.7
1.8
1.7
1.7
1.7
1.6
1.7
1.7
1.7
1.6
1.6
1.7
1.7
1.6
1.6
1.6
1.7
1.6
1.6
1.6
1.5
1.6
1.6
1.6
1.5
1.5
1.6
1.6
1.5
1.5
1.5
1.6
1.5
1.5
1.5
1.5
1,5
1,5
1.5
1.5
1,4
1,5
1,5
1,5
1,4
1,4
1.5
1.5
1.4
1.4
1.4
35
36
37
38
39
1.7
1.6
1.6
1.6
1.5
1.7
1.6
1.6
1.5
1.5
1.6
1.6
1.6
1.5
1.5
1.6
1.6
1.5
1.5
1.5
1.6
1.5
1.5
1.5
1.4
1.5
1.5
1.5
1.5
1.4
1.5
1.5
1.5
1.4
1.4
1.5
1.5
1.4
1.4
1.4
1.5
1.4
1.4
1.4
1.4
1.4
1,4
1,4
1,4
1,3
1,4
1,4
1,4
1,3
1,3
1.4
1.4
1.3
1.3
1.3
1.4
1.3
1.3
1.3
1.3
35
36
37
38
39
40
41
42
43
44
1.5
1.5
1.4
1.4
1.4
1.5
1.4
1.4
1.4
1.4
1.5
1.4
1.4
1.4
1.3
1.4
1.4
1.4
1.3
1.3
1.4
1.4
1.4
1.3
1.3
1.4
1.4
1.3
1.3
1.3
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1,3
1.3
1.2
1.3
1.3
1.3
1.2
1.2
1,3
1,3
1.2
1,2
1,2
1,3
1.3
1.2
1.2
1.2
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
40
41
42
43
44
45
46
47
48
49
1.3
1.3
1.3
1.2
1.2
1.3
1.3
1.3
1.2
1.2
1.3
1.3
1.2
1.2
1.2
1.3
1.3
1.2
1.2
1.2
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.2
1.2
1.2
1.1
1.1
1.2
1.2
1.2
1.1
1.1
1.2
1.2
1.1
1.1
1.1
1,2
1.2
1.1
1.1
1.1
1.2
1.1
1.1
1.1
1.1
1.1
1,1
1,1
1,1
1.1
1.1
1.1
45
46
47
48
49
50
51
52
53
54
1.2
1.2
1.1
1.1
1.1
1.2
1.1
1.1
1.1
1.0
1.2
1.1
1.1
1.1
1.0
1.1
1.1
1.1
1.1
1.0
1.1
1.1
1.1
1.0
1,0
1.1
1.1
1.1
1.0
1.0
1.1
1.1
1.0
1.0
1.1
1.1
1.0
1,1
1,0
1.1
50
51
52
53
54
55
56
57
58
59
60
1.0
1.0
1.0
1.0
0.9
1.0
1.0
1.0
0.9
1.0
1.0
1.0
1.0
1.0
1.0
55
56
57
58
59
60
0.8
0.8
0,8
25°
2G°
27°
28°
29°
80°
31°
82°
88°
84°
85°
86°
87°
Declination of the Hanie name as the latitude; lower transit; reduction subtraotlve.
TABLE
26.
[Page 549
Variation of Altitude in one minute from meridian passage.
Declination of a different name from the latitude; upper transit; reduction additive.
Lati-
tude.
o
Lati-
tude.
88°
89°
40°
41°
42°
48°
44°
45°
46°
47°
48°
49°
60°
II
II
" 1
II
II
II
II
II
II
II
II
II
II
o
0
2.5
2.4
2.3
2.3
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
1.7
0
1
2.5
2.4
2.3
2.2
2.1
2.1
2.0
1.9
1.9
1.8
1.7
1.7
1.6
1
2
2.4
2.3
2.3
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
1.7
1.6
2
3
2.4
2.3
2.2
2.1
2.1
2.0
1.9
1.9
1.8
1.8
1.7
1.6
1.6
3
4
2.3
2.2
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
1.7
1.6
1.6
4
5
5
2.3
2.2
2.1
2.1
2.0
1.9
1.9
1.8
1.8
1.7
1.6
1.6
1.5
6
2.2
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.5
6
7
2.2
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1.7
1.6
1.6
1.5
1.5
7
8
2.1
2.1
2.0
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.5
1.5
8
9
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1.7
1.6
1.6
1.6
1.5
1.5
9
10
2.1
2.0
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.5
1.5
1.4
10
11
2.0
2.0
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
11
12
2.0
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.5
1.5
1.4
1.4
12
13
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
1.4
13
14
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.5
1.5
1.4
1.4
1.4
14
15
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
1.4
1.4
15
16
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.5
1.5
1.4
1.4
1.4
1.3
16
17
1.8
1.8
1.7
1.7
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
17
18
1.8
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
1.4
1.4
1.3
1.3
18
19
1.7
1.7
1.7
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
19
20
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
20
21
1.7
1.6
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1,3
21
22
1.7
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
22
23'
1.6
1.6
1.6
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.2
23
24
1.6
1.6
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
24
25
1.6
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
25
26
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
26
27
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.2
27
28
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.1
28
29
1.5
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
29
30
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
30
31
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
31
32
1.4
1.4
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
1.1
32
33
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
33
34
1.4
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
34
35
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
35
36
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
36
37
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
37
38
1.3
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
38
39
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
39
40
1.2
1.2
1.2
1.2
1.1
1.1
1.1
40
41
1.2
1.2
1.2
1.1
1.1
1.1
.
41
42
1.2
1.2
1.1
1.1
1.1
42
43
1.2
1.1
1.1
1.1
43
44
1.1
1.1
1.1
44
45
46
47
48
49
1.1
1.1
1.1
45
46
47
48
49
0.9
0.9
0.9
0.8
0.9
0.9
0.9
0.9
0.9
0.9
50
51
52
53
54
55
56
57
58
0.9
0.9
0.9
0.8
0.8
0.9
0.9
0.8
0.8
0.8
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
50
51
52
53
54
0.9
0.9
0.8
0.8
0.9
0.9
0.8
0.9
0.9
0.9
0~9'
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.8
0.8
0.7
0.7
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
55
56
57
58
0.8
0.8
0.8
0.8
0.8
0.8
59
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
59
60
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
60
38°
89°
40°
41°
42°
48°
44°
45°
46°
47°
48°
49°
50°
Dec
lination
of the N
ime nan
16 as the
latitude
; lower
transit;
reductio
n Hnbtrii
ctlve.
Page 550]
TABLE
26.
Variation of Altitude in one minute from meridian passage.
Declination of a different name from the latitude: uuner transit: reduction additlre.
Lati-
tude.
o
0
Lati-
tude.
0
0
61°
62°
58°
64°.
66°
56°
57°
68°
59°
60°
61°
62°
68°
1.6
1.5
1.5
II
1.4
II
1.4
II
1.3
II
1.3
\%^
II
1.2
!
1.1
II
1.1
1.0
1.0
1
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.1
1.1
1.0
1.0
1
2
1.5
1.5
f.4
1.4
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.0
1.0
2
3
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
3
4
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
4
5
1.5
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.0
1.0
1.0
5
6
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.0
1.0
1.0
6
7
1.4
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
0.9
7
8
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
0.9
8
9
1.4
1.4
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.0
1.0
1.0
0.9
9
10
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
10
11
1.4
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
11
12
1.4
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
0.9
0.9
12
13
1.3
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.0
1.0
1.0
0.9
0.9
13
14
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
14
15
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
15
16
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
16
17
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
17
18
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
18
19
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
1.0
0.9
0.9
0.9
19
20
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
0.8
20
21
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
0.8
21
22
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
1.0
0.9
0.9
0.9
22
23
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
23
24
1.2
1.1
1.1
1.1
1.1
1.0
1.0
1.0
0.9
"0.9
24
25
1.2
1.1
1.1
1.1
1.0
1.0
1.0
1.0
0.9
25
26
1.1
1.1
1.1
1.1
1.0
1.0
1.0
0.9
26
27
1.1
1.1
1.1
1.0
1.0
1.0
1.0
27
28
1.1
1.1
1.1
1.0
1.0
1.0
28
29
1.1
1.1
1.0
1.0
1.0
29
30
30
1.1
1.1
1.0
1.0
31
1.1
1.0
1.0
31
32
33
34
1.1
1.1
1.0
32
33
34
0.8
0.7
0.8
35
36
37
38
39
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
35
36
37
38
39
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
40
41
42
43
44
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
40
41
42
43
44
45
0.9
0.8
0.8
0.8
0.9
0.9
0.8
0.9
0.9
0.9
45
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
46
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
46
47
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.6
47
48
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.6
48
49
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
49
50
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
50
51
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
51
52
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
52
53
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
53
54
0.8
0.7
1 0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
54
55
55
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
56
0.7
0.7
! 0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
56
57
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
57
58
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
58
59
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.5
59
60
1
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.5
60
51°
52°
58°
64°
55°
56°
67°
58°
59°
60°
61°
62°
68°
D
eclinatl(
)n of the
same nc
ime as t
be latitu
de; low€
r transi
I reduc
ion subt
ractlre.
TABLE
27.
■
[Page
551
Reduction to be a
pplied
to Altitudes near the Meridian.
Var.
Time from meridian passage.
Var.
1 min.
(Table
(Table
TO. S.
TO. 8.
TO. S.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
26.)
0 30
1 0
1 30
2 0
2 30
3 0
3 30
4 0
4 30
5 0
o 30
6 0
6 30
26.)
II
/ II
/ II
/ //
/ //
/ //
1 II
/ //
1 II
' II
/ II
' II
' //
' II
II
0.1
0 0
0 0
0 0
0 0
0 1
0 1
0 1
0 2
0 2
0 2
0 3
0 4
0 4
0.1
0.2
0 0
0 0
0 0
0 1
0 1
0 2
0 3
0 3
0 4
0 5
0 6
0 7
0 8
0.2
0.3
0 0
0 0
0 1
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 9
0 11
0 13
0.3
0.4
00
0 0
0 1
0 2
0 2
0 4
0 5
0 6
0 8
0 10
0 12
0 14
0 17
0.4
0.5
0 0
0 0
0 1
0 2
0 3
0 4
0 6
0 8
0 10
0 12
0 15
0 18
0 21
0.5
0.6
0 0
0 1
0 1
0 2
0 4
0 5
0 7
0 10
0 12
0 15
0 18
0 22
0 25
0.6
0.7
0 0
0 1
0 2
0 3
0 4
0 6
0 9
0 11
0 14
0 17
0 21
0 25
0 30
0.7
0.8
0 0
0 1
0 2
0 3
0 5
0 7
0 10
0 13
0 16
0 20
0 24
0 29
0 34
0.8
0.9
0 0
0 1
0 2
0 4
0 6
0 8
0 11
0 14
0 18
0 22
0 27
0 32
0 38
0.9
1.0
0 0
0 1
0 2
0 4
0 6
0 9
0 12
0 16
0 20
0 25
0 30
0 36
0 42
1.0
2.0
0 0
0 2
0 4
0 8
0 12
0 18
0 24
0 32
0 41
0 50
1 0
1 12
1 24
2.0
3.0
0 1
0 3
0 7
0 12
0 19
0 27
0 37
0 48
1 1
1 15
1 31
1 48
2 6
3.0
4.0
0 1
0 4
0 9
0 16
0 25
0 36
0 49
1 4
1 21
1 40
2 1
2 24
2 49
4.0
5.0
0 1
0 5
0 11
0 20
0 31
0 45
1 1
1 20
1 36
1 41
2 5
2 31
3 0
3 31
5.0
6.0
6.0
0 1
0 6
0 13
0 24
0 37
0 54
1 13
2 1
2 30
3 1
3 36
4 13
7.0
0 2
0 7
0 16
0 28
0 44
1 3
1 26
1 52
2 22
2 55
3 32
4 12
4 56
7.0
8.0
0 2
0 8
0 18
0 32
0 50
1 12
1 38
2 8
2 42
3 20
4 2
4 48
5 38
8.0
9.0
0 2
0 9
0 20
0 36
0 56
1 21
1 50
2 24
3 2
3 45
4 32
5 24
6 20
9.0
10.0
0 2
0 10
0 22
0 40
0 44
1 2
1 30
2 3
2 40
2 56
3 23
4 10
5 2
6 0
7 2
10.0
11.0
0 3
0 11
0 25
1 9
1 39
2 15
3 43
4 35
5 32
6 36
7 45
11.0
12.0
0 3
0 12
0 27
0 48
1 15
1 48
2 27
3 12
4 3
5 0
6 3
7 12
8 27
12.0
1.3.0
0 3
0 13
0 29
0 52
1 21
1 57
2 39
3 28
4 23
5 25
6 33
7 48
9 9
13.0
14.0
0 3
0 14
0 31
0 56
1 27
2 6
2 51
3 44
4 43
5 50
7 4
8 24
9 51
14.0
15.0
0 4
0 15
0 34
1 0
1 4
1 34
2 15
3 4
4 0
5 3
6 15
7 34
9 0
10 34
15.0
16.0
16.0
0 4
0 16
0 36
1 40
2 24
3 16
4 16
5 24
6 40
8 4
9 36
11 16
17.0
0 4
0 17
0 38
1 8
1 46
2 33
3 28
4 32
5 44
7 5
8 34
10 12
11 58
17.0
18.0
0 4
0 18
0 40
1 12
1 52
2 42
3 40
4 48
6 4
7 30
9 4
10 48
12 40
18.0
19.0
0 5
0 19
0 43
1 16
1 59
2 51
3 53
5 4
6 25
7 55
9 35
11 24
13 23
19.0
20.0
0 5
0 20
0 45
1 20
2 5
3 0
4 5
5 20
6 45
8 20
10 5
12 0
14 5
14 47
20.0
21.0
21.0
0 5
0 21
0 47
1 24
2 11
3 9
4 17
5 36
7 5
8 45
10 35
12 36
22.0
0 5
0 22
0 49
1 28
2 17
3 18
4 30
5 52
7 25
9 10
11 5
13 12
15 29
22.0
23.0
0 6
0 23
0 52
1 32
2 24
3 27
4 42
6 8
7 46
9 35
11 36
13 48
16 12
23.0
24.0
0 6
0 24
0 54
1 36
2 30
3 36
4 54
6 24
8 6
10 0
12 6
14 24
16 54
24.0
25.0
0 6
0 25
0 56
1 40
2 36
3 45
5 6
6 40
8 26
10 25
12 36
15 0
25.0
26.0
0 6
0 26
0 58
1 44
2 42
3 54
5 18
6 56
8 46
10 50
13 6
26.0
27.0
0 7
0 27
1 1
1 48
2 49
4 3
5 30
7 12
9 7
11 15
27.0
28.0
0 7
0 28
1 3
1 52
2 55
4 12
5 43
7 28
9 27
11 40
28.0
Page 662]
TABLE 27.
Reduction to be applied to Altitudes near the Meridian.
Var.
1 min.
Time from meridian passage.
Var.
(Table
m. 8.
m. s.
m. s.
m. g.
m. s.
m. s.
m. s.
m. «.
m. 8.
m. ».
m. s.
m. s.
m. K.
(Table
26.)
7 0
7 SO
8 0
H SO
» 0
9 30
10 0
10 30
11 0
11 30
12 0
12 30
13 0
26.)
0.1
0 5
0 6
0 6
0 7
0 8
' "
0 9
0 10
0 11
/ II
0 12
0 13
0 14
1 II
0 16
1 II
0 17
0.1
0.2
0 10
0 11
g 13
0 19
0 14
0 16
0 18
0 20
0 22
0 24
0 26
0 29
0 31
0 34
0.2
0.3
0 15
0 17
0 22
0 24
0 27
0 30
0 33
0 36
0 40
0 43
0 47
0 51
0.3
0.4
0.5
0 20
0 24
0 23
0 28
0 26
0 32
0 29
0 32
0 36
0 40
0 44
0 48
0 53
0 58
1 12
1 2
1 18
1 8
0.4
0 36
0 40
0 45
0 50
0 55
1 0
1 6
1 24
0.5
0.6
0 29
0 34
0 38
0 43
0 49
0 54
1 0
1 6
1 13
1 19
1 26
1 34
1 41
0.6
0.7
0 34
0 39
0 45
0 51
0 57
1 3
1 10
1 17
1 25
1 33
1 41
1 49
1 58
0.7
0.8
0 39
0 45
0 51
0 58
1 5
1 12
1 20
1 28
1 37
1 46
1 55
2 5
2 15
0.8
0.9
0 44
0 51
0 57
1 5
1 13
1 21
1 30
1 39
1 49
1 59
2 10
2 21
2 32
0.9
1.0
0 49
0 56
1 4
1 12
1 21
1 30
1 40
1 50
2 1
2 12
2 24
2 36
2 49
1.0
2.0
1 38
1 52
2 8
2 24
2 42
3 0
3 20
3 40
4 2
4 24
4 48
5 12
5 38
2.0
3.0
2 27
2 49
3 12
3 37
4 3
4 30
5 0
5 31
6 3
6 37
7 12
7 49
8 27
3.0
4.0
3 16
3 45
4 16
4 49
5 24
6 1
6 40
7 21
8 4
8 49
9 36
10 25
11 16
4.0
5.0
4 5
4 41
5 20
6 1
6 45
7 31
8 20
9 11
10 5
11 1
12 0
13 1
14 5
5.0
6.0
4 54
5 37
6 24
7 14
8 6
9 1
10 0
11 1
12 6
13 13
14 24
15 37
16 54
6.0
7.0
5 43
6 34
7 28
8 26
9 27
10 32
11 40
12 52
14 7
15 26
16 48
18 14
19 43
7.0
8.0
6 32
7 30
8 32
9 38
10 48
12 2
13 20
14 42
16 8
17 38
19 12
20 50
22 32
8.0
9.0
7 21
8 26
9 36
10 50
12 9
13 32
15 0
16 32
18 9
19 50
21 36
23 26
25 21
9.0
10.0
8 10
8 59
9 22
10 19
10 40
11 44
12 2
13 30
14 51
15 2
16 33
16 40
18 22
20 10
22 2
24 0
26 2
28 10
10.0
11.0
11.0
13 15
18 20
20 13
22 11
24 15
26 24
28 39
12.0
9 48
11 15
12 48
14 27
16 12
18 3
20 0
22 3
24 12
26 27
28 48
12.0
13.0
10 37
12 11
13 52
15 39
17 33
19 33
21 40
23 53
26 13
28 39
13.0
14.0
11 26
13 7
14 56
16 51
18 54
21 3
23 20
25 43
28 l4
14.0
15.0
12 15
14 4
16 0
18 14
20 15
22 34
25 0
27 34
15.0
16.0
13 4
15 0
17 4
19 16
21 36
24 4
26 40
16.0
17.0
13 53
15 56
18 8
20 28
22 57
25 34
17.0
18.0
14 42
16 52
19 12
21 40
24 18
18.0
19.0
15 31
17 49
20 16
19.0
20.0
16 20
18 45
20.0
21.0
17 9
21.0
TABLE
27.
[Page 553
Reduction to be applied to Altitudes near the Meridian
Var.
Time from meridian passage.
Var.
1 mln.
(Table
(Table
m. «.
m. 8.
TO. S.
m. 8.
TO. 8.
m. 8.
TO. «.
TO. 8.
TO. 8.
m. 8.
TO. 8.
m. s.
TO. 8.
26.)
18 30
14 0
14 30
15 0
15 80
16 0
16 80
17 0
17 30
18 0
18 80
19 0
19 30
26.)
„
/ II
/ II
/ II
/ II
/ //
/ II
/ //
/ //
1 II
/ II
/ II
/ II
' II
„
0.1
0 18
0 20
0 21
0 22
0 24
0 26
0 27
0 29
0 31
0 32
0 34
0 36
0 38
0.1
0.2
0 36
0 39
0 42
0 45
0 48
0 51
0 54
0 58
1 1
1 5
1 8
1 12
1 16
0.2
0.3
0 55
0 59
1 3
1 7
112
117
122
127
132
137
143
148
154
0.3
0.4
1 13
1 18
124
130
136
1 42
149
156
2 2
2 10
2 17
2 24
2 32
0.4
0.5
131
138
145
152
2 0
2 8
2 16
2 24
2 33
2 42
2 51
3 1
3 10
0.5
0.6
149
158
2 6
2 15
2 24
2 34
2 43
2 53
3 4
3 14
3 25
3 37
3 48
0.6
0.7
2 8 2 17
2 27
2 37
2 48
2 59
3 11
3 22
3 34
3 47
4 0
4 13
4 26
0.7
0.8
2 26| 2 37
2 48
3 0
312
3 25
3 38
3 51
4 5
4 19
4 34
4 49
5 4
0.8
0.9
2 44 2 56
3 9
3 22
3 36
3 50
4 5
4 20
4 36
4 52
5 8
5 25
5 42
0.9
1.0
1.0
3 2 i 3 16
3 30
3 45
4 0
4 16
4 32
4 49
5 6
5 24| 5 42
6 1
6 20
2.0
6 4 1 6 32
7 0
7 30
8 0
8 32
9 4
9 38
10 12
10 48 11 24
12 2
12 40
2.0
3.0
9 7
9 48
10 30
1115
12 1
12 48
13 38
14 27
15 19
16 12 17 7
18 3
19 1
3.0
4.0
12 9
13 14
14 1
15 0
16 1
17 4
18 9
19 16
20 25
2136
22 49
24 4
25 21
4.0
5.0
15 11
16 20
17 31
18 45
20 1
2120
22 41
24 5
25 31
27 0
28 31
5.0
6.0
18 13
19 36
21 2
22 30
24 1
25 36
27 13
6.0
7.0
21 16
22 52
24 32
26 15
28 1
7.0
8.0
24 18
26 8
28 2
8.0
9.0
27 20
9.0
Var.
T
ime fror
a meridi
anpasss
ge.
Var.
1 mill.
(Table
m. s.
m. «.
m. s.
m. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
TO. 8.
(Table
26.)
20 0
20 80
21 0
21 80
22 0
22 30
23 0
23 30
24 0
24 30
25 0
25 80
26 0
26.)
II
/ II
' //
' H
' II
' n
/ n
/ //
/ II
/ II
/ II
' //
/ //
/ //
II
0.1
0 40
0 42
0 44
0 46
0 48
0 51
0 53
0 55
0 58
1 0
1 2
1 6
1 8
0.1
0.2
120
124
128
132
137
141
146
150
155
2 0
2 5
2 10
2 15
0.2
0.3
2 0
2 6
2 12
219
2 25
2 32
2 39
2 46
2 53
3 0
3 7
3 15
3 23
0.3
0.4
2 40
2 48
2 56
3 5
3 14
3 22
3 32
3 41
350
4 0
4 10
4 20
4 30
0.4
0.5
3 20
3 30
3 41
3 51
4 2
4 13
4 24
4 36
4 48
5 0
5 12
5 25
5 38
0.5
0.6
4 0
4 12
4 25
4 37
4 50
5 4
5 17
5 31
5 46
6 0
615
6 30
6 46
0.6
0.7
4 40
4 54
5 9
5 24
5 39
5 54
6 10
6 27
6 43
7 0
7 17
7 35
7 53
0.7
0.8
5 20
5 36
5 53
6 10
6 27
6 45
7 3
7 22
7 41
8 0
8 20
8 40
9 1
0.8
0.9
6 0
6 18
6 37
6 56
7 16
7 36
7 56
8 17
8 38
9 0
9 22
9 45
10 8
0.9
1.0
1.0
6 40
7 0
7 21
7 42
8 4
8 26
8 49
9 12
9 36
10 0
10 25
10 50
1116
2.0
13 20
14 0
14 42
15 24
16 8
16 52
17 38
18 24
19 12
20 0
20 50
2140
22 32
2.0
3.0
20 0
21 0
22 3
23 7
24 12
25 19
26 27
27 37
28 48
30 0
3.0
4.0
26 40
28 1
29 24
4.0
Page 554] TABLE 28A.
For finding the Latitude of a place by Altitudes of Polaris.
[A=l8t correction. Argument, the star's hour angle (or 24i>— the star's hour angle).]
Qh ih 2h j 3h 1 41. 5h
12 00.0
11 59.9
11 59.8
11 59.6
11 59.3
11 58.9
11 58.5
11 58.0
11 57.4
11 56.7
10
11
12
13
14
15
16
17
18
19
-1 11 55.9
' 11 55.0
11 54.1
11 53.1
11 52.0
-1 11 50.8
11 49.5
1148.1
11 46.7
11 45.2
20
21
22
23
24
25
26
27
28
29
11 43.6
11 41.9
11 40.1
11 38.3
11 36.3
11 34.3
11 32.2
11 30.0
11 27.8
11 25.5
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
-1 11 23.1
11 20.6
11 18.0
11 15.3
11 12.6
-1 11 09.7
11 06.8
11 03.8
11 00.8
^057^
-1 10 54.4
10 51.1
10 47.7
10 44.2
10 40.7
-1 10 37.0
10 33.3
10 29.5
10 25.6
10 21.7
-1 10 17.6
10 13.5
10 09.3
10 05.0
10 00.7
-1 09 56.2
09 51.7
09 47.1
09 42.4
09 37.7
-1 09 32.8
.0
.1
.1*
.3
.4
-1
-1
-1
09 32.8
09 27.9
09 22.9
09 17.9
09 12.7
09 07.4
09 02.1
08 56.7
08 51.3
08 45.8
08 40.2
08 34.4
08 28.6
08 22.7
08 16.8
08 10.8
08 04.7
07 58.5
07 52.3
07 46.0
07 39.6
07 33.1
07 26.5
07 19.9
07 13.1
07 06.3
06 59.5
06 52.5
06 45.5
06 38.4
06 31.2
06 24.0
06 16.7
06 09.3
06 01.8
05 54.2
05 46.6
05 38.9
05 31.1
05 23.3
05 15.3
05 07.3
04 59.3
04 51.1
04 42.9
04 34.6
04 26.2
04 17.8
04 09.3
04 00.7
— 1
llh
03 52.0
03 43.3
03 34.5
03 25.6
03 16.6
03 07.6
02 58.6
02 49.4
02 40.2
02 30.8
02 21.4
4.9,
5.0
5.0;
5.2,
5.3
5.3
m;
5.4'
5.5|
5.6,
5.8
5.8|
5.9;
5.9
6.0
6.1;
6.2'
6.2,
6.3,
G.4
G.5
6.6;
6.6
6.8
6.8
6.8
7.0'
7.0'
7.1'
7.2
7.2
7.3!
7.4'
7.5'
7.6'
7.6
7.7^
7.8!
7.8
8.0
8.0'
8.0!
8.2'
8.31
8.4|-
8.4,
8.5
8.6;
8.7;-
8.7: ■
9.0
9.0;
9.0:
9.2
9.2|
9.4
9.4
-1 02 21
02 11.
02 02.
0152.
0143.
-1 01 33.
0123.
0113.
0103.
00 53.
4 — '
^ 9.5
9.5
9.6
9.7^
-1 00 43.
00 33.
00 23.
00 12.
00 02.
-0 59 52,
59 41
59 31.
59 20.
59 09.
-0 58 58,
58 48,
58 37,
58 26
58 15,
-0 58 04
57 52
57 41
57 30
57 18
-0 57 0
56 56
56 44
56 32.
56 21.
-0 56 09.
55 57.
55 45.
55 33.
55 21.
-0 55 09.
54 57.
54 45.
54 32.
54 20.
-0 54 08.
53 55.
53 43.
53 30.
53 18.
-0 53 05
52 52
52 39
52 26
52 13
-0 52 00
5147
5134
5121
5108,
-0 50 54,
9.8:
9.9;
10.0'
I
10.1
10.2
10.21
IO.3I
10.3:
10.5|
10.5
10.6
10.6;
10.7;
10.8
10.9'
10.9!
10.9
11.1
ll.l|
11.2'
11.2;
11.3
11.4'
I
11.4
11.6
11.6
11.6
11.7'
11.8
11.8:
11.9
12.0'
12.0
12.1
12.1
12.2
12.3|
12.3
12.4!
12.5j
12.5,
12.6
12.6
12.7
12.8
12.8;
12.9
13.0
13.0
13.0
13.1
13.2
13.3
13.3
-0 50 54.
50 41.
50 28.
50 14.
50 01.
-0 49 47.
49 33.
49 20.
49 06.
48 52.
-0 48 38.
48 24.
48 10.
47 56.
47 42.
-0 47 28.
47 14,
47 00.
46 45.
46 31,
-0 46 17
46 02
45 48
45 33
45 18
-0 45 04
44 49
44 34
44 19
44 04
-0 43 50
43 35
43 20
43 05
42 49
-0 42 34
42 19
42 04
4148
4133
-0 41 18
4102
40 47
40 31
4016
-0 40 00,
39 44
39 28
39 13
38 57
-0 38 41
38 25
38 09
37 53
37 37
-0 37 21
37 05
36 48
36 32
36 16
-0 36 00
13.3
13.4;
13..5
13.5
13.6;
13.7,
13.71
13.7
13.8:
13.9,
14.0
14.0
14.0
14.1
14.1
14.2
14.2
14.3;
14.4,
•14.4
14.5
14.5;
14.6]
14.6
14.7|
14.8
14.8!
14.8;
14.9
i
14.9
15.0
15.0!
15.0'
15.1!
15.2;
15.2J
15.3
15.3;
15.3:
15.4
15.5;
15.5
15.6'
15.6|
15.71
15.7
15.7;
15.8;
15.8
15.9
15.9
16.0
16.0
16.1
16.1
16.2
16.2
16.3
16.3
I6.3!
-0 36 00
35 43
35 27
35 10.
34 54.
-0 34 38.
34 21.
34 05.
33 48.
33 31.
-0 33 15^
32 58.
32 41,
32 24.
32 07,
-0 31 50,
31 34,
31 27,
31 10,
30 53,
-0 30 36,
30 18,
30 01,
29 44,
29 17,
-0 29 00,
28 42,
28 25
28 08
27 50
-0 27 33
27 16
26 58
26 41
26 23
-0 26 05
25 48
25 30
25 13
24 55
-0 24 37
24 20
24 02
23 44
23 26
-0 23 08
22 50
22 33
22 15
2157
-0 21 39
2121
2103
20 45
20 27
-0 20 09
19 50
19 32
19 14
18 56
-0 18 38
16.3
16.4
16.4
16.4
16.4
16.5
16.6;
16.6
16.7
16.7
16.8
16.8
16.8
16.8
16.9
I6.9;
16.9
17.0
17.1;
17.0
17.1
17.2
17.2
17.2
17.2
17.3j
17.3;
17.4;
17.4
17.4
17.5
17.5:
17.5;
17.6
17.6
17.6
17.6
17.7
17.
17.7
17.8
17.8!
17.8
17.8'
17.9
17.9
17.9
17.9
18.0
18.0
18.0
18.0,
18.1
18.1
18.1
18.1
18.2
I8.2'
18.2
4
.0
.5
0
5
9
3
.7
.1
A
.7 ,-- —
-0 18 38.
18 20.
18 01.
17 43.
17 25.
-0 17 06.
16 48.
16 30.
16 11.
15 53.
-0 15 35
15 16.
14 58.
14 39
14 21,
-0 14 03
13 44
13 26,
13 07
12 48
-0 12 30.
12 11,
1153.
1134.
1115.
-0 10 57
10 38
10 20
10 01
09 42
-0 09 24
09 05
08 46
08 27
08 09
-0 07 50
07 31
07 12,
06 54
06 35
lOh
9h
Sh
Ih
0 06 16
05 57
05 39
05 20
05 01
-0 04 42
04 23
04 05
03 46
03 27
-0 03 08
02 49
02 30
02 12
01 53
-0 01 34
0115
00 56
00 37
00 18
-0 00 00,
01'
18.2
18.2
18.3
18.3
18.3
18.3
18.3
18.4
18.4
18.4'
18.4!
I8.4!
18.4'
18.4J
18.5!
I8.5;
18.5
18.5
18.6;
18.6-
18.6|
18.6
18.6
18.6
18.7
18.6
18.6
18.6
I8.7'
18.7-
18.7|
18.71
I8.7'
18.7
18.7;
18.71
18.7;
18.8!
18.8
18.7
18.8'
18.8;
18.8,
18.8;
18.8'
18.8!
18.8
18.8
18.8
18.9
18.8;
18.8
18.9
18.8
18.8
18.9
18.8
18.9
18.9
18.9
60
59
58
57
5<>
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
Jl_
10
Change the sign to + when the argument is found at tlie bottom.
TABLE 28B.
[Page 555
For finding the Latitude of a
L place by Altitudes of Polaris.
[B=the 2d correction. This correction is always additive.]
Star's
Star's altitude. 1
star's
hour
angle.
hour
angle.
10°
15°
16°
17°
18°
^ 19°
20°
21°
22°
23°
h. m.
//
//
II
II
II
//
//
II
II
// '
h. m.
0 00
0.0 0
0.0 0
0.0 0
0.0 n
0.0 0
0-0.0
0-0.0
0-0.0
0.0.0
0-0.0
12 00
10
0.0 ',
0.0?
0.0 ',
0.0
1
0.0 1
0.0 "
0.0 1
0.0 "
0.0 1
0.0 1
11 50
20
0.1-
0.1-
0.1-
0.1
\
0.1 •;
0.1 •;
0.1 0
0.1 \
0-1 \
0.1 \
40
30
0.2 \
0.2'
0.2'
0.2
0
0.2 \
0.2 1
0.3-2
0.3-5
0.3-3
0.3-3
30
40
0.3-
0.3 2
0.4"
0.4
0
0.4'^
0.5-3
0.5-3
0.5-3
0-63
0-6-3
20
50
0.4-
0.5 t,
0.6'
0.6
3
0.7 -J
0.8-3
0.8 3
0.8-3
0-9-3
0.9 -,
10
1 00
0.5-
0._8-
1.1 !
0.9-
0.9
3
1.0-
1-1 ■,
1-1
1-1 ■
1.2'
1.3'
00
10
0.7-;
1.2-3
1-8 1
2.3-5
2.8-
3- 2'
1.2
1.3-4
1.4-^
1-45
1.5-5
1.6 -J
1-75
10 50
20
1.1 'll 1.8 •:
1.4 -'l 2.2-!
1.6
1.7-1
2.6 -J
3-1 1
3.6-
1-8-6
1-9 1
2-0 -J
2-1 1
2-7-
2-2-6
40
30
2.0
i
2.3-,
2-4 -5
2-5-6
2-8-6
30
40
2.4
2-8 1
2-9-6
3-1 1
3.7-
4.4-^
3-2 •«
3.8-;
4.5-^
a
3-4-6
20
50
1.7-
2.0"'
2.3-^
2.6-4
3.5 -J
2.9
3-3 -fi
3.9-
3-5-6
4.0-5
10
2 00
3.4
ts
4.1-
4.7-
00
10
3.7 -fi
4.3-
4.8 -J
5.3-!
5-9 -«
7-0 1
8.7-,
3.9
6
6
6
4.9 -J
5.5 -J
6.7-;
7.4-^
4-5 fi
5.1-
5.8-'
6.4-
7.1-;
8.4-?
9.1-
9.8 •'
10.4 -;
4.8-;
5.4-
6.1 -;
6.8-,
7.5-;
8.3-^
5.0-5
5.7-;
6.4-;
8.7-^
9.4 -J
10.2 -,
10.9 -,
11.6 -,
5.3-5
6-0 •;
6.8-5
8.3 -J
9.1 •*
5.6-"
7-1 8
7-9-8
8-7-8
9 50
20
2.6-:
4.0 •;
4.5
40
30
2.9'^
4.5-^
5.1
30
40
3.3 t
5.0-:^
5.7
20
50
3.6'^
5.5 -J
6.3
10
3 00
4.0-''
6.0-^
6.9
6
6
5
6
6
00
10
4.3 -J
6.6-^
7.5
8-0 •«
8.9-2
9-6 -«
10.4-^
9.9 -J
10. 7 -J
10.4 -'
11-3-8
12-1-8
12.9-^
8 50
20
4.7-^
7.1 -J
8.1
8.6-'
40
30
5.0-^
7.6-;
8.6
9.2-5
11.5 -,
30
40
5.3 -J
8.1 •;
9.2
9-9 I
11.0 •?
12.2 -J
20
50
5.7-^
8.6-^
9.2-^
9.8
10.5-^
11.1 •!
11. 7-'
12.3 •;
13.0-5
13. 7-!
10
4 00
6.0-^
9.1-^
9.7-^
10.4
h
11.0-^
11.7-'^
12.3-"
13.0-^
13.7-^
14.4-^
00
10
6.3-^
9.6-;;
10.2-^
10.9
11.6-^
12.2-^
13.0-^
13.6-^
14-3 -'
15.0-5
7 50
20
6.6,
10.0'^
10.7-^
11.3
12.1 1
12.8 ■.
13.6-°
14.3-^
14.9-^
15-7 -„
40
30
6.8-^
10.4-^
11. 1-!
11.7
12:5 -f
13.3-^
14. 0-*
14.8 -,
15.6 •!
16.3-^
30
40
7.0-
10.8 -J
11.4^
12.1
13.0 -,
13.8 -,
14.5-^
15.3-^
16.1 -l
16.9-°
20
50
7.3-^
11.1 -l
11.8 -J
12.5
4
13.4 -J
14.2 J
15.0-^
15.8 ,
16.6-^
17.5-^
10
5 00
7.5-^
11.4-^
12.1 -^
12.9
13.7 -^
14.5 -^
15.4-^
16.2-^
17.1 -^
17.9-^
00
10
7.6-;
11.6-^
12.4 -J
13.2
14.0 -J
14.8-^
15.7-^
16.5-^
17.4-3
18.3-^
6 50
20
7.8 -f
11.7-^
12.6 ,
13.4
2
14.2 ■;
15.1 -l
16.0-^
16.8-^
17.7-^
18.6-^
40
30
7.9-,
11.9 f
12.7 ■,
13.6
14.4-2
15.3-2
16.2 -;
17.1-.'
18.0 -^
18.9 -f
30
40
7.9-^
12.0 "I
12.9 -f
13.7
14.6 -^
15.5-2
16.4-2
17.3-2
18.1 -^
19.0 -,
20
50
7.9-^
12.1 -^
13.0 -^
13.8
14. 7 -^
15.6 -^
16.5-^
17.3 •«
18.2-1
19.1 ■]
10
6 00
7.9-^
12.2-^
13.0 •"
13.9-^
14.7-°
15.6-0
16.5 •"
17.3-0
18.3 -1
19.2-1
6 00
TABI
.E 28C.
[C=the 3d correction.
Hor. Arg.
the star's
declination. Vert. Arg., B=the
2d correct
ion.]
B.
88° 47'
88° 48'
88° 49' 1
20"
30"
40"
50"
0"
10"
20"
80"
40"
50"
0"
10"
20"
//
//
«
II
II
II
1 "
II
II
II
II
II
II
II
0
0.0
0.0
0.0
0.0
o.c
) 0.0
0.0
0.0
0.0
0.0
0
.0
0.0
0.0
10
+0.2
+0.1
+0.1
+
0.0
0.(
) -0.0
-0.1
-0.1
-0.2
-
-0.2
-0
.3
—0.4
-0.4
20
0.4
0.3
0.2
0. 1 0. (
) 0.1
t 0.2 ; 0.3
0.4
0.5
0
.6
0.7
0.8
30
0.6
0.5
0.3
0.1
o.c
) 0.1
0. 3 0. 5
0.6
0.7
0
.8
1.1
1.2
40
0.8
0.6
0.4
0.2
o.c
) 0.2
0.4
0.6
0.8
1.0
1
.2
1.5
1.6
50
+1.0
4-0.7
+0.5
+
0.2
o.c
) -0.2
0.5
-0.9
-1.0
-
-1.2
-1
.5
-1.7
-2.1
Note. — Below 15° B is nearly proportional to the altitude.
Page 656]
TABLE 28B
For finding the Latitude of a place by Altitudes of Polaris.
[B=the 2d correction. This correction
is always additive.]
Star's
hour
Star's altitude. 1
SUir's
hour
angle.
24°
26°
26°
27°
28°
28°
80°
31°
82°
Z9fi
angle.
h. m.
» II
II
//
II
//
//
//
II
II
II
h. in.
0 00
0.0 „
0-0.0
0.0 .
0.0 l
0.2 •;
0.4 l
0.7 l
1-1 1
1.5 •"
0.0 ^
0.0 -l
0.2 -i
0.4 l
0.7 -^
1.1 4
1.5 -^
0.0 „
0.0 •°
0.2 -i
0.4 'l
0.7 l
1-1 1
1.6 -^
0.0 „
0.0 •°
0.2 -t
0.4 'l
0.7 l
1.1 -J
1.7 ■'
2.3 -^
2.9 ■;
3.6 •;
0.0 ^
0.0 •°
0.2 -t
0.4 'l
0.8 ,
1.2 -J
1.7 -^
0.0 ^
0.0 •"
0.0 „
0.0 ,,
12 00
10
0.0 -J
0. o*-?
0.0 •;
0.0 -°
11 50
20
0.1 •
0.1 i
0.2 •;
0.5 5
0.2 -2
0.2 -2
40
80
0.3 •:
0.3 -^
0.5 \
0.5 -,
30
40
0.6 ■,
0.6 .
0.8 ■:
1.3 -^
0.8 z
1.3 -l
0.9 -.
20
50
1.0 ■'
1.0 J
1.4 'X
10
1 00
1.4 ■'
1.4 •'
1.9 •;
1.8 •'
1.9 •'^
1.9 -'
00
10
1.8 ■'
2.0 i
2.1 -^
2.2 -J
2.8 •;
3.5 l
4.3 -^
5.1 -l
2.3 ■;
3.0 -J
3.8 -l
4.7 -^
5.6 'l
6.5 -^
7.51-°
2.4 -^
2.5 -^
2.6 -:
10 50
20
2.3 ■:
2.4 -l
2.5 ,
2.7 -^
3.2 -J
3.3 'l
3.4 'l
40
30
2.9 !
3.1 ■;
3.8 •;
3.2 ■;
3.4 !
4.0 -l
4.1 -^
4-3/0
30
40
3.6 •:
4.0 -i
4.7 •!
4-1 ■«
4.5 -l
5.3 ■;
4.9 •;
S-Oi'o
5.31-°
20
5f)
4.3 •:
4.5 -l
4.9 -^
5.8 -J
6.0 -J
6.2,-;
10
2 00
5.0 ■'
5.3 -^
5.5 ■«
5.8 -^
6.0 -^
6.2 -^
6.8l-°
7.0i-°
7. 3 1-1
00
10
5.8 -J
6.1 •;
6.4 -^
6.7 'l
7.0l-°
7.2i-°
7.91-1
8. 2 1-2
8.51-2
9 50
20
6.6 'l
7.0 -^
7.3 -l
7.6 -^
7-9,n
8.3-1
8.61-;
8.9 -J
9.31-1
9.6-1
40
30
i.b
7.9 -l
8.2 -^
8-5/n
8.9 ■;
9.3 -J
9.6 •°
10.0 1-1
10.4 -
10.81-2
30
40
8. 3- 'l
8.7 -^
9.1 'l
9.51-°
10.0 11
10.4 1
10.8 -J
11.21-2
11.6-2
12.0 1-2
20
50
9.2 'l
9.6 'l
10.0 •„
10.51°
ii.oi°
11.41°
11. 9 1-
12.4!-^
12. 9 i-„
13. 3 1-^
10
3 00
10.0 -^
10.5 -^
11.01°
11. 5 1-°
12.0l°
12. 5 11
13.0 1-1
13.61-2
14.11-2
14. 6 1-**
00
10
10.9 'l
11-4/2
12.0;°
12.51°
i3.di°
13.611
T4.2i-'f
14. 7 1-1
I5.4I-5
16. oj-;
8 50
20
11.8 'l
12.41°
13.0i°
13.5 O
14. 1 11
14.7 ■
15.3 •
15.9-2
16.61-2
17.3 -^
40
30
12.6 'l
13.3 -l
13.9 -l
14.5 -J
15.ll°
15.8-1
16.4 ■
17.1 1-2
17.8-2
18.5-2
30
40
13.5 •;
14.2 J
14.8 -^
15.51°
16-1 n
16. 8 1-°
17.5-1
18. 2 1-1
19. 0 1-2
19.7-2
20
50
14.3 'l
15.0 'l
15.7 -l
16.4 -l
17.1 ^
17.8 •"
18.5 -^
19.4-2
20. 1 1-1
20. 9 1-2
10
4 00
10
15.1 •*'
15.9 -t
15.8 •'^
16.6 -^
16.5 -^
17.3 •«
17.3 -^
18.1 •*
18. 1 1-°
18. 8 1-°
19.7 -l
19.61-1
20.41°
21.41-°
21. 2 1-1
22. 3 1-1
22.0 1-1
00
19.0 'l
20. 6 1-°
23. 1 1-1
7 50
20
16.6 •;
17.3 !
18.1 -Z
19.0 •;
19.8 •«
20.6 'l
21.5 -l
22.41-°
23.2 -„
24.1 -°
40
30
17.2 J
18.0 -J
18.8 -^
19.7 !
20.5 -l
21.4 •"
22.3 -Z
23.2 'l
24.1 \
25.li-°
30
40
17.8 i
18.6 'l
19.5 -l
20.3 -^
21.2 •:
22.1 -l
23.0 -^
24.0 i
24.9 'l
25.9 -^
20
50
18.3 i
19.2 -^
20.1 -^
21.0 !
21.9 •'
22.8 -l
23.7 -'
24.6 •_
Ih.l -_
26.7 -l
10
5 00
18.8 -^
19.2 -f
19.7 -5
20.6 -^
21.1 •;
21. {
22.4 -^
23.4 -^
23.9 -^
24.4 •'
24.9 -f
25.3
.5
26.4
.6
27.4 •'
28.0 -^
00
10
20.1 ■]
22. (
22.9 ••'
25.8
27.0
6 50
20
19.5 i
20.5 -^
21.4 l
22.4 -^
23.3 -t
24.3 -t
25.4 •;
26.2 -^
27.4 -^
28.5 -5
40
30
19.8 -l
20.7 •
21.7 -l
22.6 -l
23.6 'l
24.6 -^
25.7 -l
26.6 -J
27.8 -t
28.8 l
30
40
20.0 -2
20.9 f
21.9 -^
22.8 -2
23.9 -^
24.9 -f
25.9 -2
26.9 -^
28.0 -2
29.1 -^
20
50
20.1 -^
21.0 -1
22.0 -1
23.0 ■]
24.0 1
25.0 -1
26.0 -1
27.0 -1
28.2 -2
29.3 ■;
10
6 00
20.2 -^
21.1 -1
22.0 •"
23.1 1
24.1 -1
25.1 -1
26.1 -1
27.1 -1
28.3 1
29.4 •'
6 00
TABLE 28C
[C=the 3d c
orrection.
Her. Arg., the star's declinatio
n. Vert. Arg., B=th€
2d correct
ion.]
B.
88° 4
V
88
° 48'
88-^ 49' 1
20"
80"
40"
50"
0"
10"
20"
80"
40"
50"
0"
10"
20"
II
w
//
II
II
II
II
II
II
II
II
/
1
II
ii
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
.0
0.0
0.0
10
+0.2
+0.1
+0.1
■+
0.0
0.0
-0.0
-0.1
-0.1
-0.2
-0.2
-0
.3
-0.4
-0.4
20
0.4
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
0
.6
0.7
0.8
30
0.6
0.5
0.3
0.1
0.0
0.1
0.3
0.5
0.6
0.7
0
.8
1.1
1.2
40
0.8
0.6
0.4
0.2
0.0
0.2
0,4
0.6
0.8
1.0
1
.2
1.5
1.6
50
+1.0
+0.7
+0.5
4
-0.2
0.0
-0.2
-0:5
-0.7
-1.0
-1.2
-1
.5
-1.7
-2.1
TABLE 28B.
For finding the Latitude of a place by Altitudes of Polaris.
[B = the 2d correction. This correction is always additive.]
[Page 557
star's
hour
angle.
h. in.
0 00
10
20
30
40
50
1 00
10
20
30
40
50
00
10
20
30
40
50
3 00
10
20
30
40
50
4 00
10
20
30
40
50
5 00
10
20
30
40
50
6 00
Star's altitude.
0.0
0.1
0.2
0.5
0.9
1.5
2.0
S.8
10.0
11.3
12.6
13.9
15.2
16,6
17.9
2
20.5
21.7
22.8
24.0
25.0
26.1
27.0
27.8
28.4
29.1
29.6
30.0
30.3
30.5
30.5
24.9
26.0
27.1
27.9
28.8
29.6
30.2
30.7
31.1
31.4
31.6
31.7
38°
89°
0.0
0.1
0.3
0.6
1. 1
1.7
2.4
3.3
4.3
5.3
6.6
7.8
9.2
10.6
12.1
13.6
15.1
16.7
18.3
19.9,
21.5,
23.1,
24.6;
26.1,
27.5
28.8
40°
0.0
0.1
0.3
0.6
1.1
1.8
2.5
3.4
4.5
5.6
6.8
8.1
9.5
29.9
31.2
32.4
33.5
34.4
35.3
36.1
36.8
37.3
37.6
37.8
37.9
0.0
0.1
0.3
0.7
1.2
1.9
2.7
3.6
4.6
5.8
7.0
8.3
11.3
13.0
14.6
16.2
18.0
19.7
21.4
23.1
24.7
26.4
27.9
29.5
30.9
32.3
33.5
34.7
35.8
36.7
37.5
38.2
38.6
39.0
39.3
39.4
42°
11.7:
13.4
15.1
16.8
18. 5:
20.3:
38.8
39.5
40.0
40.4
40.7
40.8
48°
9.0:
10.5:
12.1;
13.9;
15.6:
26.5:
28.3:
30. 0:
Star's
hour
angle.
/(. ?;(.
12 00
11 50
40
30
20
10
00^
10 50
40
30
20
10
00
6 50
40
30
20
10
6 00
TABLE 28C.
[C = the 3d correction. Hor. Arg., the star's declination. Vert. Arg.j B = the 2d correction.]
B.
0
10
20
30
40
50
20'
0.0
+0.2
0.4
0.6
0.8
+1.0
88° 47'
80'
0.0
+0.1
0.3
0.5
0.6
+0.7
40'
0.0
+0.1
0.2
0.3
0.4
+0.5
60'
0.0
+0.0
0.1
0.1
0.2
+0.2
88° 48'
0.0
0.0
0.0
0.0
0.0
0.0
10'
0.0
-0.0
0.1
0.1
0.2
-0.2
20"
0.0
80'
0.0
-0.1
0.3
0.5
0.6
-0.7
40'
0.0
-0.2
0.4
0.6
0.8
-1.0
50'
0.0
-0.2
0.5
0.7
1.0
-1.2
0.0
-0.3
0.6
0.8
1.2
-1.5
88° 49'
10"
0.0
-0.4
0.7
1.1
1.5
-1.7
20'
0.0
-0.4
0.8
1.2
1.6
-2.1
Page 558]
TABLE 28B.
For finding the Latitude of a place by Altitudes of Polaris.
[B=the 2d correction. This correction is always additive.]
star's
hour
Star's altitude. 1
star's
liour
angle.
44°
45°
46°
47°
48°
49°
50°
51°
52°
angle.
h. m.
„
//
„
II
//
„
„
„
„
//. m.
0 00
0.0 1
0.0 ,
0.0 ,
0.0 1
0.0 1
0.0 1
0.0 ,
0.0 ,
0.0 ,
12 00
10
0.1
o
0.1. -2
0.1 2
0.1 2
0.1 .3
0-1 :3
0.1 :3
0.1 -3
0.1 i
11 50
20
0.3
1
0.3 4
0.3-5
0.3 5
0.4 .5
0.4 5
0.4 5
0.4 6
0.4 i
.] 40
30
0.7
(i
0.7 \
0.8 %
0.8 ;
0.9 6
0.9 ;
0.9 7
1.0 7
1.0 8
30
40
1.3
7
1.4 •;
1.4 %
1.5 \
1-5 8
1.6 8
1-6 :9
1.7 9
1. 8 i-,3
20
50
2.0
9
2-1 :9
2.2i:
2.3 9
2.3i
2. 4 1.1
2. 5 1.1
2.61:
2.8 •
10
1 00
2.9
3.0^^
^•2io
3.2^„
^•^1
3.5,.
•^•^3
3-7i3
3.9 •
00
10
4.0
1
4.iil.2
4.2 :3
4.4 :3
4.5 :
4.7 :4
4.9 4
5.0 1:6
5.3 •
10 50
20
5.1
^
^' ^ 1.3
5. 5 1.4
5- 7 1.4
5. 9 1.5
6.1 1.5
6. 3 1.6
6. 6 1.6
6. 8 ;•-
40
30
6.4
4
6.61.5
6.9i4
' • 1 1.6
7. 4 1.0
7.61.7
7. 9 1.7
8. 2 1.8
8.5 •;
30
40
7.8,
8-1 1.5
8. 3 1.7
8. 7 1.7
H-2l-7
9. 3 1.8
9. 6 1.9
10.0 1.9
10-3 20
20
50
9.3t
f)
9.61.7
10. 0 1 7
10- 4 1.8
10. 7 1.9
11.1 1.9
11.5 2.0
11.9 2.0
12. 3 22
10
2 00
10
10.9
12. 6 T
7
11.3
13. 0^:;
11.'
U.8
>iq
12-2is
12.6
1.9
13-0 2.0
I5.O21
13-5 2.1
15.621
13.9,
2
a
14-5'-
00
13. J
14.0 :
14.5
16.1 2
16.7^2
19-0 25
9 50
20
14.3,
q
14. 9 1.9
15.4i:9
16.0 2.0
16.5 2.1
17.1 2.2
17.7 2.3
18.42:3
40
30
16.2,
^
16. 8 1.9
17.3 2.1
18.0 2.0
18. 621
ly. *j 2 2
20.0 2.3
20. 7 2 4
21.5;'
23.9^'
30
40
18.1,
8
18.7 2.0
19.4 2.0
20.0,,
20. 7 20
Zl, t) 2 2
22.3 2.3
23.12:4
20
50
19.9^
n
20. 7 1.9
21.4 2.0
22.12:1
22. 9 22
23, 7 2.3
24.62.4
25.524
26.4 2
28. 9 ^-"^
31-5 25
34. 0 ,-
36. 5 ^J
10
3 00
21.9
22.6,^
23-4„o
24.2_
25-122
26.0,3
27-023
27- 9 06
00
10
23. 7 1
<»
24.62:0
25.4;:;
26. 4 21
97 3
■^'. •'2.2
^o* ^00
.^y. *^ 2 4
30.4 24
8 50
20
25. 6 ,
q
26. 61 9
27. 5 2.0
28. 5 2 0
29.52 1
30. 5 2 2
31.7 22
32. 8 "4
40
80
27. 5 1
8
28. 5 1.9
29. 5 1.9
30. 5 2 1
31.621
32. 7 22
00, y 2 3
35.22:3
30
40
29.3,
8
30. 4 1.8
31. 4 1.9
32.61:9
33. 7 20
34.9 2.1
36. 2 2 1
37. 5 2.3
38.9 2,
41. 2
20
50
31.1,
6
32.2i7
33. 3 19
34.5,0
35. 7 20
37.0 2.0
38. 3 2.1
OU, ^01
10
4 00
32.7
6
33.9/^
35.2 •
36. 4 ^-g
37.7^3
39.0,^
40.4,,
41.9,-,
00
10
34.3,
35. 6 1 g
36. 9 1:6
38.2,'7
39. 5 18
41. 0^8
42.5^:8
44.01:9
45-5 2-;
47.5;-;
49.4 !
51. 1 ;■!
52.7 •
54. 0 ^-^
7 50
20
35. 9 ,
1
37. 2 1.4
38. 5 1.5
39. 9 1:5
41- 3 1.5
42.81.6
44. 3 1.7
45. 9 1.8
40
30
37. 3 ,
S
38. 6 1 3
4o.o;-4
41.4;.4
42.81.6
44. 4 1.5
46.0 1.6
47. 7 1.6
30
40
38.6,
'>
oy. y 1 0
41.4
42.81.3
44.41.3
45. 9 1.4
47.61.4
49. 3 1.5
20
50
39.8
q
4i.ii:i
42.61.1
44.1 1.2
45. 7 1.2
47. 3 1.3
49.0 1.3
50. 8 1 0
10
5 00
40.7
9
e
42.2 •„
43.7 •
45-3io
46-9io
48-6ii
50.3,,
52.1,-,
00
10
41.6
43.1 8
44.6 \
46.3'-°
47. 9 'g
49.7 .
51.5 .9
53. 2 1 Q
55.2 1-2
6 50
20
42.4
"
43.9 \
45.4 7
47.1 6
48.7 7
50.5 7
52.4 7
54. 2 7
56.1 'l
40
30
42.9
1
44.5 4
46.1 "4
47.7 \
49.4 -5
51.2 \
53.1 -5
54.9 'e
56.9 'l
30
40
43.3
3
44.9 2
46.5 \
48.1 3
49.9 "2
51.7 ■;
53.6 0
55.5 2
57.5 'l
20
50
43.6
45.1 0
46.7 ■,
48.4 1
50.1 ■,
51.9 '0
53.9 ■-,
55.7 \
57.8 -f
10
6 00
43.7 "^
45.3 ■
46.8 ■
48.5 ■
50.2 ■
52.1 ■
54.0 ■
55.9 ■
57.9 -1
6 00
TABLE 28C.
[C
=the 3d correction. Hor. Arg., the star's declination. Vert. Arg., B=t
he 2d corre(
Jtion.]
B.
88° 47'
88° 48'
88° 49' 1
20"
80"
40"
50"
0"
10"
20"
80"
40"
60"
0"
10"
20"
30
+0.6
+0.5
II
+0.3
II
+0.1
0.0
-0.1
II
-0.3
-0.5
II
-0.6
II
-0.7
II
0.8
II
-1.1
-1.2
40
0.9
0.6
0. 4 1 0. 2
0.0
0.2
0.4
0.6
0.9
1.0
1.2
1.4
1.6
50
1.0
0.7
0.5
0.2
0.0
0.2
0.5
0.7
1.0
1.2
1.5
1.7
i 2.0
60
1.2
0.9
0.6
0.2
0.0
0.2
0.6
0.9
1.2
1.5
1.8
2.1
2.5
70
1.5
1 1-1
0.7
0.4
0.0
0.4
0.7
1.1
1.5
1.8
2.1
2.5
2.8
80
+1.6
+1.2
+0.8
+0.4
0.0
-0.4
-0.8
-1.2
-1.6
-2.1
■2.5
-2.8
-3.3
TABLE 28B.
[Page 559
For finding the Latitude of a place by Altitudes <jf Polaris.
LB = the 2d c
orrecti
on. This
star's a
correction is always additive.]
star's
Ititude.
Star's
hour
hour
angle.
58°
54°
55°
56°
57°
58°
59°
60°
angle.
//. m.
/ ,>
/ /'
/ n
/
„
/ ,,
, ,/
/ //
h. m.
0 00
0 0.0 0.1
0 0.0 0.1
0 0.0 0.1
0
0.0 0.2
0 0. 0 0 2
0 O.Ooo
0 0. 0 0 0
0 0. 0 0 2
12 00
10
0. 1 0.4
0-1 0.4
0-1 0.4
0.2o3
0.2 0:3
0.2 0:4
0-2 0:4
0.2o4
11 .50
20
0-'^0.6
0-5 0.5
0-5 0.6
0.5o6
0.0 0.7
0-60.6
0.60.7
0.60.7
40
30
1-0 0.8
1-0 0.8
1-1 0.8
I-I09
1-2 0.9
1-2 1.0
1-3 0.9
1-3 1.0
30
40
1-8 1.0
1-«1.1
1-9 1.1
2.O11
2.1 1.1
2- 2 1.2
2. 2 1.3
2.3i3
20
50
2.81.2
2. 9 1.3
3.0 1.3
3.1i4
3. 2 1.5
3- 4 1.5
3. 5 1.5
3.617
10
1 00
4.0- .
4.2, ,
4.3,^
4.5,,
4.7
4. 9
5.0
5.3
00
1.4
1 fi
0 5.8;-7
T
6.1-^8
0 6. 3 1:9
0 6.61:8
0 6.8 2'o
0 7.1^:2
10
0 5.4
0 5.6/7
10 50
20
7.0 1.8
7. 3 1:8
7. 5 2.0
7.^19
8-2 2.0
8.4 2.2
0. 0 0 0
9.1 24
40
30
^- ^ 1.9
^- 1 2.0
9. 5 20
9. 8 2.1
10.22.3
10.624
11.02:4
11-5 2.5
30
40
10.7 2.1
11-12.2
11.5 2.3
11.9.4
12.5 2.3
13.02:5
13.4 2.6
14.02?
20
50
12. 8 2.2
13. 3 2.3
13. 8 2.3
14.3,.,
14.82.6
15. 5 2 6
16.0 2.8
16. 7 2 9
10
2 00
15.0.,,
15. 6„,
16. 1 „ .
16. 8„,
17. 4„,
18. 1 „
18.8 °
19.6
00
0 22.632
10
0 17.324
0 18. 0 2 5
0 18.6"
0
19. 3 2 8
0 20. 1 28
020.830
0 21.7
9 50
20
19.7 2.5
20.52:6
21.32:7
22.1,8
22. 9 2.9
23. 8 go
24.83
25. 8 33
40
30
ZZ, '^2 6
23.1 2.6
^!-^-7
24.9, «
25. 8 3 0
26.83.1
27.93.2
29.1 33
30
40
24. 8 2.C
25.7 2.7
26.7 2.8
27. V,,
28. 8 3 0
29.93.1
31.1 3.2
32.434
20
50
27.4 2.7
28.4 2.7
29. 5 2.8
30. 6 2 q
31. 8 3 0
33.0 32
34. 3 33
35. 834
10
' 3 00
30. 1 „ ^
31.1„.,
32. 3„,
33. 5 ■„
34. 8 "
36. 2
37. 6 „
39. 2
00
0 42.6^J
10
0 32.626
0 33. 8 27
0 35. 1 2 8
0 36. 5 ;■;
037.93:0
0 39.4^7
0 40.9 3.3
8 50
20
35. 2 2.6
36. 5 2*7
37.9 2.8
39.428
40.9 2.9
42.53
44.232
46.0 33
40
30
37.82.5
39. 2 2 6
40.7 2.6
42.2,,
43. 8 2.9
45.63:0
47.43:1
49. 3 3 3
30
40
40.3 2.4
41-82.5
43. 3 2.6
45.0,7
46. 7 2 9
48.629
50. 5 3 0
52.631
20
50
42.7 2.3
44.3 2.4
45.9 2.5
47. V, 6
49.62:6
51.5 28
53. 5 2.9
55. 7 3 1
10
' 4 00
- 45.0^2
46.7^,3
^A4 2 4
50.3.,,
52.2
54.3^"
0 56. 9 \\
56. 4
0 59.2,7
1 1.6 •
00
10
0 47.2 21
0 49. 0 "\
0 50. 8 ;l
0 52. 8 ;■,
0 54.824
7 50
20
49.32:0
51.12:0
53. 1 21
55. loo
57.22:3
59.4 24
1 1.9.^-J
1 4.4^^
40
30
51. 3 1.8
53.1 1.9
55. 2 1:9
57. 3,9
59.52 1
1 \.%^\
1 4.3 •*
1 6.92:3
30
40
53.1 1.5
o5.0i6
^Hl-7
5y-2i8
1 1-6 1.8
1 3.9 2.0
1 6.52:0
1 9.2 2^
20
50
54.61.5
56-61.5
. ^^•^•5
l-Oifi
^ ^-^-6
1 5.9i7
1 8.5i^^
lll-3i8
10
5 00
56.1^.,
^^•^3
1 ^-^3
^•So
1 ^-014
1 6.4i2
1 7.6
110.3 •;
1 11.8ii
113.1 -^
00
10
0 57. 3 0.9
0 59.4^:0
1 1-6 :
3.9-
1 9.0 :2
114.7 •
6 50
20
5|^- 2 0.8
1 0-4 0.8
} f-Io-8
5-O09
1 7.60.9
110.2 ^
1 13.1 0:9
1 16.1 0:9
40
30
59.0 0.6
} }-h-^
1 3. 5 0.7
5-^07
1 8- 5 0.7
1 11- 2 0.6
114.0^8
1 17. Oj-^
30
40
59.60.3
1 1-80.3
1 4. 2 0.3
6-604
1 9. 2 0.4
1 11.80.4
1 14.8j°
117.804
20
50
59.9oi
1 2.I02
1 4.5oo
7.001
1 9.601
1 12. 2 02
1 12.4"-
1 15. 2 J-^
1 15.4 •
118. 2 02
1 18.4
10
6 00
1 0.0°-^
1 2.3
1 4.7°-
7.1°-^
1 9.7°-^
6 00
TABLE 28C.
[C = the 3d correction. Hor. Arg., the star's declination.
Vert. Arg., B = the 2d corr
ection.]
B.
88° 47'
88° 48'
88° 49' 1
20"
80"
40"
50"
0"
10"
20" 8
tO"
40"
50"
0" 10"
20"
„
„
„
„
„
„
II
//
„
„
„
„
II
„
30
-rO.6
+0.5
+0.3
+0.1
0.0
-0.1
-0.3 -
0.5
-0.6
-0.7
-0.8
-1.1
-1.2
40
0.9
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.9
1.0
1.2
1.4
1.6
50
1.0
0.7
0.5
0.2
0.0
0.2
0.5
0.7
1.0
1.2
1.5
1.7
2.0
60
1.2
0.9
0.6
0.2
0.0
0.2
0.6
0.9
1.2
1.5
1.8
2.1
2.5
70
1.5
1.1
0.7
0.4
0.0
0.4
0.7
1.1
1.5
1.8
2.1
2.5
2.8
80
+1.6
+1.2
+0.8
+0.4
0.0
-0.4
-0.8
—
1.2
-1.6
-2.1
-2.5 -2.8
-3.3
Page 660]
TABLE 28D.
For finding the Latitude of a place by Altitudes of Polaris.
[D=the 4th correction. (D has the same sign as A when the Dec. <88°48', the oppo.^ite sign when the Dec. >88° 48'.)]
[Vertical Argument, A = the 1st correction. Horizontal Argument, the star's declination.]
A.
10
12
14
16
18
20
22
24
68
70
72
0 20
0 40
1 00
1 20
1 40
2 00
Declination, 88° 47'
20" 25
0.0
1.1
2.2
3.3
4.4
5.6
6.7
7.8
8.9
10.0
11.1
12.2
13.3
27.8
28.9
30.0
31.1
32. 2
33.3
34.4
35.6
36.7
37.8
38.9
40.0
0.0
1.0
1.9
2.9
3.9
4.9
5.8
6.8
7.8
8.8
9.7
10.7
11.7
12.7
13.6
14.6
15.6
16.6
17.5
18.4
19.4
20.4
21.4
22.3
23.3
24.3
25.3
26.2
27.2
28.2
29.2
30.1
31^1
32. 1
33.0
34.0
35.0
«0"
o.t
0.8
1.7
2.5
3.3
4.2
5.0
5.8
^•1
7.5
8.3
9.2
10^
10.8
11.7
12.5
13.3
14.2
15.0
15.8
16^7
"17. 6
18.3
19.2
20.0
20.8
21.7
22.5
23.3
24.2
25.0
25.8
26.7
27.5
28.3
29.2
30.0
85'
0.0
0.7
1.4
2.1
2.8
11.8
12.5
13.2
13.9
14.6
15.3
16.0
16.7
17.3"
18.0
18.8
19.4
20.1
20.8
21.5
22.2
"22.9
23.6
24.3
25.0
40"
0.0
0.6
1.1
1.7
2.2
2.8
3.3
3.9
4.4
6.0
5.5
6.1
6.7
7.2
7.8
8.3
8.9
9.4
10.0
10.6
11.1
11.7
12.2
12.8
13.3
13. 9"
14.4
15.0
15.6
16.1
16.7
17.2
17.8
18.3
18.9
19.4
20.0
45'
0.0
0.4
0.8
1.2
1.7
2.1
2.5
2.9
3.3
3.8
4.2
4.6
AO
5.4
5.8
6.2
7.9
8.3
8.8
9.2
9.6
10.0
10.4
10.8
11.2
11.7
12.1
12.5
12.9
13.3
13.8
14.2
14.6
15.0
2.5
2.8
3.0
3.3
3.6
3.9
4.2
4.4
4.7
5.0
5.3
5.6
5.8
6.1
6.4
6.7
6.9
7.2
7.5
7.8
8.0
8.3
8.6
_8^9
9.2
9.4
9.7
10.0
0.0
0.1
0.3
0.4
06
0.7
0.8
1.0
1.1
1.2
1.4
1.6
1.7
1.8
1.9
2.1
2^2
"2.3
2.5
2.7
2.8
2.9
3.0
3.2
3.3
3.4
3.6
3.8
3.9
4.0
4.2
4.3
4.4
4.6
4.7
4.9
5,0
88° 48'
0.0
1.2
0.0
1.4
0.0
1.6
0.0
1.7
0.0
1.8
0.0
1.9
0.0
2.1
0.0
2.2
0.0
0.0
0.0
0^0
0.0
0.0
0.0
OJ)
0.0"
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1
0.3
0.4
0^
0.7
0.8
1.0
1.1
2.3
2.5
2.7
2.8
2.9
3.0
3.2
3.3
3.4
3.6
3.8
3.9
4.0
4.2
4.3
4.4
4.6
4.7
4.9
5.0
10" 15
4.7
5.0
5.3
5.6
5.8
6.1
6.4
6.7
6.9
7.2
7.5
7.8
8.0
8.3
8.6
8.9
9.
2
4
9.7
10.0
0.0
0.4
0.8
1.2
1.7
2.1
2.5
2.9
3.3
3.8
4.2
4.6
5.0
5.4
5.8
6.2
6.7
7.1
7.5
7.9
8.3
9.2
9.6
10.0
10.4
10.8
11.2
11.7
12.1
12.5
12.9
13.3
13.8
14.2
14.6
X5.0
20'
0.0
0.6
1.1
1.7
2.2
2.8"
3.3
3.9
4.4
25"
0.0
0.7
1.4
2.1
2.8
5.0
5.5
6.1
6.7
3.4
4.1
4.9
5.5
7.2
7.8
8.3
9.4
10.0
10.6
11.1
11.7
12.2
12.8
13.3
13.9
14.4
15.0
15.6
16.1
16.7
17.2
17.8
18.3
18.9
19.4
20.0
6.2
6.9
7.7
8.3
9.0
9.7
10.4
11.1
Proportional parts.
0.0
0.0
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.3
11.8
12.5
13.2
13.9
14.6
15.3
16.0
16.7
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.7
17.3 0.7
18.0 0.7
18.810.7
19.410.8
20.1
20.8
21.5
22.2
0.8
0.8
0.9
0.9
0.0
0.0
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0^
"0.9
1.0
1.1
1.1
22.9 0.9
23.6 0.9
24.3 1.0
25.0 1.0
1.2
1.2
1.3
1^3
1.4
1.4
1.5
jL6
1.6
1.7
1.7
L_8
1.8
1.9
1.9
2.0
0.0
0.1
0.2
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.1
1.3
1.3
1.4
1.5
1.6
1^
1.7
1.8
1.9
2^^
'2.1
2.2
2.2
2.^
2.4
2.5
2.6
2^
"2.8
2.8
2.9
3.0
4'
0.0
0.1
0.2
0,3
0.4
0.6
0.6
0.8
0.9
1.0
1.1
1.3
1.4
2.3
2.4
2.6
2.6
2.8
2.9
3.0
3.1
Proportional parts.
0.2
0.4
0.6
0.7
0.9
1.1
„
„
„
„
„
„
„
„
n
„
II
II
0.2
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.1
0.1
0.3
0.3
0.2
0.2
0.1
0.0
0.0
0.0
0.0
0.0
0.1
0.2
0.5
0.4
0.4
0.3
0.2
0.1
0.1
0.0
0.1
0.1
0.2
0.3
0.7
0.5
0.5
0.4
0.2
0.1
0.1
0.0
0.1
0.1
0.2
0.4
0.8
0.7
0.6
0.5
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.5
1.0
0.8
0.7
0.6
0.4
0.2
0.1
0.0
0.1
0.2
0.4
0.6
0.1
0.2
0.4
0.5
0.6
0.7
TABLE
28D.
[Page 561 |
For
finding the Latitude of a place by
Altitudes of Polaris.
[D=
the 4th correction. (D has the same sign
as A when the Dec. <88° 48', the oppo.site sign when the Dec
>88°48'.)]
[Vertical Argument A=the 1st correction. Horizontal Argument, the star's declination.]
A.
Declination, 88° 48'
88° 49' 1
Proportional parts. 1
80"
36"
40"
45"
60"
65"
0"
5"
10"
16"
20"
1"
2"
8"
4"
0
0.0
0.0
0.0
II
0.0
II
0.0
0.0
II
0.0
II
0.0
0.0
0.0
II
0.0
II
0.0
0.0
0.0
0.0
2
0.8
1.0
1.1
1.2
1.4
1.6
1.7
1.8
1.9
2.1
2.2
0.0
0.1
0.1
0.1
4
1.7
1.9
2.2
2.5
2.8
3.1
3.3
8.6
8.9
4.2
4.4
0.1
0.1
0.1
0.2
6
2.5
2.9
3.3
3.8
4.2
4.6
5.0
5.3
5.8
6.2
6.7
0.1
0.2
0.2
0.8
8
8.3
3.9
4.4
5.0
5.6
6.1
6.7
7.2
7.8
8.3
8.9
0.1
0.2
0.3
0.4
10
4.2
4.9
5.6
6.2
6.9
7.6
8.3
9.0
9.7
10.4
11.1
0.1
0.3
0.4
0.6
12
5.0
5.8
6.7
7.5
8.3
9.2
10.0
10.8
11.7
12.5
13.3
0.2
0.3
0.5
0.7
14
5.8
6.8
7.8
8.8
9.8
10.8
11.8
12.7
13.7
14.6
15.6
0.2
0.4
0.6
0.8
16
18
6.7
7.8
8.9
10.0
11.1
12.2
13.3
14.4
15.6
16.7
17.8
0.2
0.2
0.4
0.7
0.9
7.5
8.8
10.0
11.2
12.5
13.8
15.0
16.2
17.5
18.8
20.0
0.5
0.7
1.0
20
8.3
9.7
11.1
12.5
13.9
15.3
16.7
18.1
19.4
20.9
22.2
0.3
0.6
0.8
1.1
22
9.2
10.7
12.2
13.8
15.3
16.8
18.3
19.8
21.4
22.9
24.4
0.3
0.6
1.0
1.3
24
10.0
11.7
13.3
15.0
16.7
18.4
20.0
21.7
23.8
25.0
26.7
0.3
0.4
0.7
1.0
1.4
26
10.8
12.7
14.4
16.2
18.0
19.9
21.7
23.5
25.3
27.1
28.9
0.7
1.1
1.4
28
11.7
13.6
15.6
17.5
19.4
21.4
23.3
25.3
27.2
29.2
31.1
0.4
0.8
1.2
1.6
80
12.5
14.6
16.7
18.8
20.8
22.9
25.0
27.1
29.2
31.2
38.3
0.4
0.8
1.2
1.6
32
13.3
15.6
17.8
20.0
22.2
24.4
26.0
26.7
28.4
28.9
31.1
83.8
35.5
0.4
0.9
1.3
1.8
84
14.2
16.6
18.9
21.2
23.6
30.7
33.1
35.4
37.8
0.5
0.9
1.4
1.9
86
15.0
17.5
20.0
22.5
25.0
27.5
30.0
32.5
35.0
37.5
40.0
0.5
1.0
1.5
2.0
88
15.8
18.4
21.1
23.8
26.4
29.0
81.6
34.2
87.0
39.6
42.2
0.5
1.1
1.6
2.2
40
42
16.7
19.4
22.2
25.0
27.8
30.6
83.3
36.1
88.9
41.7
44.4
0.6
1.1
1.7
2.2
17.6
20.4
23.3
26.2
29.2
32.1
85.0
37.9
40.8
48.8
46.7
0.6
1.2
1.8
2.4
44
18.3
21.4
24.4
27.5
30.6
33.7
36.8
39.8
42.8
45.9
48.9
0.6
1.2
1.8
2.4
46
19.2
22.3
25.6
28.8
32.0
35.1
38.3
41.5
44.8
47.9
51.1
0.6
1.3
1.9
2.6
48
50
20.0
23.3
26.7
30.0
33.3
36.7
88.2
40.0
43.8
45.1
46.7
50.0
58.3
0.7
1.3
2.0
2.7
20.8
24.3
27.8
31.2
34.7
41.7
48.6
52.1
55.5
0.7
1.4
2.1
2.8
52
21.7
25.3
28.9
32.5
36.1
39.7
43.3
46.9
50.5
54.2
57.8
0.7
1.4
2.2
2.9
54
22.5
26.2
30.0
33.8
37.5
41.2
45.0
48.7
52.5
56.2
60.0
0.7
1.5
2.2
8.0
56
58
23.3
27.2
31.1
35.0
88.9
42.8
46.7
50.5
52. 3
54.4
58.8
62.2
0.8
1.6
2.3
3.1
24.2
28.2
32.2
36.2
40.3
44.3
48.8
56.4
60.4
64.4
0.8
1.6
2.4
3.2
60
25.0
29.2
33.3
37.5
41.7
45.9
50.0
54.2
58.3
62.5
66.7
0.8
1.7
2.5
3.8
62
25.8
30.1
34.4
38.8
43.0
47.3
51.7
56.0
60.3
64.6
68.9
0.9
1.7
2.6
3.4
64
66
26.7
31.1
35.6
40.0
44.4
48.9
53.3
57.8
62.2
66.7
71.1
0.9
1.8
2.7
2.7
3.6
27.5
32.1
36.7
41.2
45.8
50.4
55.0
59.6
64.2
68.8
73.3
0.9
1.8
3.6
68
28.3
33.0
37.8
42.5
47.2
52.0
56.7
61.3
66.1
70.9
75.5
0.9
1.9
2.8
3.8
70
29.2
34.0
38.9
43.8
48.6
53.5
58.3
63.1
68.0
72.9
77.7
1.0
1.9
2.9
3.9
72
0 20
30.0
35.0
40.0
45.0
50.0
55.0
60.0
65.0
70.0
75.0
80.0
1.0
2.0
3.0
4.0
Proportional parts.
0.1
0.1
0.1
II
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.4
0 40
0.2
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.7
0.7
100
0.4
0.5
0.6
0.6
0.7
0.8
0.8
0.9
0.9
1.0
1.1
120
0.5
0.7
0.7
0.8
0.9
1.1
1.1
1.2
1.3
1.4
1.5
140
0.6
0.8
0.9
1.0
1.1
1.3
1.4
1.5
1.6
1.7
1.8
2 00
0.8
1.0
1.1
1.2
1.4
1.6
1.7
1.8
1.9
2.1
2.2
22489—03-
-36
Page 562]
TABLE 29.
Conversion Tables for Nautical and Statute Miles.
XmUical miles into statute miles.
Statute miles into naiUical miles.
1 nautical mile or knot = 6,080 feet.
1 statute mile
= 5,280 feet.
1 statute mile
=6,280 feet.
1 nautical mile or knot = 6,080 feet.
'
Nautical
Statute
Nautical
Statute
Nautical
statute
Statute
Nautical
Statute
Nautical
Statute
Nautical
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
1.00
1.151
8.75
10. 075
16.50
18. 999
1.00
0.868
^00
7.815
17.00
14. 763
1.25
1.439
9.00
10. 363
16.75
19. 287
1.25
1.085
9.25
8.032
17.25
14.980
1.50
1.727
9.25
10.651
17.00
19. 575
1.50
1.302
9.50
8.249
17.50
15. 197
1.75
2.015
9.50
10. 939
17.25
19. 863
1.75
1.519
9.75
8.467
17.75
15.414
2.00
2.303
9.75
11.227
17.50
20. 151
2.00
1.736
10.00
8.684
18.00
15. 632
2.25
2.590
10.00
11.515
17.75
20. 439
2.25
1.953
10.25
8.901
18. 25
15. 849
2.50
2.878
10.25
11.803
18.00
20. 727
2.50
2.170
10.50
9.118
18.50
16. 066
2.75
3.166
10.50
12. 090
18.25
21.015
2.75
2.387
10.75
9.335
18.75
16. 283
3.00
3.454
10.75
12. 378
18.50
21. 303
3.00
2.604
11.00
9.552
19.00
16.500
3.25
3.742
11.00
12. 666
18.75
21. 590
3.25
2.821
11.25
9.769
19.25
16.717
3.50
4.030
11.25
12. 954
19.00
21.878
3.50
3.038
11.50
9.986
19.50
16. 934
3.75
4.318
11.50
13. 242
19.25
22. 166
3.75
3.256
11.75
10. 203
19.75
17.151
4.00
4.606
11.75
13. 530
19.50
22. 454
4.00
3.473
12.00
10. 420
20.00
17. 369
4.25
4.893
12.00
13. 818
19.75
22. 742
4.25
3.690
12.25
10. 638
20.25
17. 586
4.50
5.181
12.25
14. 106
20.00
23. 030
4.50
3.907
12.50
10. 855
20.50
17. 803
4.75
5.469
12.50
14. 393
20.25
23. 318
4.75
4.124
12.75
11. 072
20.75
18. 020
5.00
5.757
12.75
14. 681
20.50
23. 606
5.00
4.341
13.00
11. 289
21.00
18. 237
5.25
6.045
13.00
14. 969
20.75
23. 893
5.25
4.559
13.25
11. 507
21.25
18. 454
5.50
6.333
13.25
15. 257
21.00
24. 181
5.50
4.776
13. 50
11. 724
21.50
18. 671
5.75
6.621
13.50
15. 545
21.25
24. 469
5.75
4.994
13.75
11. 941
21.75
18.888
6.00
6.909
13.75
15. 833
21.50
24. 757
6.00
5.211
14.00
12. 158
22.00
19. 105
6.25
7.196
14.00
16. 121
21.75
25.045
6.25
5.428
14.25
12. 376
22.25
19. 322
6.50
7.484
14.25
16.409
22.00
25. 333
6.50
5.645
14.50
12. 593
22.50
19. 539
6.75
7.772
14.50
16. 696
22.25
25. 621
6.75
5.862
14.75
12. 810
22.75
19. 756
7.00
8.060
14.75
16.984
22.50
25. 909
7.00
6.079
15.00
13. 027
23.00
19. 973
7.25
8.348
15.00
17. 272
22.75
26. 196
7.25
6.296
15.25
13.244
23.25
20. 191
7.50
8.636
15.25
17. 560
23.00
26. 484
7.50
6.513
15.50
13. 461
23.50
20. 408
7.75
8.924
15.50
17. 848
23.50
27. 060
7.75
6.730
15.75
13. 678
23.75
20. 625
8.00
9.212
15.75
18. 136
24.00
27. 636
8.00
6.947
16.00
13. 895
24.00
20.842
8.25
9.500
16.00
18. 424
24.50
28. 212
8.25
7.164
16.25
14. 112
24.25
21. 060
8.50
9.787
16.25
18.712
25.00
28. 787
8.50
7.381
16.50
14. 329
24.50
21. 277
8.75
7.598
16.75
14. 546
25.00
21.711
TABLE 30. [Page 563
Conversion Tables for Metric and English Linear Measure.
Metric to Eiiglwi.
Meters.
Feet.
Yards.
Statute miles.
Nautical miles.
1
2
3
4
3. 280 833 3
6. 561 666 7
9.842 500 0
13.123 333 3
1.093 611 1
2.187 222 2
3.280 833 3
4.374 444 4
0.000 621 369
.001 242 738
.001 864 106
.002 485 475
.003 106 844
.003 728 213
.004 349 582
.004 970 950
.005 592 319
0. 000 539 593
.001 079 185
.001 618 778
.002 158 370
5
6
7
8
9
16.404 166 7
19.685 000 0
22.965 833 3
26.246 666 7
29.527 500 0
5. 468 055 6
6.561 666 7
7.655 277 8
8.748 888 9
9. 842 500 0
.002 697 963
.003 237 556
.003 777 148
.004 316 741
.004 856 333
English to metric.
No.
Feet to meters.
Yards to meters.
Statute miles to meters.
Nautical miles to meters.
1
2
3
4
0.304 800 6
0.609 601 2
0.914 401 8
1.219 202 4
0.914 401 8
1.828 803 7
2.743 205 5
3.657 607 3
1,609.35
3, 218. 70
4, 828. 05
6, 437. 40
1, 853. 25
3, 706. 50
5, 559. 75
7, 413. 00
5
6
7
8
9
1.524 003 0
1.828 803 7
2.133 604 3
2.438 404 9
2.743 205 5
4. 572 009 1
5.486 411 0
6.400 812 8
7.315 214 6
8.229 616 5
8, 046. 75
9, 656. 10
11,265.45
12, 874. 80
14,484.15
9, 266. 25
11, 119. 50
12, 972. 75
14, 826. 00
16, 679. 25
Page 564]
TABLE 31.
Conversion Tables for Thermometer Scales.
[F°=Fahrenheit temperature; C°=Centigrade temperature; R°=R6aumur temperature.]
Equivalent temperatures— Fahr., Cent.,
Mail
R°=* C°=i (F°-
-32°).
C
3=JRO = g (F°-
-32°).
S
F°.
C°.
R°.
r
C°.
R°.
1
-17.2
-13.8
51
+10.6
+ 8.4
2
16.7
13.3
52
11.1
8.9
Equivalent temperatures— Centigrade and Fahrenheit.
3
4
16.1
15.6
12.9
12.4
53
54
11.7
12.2
9.3
9.8
F°= 1 C°-h32°.
5
6
7
15.0
14.4
13.9
12.0
11.6
11.1
55
56
57
12.8
13.3
13.9
10.2
10.7
11.1
C°.
pa
C°.
F°.
c°
F°.
c°.
F°.
C°.
F°.
8
13.3
10.7
58
14.4
11.6
-10
14.0
0
32.0
10
50.0
20
68.0
30
86.0
9
12.8
10.2
59
15.0
12.0
— 9
15.8
1
33.8
11
51.8
21
69.8
31
87.8
10
12.2
9.8
60
15.6
12.4
- 8
17.6
2
35.6
12
53.6
22
71.6
32
89.6
11
11.7
9.3
61
16.1
12.9
— 7
19.4
3
37.4
13
55.4
23
73.4
33
91.4
12
11.1
8.9
62
16.7
13.3
— 6
21.2
4
39.2
14
57.2
24
75.2
34
93.2
13
10.6
8.4
63
17.2
13.8
— 5
23.0
5
41.0
15
59.0
25
77.0
35
95.0
14
10.0
8.0
64
17.8
14.2
- 4
24.8
6
42.8
16
60.8
26
78.8
36
96.8
15
9.4
7.6
65
18.3
14.7
- 3
26.6
7
44.6
17
62.6
27
80.6
37
98.6
16
8.9
7.1
66
18.9
15.1
_ 2
28.4
8
46.4
18
64.4
28
82.4
38
100.4
17
8.3
6.7
67
19.4
15.6
— 1
30.2
9
48.2
19
66.2
29
84.2
39
102.2
18
19
7.8
7.2
6.2
5.8
68
69
20.0
20.6
16.0
16.4
1
20
6.7
5.3
70
21.1
16.9
21
6.1
4.9
71
21.7
17.3
22
5.6
4.4
72
22.2
17.8
23
5.0
4.0
73
22.8
18.2
24
4.4
3.6
74
23.3
18.7
25
3.9
3.1
75
23.9
19.1
26
3.3
2.7
76
24.4
19.6
27
2.8
2.2
77
25.0
20.0
Equivalent temperatures— Riaumitr and Fahrenheit.
28
2.2
1.8
78
2.5.6
20.4
• • F°=| R°-|-32°.
29
30
1.7
1.1
1.3
0.9
79
80
26.1
26.7
20.9
21.3
R°.
F°.
R°.
F°.
R°.
F°.
R°.
F°.
31
32
33
34
35
36
37
38
39
40
41.
42
-0.6
0.0
+ 0.6
1.1
1.7
2.2
2.8
3.3
3.9
4.4
5.0
5.6
-0.4
0.0
+ 0.4
0.9
1.3
1.8
2.2
2.7
3.1
3.6
4.0
4.4
81
82
83
84
85
86
87
88
89
90
91
92
27.2
27.8
28.3
28.9
29.4
30.0
30.6
31.1
31.7
32.2
32.8
33.3
21.8
22.2
22.7
23.1
23.6
24.0
24.4
24.9
25.3
25.8
26.2
26.7
0
1
2
3
4
5
6
7
8
9
-10
- 9
- 8
- 7
- 6
- 5
- 4
- 3
- 2
- 1
9.5
11.8
14.0
16.2
18.5
20.8
23.0
25.2
27.5
29.8
32.0
34.2
36.5
38.8
41.0
43.2
45.5
47.8
50.0
52.2
10
11
12
13
14
15
16
17
18
19
54.5
56.8
59.0
61.2
63.5
65.8
68.0
70.2
72.5
74.8
20
21
22
23
24
25
26
27
28
29
77.0
79.2
81.5
83.8
86.0
88.2
90.5
92.8
95.0
97.2
43
6. 1
4.9
93
33.9
27. 1
44
6! 7
5! 3
94
34^4
27! 6
45
7.2
5.8
95
35.0
28.0
46
7.8
6.2
96
35.6
28.4
47
8.3
, 6.7
97
36.1
28.9
48
8.9
7.1
98
36.7
29.3
49
9.4
7.6
99
37.2
29.8
50
+10.0
+ 8.0
100
+37.8
+ 30.2
TABLE 32.
[Page 565
To obtain the True Force and Direction of the Wind from its Apparent Force and Direction on a
Moving Vessel.
•atBOS ^jojiiBaa 'aojoj orux
C<105iOC0'*iO-^iOtOmtOt~!Ot~00l>'3DCC0000a>CCO>O0>Oi-IOt-lT-lr-(iHC^C^C^(N0JC^IM
Moq am no s;u{od 'uoTjoajip aiux
COCO^^OO^O^CD^OCO^^^^j^^COtOO^OtDtOO^OtOCOOOkOeO^OSOCDO^eOO
•aiBOS jjojnBag 'aoaoj arux
N«iOmTf<iO'^iOtOintOt-!Ol^Q0C~a000000001000>OOO^Oi-(rHi-li-lc^iMC^C^~104C^
■Moq aqi J90 s^uiod 'uoijoajip atux
CO<lOtOtD<OOiO«OCOlC»C?OiCiC^iCiOidC»OiOlft>'5iCi^i/2iCiO»Cif5Uci05DiOiClOtCiCiO
■81B08 :)jojnB8a 'aajoj atux
C^CCOCO-^iO-^iCOiOOt^^t^oDt^OOOOQOODOsaOCSOOSOOOr-li-iUHT-lc^C^C^C^KMC^C^
•Moq aqj yo sjuiod 'uoijaaiip arux
iOOCOii^iCiOiCiOi^iCiOiC»C»0»CiCiCiC"^iC'^-^idO"^iCiC'^-^»C •^TT'iC'^'^-f-^-^T^
•ajBas :)jojn'Baa 'aaaoj atux
c^cciocO'^iC'^icto»ceot^«ot^oot*t^cct*ooa^oO'35ascsoooi-*i-iU-ii-(c^c^e^c^(NMej
■Aioq aqi jjo s^uiod 'uojiaajip arux
iootoidninTjiiom"»''*iO'*'*-*Tf9<r)<i)<'^T(<T(<->jiTj<..ji.^ij< «-»<■<>' cc^'«<cotj"'^ MM-*
•aiBOS jjojtiBaa 'aajoj arux
(NM'«J<MTjllOr}imtO>/5t0t~«Or"t^t»t»00t~0Ca000 050>05OOOOr-tr-li-mC^e^C^C^C^C^
'Aioq aqi yo s^ujod 'uopoajip arux
li^iOtO-^iOiC't'^iO^'^-^M'^'V M-^-^MM-^MMMMMMMMM MMMC<IMMC^MM
•axuas ■jjojnBaa 'aaaoj arux
(^^M'9lM-*l0^lCtOlOtotOlra^oc~!0^»■ooc~oooooooDOiO»o^oooo^-l.-l1-lr-lm^c^(^^c^
•Moq aq; jjo sjuiod 'uorioajip arux
lOlOlC■*■^lreM-*■*MM-*MM"*c>)MMe^MMI^lc^Mc^lMMc^IMc^INN(^J^^l^^c^<^^M^^
•aiBas jjojn'Baa; 'aajoj arux
INMTt<M'S<i'2M'*iO-*idOU5«3t-«5t~t-t~t>0D0000ai0>0»OOOOr-li-li-li-liMC^iM(N:^
•Avoq aqj BO sjaiod 'uoijoajjp arux
lOmiO'"»"fl<>OMM-*<«MMe^C4MC^e^Mr-ie>«C^rHe^drHi-IC<r-li-l(Nl-(i-li-Hi-(r-lr-lrti-Ci-l
•aXBas ^jojnBaa 'aojoj arux
e^MT»ie<M'^eO"«'iO'*iO<om<o<okoot~t~t-t~i>ooooooo>o>o»oooi-<>-i!-ii-i(N<NNc^
•Aioq aqi BO s^urod 'uoipajip arux
lCiniCM-^'<J<C<M-*01HM^«C^li-IIN<NrJi-IC^O"-l>-IOT-l.-IOO'-liOOi-lOOOOOO
•aXBOS '4J0jnBaa 'aoJOj arux
CJM'^C^M'<1*M'^iC'^-^iC-^iCtOu050«OtOt*l:^t^t^00000005C>CiOSOOOt-lT--rHC^C^M
• Avoq aqj BO sjurod 'uoi:>aajrp arux
miOiOM-^-^e-lMMi-HMMOfHC^l Or-IC^OO^mO-HOJOOO>00 OS0500>OSOO>C50>
'ai^Ds ^jojnBaa 'aajoj arux
C4o9^e<M^eo«o^e<9vm^i(5iou5io«o«D<or~t»r-t»»ooaoe»05oooooi-ir-ir-(c^Nc^
•Moq aq:) bo 8:}rrrod 'uorjaaarp arux
lOiOiCMf-^i-tC^MOf-'C^O^C^ asOV-IOiOOOOOaOCOOiO>OOOaOi 0000O>0000OS«GC00
•axBos laojnBaa 'aojoj arux
c<M'^NW*Nm'^weiS'*'^'^-^io>OiOtD«o«oi~«ct»ooooooo»aooooo>a>r-(^0(NC<ie<i
•Moq aq? BO s^uiod 'uorjoajrp anix
ioicmc^'*'*oe^MO»i-ic^o»o>-i!ooosoooo>ot-.ooo>t~ooo»t~xoot»t~aot-t»oot~t>-t»
•a[BOs iiojn'Bag 'aajoj arux
4C^-»1<i-IMMC^C^MC^MMMM-*'^-*MiOiOiO<00'Ot»t~t^CCOOaOO»0>01000?^r-'r-l
•AVoq aqi bo s-juiod 'uorjoaarp arux
io>nme^"»'"*oc^MaoorJooo»oi-~-ooot~ooo>tot»aotot»ootDtoi»totot-«i;ct-;ctoto
•aiBDS jjojnBag 'aojoj arux
i-(iMTtir-ic^MiHe^MNC<we<9eOOT'*e<5MiO'*^toiomt~c~eoaDoot~o>o>ooooOr-ir-i-H
•M.oq aqj bo sjniod 'uoijaaarp arux
iOiCiCC^-1''^P>C^M30OC^t-CCO 50t^05 0t>-OOiCOt>»C!OCOidC«OidC«OiCiCiO-V»CiO
•aiBos jjojnBag 'aojoj arux
l-IC^'<)<r-IC<MiH.HNC<rHNC^Ne<e0MM'*-<>"M«>lO"9<t~!OtO00t^t^0»a000OO01i^--<.-(
• Moq aqi bo s^nrod 'uorjoaarp arux
K3icnoc^'«»">coo<NM<eo»Ntot»o in!3ao'^iot~^io<e'*^iO'«j"<»'ift ■^■^^^^tjimtji'v
•aiBos jjojriBaa 'aojoj arux
rHC^MOC^MOr-iC^iHrHi-l!NrHr-l,e>5C^C^-<«"MC^lO-<)<-<(<t>tOlO»t~tDOSOOOOOO>3S-H — O
•Aioq aqj go sjutod 'uoijoaJlp arux
lO'^OM-^iCt-C^-^iOOOC^-^^Oa
MlOt~M'^iCMM^MM'^CMMMCMMMC^MMC^e^M
•aXBDs iJojUBag 'aajoj arux
r-ie^MOrHC^OOe^rlOrHC^rHO
MPjTH'*MC^iO-*MtD<OmXlt»50»COt»00»0>r-lr-IO
•Avoq aq:> bo sjurod 'uor^aajrp arux
«ototOT)<ic>ntoM>oweceocjr(<o>
NMUtC^C4Mrt(NINrtC^C^r-(rHC^
•aiBos ^jojnBag aojoj arux
iHC^MOr-IC^OOrtr-IOOC^rHO
MCJO-»J<MC^iO-rl<M«OiO'<»'OOt^«>
OiOOt>OOiOir-'t— 'O
Moqaq^ Bosjnrod 'uopoai}p arux
cooec^o^otooooooo
ooooooooooooooo
ooooooooo
•s^ouj[ 'xassaA jo paadg
OiOOOiCOOiCOOiOOOiOO
r-li-l(NrH^!NiHT-IC^i-(i-ie^i-(r-lC^
oireoo>oooioooiooo>oo
rHi-lC^i-lrH(Ni-li-IOJi-lT-l(NrtrH(M
oioooinooiao
O rH C^ M
00 o>
Page 566]
TABLE 33.
Distance by Vertical Angle.
05
Q CC t^ ^ Vi
N e^ M T-- r-l
^ iOeO(NrH
OCPJMOOQ
I-Hr-IOIOT
OlOOOlN
■Ir-lrtr-l 00000
^ ^ CC CQ CC
00000
00000
i-lrHSc
■^t^ i-Ht^ CC
i-I>-ItHOO
3 tir~ooo
^.-lOOO
OkOiC-^ -^
r-(0000
~ (MT)'0(NiOCC(Nr-IO
o OTjiece^
. CCOOOl-*
^ li5<MlOr-l
O 00-<J'(MCJ
. - -( t^-^o
lO >o -^ "^ "^
00000
> t^t^o
SrHOO
■.^ ■f54Tj<CC
00000
CSrHTfO
O 00-*(NC^
c^Jioec^i t^
— irtOlO
H,-I.HO
~ >cS-<}<o
" M-.J'CcS
O t~CCINrH
QiO>2t~0
CCtHOiO in
1-lr-IOO
occc>iT)>
O r-CCO)rH
iCt-H rH CCI>
Mi-lOiO-*
tHi-Ii-HOO
O OCCI^i-l
. 00O5 CCiO
CC ■'T »r5 c^
» oxj-r »
r-lCC'^.-l
O iONtHiH
Til (N CC tH
O ■<)< cq r-l rH
O •<9' (M r-( r-l
^ cocci/sr*
*■ T)<lflr-im
O CCi-Hi-IO
O-^"^ CC CC
00000
lO'^Tf.J^'^hj'CCCCCCCC
0000000000
CC CC CC CC CC CC
00000 00000
lOiNOOCS
^ ^ ■^ CC CC
00000
.-loit^iocc
Tf CC CC CC CC
00000
CC CC CC CC C4
ooooo
ccccfSo) (N
ooooo
ooooo
ccccecccM
ooooo
■* <N O 00 l-
CCCCCCCNC-^
ooooo
ooooo
00 !•» lO ■^ M
ooooo
CCCC64fSM
ooooo
^ 00 t^ O iC
ooooo
- JiQ'^CC
ojmSic^(N
ooooo
ooooo
- < o a> 00 00 1^
O) (N tH tH .H r-l
ocoooo
•O v(5 CC 51 r-(
ooooo
ooQor* co^
lO CC C-1 p o>
ooooo
OCt^l^tOiftiO
000000
ooooo
t>- CO iCiC ■*** -^
000000
i-HOOOl-tD
«0 lO ■* '<' CC c^
ooooo
000000
ec?i>Hoo
ooooo
ooooo
rH rH 001 Oi
lO-q'CClN^lOOOlOOOO
>o»occaOT)iot~-* jJOoot^iC'^ccoii-io
>eq00>0 'J' Tfi TT CC CC CCCC(N04lN 'C^M!N<m55
4rHrHr-IO OOOOO OOOOO OOOOO
OS to I^ CI -^
rHOOO
■^■-HCCtOrH
rHOift ■*■*
i-hOOO
gt^oOC^QO
inT)<Ti!cc
0000
m-^cccc
i-HOOOO
t^t^OlOf-H
UD ^ ^ CC CC
OOOOO
lOiHOOlO C^
T}*-^CCCC CC
OOOOO
cj OS i<5 CC o
■• -5C<iCCCC
ooooo
CC?S MC<IIM
ooooo
CCC^f-tOa>QDt^t^«<C'
ooooo ooooo
ooooo
CCCCCCOl
ooooo
r* ccr-t 000
T* 1-H 00 «5 ■"»<
ccccc5c^c^
ooooo
to iQ CC C-) .H
CM C<l C^ (N C^
ooooo
iCCC<M 005
ooooo
ooooo
i-H 00 O -^ C-1 It-h (3i OC' l^ to
cccm^mM
ooooo ooooo
COtO'*C^O
ooooo
rHCqOC^lOOlCCCrHOOO
lO'^CCCCO)
ooooo
iCl 00 <N 00 IQ
•<*< CC CC fl C<l
ooooo
iO5Ot~-00O5
ooooo
3>00 t^tOlO
ooooo
t^toic -^cc
ooooo
ooooo
OrHCqCC^
lO-^CCCCO)
OOOOO
10 or* 00 OS
OSOOOD t^t^
ooooo
T-IOOOOOO
OOOOO
OOOOO
o a>oo t>-i^
OOOOO
00 X t^ to in
ooooo
I^ tOiO-^ -^
ooooo
to »o '^ -^ CC
ooooo
■*Tf CClMffJ
ooooo
CCCCOIOt-I
ooooo
i-<-HOOO
ooooo
Or-lC^CC*
to iCiC ■'I* ■^
OOOOO
a>oo t^toio
OOOOO
Tj* ^ CC CC C^ r^
000000
CO t^ tO>OTj<
ooooo
t- to lO ■«<" CC
ooooo
to 10 "* CC CC
ooooo
in-^cocc^j
ooooo
^CCC^Ni-l
ooooo
CCC4C^r-IO
ooooo
iC-^ ^ cccc c^
ooooo o
CCCCOCJi-H
ooooo
ooooo
.-I rHOOO
ooooo
1-1 000105
ooooo
0>0>0>0000
0000©
iCCOI~*00O>
ONtJIOOO
CC CC C^ C< i-H r-l
000000
CC CJ C^ rH 1-1 O
000000
C^rH— 1000
000000
ON'* to 000
TABLE 33.
Distance bv Vertical Angle.
[Page 567
CO O
55
- r-i C^ O
00 =0000 CO
O t0 51000
rHC05irHT-t|C^CClO(NiO
0»T»((NQO
OiOCOINrH
OOiCOOC^
rl 0)10 0110
,-(005 OS 00
tOi-ltOMOO lOt^Olt^O^
t^COOOOtOi-*050Ii-<0
01c3c4rHrH,i-lTHiHr-li-l
0 -T^QcccOT-txaiOicco
lO Tj<0r-I001i0 1'i0001
01 -^rHOOOf'oi^-lOOOJ
C-leCiOOKM
COr-ITl<lOC^
rloOiCMOl
OOOOO^
i-Hi-IOloSO
i-ioa>ooao
■^ .-* Ice O CC l^ r-l
•^ (M ^>-l Ol i-H M O)
00 Ol lOOlOCOr-IO
55 Ol |iH r-l rH i-H rH
0 05 0
lOC^OJ
_ OOTt-IOO>
01(?J .-(rHiHr-l
lOOlOlOOi
■*lMC001i-l
(NOOiOO
lOOirHrl
OlOOiOOt^
tH rt lO
OOOM
o>oot-t-«>
lO O Ol O Ol
OJ'^OCOO
00t>t-«O5O
OOrHOJin
rH<NOOi-l
OOOOIIMCO
Ol '^ -^lO i-H
OS t* OiOiC
O WJ Ol
C3010:OiOO)(Ni-l
1-(01M «.-(OlTJ>r-<
ooojo> r»^iO'*»j'
CO -^ O cc O
iO'^T)<eoco
rHOtrH'^
O 00 OitO-^
. i-H M 1- 00
^ OJiOiO O)
o r^ooiOT^
C^COOiCiO
*1* 05 O* '^ c^
coiooio'*
Oio loirs'^
0-*(M0
- _500Oa-Ji
lO Ol*^ i-H lO
O>CJ>O0O0t~
■*i-ICOt^iO
TJi rH -^ ^ lO
00 GC t^ t^ CO
rHlOC0»-llO
?0 lO lO lO "^
00 t^ OiOl t^
C0i-li0'*0»
lO lO -^ -^ -^
0-^<N i-HiO
IC T)l Tl< TJI CO
Q CO 1^ Ol 00
« rHiO '^ Ol
t~ r- o -o o
iC-HOi-iOjiiOOiOOIQ
OJO-VlNOjTfcOiHOio
oooor-t^t--toototOiO
lO Ol O) CO l^
- _5 I--. iO lO CO
■* (M I— C3 lO ■.»<
f* ^ Tf CO CO
00 1^ OS n i^
lO lO ^ ^ ^
OOCOSOliO-JI^-fOlrH
-)■ lo OS "i< o>
CO Tl lO ■>J< ?l
*-0 O lO iC iC
iOlOiO"iJ<')'Ujc.JiTjiT>iC0
■J5 -* CO 0> OJ
i-fOiOT»<cO
lO lO T)< ■.p Tjl
ojosr-ioio
— -^i-cOiO
Tj< ^ ^ •<}< CO
•^COCMOlrl
CO CO CO CO CO
-^ Ol »-l rH Ol
i-H OlO -^t* CO
^ ^ CO CO CO
CO CO X ^1 lO
O) rH OOiO
CO COCO CO (N
-O lO lO CO 00
TCCOOlrt o
CO CO CO CO CO
CO t~ O) O 00
oioiO'j'oi
1<-^ CO CO CO
OOOOOIMlO
T-lOOlO-*
CO CO cooler
i-t Ol CO ,H 00
cot^oiooo
OlOiO'^O)
tT'^COCOCO
r><COr-IOiO
CO CO CO CO CI
lOI^^OCO
CO IC lO CO GC' ,-t
■* C0 0)i-(00
coco CO CO CO CO
30 « O O lO 00
iHOOiO'^CO
CO CO cool (MO)
OS ^ -^ t^i-H CO
^ ■* CO Ol Ol rH
0)0)010)010)
1-1 lO 00 CO 00 CO
OlrHOOiCiO
COOIOIOIO) 0)010)01>-i>H
OS OS O 1-1 -r t^ r-( CO ^^ CO c
TCOCOOIr-liOOlOiO'^'
0)0101010) O) O) 1-1 r-( .H r
.^^1^,-tCO r-*^C0COOS
OiO-*'>1<CO COO)i-lOiO
C0 0)0)010)010)0101i-I
COCOOlOlrH
010)01010)
^ooco oo'fl'o
J -^ -.a* CO CO CO
oi3|coQ:g"Os-^Qcoo)os
i-iOiSio-^ cocoeoo)0)iH
OlOlf-lT-
COOlOSOOCCOSr-lTj'f.i-l'COOCOiHt^
■TCOi-IOiOTfi-^COOlOli-d-IOOiO
COCOCOCOOl Ol Ol Ol Ol Ol OI Ol Ol Ol T-l
O) (■- lO t^ O)
•cCrHlOCOO)
Tj* T^ CO CO CO
t^coi^ gs
lO -tiCOOl
COOIOIOIOI
COiOOp-^iH
■^ Ol OiO -^
CO CO cool 01
1-t ^ coco OS
COOlrHOlO
01010)0) iH
Osfi-IOt-i
■*eoo)T-io
0)0)0)0)01
Scoo3;os
■^'S'COOl
CQCCr-lr-ICO CO CO •* t^ >-l
^©■"tOlO lOrfcOOlOl
eocoo)oioi
iC »-(t^cOO
1-1 iH o o o
lO OS CO -* OS
CO iC CO 1— I lO
COOIO) Olr-I
r-QOOco t^
TTCOCOOlr-l
^ OSiOOO-^ COOsiOt^
^ OlOlCOrH -' — -• —
O COOOiO'*
^ r* CO OS o
^ COiOiH O
Q lO t^ lO ■^
COOsiO t^ CO
oS-^oioio
COO)0101rH
0)Qt~Ot~
1-1^1-1 0-*
COOlOlOlrH
» lOOi-icg
•cP CO o ^
Q ^ t* us CO
SeoQ
COOJOliHrH
lOCOt^OOOs
leoioooc
>C0Oli-lr
CO 0)0)1-10
Oi-IOlCO'*
Olt^COQt
r-tO OOi
1-liHOO
SOt^COiH
O iCiO to
HOOO
St^COQOO
SiOiOiO^
HOOOO
lO i-IJ^ -nj" rH 5C
ol O) rt iH 1-1 S
i-liOOOCOQC'jCOOSiOi-II^I'I'OOCOOS-.^f
"i-iooioiif'^' — ^^' — "
Ol OIOIO
"'J"'^CO:COO)01rHi-(
010)i-li-liH
r»^i-iosr-
- lOlOTjlTjl
OOOOO
■^ 1-1 OSI>iO
lO lO ij' 'J' ■«<
OOOOO
1-1 00 CO 31 o)
OOOOO
3D CO-* 0)0
COO)0)0)i-i
S;^SSS
OOiOCOi-IQO t-*C0Ot^iO
OOOOiOjiOiOiO'^Tji
Hr-(i-lO OOOOO
- I<0)Q0S
OOOOO
-* CO CO CO w
OOOOO
r-l t^ -r 1-1 0> !■-
i-IOOOiOiO
T-li-lr-lrtOO
t^ -* 1-1 OS r^ »o
lO lO lO ^ *1i *
OOOOOO
O)00st-i0'*
■* 'J' CO 95 CO CO
OOOOOO
ociocoi-iooQr-coio-*co
eocOeococop)oiO)0«o)o5
OOOOO OOOOOO
C0'*0)000 t^CO-«iC0O)i-c
COCOCOCOOl 010101010)C<
OOOOO OOOOOO
■^ 0)000 1>
CO CO CO O) O)
OOOOO
aot~co-<t|co o)OoQ«^io
COCOCOCOCO COCOOiO)OI
OOOOO OOOOO
lOCOi-fOSOQ cpiO'^Oli-H
^ 1J1 ^ CO CO CO CO CO CO CO
OOOOO OOOOO
lO ■* cool 1-1 o
0)0)0)0)0101
OOOOOO
■*C0 01i-< OOs
0)05 0)01 O) rH
OOOOOO
ooor^iOTjicooii-iposoo
cooioioioiiNoiois5i-ii-i
OOOOOOOOOOO
iOC0t^000SOrH01C0'.^i0C0t^000SO0)-^O«O0)'*C000O
Page 568] TABLE 34.
For finding the distance of an object by an angle, measured from an elevated position, between the
object and the horizon beyond.
Dlst.,
yards.
Height of the Eye Above the Level of the Sea, In Feet.
Dist,
yards.
20
30
40
50
60
TO
80
»o
lOO
no
ISO
100
200
300
400
500
0 /
3 44
1 50
1 12
52
41
0 1
5 37
2 46
1 4%
1 21
1 03
0 (
7 29
3 43
2 26
1 48
1 25
0 /
9 21
4 39
3 04
2 16
1 48
0 r
11 11
5 35
3 41
2 44
2 10
o /
13 00
6 31
4 19
3 12
2 32
o /
14 47
7 27
4 56
3 40
2 54
o /
16 34
8 23
5 33
4 08
3 17
o /
18 16
9 18
6 11
4 36
3 39
O 1
19 58
10 13
6 48
5 04
4 01
o /
21 37
11 08
7 25
5 32
4 24
100
200
300
400
500
600
700
800
900
1,000
34
28
24
21
18
52
44
38
33
29
1 10
1 01
51
45
40
1 29
1 15
1 05
57
50
1 47
1 31
1 18
1 09
1 01
2 05
1 46
1 32
1 22
1 12
2 24
2 01
1 46
1 33
1 23
1 15
1 08
1 02
57
52
2 42
2 18
2 00
1 45
1 34
3 01
2 34
2 13
1 57
1 45
3 20
2 50
2 27
2 10
1 56
3 38
3 05
2 41
2 22
2 07
600
700
800
900
1,000
1,100
1,200
1,300
1,400
1,500
1,600
1,700
1,800
1,900
2,000
16
15
13
12
11
26
23
21
19
18
35
32
29
27
24
45
41
37
34
31
55
50
45
41
38
1 05
59
53
49
45
1 24
1 17
1 10
1 04
59
1 34
1 26
1 18
1 12
1 07
1 44
1 35
1 27
1 20
1 14
1 54
1 44
1 35
1 27
1 21
1,100
1,200
1,300
1,400
1,500
10
16
15
14
13
12
22
21
19
18
17
29
27
25
23
22
35
33
31
29
27
42
39
36
34
32
48
45
42
39
37
55
51
48
45
42
1 02
58
54
50
47
1 08
1 04
1 00
56
53
1 15
1 10
1 06
1 02
58
1,600
1,700
1,800
1,900
2,000
2,100
2,200
2,300
2,400
2,500
11
10
16
15
14
13
12
20
19
18
17
16
25
24
22
21
20
30
28
27
25
24
35
33
31
29
28
40
38
36
34
32-
45
42
40
38
36
50
47
45
42
40
55
52
49
47
44
2,100
2,200
2,300
2,400
2, 500
2,600
2,700
2,800
2,900
3,000
11
11
10
15
14
14
13
12
19
18
17
16
15
23
22
20
19
19
26
25
24
23
22
30
29
28
26
25
34
33
31
30
28
38
36
35
33
32
42
40
38
37
35
2,600
2,700
2,800
2,900
3, 000
3,100
3,200
3,300
3, 400
3,500
12
11
10
15
14
13
13
12
18
17
16
15
15
21
20
19
18
17
24
23
22
21
20
27
26
25
24
23
30
29
28
27
26
34
32
31
30
29
3,100
3,200
3,300
3,400
3,500
3,600
3,700
3,800
3,900
4,000
12
11
11
10
14
13
13
12
12
17
16
15
15
14
19
19
18
17
16
22
21
20
20
19
25
24
23
22
21
27
26
25
25
24
3,600
3,700
3,800
3,900
4,000
4,100
4,200
4,300
4,400
4,500
11
11
10
14
13
13
12
12
16
15
15
14
14
18
17
17
16
16
20
20
19
18
18
23
22
21
21
20
4,100
4,200
4,300
4,400
4,500
4,600
4,700
4,800
4,900
5,000
11
11
10
13
13
12
12
11
15
15
14
14
13
17
17
16
15
15
19
19
18
17
17
4,600
4,700
4,800
4,900
5,000
TABLE 35.
[Page 569
Speed in knots per hour developed by a
vessel traversing a measured nautical mile in any given 1
number of minutes and seconds.
1
Number of minutes.
1
2
8
4
5
6 7
8
9
10
11
12
Knots.
Knots.
Knots.
Knots.
Knots.
Knots.
Knots.
Knots.
Knots.
Knots.
Knots.
Knots.
0
60.000
30. 000
20. 000
15. 000
12. 000
10. 000
8.571
7.500
6.666
6.000
5.455
5.000
0
1
59. 016
29. 752
19. 890
14. 938
11.960
9.972
8.551
7.484
6.654
5.990
5.446
4.993
1
2
58. 065
29. 508
19. 780
14. 876
11.920
9.944
8.530
7.468
6.642
5.980
5.438
4.986
2
8
57. 143
29. 268
19. 672
14. 815
11.880
9.917
8.510
7.453
6.629
5.970
5.429
4.979
3
4
5
56. 250
55. 385
29. 032
28. 800
19. 565
14. 754
11. 841
11. 803
9.890
8.490
7.438
6.617
5.960
5.421
4.972
4.965
4
5
19. 460
14. 694
9.863
8.470
7.422
6.605
5.950
5.413
6
54. 545
28. 571
19. 355
14. 634
11.764
9.836
8.450
7.407
6.593
5.940
5.405
4.958
6
7
53. 731
28.346
19. 251
14. 575
11. 726
9.809
8.430
7.392
6.581
5.930
5.397
4.951
7
8
52. 941
28. 125
19. 149
14, 516
11. 688
9.783
8.411
7.377
6.569
5.921
5.389
4.945
8
9
10
52. 174
27. 907
27. 692
19. 048
"18:947
14. 458
11.650
9.756
8.392
7.362
7.346
6.557
5.911
5.381
4.938
9
51.429
14. 400
"11.613
9.729
8.372
6.545
5.902
5.373
4.932
10
11
50. 704
27. 481
18. 848
14. 342
11.575
9.703
8. 353
7.331
6.533
5.892
5.365
4.924
11
12
50. 000
27. 273
18. 750
14. 286
11.538
9.677
8.334
7.317
6.521
5.882
5.357
4.918
12
13
49. 315
27. 068
18. 652
14. 229
11.501
9.651
8.315
7.302
6.509
5.872
5.349
4.911
13
14
15
48. 649
48. 000
26. 866
18. 556
18. 461
14. 173
l4ril8
11.465
9.625
8.295
7.287
6.498
6.486
5.863
5. 853
5.341
4.904
14
15
26. 667
11.428
9.600
8.276
7.272
5.333
4.897
16
47. 368
26. 471
18. 367
14. 063
11.392
9.574
8.257 ! 7.258
6.474
5.844
5.325
4.891
16
17
46. 753
26. 277
18. 274
14. 008
11.356
9.549
8.238 1 7.243
6.463
5.834
5.317
4.884
17
18
46. 154
26. 087
18. 182
13. 953
11.321
9.524
8.219 7.229
6.451
5.825
5.309
4.878
18
19
20
45. 570
25. 899
18. 090
18.000
13. 900
13. 846
11.285
11. 250
9.499
8.200 i 7.214
6.440
6.428
5.815
5.301
4.871
19
45. 000
25. 714
9. 473 ! 8. 181 7. 200
5.806
5.294
4.865
20
21
44. 444
25. 532
17.910
13. 793
11.214
9. 448 8. 163 7. 185
6.417
5.797
5.286
4.858
21
22
43. 902
25. 352
17. 822
13. 740
11. 180
9.424 8.144 7.171
6.405
5.787
5.278
4.851
22
23
43. 373
25. 175
17.734
13. 688
11.146
9. 399 8. 126 7. 157
6.394
5.778
5.270
4.845
23
1
42. 857
25.000
17.647
17:560
13. 636
13.584
11.111
"11.077
9.375 8.108 : 7.142
9.350 8.090 7.128
6.383
6.371
5.769
5.263
4.838
24
25
42. 353
24. 828
5.760
5. 255
4.832
26
41. 860
24. 658
17.475
13. 533
11.043
9. 326 8. 071 ! 7. 114
6.360
5.750
5.247
4.825
26
27
41.379
24. 490
17. 391
13. 483
11.009
9.302: 8.053
7.100
6.349
5.741
5.240
4.819
27
28
40. 909
24. 324
17. 307
13. 433 1 10. 975
9. 278 1 8. 035
7.086
6.338
5.732
5.232
4.812
28
29
30
40. 449
40. 000
24. 161
24. 000
17. 225
13. 383 1 10. 942
9.254
9.230
8.017
7.072
6. 327
5. 723
5. 714
5.224
4.806
29
17. 143
13. 333
10. 909
8.000
7.059
6.315
5.217
4.800
30
31
39. 560
23. 841
17.061
13. 284
10. 876
9.207
7.982
7.045
6.304
5.705
5.210
4.793
31
32
39. 130
23. 684
16. 981
13. 235
10. 843
9. 183
7.964 i 7.031
6.293
5.696
5.202
4.787
32
33
38. 710
23. 529
16. 901
13. 186
10.810
9.160
7.947
7.017
6.282
5.687
5.195
4.780
33
34
35
38. 298
23. 377
23. 226
16. 822
16. 744
13. 138
10. 778
9.137
7.929
7.912
7.004
6.990
6. 271 5. 678
6.260 1 5.669
5.187
5.179
4.774
"4. 768
34
35
37. 895
13. 091
10. 746
9.113
36
37. 500
23. 077
16. 667
13. 043
10. 714
9.090
7.895
6.977
6.250
5.660
5.172
4.761
36
37
37. 113
22. 930
16. 590
12. 996
10. 682
9.068 7.877
6.963
6.239 1 5.651
5.164
4. 755
37
38
36. 735
22. 785
16.514
12. 950
10. 651
9.045
7.860
6.950
6.228
5.642
5.157
4.749
38
39
40
36. 364
36. 000'
22.642
16. 438
12. 903
10.619
9.022
7.843
6.936 6.217
5.633
5. 150 4. 743 1
39
40
22. 500
16. 363
12. 857
10. 588
9.000 7.826
6.923
6.207
5.625
5.143
4.737
41
35.644
22. 360
16. 289
12.811
10. 557
8.9771 7.809
6.909
6.196
5.616
5.135
4.731
41
42
35. 294
22. 222
16.216
12. 766
10. 526
8.955 7.792
6.896
6.185
5.607
5.128
4.724
42
43
34. 951
22. 086
16. 143
12. 721
10. 495
8.933 7.775
6.883
6.174
5.598
5.121
4.718
43
44
45
34. 615
21. 951
16. 071
12. 676
10. 465
8.911 7.758
6.870
6.164
5.590
5.114
4.712
44
45
34. 286
21.818
16.000
12. 631
10.434
8.889
7.741
6.857
6.153
5.581
5.106
4.706
46
33. 962
21. 687
15. 929
12. 587
10.404
8.867
7.725
6.844
6.143
6.572
5.099
4.700
46
47
33.645
21.557
15. 859
12. 543
10. 375
8. 845
7.708
6.831
6.132
5.564
5.091
4.693
47
48
33. 333
21.429
15. 789
12.500
10. 345
8.823
7.692
6.818
6.122
5.555
5.084
4.687
48
49
50
33. 028
21. 302
15. 721
15.652
12. 456
10. 315
8.801
7.675
7.659
6.805
6.792
6.112
6.101
5.547
5.077
4.681
49
50
32. 727
21. 176
12.413
10. 286
8.780
5.538
5.070
4.675
51
32. 432
21.053
15. 584
12. 371
10. 256
8.759
7.643
6.779
6.091
5. 530
5.063
4.669
51
52
32. 143
20. 930
15.517
12. 329
10. 227
8.737
7.627
6.766
6.081
5.521
5.056
4.663
52
53
31.858
20. 809
15. 450
12. 287
10. 198
8.716
7.611
6.754
6.071
5. 513
5.049
4.657
53
54
55
31.579
20. 690
20. 571
15. 384
12. 245
12. 203"
10. 169
8.695
8.675
7.595
7.579
6.741
6.739
6.060
6.050
5.504
5.496
5.042
4.651
54
55
31. 304
15.319
10. 140
5. 035
4. 645
56
31. 034
20. 455
15. 254
12. 162
10. 112
8.654
7.563
6.716
6.040
5.487
5.028
4.639
56
57
30. 769
20. 339
15. 190
12. 121
10. 084
8.633
7.547
6.704
6.030
5.479
5.020
4.633
57
58
30. 508
20. 225
15. 126
12. 080
10. 055
8.612
7.531
6.691
6.020
5.471
5.013
4.627
58
59
30. 252
20. 112
15. 062
12. 040
10. 027
8.591
7.515
6.679
6.010
5.463
5.006
4.621
59
Sec.
Sec.
1
2
3
4
5
6
7
8
«
10
11
12
Page 670] TABLE 36.
Eeduction of Local Mean Time to Standard Meridian Time, and the reverse.
[If local meridian is east of standard meridian, subtract from local mean time, or add to standard meridian time. If local
meridian is west of standard meridian, add to local mean time, or subtract from standard meridian time.]
Difference of longitude be-
Reduction to
be applied
to local mean
time.
Difference of longitude be-
Reduction to
tween local meridian and
standard meridian.
tween local meridian and
standard meridian.
De appiieci
to local mean
time.
o / o /
^f^7mtes.
O ' 0 '
Minutes.
0 oft to 0 07
0
7 23 to 7 37
30
0 08 to 0 22
1
7 38 to 7 52
31
0 23 to 0 37
2
7 53 to 8 07
32
0 38 to 0 52
3
8 08 to 8 22
33
0 53 to 1 07
4
8 23 to 8 37
34
1 08 to 1 22
5
8 38 to 8 52
35
1 23 to 1 37
6
8 53 to 9 07
36
1 38 to 1 52
7
9 08 to 9 22
37
1 53 to 2 07
8
9 23 to 9 37
38
2 08 to 2 22
9
9 38 to 9 52
39
2 23 to 2 37
10
9 53 to 10 07
40
2 38 to 2 52
11
10 08 to 10 22
41
2 53 to 3 07
12
10 23 to 10 37
42
3 08 to 3 22
13
10 38 to 10 52
43
3 23 to 3 37
14
10 53 to 11 07
44
3 38 to 3 52
15
11 08 to 11 22
45
3 53 to 4 07
16
11 23 to 11 37
46
4 08 to 4 22
17
11 38 to 11 52
47
4 23 to 4 37
18
11 53 to 12 07
48
4 38 to 4 52
19
12 08 to 12 22
49
4 53 to 5 07
20
12 23 to 12 37
50
5 08 to 5 22
21
12 38 to 12 52
51
5 23 to 5 37
22
12 53 to 13 07
52
5 38 to 5 52
23
13 08 to 13 22
53
5 53 to 6 07
24
13 23 to 13 37
54
6 08 to 6 22
25
13 38 to 13 52
55
6 23 to 6 37
26
13 53 to 14 07
56
6 38 to 6 52
27
14 08 to 14 22
57
6 53 to 7 07
28
14 23 to 14 37
58
7 08 to 7 22
29
14 38 to 14 52
59
TABLE 37.
[Page 571
Log. A and Log. B.
For Computing the Equation of Equal Altitudes. For Noon, A-;
for Midnight, A+;
for Noon or Midnight, B+. |
Argument=Elapsed Time.]
05 -^
Oh
1
h
2h
gh
4h
5)> 1
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
m.
0
9. 4059
9. 4059
9. 4072
9. 4034
9. 4109
9. 3959
9. 4172
9. 3828
9.4260
9. 3635
9. 4374
9. 3369
1
.4059
.4059
.4072
.4034
.4110
.3957
.4173
. 3825
.4261
.3631
. 4376
.3364
2
.4059
.4059
.4073
.4033
.4111
.3955
.4174
.3822
.4263
.3627
.4378
. 3358
3
. 4059
.4059
.4073
.4032
.4112
.3953
.4175
.3820
.4265
.3624
.4380
.3353
4
.4059
.4059
9. 4059
.4074
.4031
.4113
.3952
.4177
.3817
9. 3814
.4266
.3620
.4383
.3348
5
9. 4059
9. 4074
9. 4030
9.4113
9. 3950
9. 4178
9. 4268
9. 3616
9. 4385
9. 3343
6
.4060
.4059
.4074
.4029
.4114
.3948
.4179
.3811
.4270
.3612
.4387
.3337
7
.4060
.4059
.4075
.4028
.4115
.3946
.4181
. 3809
.4272
.3608
.4389
.3332
8
.4060
.4059
. 4075
.4027
.4116
.3944
.4182
.3806
.4273
.3604
.4391
.3327
9
10'
.4060
9. 4060
.4059
9. 4059
.4076
9. 4076
.4026
"9. 4025
.4117
.3943
.4183
.3803
9. 3800
.4275
9. 4277
.3600
.4393
9. 4396
.3221
9. 3316
9. 4118
9. 3941
9. 4184
9. 3596
11
.4060
.4059
.4077
.4024
.4119
.3939
.4186
.3797
.4279
.3592
.4398
.3311
12
.4060
. 4058
.4077
. 4023
.4120
.3937
.4187
.3794
.4280
.3588
.4400
.3305
13
.4060
. 4058
.4078
.4022
.4121
.3935
.4188
. 3792
.4282
.3584
.4402
.3300
14
15
.4060
.4058
.4078
.4021
.4121
.3933
.4190
.3789
9. 3786'
.4284
9. 4'286
.3580
.4405
.3294
9. 4060
9. 4058
9. 4079
9. 4020
9. 4122
9. 3931
9. 4191
9. 3576
9. 4407
9. 3289
16
.4060
.4058
.4079
.4019
.4123
.3929
.4193
.3783
.4288
.3572
.4409
.3283
17
.4060
.4057
.4080
.4018
.4124
.3927
.4194
.3780
.4289
. 3568
.4411
.3278
18
.4061
.4057
.4080
.4017
.4125
.3925
.4195
. 3777
.4291
.3564
.4414
.3272
19
20
.4061
.4057
.4081
.4016
9. 4015
.4126
.3923
.4197
.3774
.4293
9. 4295
.3559
.4416
.3266
9. 4061
9. 4057
9. 4081
9. 4127
9. 3921
9. 4198
9. 3771
9. 3555
9.4418
9. 3261
21
.4061
.4056
.4082
.4014
.4128
.3919
.4199
. 3768
.4297
.3551
.4420
.3255
22
.4061
.4056
.4083
.4013
.4129
.3917
.4201
.3765
. 4299
.3547
.4423
.3249
23
.4061
.4056
. 4083
.4012
.4130
.3915
.4202
.3762
.4300
.3542
.4425
.3244
24
25
.4061
.4055
.4084
9. 4084
.4010
9.4009
.4131
.3913
.4204
.3759
.4302
. 3538
.4427
.3238
9. 4062
9. 4055
9. 4132
9. 3911
9. 4205
9. 3756
9. 4304
9.3534
9.4430
9. 3232
26
.4062
.4055
.4085
.4008
.4133
.3909
.4207
.3752
.4306
. 3530
.4432
.3226
27
.4062
.4054
.4086
.4007
.4134
.3907
.4208
.3749
.4308
.3525
.4434
. 3220
28
.4062
.4054
.4086
.4006
.4135
.3905
.4209
.3746
.4310
.3521
.4437
.3214
29
30
.4062
9. 4062
.4054
9. 4053
.4087
.4004
9.4003
.4136
.3903
.4211
.3743
.4312
.3516
.4439
.3208
9. 4087
9. 4137
9.3900
9. 4212
9.3740
9. 4314
9. 3512
9.4441
9. 3203
31
. 4063
.4053
.4088
.4002
. 4138
.3898
.4214
.3737
.4315
.3508
.4444
.3197
32
.4063
.4052
.4089
.4001
.4139
. 3896
.4215
.3733
.4317
. 3503
.4446
.3191
33
.4063
.4052
.4089
. 3999
.4140
.3894
.4217
.3730
.4319
.3499
.4448
.3185
34
. 4063
.4051
.4090
9. 4091
. 3998
9. 3997
.4141
.3892
.4218
9. 4220
.3727
.4321
. 3494
.4451
.3178
35
9. 4064
9. 4051
9. 4142
9. 3889
9. 3723
9. 4323
9.3490
9.4453
9. 3172
36
.4064
.4050
. 4091
. 3995
.4144
.3887
.4221
.3720
.4325
.3485
.4456
.3166
37
.4064
. 4050
.4092
. 3994
.4145
.3885
.4223
.3717
.4327
.3480
.4458
.3160
38
.4064
.4049
.4093
.3993
.4146
.3882
.4224
.3713
.4329
.3476
.4460
.3154
39
. 4065
.4049
.4093
. 3991
.4147
9. 4148
.3880
9. 3878
.4226
9. 4227
.3710
9. 3707
.4331
9. 4333
.3471
.4463
.3148
40
9. 4065
9. 4048
9. 4094
9. 3990
9. 3467
9.4465
9. 3142
41
.4065
.4048
. 4095
.3988
.4149
.3875
.4229
.3703
.4335
.3462
.4468
.3135
42
.4065
.4047
.4095
.3987
.4150
.3873
.4231
.3700
.4337
.3457
.4470
.3129
43
.4066
.4047
.4096
.3985
.4151
.3871
.4232
.3696
.4339
.3453
.4473
.3123
44
45
.4066
.4046
9. 4045
.4097
.3984
.4152
.3868
.4234
.3693
9. 3690
.4341
9. 4343
.3448
.4475
.3116
9. 4066
9. 4097
9. 3982
9. 4154
9. 3866
9. 4235
9. 3443
9. 4477
9.3110
46
.4067
.4045
.4098
.3981
.4155
.3863
.4237
.3686
.4345
. 3438
.4480
. 3103
47
.4067
.4044
.4099
.3979
. 4156
.3861
.4238
.3683
.4347
.3433
.4482
.3097
48
.4067
.4043
.4100
.3978
.4157
.3859
.4240
. 3679
.4349
.3429
.4485
. 3091
49
50
.4068
.4043
.4100
9. 4101
.3976
9."3975
.4158
9. 4159
.3856
9. 3854
.4242
. 3675
9. 3672
.4351
"9. 4353'
.3424
.4487
.3084
9. 4068
9. 4042
9. 4243
9. 3419
9. 4490
9. 3078
51
.4068
.4041
.4102
. 3973
. 4161
.3851
.4245
.3668
. 4355
.3414
.4492
.3071
52
.4069
.4041
.4103
. 3972
.4162
.3849
.4246
. 3665
.4357
.3409
.4494
.3064
53
.4069
.4040
. 4103
.3970
.4163
.3846
.4248
.3661
. 4359
.3404
.4497
. 3058
54
55
.4069
9. 4070
.4039
9. 4038
.4104
9. 4105
.3969
.4164
9.4165
.3843
9. 3841
.4250
.3657
9. 3654
. 4361
9. 4363
.3399
.4500
9. 4503
.3051
9. 3967
9. 4251
9. 3394
9. 3044
56
.4070
.4038
.4106
.3965
.4167
.3838
.4253
.3650
.4366
.3389
.4505
.3038
57
.4071
.4037
.4107
.3964
.4168
.3836
.4255
.3646
. 4368
. 3384
.4508
.3031
58
.4071
.4036
.4107
.3962
.4169
. 3833
.4256
.3643
.4370
.3379
.4510
. 3024
59
60
.4071
9. 4072
.4035
9. 4034
.4108
9.'4T09
.3960
9. 3959
.4170
. 3830
9. 3828
.4258
.3639
.4372
.3374
.4513
.3017
9.4172
9. 4260
9. 3635
9. 4374
9. 3369
9. 4515
9. 3010
Page 572]
TABLE 37.
Log. A and Log. B.
[For Computing the Equation of Equal Altitudes. For Noon, A-; for Midnight, A + ; for Noon or Midnight, B+. |
Argument=Elapsed Time.]
0
h
7
h
- I
1
10^ 1
Ilk 1
Log. A.
Log.B.
Log. A.
Log.B.
Log. A.
Log. B.
Log. A.
Log.B.
Log. A.
Log.B.
Log. A.
Log.B.
m.
0
9. 4515
9. 3010
9^4685
9. 2530
9. 4884
9. 1874
9.5115
9. 0943
9. 5379
8. 9509
9. 5680
8. 6837
1
.4518
.3003
.4688
.2520
.4888
.1861
.5119
.0925
.5384
.9478
.5685
.6770
2
.4521
.2996
.4691
.2511
.4892
.1848
.5123
.0906
.5389
.9447
.5691
.6701
3
. 4523
.2989
.4694
.2502
.4895
.1835
.5127
.0887
.5393
.9416
.5696
.6632
4
5
.4526
9. 4528
.2982
.4697
.2492
.4899
9. 4902
.1822
9. 1809
.5132
9. 5136
.0867
.5398
.9384
.5701
.6560
8. 6488
9. 2975
9. 4701
9. 2483
9. 0848
9.5403
8. 9352
9. 5707
6
.4531
.2968
.4704
.2473
.4906
.1796
.5140
.0828
.5408
.9320
. 5712
.6414
7
.4534
.2961
.4707
.2463
.4910
.1782
.5144
.0809
.5412
.9287
.5718
.6339
8
.4536
.2954
.4710
.2454
.4913
.1769
.5148
.0789
.5417
.9254
.5723
.6262
9
10
.4539
.2947
.4713
.2444
9. 2434
.4917
.1756
9. 1742
.5153
.0769
.5422
.9221
.5728
.6183
9. 4542
9. 2940
9. 4716
9. 4921
9. 5157
9. 0749
9. 5427
8.9187
9.5734
8. 6103
11
.4544
.2932
.4719
. 2425
.4924
.1728
. 5161
.0729
.5432
.9153
. 5739
.6021
12
.4547
.2925
.4723
.2415
.4928
.1715
. 5165
.0708
.5436
.9118
.5745
.5937
13
.4550
.2918
.4726
.2405
.4932
.1701
.5169
.0688
.5441
.9083
.5750
.5852
14
.4552
.2911
9. 2903
.4729
.2395
.4935
.1687
.5174
.0667
.5446
.9048
.5756
.5764
15
9. 4555
9. 4732
9. 2385
9. 4939
9. 1673
9.5178
9. 0646
9. 5451
8. 9013
9. 5761
8. 5674
16
.4558
.2896
.4735
.2375
. 4943
.1659
.5182
.0625
.5456
.8977
.5767
.5583
17
.4561
.2888
.4738
.2365
.4946
.1645
.5186
.0604
.5461
.8940
.5772
.5488
18
.4563
.2881
.4742
.2355
.4950
.1630
.5191
.0583
. 5466
.8903
.5778
.5392
19
20
.4566
.2873
'9. 28*66
.4745
.2344
.4954
9. 4958
.1616
. 5195
.0561
.5470
.8866
.5783
.5293
9. 4569
9. 4748
9. 2334
9. 1602
9.5199
9. 0540
9. 5475
8. 8829
9. 5789
8. 5192
21
.4572
. 2858
.4751
.2324
.4961
.1587
.5204
.0518
.5480
.8791
.5794
.5088
22
. 4574
.2850
.4755
.2313
.4965
.1573
. 5208
.0496
.5485
.8752
.5800
.4981
23
.4577
.2843
.4758
.2303
.4969
.1558
.5212
.0474
.5490
.8713
.5806
.4871
24
.4580
.2835
.4761
.2292
.4973
.1543
.5217
.0452
. 5495
9. 5500
.8674
.5811
. 4758
25
9. 4583
9. 2827
9. 4764
9. 2282
9. 4977
9. 1528
9. 5221
9. 0429
8. 8634
9. 5817
8. 4641
26
.4585
.2819
.4768
. 2271
.4980
.1513
.5225
.0406
.5505
.8594
.5822
.4521
27
.4588
.2812
.4771
. 2261
.4984
.1498
.5230
.0383
.5510
. 8553
.5828
. 4397
28
.4591
.2804
.4774
.2250
.4988
.1483
.5234
.0360
.5515
. 8512
.5834
.4270
29
30
.4594
.2796
9. 2788
.4778
.2239
.4992
9. 4996
.1468
.5238
9. 5243
. 0337
.5520
.8470
.5839
. 4138
9. 4597
9. 4781
9. 2228
9. 1453
9. 0314
9. 5525
8. 8427
9. 5845
8. 4001
31
.4600
.2780
.4784
.2217
.5000
.1437
.5247
.0290
.5530
.8384
.5851
.3860
32
.4602
.2772
.4788
.2206
.5003
.1422
.5252
.0266
. 5535
.8341
.5856
.3713
33
.4605
.2764
.4791
.2195
.5007
.1406
.5256
.0242
. 5540
.8297
.5862
. 3561
34
.4608
. 2756
.4794
.2184
9. 2173
.5011
.1390
5261
9. 5265
.0218
.5545
9. 5550
.8253
.5868
. 3403
8. 3239
35
9. 4611
9. 2747
9. 4798
9. 5015
9. 1375
9. 0194
8. 8208
9. 5874
36
.4614
.2739
.4801
.2162
.5019
.1359
.5269
.0169
.5555
.8162
.5879
.3067
37
.4617
.2731
.4804
.2151
.5023
.1343
.5274
.0144
.5560
.8115
.5885
.2888
38
.4620
.2723
.4808
.2140
.5027
.1327
.5278
.0119
.5565
.8068
.5891
.2701
39
40
.4622
9. 4625
.2714
9. 2706
.4811
.2128
.5031
.1310
.5283
9.5287
.0094
.5570
.8020
.5897
.2505
9.4815
9.2117
9. 5035
9.1294
9. 0069
9. 5576
8. 7972
9. 5902
8. 2299
41
.4628
.2698
.4818
.2105
.5038
.1278
.5292
.0043
.5581
.7923
.5908
.2082
42
.4631
.2689
.4821
.2094
.5042
.1261
. 5296
.0017
.5586
.7873
.5914
.1853
43
. 4634
.2681
.4825
.2082
.5046
.1244
.5301
8. 9991
.5591
.7823
.5920
.1611
44
45
.4637
.2672
.4828
.2070
9.2059
.5050
.1228
.5305
.9965
8. 9938
. 5596
9. 5601
.7772
.5926
.1354
9. 4640
9.2664
9. 4832
9. 5054
9.1211
9. 5310
8.7720
9. 5931
8. 1080
46
.4643
.2655
.4835
.2047
. 5058
.1194
.5315
.9911
.5606
.7668
.5937
.0786
47
.4646
.2646
.4839
.2035
.5062
.1177
. 5319
.9884
.5612
.7614
.5943
.0470
48
.4649
.2638
.4842
.2023
.5066
.1159
.5324
.9857
.5617
.7560
.5949
.0128
49
50
.4652
.2629
9. 2620
.4846
.2011
.5070
.1142
9. 1125
.5328
.9830
8. 9802
.5622
.7505
8. 7449
.5955
7. 9756
9. 4655
9.4849
9. 1999
9. 5074
9. 5333
9. 5627
9. 5961
7. 9348
51
.4658
.2611
.4853
.1987
.5078
.1107
.5337
.9774
.5632
.7392
.5967
.8897
52
.4661
.2602
.4856
.1974
.5082
.1089
.5342
.9745
.5638
.7335
. 5973
.8391
53
.4664
.2593
.4860
.1962
.5086
.1072
.5347
.9717
.5643
.7276
.5979
.7817
54
.4667
.2584
9. 2575
.4863
9. 4867
.1950
.5091
.1054
.5351
.9688
8. 9659
.5648
9.5654
.7217
8. 7156
.5985
.7154
55
9. 4670
9. 1937
9. 5095
9. 1036
9. 5356
9. 5991
7. 6368
56
.4673
.2566
.4870
.1925
.5099
.1017
.5361
.9630
.5659
.7094
.5997
.5405
57
.4676
.2557
.4874
.1912
.5103
.0999
. 5365
.9600
.5664
.7032
.6003
.4162
58
.4679
.2548
.4877
.1900
.5107
.0981
.5370
.9570
.5669
.6968
.6009
.2407
59
60
.4682
.2539
9. 2530
.4881
. 1887
.5111
.0962
9. 0943
.5375
9. 5379
.9540
8.9509
.5675
9. 5680
.6903
.6015
6. 9591
9. 4685
9. 4884
9. 1874
9. 5115
8. 6837
9.6021
Inf.
f OF THE ^ X
%£^LypnBKa>._^
/
TABLE 37.
[Page 573
Log. A and Log. B.
[For Computing the Equation
of Equal
Altitudes. For Noon, A — ;
for Midnight, A +;
for Noon or Midnlgh
t, B-.
Argument = Elapsed Time. 1
■ . lai"
18"
14h
loh
itt-
1
7"
Log. A.
Log. B.
Inf.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
in.
0
9. 6021
9.6406
8. 7563
9. 6841
9. 0971
9. 7333
9. 3162
9. 7895
9.4884
9. 8539
9. 6383
1
.6027
6. 9608
.6412
.7641
. 6848
.1014
.7:342
. 3194
.7905
.4911
.8550
.6407
9
.6038
7. 2431
. 6419
.7718
.6856
. 1057
. 7351
. 8225
.7915
.4937
. 8562
.6431
8
.6039
.4198
.6426
.7794
.6864
.1099
.7360
.8256
.7925
.4963
.8573
.6455
4
5
.6045
. 5453
7. 6428
. 6438
9.6440
.7868
.6872
.1141
9. 1183
.7369
9. 7378
.8287
.7935
.4990
.8585
.6478
9. 6051
8. 7942
9. 6879
9. 3319
9. 7945
9. 5016
9. 8597
9. 6502
B
. 6057
.7226
.6447
. 8015
.6887
.1224
. 7386
.3350
. 7955
.5042
.8608
.6526
7
. 6063
.7902
. 6454
.8087
. 6895
. 1265
.7395
.3880
.7965
. 5068
.8620
.6550
8
.6069
.8488
.6461
.8158
.6903
.1806
.7404
.8411
.7975
.5094
. 8632
. 6573
9
10
. 6075
.9005
.6467
9.6474
.8227
8. 8296
.6911
9. 6919
.1347
9. 1887
.7418
.3442
9. 8472
.7986
9. 7996'
.5120
9. 5146
.8644
.6597
9. 6082
7. 9469
9. 7422
9. 8655
9. 6621
n
.6088
.9889
.6481
.8364
.6926
.1428
.7431
. 8503
.8006
.5171
.8667
.6644
12
.6094
8. 0273
.6488
. 8482
.6934
.1468
.7440
. 3533
.8016
.5197
.8679
. 6668
18
.6100
.0627
.6495
.8498
.6942
.1507
.7449
.3563
.8027
. 5223
.8691
.6691
14
15
.6106
9.6112
.0955
8. 1260
.6502
9. 6509
. 8564
8. 8628
.6950
9. 6958
.1547
9. 1586
.7458
. 3593
9.8628
. 8037
9. 8047'
.5248
. 8708
.6715
9. 6738
9. 7467
9. 5274
9.8715
16
.6119
. 1547
.6516
.8692
.6966
.1625
.7476
.3653
.8058
.5800
.8727
.6762
17
.6125
.1816
. 6523
.8756
.6974
.1664
. 7485
. 3688
.8068
.5325
.8789
.6785
18
.6131
.2071
.6580
.8818
.6982
.1703
.7494
.3713
.8078
.5851
.8751
.6809
19
.6137
. 2312
. 6538
.8880
.6990
9. 6998
.1741
.7503
. 3742
9. 3772^
.8089
9. 8099
.5376
9. 5401
.8763
9. 8775
.6832
20
9.6144
8. 2541
9. 6545
8. 8941
9. 1779
9. 7512
9. 6856
21
.6150
.2759
. 6552
.9002
.7006
.1817
.7522
.3801
.8110
.5427
.8787
.6879
22
.6156
.2967
.6559
.9062
.7014
.1855
.7531
.3831
.8120
.5452
.8799
.6903
28
.6163
.3166
.6566
.9121
.7022
.1893
.7540
.8860
.8131
.5477
.8812
.6926
24
25
.6169
.8357
.6573
9. 6580
.9180
8. 9288
.7030
9. 7088
.1930
.7549
. 3889
9. 3918
.8141
9. 8152
.5502
9. 5528
.8824
.6949
9. 6973
9.6175
8. 3540
9. 1967
9. 7558
9. 8836
26
.6182
.3717
.6588
.9295
.7047
.2004
.7568
.3947
.8162
.5553
.8848
.6996
27
.6188
.3887
. 6595
. 9852
.7055
.2041
.7577
.3976
.8173
. 5578
.8861
.7019
28
.6194
. 4051
.6602
.9408
.7063
.2078
.7586
.4005
.8184
. 5603
.8873
.7043
29
80
.6201
9. 6207
.4210
8. 4363
.6609
.9464
8. 9519
.7071
9. 7079
.2114
9. 2150
.7595
.4083
9. 4062
.8194
. 5628
.8885
.7066
9. 6616
9. 7605
9. 8205
9. 5653
9. 8898
9. 7089
81
. 6214
.4512
.6624
.9573
.7088
.2186
.7614
.4090
.8216
.5677
.8910
.7112
82
.6220
. 4657
. 6631
.9627
.7096
.2222
.7624
.4119
.8227
.5702
.8923
.7186
88
.6226
.4796
. 6638
.9681
.7104
.2258
.7638
.4147
.8237
.5727
. 8935
.7159
34
85
.6233
9. 6239
. 4932
8. 5064
. 6645
. 9734
8. 9787
.7112
.2293
.7642
.4175
.8248
.5752
.8948
.7182
9. 6653
9. 7121
9. 2329
9. 7652
9. 4204
9. 8259
9. 5777
9. 8961
9. 7205
86
.6246
.5192
.6660
. 9889
.7129
.2364
.7661
.4232
.8270
.5801
.8973
.7228
87
.6252
.5318
.6667
.9891
.7137
.2399
.7671
.4260
.8281
.5826
.8986
.7251
88
.6259
.5440
.6675
.9942
.7146
.2434
.7680
.4288
.8292
.5850
.8999
.7275
39
40
.6265
. 5559
.6682
9. 6690
. 9993
.7154
.2468
.7690
.4316
.8803
.5875
.9011
.7298
9. 6272
8. 5675
9. 0043
9. 7162
9. 2508
9. 7699
9. 4348
9. 8314
9. 5900
9. 9024
9. 7821
41
.6279
.5788
.6697
.0093
.7171
. 2587
.7709
.4371
.8325
.5924
. 9037
.7344
42
.6285
.5899
.6704
.0142
.7179
.2571
.7718
.439^
. 8336
. 5948
.9050
.7367
48
.6292
.6008
.6712
.0191
.7187
.2605
.7728
.4426
.8347
.5973
.9063
.7390
44
45
.6298
.6114
8. 6218
.6719
.0240
.7196
9. 7204
.2639
.7788
.4454
.8358
.5997
9.6022
.9075
.7413
9. 6305
9. 6727
9. 0288
9. 2673
9. 7747
9.4481
9. 8369
9. 9088
9. 7436
46
.6311
.6320
.6734
.0336
.7213
.2706
. 7757
.4509
.8380
.6046
.9101
.7459
47
.6318
.6419
.6742
.0384
.7221
.2740
.7767
.4536
. 8391
.6070
.9114
.7482
48
.6325
.6517
.6749
.0431
.7230
. 2773
.7776
.4563
.8402
.6094
.9127
.7505
49
50
.6381
9. 6338
.6613
8. 6707
.6757
9. 6764
.0478
9. 0524
.7238
.2806
.7786
.4590
.8414
.6119
.9140
.7529
9. 7247
9. 2839
9. 7796
9.4617
9. 8425
9. 6143
9. 9154
9. 7552
51
.6345
.6799
.6772
.0570
.7256
.2872
.7806
.4644
.8486
.6167
.9167
.7575
52
.6351
.6890
.6779
.0616
.7264
.2905
.7815
.4671
.8447
.6191
.9180
.7598
53
. 6358
.6979
.6787
.0662
.7273
.2937
.7825
.4698
.8459
.6215
.9193
.7621
54
.6365
.7067
.6795
9. 6802
.0707
9. 0752
.7281
.2970
9. 8002
. 7835
.4725
9. 4752
.8470
9.8481
.6239
.9206
.7644
55
9. 6372
8. 7153
9. 7290
9. 7845
9. 6263
9. 9220
9. 7667
56
.6378
.7237
.6810
.0796
.7299
. 8034
.7855
. 4778
.8493
.6287
.9233
.7690
57
.6385
.7321
.6818
.0840
.7307
.3066
.7865
.4805
.8504
.6311
.9246
.7713
58
.6392
.7402
.6825
.0884
.7316
.3098
.7875
.4831
.8516
.6335
.9260
.7736
59
.6399
. 7483
.6833
.0928
.7324
.3130
.7885
.4858
.8527
.6359
.9273
.7759
60
9.6406
8. 7568
9.6841
9.0971
9. 7333
9. 3162
9. 7895
9.4884
9. 8539
9. 6383
9. 9287
9. 7782
Page 574
TABLE 37.
Log. A and Log. B.
[For Computing the Equation of Equal Altittide.s
. For Noon, A — ; for Midnight, A +;
for Noon or Midnight, B -. 1
Argument = Elapsed Time.]
fa
l|
18"
IS"
200
2ih
221-
o
jh
Ivog. A.
Log.B.
Log. A.
Log.B.
Log. A.
Log.B.
Log. A.
0. 2623
Log.B.
Log. A.
Log. B.
Log. A.
Log. B.
m.
0
9. 9287
9. 7782
•
0. 0172
9. 9167
0. 1249
0. 0625
0. 2279
0. 4523
0. 4372
0. 7689
0. 7652
1
.9300
.7804
. 0188
.9190
.1269
.0650
.2649
.2309
.4562
.4414
. 7765
.7729
2
.9314
.7827
. 0204
. 9213
.1290
.0676
.2676
. 2339
.4601
.4455
.7842
.7807
3
. 9327
.7850
.0221
.9237
.1310
.0701
.2702
.2370
.4640
.4497
.7920
.7886
4
5
.9341
9.9355
.7873
.0237
.9260
. 1330
.0727
.2729
.2401
0.2431
.4680
0. 4720
. 4540
.8000
0. 8081
.7967
9. 7896
0. 0253
9. 9284
0.1351
0. 0753
0. 2756
0. 4582
0.8049
6
.9368
.7919
.0270
.9307
.1371
.0779
. 2783
.2462
.4761
.4625
.8163
.8133
7
.9382
.7942
.0286
.9331
.1392
.0805
.2810
.2493
.4801
.4668
.8247
.8218
8
.9396
.7965
.0303
. 9355
.1412
.0830
.2838
. 2524
.4842
.4711
. 8333
.8305
9
.9410
.7988
.0319
0. 0336
.9378
. 1433
0. 1454
.0856
.2865
. 2556
0.2587
.4884
0. 4926
.4755
.8420
. 8393
0. 8483
10
9. 9424
9.8011
9. 9402
0. 0882
0. 2893
0.4799
0. 8508
11
.9437
.8034
. 0353
.9426
.1475
.0909
.2921
.2619
.4968
.4844
. 8599
.8574
12
.9451
.8057
.0370
.9449
.1496
.0935
.2949
.2650
.5010
.4889
.8691
.8667
13
.9465
.8080
.0386
.9473
.1517
.0961
.2977
.2682
.5053
.4934
.8786
.8763
14
15
.9479
.8103
.0403
.9497
.1538
.0987
.3005
.2714
0. 2746
.5097
.4980
.8882
.8860
9. 9493
9. 8126
0. 0420
9. 9520
0. 1559
0. 1013
0. 3034
0. 5140
0. 5026
0. 8980
0. 8959
16
.9508
.8149
.0437
.9544
.1581
.1040
.3063
.2778
.5184
.5072
.9080
.9060
17
.9522
.8172
.0454
.9568
.1602
.1066
. 3091
.2811
. 5229
.5118
.9183
.9164
18
.9536
.8195
.0472
.9592
.1623
.1093
.3120
.2843
.5274
.5165
.9288
.9270
19
20
.9550
9.9564
.8218
9. 8241
.0489
.9616
.1645
.1119
. 3150
.2876
"0. 2909
. 5319
0. 5365
. 5213
0. 5261
. 9396
.9378
0. 0506
9.9640
0. 1667
0. 1146
0. 3179
0. 9506
0. 9489
21
.9579
.8264
.0523
.9664
.1689
.1173
.3208
.2942
■ . 5411
.5309
.9618
.9603
22
.9593
.8287
.0541
.9687
.1711
.1200
.3238
.2975
. 5458
.5358
.9734
.9719
23
.9607
.8310
.0558
.9711
.1733
.1226
.3268
.3008
.5505
.5407
.9853
.9839
24
25
.9622
9. 9636
.8333
. 0576
.9735
.1755
.1253
0. 1280
.3298
.3041
. 5553
.5457
.9975
.9961
9. 8356
0. 0593
9. 9760
0. 1777
0. 3328
0. 3075
0. 5601
0. 5507
1.0100
1.0087
26
.9651
.8379
.0611
.9784
.1799
.1308
.3359
.3109
.5649
.5557
.0228
.0216
27
.9665
.8402
.0628
.9808
.1821
.1335
.3389
.3143
.5698
.5608
.0361
.0350
28
.9680
.8425
.0646
.9832
.1844
.1362
.3420
.3177
.5748
.5660
.0497
.0487
29
30
.9695
9. 9709
.8448
.0664
.9856
.1867
.1389
0. 1417
.3451
0. 3482
.3211
0. 3245
.5798
0.5848
.5712
.0638
.0628
9. 8471
0. 0682
9. 9880
0. 1889
0.5764
1 1. 0783
1. 0774
31
.9724
.8494
.0700
.9904
.1912
.1444
.3514
.3280
. 5899
.5817
.0934
.0925
32
.9739
. 8517
.0718
.9929
.1935
.1472
.3545
.3315
. 5951
.5871
.1089
.1081
33
.9754
.8540
.0736
.9953
.1958
.1499
.3577
.3350
.6003
.5925
.1250
.1242
34
.9769
.8563
.0754
.9977
.1981
.1527
0. 1555
.3609
.3385
0. 3420'
.6056
.5979
.1416
.1409
35
9.9784
9. 8586
0. 0772
0.0002
0. 2004
0. 3641
0. 6110
0.6034
1. 1590
1. 1583
36
.9798
.8609
.0790
.0026
.2028
.1582
.3674
.3456
.6164
.6090
.1770
.1764
37
.9813
.8632
.0809
.0051
.2051
.1610
.3706
.3491
.6218
.6147
.1958
.1952
38
.9829
.8655
.0827
.0075
.2075
.1638
.3739
.3527
.6273
.6204
.2154
.2149
39
40
.9844
.8678
. 0845
.0100
.2098
.1667
.3772
.3563
.6329
.6261
0. 6319
.2359
. 2354
1. 2569
9. 9859
9. 8701
0.0864
0. 0124
0. 2122
0. 1695
0. 3805
0. 3599
0. 6386
1. 2573
41
.9874
.8724
.0883
.0149
.2146
.1723
.3839
.3636
.6443
.6378
.2799
.2795
42
.9889
.8748
.0901
.0173
.2170
.1751
.3873
.3673
.6501
.6438
.3037
.3033
43
.9904
.8771
.0920
.0198
.2194
.1780
.3907
.3710
.6560
.6498
.3288
.3285
44
45
.9920
9. 9935
.8794
.0939
0. 0958
.0223
.2218
.1808
.3941
.3747
0. 3784
.6619
0.6679
.6559
.3554
.3552
9. 8817
0. 0248
0. 2243
0. 1837
0. 3975
0. 6621
1. 3837
1.3835
46
.9951
.8840
.0976
.0272
.2267
.1866
.4010
.3822
.6740
.6684
.4140
.4138
47
.9966
.8863
.0995
.0297
.2292
.1895
.4045
.3859
.6802
.6747
.4465
.4463
48
.9982
.8887
.1015
.0322
.2316
.1924
.4080
.3897
.6865
.6811
.4815
.4814
49
50
.9998
.8910
.1034
.0347
.2341
.1953
.4115
.3936
0. 3974
.6928
0. 6993
.6876
.5196
1. 5613
.5195
0.0013
9. 8933
0. 1053
0. 0372
0. 2366
0. 1982
0. 4151
0. 6942
1.5612
51
.0029
.8956
.1072
.0397
.2391
.2011
.4187
.4013
.7058
.7008
.6074
.6073
52
.0044
.8980
.1092
.0422
.2416
.2040
.4223
. 4052
.7124
.7076
.6588
.6587
53
.0060
.9003
.1111
.0447
.2442
.2070
.4260
.4091
.7191
.7144
.7171
.7171
54
.0076
.9026
.1131
.0473
.2467
.2099
.4297
.4130
0. 41 70
.7259
0. 7328'
.7214
.7844
.7843
55
0.0092
9. 9050
0. 1150
0. 0498
0. 2493
0.2129
0. 4334
0. 7284
1. 8638
1. 8638
56
.0108
.9073
.1170
.0523
.2518
.2159
. 4371
.4210
.7398
. 7355
.9610
.9610
57
.0124
.9096
.1190
.0548
.2544
.2189
.4408
.4250
.7469
.7428
2. 0863
2. 0863
58
.0140
.9120
.1209
. 0574
. 2570
.2219
.4446
.4291
.7541
.7501
.2627
.2627
59
60
.0156
0. 0172
.9143
.1229
. 0599
.2596
.2249
. 4485
. 4331
.7615
.7576
2.5640
2.5640
9. 9167
0. 1249
0. 0625
0. 2623
0. 2279
0. 4523
0. 4372
0. 7689
0.7652
Inf.
Inf.
TABLE 38. [Page 575 1
Error in Longitude due to one minute Error of Latitude.
2
3 —
Latitude. •
03 d
00 -a
3
0°
5°
10°
15°
•20°
•25°
30°
35°
40°
45°
60°
66°
60°
66°
70°
75°
o
0
/
1
1
,
,
,
1
/
/
,
/
/
/
1
/
O
o
10
110
.4
.4
.4
.5
.5
.6
.7
.8
1.0
1.8
L8
2.9
110
10
?.o
.4
.4
.5
.6
.7
.8
1.0
1.2
1.6
2.6
20
80
.4
. 0
.6
.7
.9
1.1
1.5
2.3
30
40
.5
.6
.8
1.0
1.3
40
50
.7
.9
1.2
50
60
10
.9
.8
.9
1.2
1.8
3.0
105
60
10
105
.8
.8
.3
.3
.4
.4
.5
.6
9.0
.8
.8
.4
.4
.5
.6
.7
.9
1.2
L6
2.7
20
80
.8
.4
.5
.6
.7
.8
1.1
1.5
2.4
30
40
.4
.5
.6
. t
1.0
1.3
40
50
.4
.6
.8
1.2
50
60
.6
.9
60
15
100
.2
.2
.2
.3
.3
.4
.4
.5
.6
.8
1.1
1.6
2.9
100
15
20
.2
,2
.8
.3
.4
.5
.5
.7
.9
1.1
1.6
2.7
20
80
.2
.8
.8
.4
.5
.6
.8
1.1
1.5
2.4
30
40
.2
.3
.4
.6
.7
.9
1.3
2.1
40
50
.8
.4
.6
.8
1.2
50
60
.8
.6
.9
.5
.6
.8
1.1
1.7
3.0
95
60
15
15
95
.1
.1
.2
.2
.3
.3
.4
20
.1
.2
. 2
.8
.3
.4
.5
.6
.8
1.1
1.6
2.8
20
80
.2
.2
.3
.4
.5
.6
.8
LO
L5
2.5
80
40
.2
.3
.4
.5
.7
.9
1.3
2.1
40
50
.3
.4
.6
.8
1.1
50
60
.2
.3
.6
.9
60
20
90
.0
.0
.1
.1
.1
.2
.2
.3
.4
.6
.7
1.1
1.6
3.0
90
20
80
.0
.1
.1
.2
.2
.3
.4
.5
.7
1.0
L5
2.7
80
40
.0
.1
.2
.3
.8
.5
.6
.9
1.3
2.2
40
50
.0
.1
.2
.4
.5
.8
1.1
50
60
.0
.2
.3
.5
.9
60
70
.0
.2
.6
1.1
LO
L6
3.1
70
20
85
.1*
.1*
.0
.0
.0
.1
.1
.2
.3
.3
.5
.7
85
20
80
.1*
.0
.0
.1
.1
.2
.2
.4
.5
.7
LO
L5
2.7
30
40
.1*
.0
.0
.1
.2
.3
.4
.6
.9
1.3
2.3
40
50
.1*
.0
.1
.2
.8
.5
.7
1.1
50
60
.2*
.0
.1
.3
.5
.9
60
70
20
.3*
.0
.2
.6
1.1
.1
.1
.2
TT
.5
.9
1.5
3.1
70
80
.2*
.2*
.1*
.1*
.1*
.0
.0
.0
80
20
80
.2*
.2*
.1*
.0
.0
.1
.1
.2
.3
.4
.6
.9
1.5
2.8
30
40
.2*
.2*
.1*
.0
.1
.2
.3
.4
.6
.9
1.3
2.4
40
50
.8*
.2*
.1*
.1
.2
.3
.5
.7
1.1
50
60
.4*
.2*
.0
.1
.3
.5
.9
60
70
20
75
.6*
.3*
.0
.2
.6
1.2
.1*
.0
To"
.1
.2
.3
.6
1.2
70
.3*
.3*
.2*
.2*
.2*
.1*
.1*
.1*
75
20
80
.8*
.3*
.2*
.2*
.1*
.1*
.0
.1
.1
.2
.4
.6
.9
1.5
3.0
30
40
.4*
.3*
.2*
.1*
.1*
.0
.1
.2
.4
.5
.8
1.3
2.5
40
50
.4*
.3*
.2*
.1*
.0
.1
.3
.5
.7
1.1
50
60
.6*
.4*
.2*
.1*
.1
.3
.5
.9
60
70
20
1.2*
.6*
.3*
.0
.2
.6
1.2
.2*
.2*
.2*
.2*
.2*
.2*
.2*
.2*
70
70
20
70
.4*
.4*
.3*
.8*
.8*
.3*
.2*
.2*
80
.4*
.4*
.3*
.3*
.2*
.2*
.1*
.1*
.0
.0
.1
.2
.6
.8
L5
3.1
30
40
.5*
.4*
.3*
.8*
.2*
.1*
.0
.1
.2
.3
.5
.8
1.3
2.6
40
50
.6*
.5*
.3*
.2*
.2*
.0
.1
.3
.4
.7
1.1
50
60
.9*
.6*
.4*
.3*
.1*
.1
.2
.5
.9
60
70
1.2*
.6*
.3*
.1*
.2
.6
L2
70
•h
H *^
s
0°
6°
10°
15°
20°
26°
80°
86°
40°
46°
60°
66°
60°
65°
70°
76°
«g
Ph
Latitude.
Page 576]
TABLE 39.
Amplitudes.
Declination.
Lati-
tude.
Lati-
tude.
o°.o
0°.6
1°.0
1°.5
2^.0
2°. 5
8°.0
8°. 6
4°.0
4°. 5
5°.0
o°.5
6°.0
o
0
0
0
0
0
0
o
0
0
0
0
o
0
0
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
0
10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.1
4.6
5.1
5.6
6.1
10
15
0.0
0.5
1.5
2.1
2.6
3.1
3.6
4.2
4.7
5.2
5.7
6.2
15
20
0.0
0.5
1.1
1.6
2.1
2.7
3.2
3.7
4.3
4.8
5.3
5.8
6.4
20
25
0.0
0.5
1.1
1.6
2.2
2.8
3.3
3.8
4.4
5.0
5.5
6.0
6.6
25
30
0.0
0.6
1.2
1.7
2.3
2.9
3.4
4.0
4.6
5.2
5.8
6.3
6.9
30
32
0.0
0.6
1.2
1.8
2.4
2.9
3.5
4.1
4.7
5.3
5.9
6.5
7.0
32
34
0.0
0.6
1.2
1.8
2.4
3.0
3.6
4.2
4.8
5.4
6.0
6.6
7.2
34
36
0.0
0.6
1.2
1.8
2.5
3.1
3.7
4.3
4.9
5.6
6.1
6.8
7.4
36
38
0.0
0.6
1.3
1.9
2.5
3.2
3.8
4.4
5.1
5.7
6.3
7.0
7.6
38
40
0.0
0.7
1.3
2.0
2.6
3.3
3.9
4.6
5.2
5.9
6.5
7.2
7.8
40
42
0.0
0.7
1.3
2.0
2.7
3.4
4.0
4.7
5.4
6.1
6.7
7.4
8.0
42
44
0.0
0.7
1.4
2.1
2.8
3.5
4.2
4.9
5.6
6.3
6.9
7.6
8.3
44
46
0.0
0.7
1.4
2.2
2.9
3.6
4.3
5.0
5.8
6.5
7.2
7.9
■8.6
46
48
0.0
0.7
1.5
2.2
3.0
3.7
4.5
5.2
6.0
6.7
7.5
8.2
9.0
9.3
48
50
0.0
0.8
1.5
2.3
3.1
3.9
4.7
5.4
6.2
7.0
7.8
8.6
50
51
0.0
0.8
1.6
2.4
3.2
4.0
4.8
5.6
6.4
7.2
8.0
8.8
9.5
51
52
0.0
0.8
1.6
2.4
3.3
4.1
4.9
5.7
6.5
7.3
8.1
9.0
9.7
52
53
0.0
0.8
1.6
2.5
3.3
4.2
5.0
5.8
6.7
7.5
8.3
9.2
10.0
53
54
0.0
0.9
1.7
2.5
3.4
4.3
5.1
6.0
6.8
7.7
8.5
8.7
9.4
9.6
0.2
54
55
0.0
0.9
1.7
2.6
3.5
4.4
5.2
6.1
7.0
7.9
10.5
55
56
0.0
0.9
1.8
2.7
3.6
4.5
5.4
6.3
7.2
8.1
9.0
9.9
0.8
56
57
0.0
0.9
1.8
2.7
3.7
4.6
5.5
6.4
7.4
8.3
9.2
10.1
1.1
57
58
0.0
0.9
1.9
2.8
3.8
4.7
5.7
6.6
7.6
-8.5
9.5
0.4
1.4
58
59
0.0
1.0
1.9
2.9
3.9
4.9
5.8
6.8
7.8
8.8
9.7
0.7
1.7
59
60
60
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.1
61
0.0
1.0
2.1
3.1
4.1
5.2
6.2
7.2
8.3
9.3
0.3
1.4
2.5
61
62
0.0
1.1
2.1
3.2
4.3
5.3
6.4
7.5
8.5
9.6
0.7
1.8
2.9
62
63
0.0
1.1
2.2
3.3
4.5
5.5
6.6
7. 7
8.8
9.9
1.1
2.2
3.4
63
64
0.0
1.1
2.3
3.4
4.6
5.7
6.9
S.O
9.2
10.3
1.5
2.6
3.9
64
65.0
0.0
1.2
2.4
3.5
4.8
5.9
7.1
8.3
9.5
10.7
11.9
13.1
14.4
65.0
5.5
0.0
1.2
2.4
3.6
4.8
6.0
7.2
8.5
9.7
0.9
2.1
3.4
4.6
5.5
6.0
0.0
1.2
2.5
3.7
4.9
6.1
7.4
8.6
9.9
1.1
2.4
3.6
4.9
6.0
6.5
0.0
1.2
2.5
3.8
5.0
6.3
7.5
8.8
10.1
1.3
2.6
3.9
5.2
6.5
7.0
0.0
1.3
2.6
3.8
5.1
6.4
7.7
9.0
0.3
1.6
2.9
4.2
5.5
7.0
67.5
0.0
1.3
2.6
3.9
5.2
6.5
7.9
9.2
10.5
11.8
13.2
14.5
15.9
67.5
8.0
0.0
1.3
2.7
4.0
5.3
6.7
8.0
9.4
0.7
2.1
3.5
4.8
6.2
8.0
8.5
0.0
1.4
2.7
4.1
5.4
6.8
8.2
9.6
1.0
2.4
3.8
5.2
6.6
8.5
9.0
0.0
1.4
2.8
4.2
5.5
7.0
8.4
9.8
1.2
2.6
4.1
5.5
7.0
9.0
9.5
0.0
1.4
2.9
4.3
5.7
7.2
8.6
10.0
1.5
2.9
4.4
5.9
7.4
9.5
70.0
0.0
1.5
2.9
4.4
5.8
7.3
8.8
10.3
11.8
13.3
14.8
16.3
17.8
70.0
0.5
0.0
1.5
3.0
4.5
6.0
7.5
9.0
0.5
2.1
3.6
5.1
6.7
8.2
0.5
1.0
0.0
1.5
3.1
4.6
6.2
7.7
9.3
0.8
2.4
3.9
5.5
7.1
8.7
1.0
1.5
0.0
1.6
3.2
4.7
6.3
7.9
9.5
1.1
2.7
4.3
5.9
7.8
9.2
1.5
2.0
0.0
1.6
3.2
4.9
5.0
6.5
6.7
8.1
9.8
1.4
3.0
4.7
6.4
8.1
9.8
2.0
72.5
0.0
1.7
3.3
8.3
10.0
11.7
13.4
15.1
16.9
18.6
20.3
72.5
3.0
0.0
1.7
3.4
5.1
6.9
8.6
0.3
2.0
3.8
5.5
7.4
9.1
0.9
3.0
3.5
0.0
1.8
3.5
5.2
7.1
8.8
0.6
2.4
4.2
6.0
7.9
9.7
1.6
3.5
4.0
0.0
1.8
3.6
5.4
7.3
9.1
0.9
2.8
4.6
6.5
8.4
20.3
2.3
4.0
4.5
0.0
1.9
3.7
5.6
7.5
9.4
1.3
3.2
5.1
7.1
9.0
1.0
3.0
4.5
75.0
0.0
1.9
3.8
5.8
7.7
9.7
11.7
13.6
15.6
17.7
19.7
21.7
23.8
75.0
5.5
0.0
2.0
3.9
6.0
8.0
10.0
2.1
4.1
6.2
8.3
20.4
2.5
4.7
5.5
6.0
0.0
2.1
4.0
6.2
8.3
0.4
2.5
4.6
6.8
8.9
1.1
3.3
5.6
6.0
6.5
0.0
2.1
4.2
6.4
8.6
0.8
3.0
5.2
7.4
9.6
1.9
4.2
6.6
6.5
7.0
0.0
2.2
4.4
6.6
8.9
1.2
3.5
5.8
8.1
20.4
2.8
5.2
7.7
7.0
TABLE
39.
[Page
577
Amplitud
es.
Declination.
Lati-
tude.
Lati-
tude.
6°.0
6°. 6
;°.o
7°. 5
8°,0 j
8°.o j 9°.0 ,
9°, 5
10°.0
10°. 5
11°.0
11°. 5 12°.0
o
o
o
o
o
. ° ° \
0
o
o
o
0
o
o
0
6.0
6.5
7.0
7.5
8.0
8.5 9.0 1
9.5
10.0
10.5
11.0
11.5
12.0
0
10
6.1
6.6
7.1
7.6
8.1
8.6 ; 9.1 1
9.7
0.1
0.7
1.2
1.7
2.2
10
15
6.2
6.7
7.2
7.8
8.3
8.8 1 9.3
9.8
0.4
0.9
1.4
1.9
2.5
15
20
6.4
6.9
7.4
8.0
8.5
9.1 1 9.6 :
10.1
0.7
1.2
1.7
2. 3 2. 8 1
20
25
30
6.6
7.1
7.7
8.3
8.8
9.4 1 9.9
0.5
1.1
1.6
2.2
2.8
3.3
25
30
6.9
7.5
8.1
8.7
9.3
9.8 10.4
11.0
11.5
12.1
12.7
13.3
13.9
82
7.0
7.7
8.3
8.8
9.5
10.0 0.6
1.2
1.8
2.4
3.0
3.6
4.2
32
34
7.2
7.8
8.5
9.0
9.7
0. 3 0. 8
1.5
2.1
2.7
3.3
3.9
4.5
34
36
7.4
8.0
8.7
9.3
9.9
0.5 1 1.1
1.8
2.4
3.0
3.6
'4.3
4.9
36
38
7.6
8.2
8.9
9.5
10.2
0.8 ! 1.4
2.1
2.7
3.4
4.0
4.7
5.3
38
40
7.8
8.5
9.1
9.8
10.5
11.1 11.7
12.4
13.1
13.8
14.4
15.1
15.7
40
42
8.0
8.8
9.4
10.1
0.8
1.5 2.1
2.8
3.5
4.2
4.8
5.6
6.2
42
44
8.3
9.1
9.7
0.5
1.1
1.9 2.5
3.3
4.0
4.7
5.3
6.1
6.8
44
46
8.6
9.4
10.1
0.8
1.5
2. 3 3. 0
3.8
4.5
5.2
5.9
6.7
7.4
46
48
50
9.0
9.7
0.5
1.2
2.0
2. 8 3. 5
4.3
5.0
5.8
6.6
7.3
8.1
48
9.3
10.1
10.9
11.7
12.5
13.3 14.1
14.9
15.7
16.5
17.3
18.1 18.9
50
51
9.5
0.4
1.2
2.0
2.8
3. 6 4. 4
5.2
6.0
6.8
7. 7
8.5 , 9.3
51
52
9.7
0.6
1.4
2.2
3.1
3. 9 4. 7
5.6
6.4
7.2
8.1
8. 9 i 9. 7
52
53
10.0
0.8
1.7
2.5
3.4
4.2 5.1
5.9
6.8
7.6
8.5
9. 4 20. 2
53
54
0.2
1.1
2.0
2.8
3.7
4.6 5.4
6.3
7.2
8.1
8.9
9. 8 0. 7
54
55
10.5
11.4
12.3
13.1
14.0
14.9 15.8
16.7
17.6
18.5
19.4
20.3 21.2
55
56
0.8
1.7
2.6
3.5
4.4
6.3 i 6.2
7.2
8.1
9.0
9.9
0.9 1.8
56
57
1.1
2.0
2.9
3.9
4.8
5. 8 6. 7
7.7
8.6
9.6
20.5
1.5 2.4
57
58
1.4
2.3
3.3
4.3
5.2
6. 2 7. 2
8.2
9.1
20.1
1.1
2.1 i 3.1
58
59
60
1.7
2.7
3.7
4.7
5.7
6. 7 7. 7
8.7
9.7
0.7
1.7
2.8
3.8
24.6
59
60
12.1
13.1
14.1
15.1
16.2
17.2 i 18.2
19.3
20.3
21.4 22.4
23.5
61
2.5
3.5
4.6
5.6
6.7
7.8 i 8.8
9.9
1.0
2.1 1 3.1
4.3 5.4
61
62
2.9
3.9
5.1
6.1
7.3
8.4 9.4
20.6
1.7
2.9 1 3.9
5.2 6.3
62
63
3.4
4.4
5.6
6.7
7.9
9. 0 20. 1
1.3
2.5
3.7
4.8
6.1 i 7.2
63
64
3.9
14.4
5.0
6.2
7.3
8.5
9. 7 0. 9
2.1
3.3
4.6
5.7
7.1
28.2
8.3
64
65.0
15.5
16.8
18.0
19.3
20.5 21.7
23.0
24.2
25.6 1 26.8
29.5
65.0
5.5
4.6
5.8
7.1
8.3
9.6
0.9 2.2
3.5
4.7
6.1
7.4
8. 7 30. 1
5.5
6.0
4.9
6.2
7.4
8.7
20.0
1.3
2.6
3.9
5.3
6.6
8.0
9.3 0.7
6.0
6.5
5.2
6.5
7.8
9.1
0.4
1.8
3.1
4.4
5.8
7.2
8.6
30.0 1.4
6.5
7.0
67. 5
5.5
6.8
8.2
9.5
19.9
0.9
2.2
3.6
5.0
6.4
7.8
9.2
29.9
0.7 2.1
31.4 .32.9
7.0
15.9
17.2
18.6
21.3
22.7 24.1
25.5
27.0
28.4
67.5
8.0
6.2
7.6
9.0
20.4
1.8
3. 2 4. 7
6.1
7.6
9.1
30.6
2. 2 3. 7
8.0
8.5
6.6
8.0
9.4
0.9
2.3
3. 8 5. 3
6.8
8.3
9.8
1.4
3. 0 4. 6
8.5
9.0
7.0
8.4
9.9
1.4
2.8
4. 4 5. 9
7.4
9.0
30.6
2.2
3.8 5.5
9.0
9.5
7.4
8.9
20.4
1.9
3.4
5. 0 6. 5
25. 6 ; 27. 2
8.1
28.8
9.7
1.4
3.0
4.7 6.4
9.5
70.0
70.0
17.8
19.3
20.9
22.4
24.0
.30.5
32.2
33.9
35.7 1 37.4
0.5
8.2
9.8
1.4
3.0
4.6
6. 3 7. 9
9.6
1.3
3.1
4.9
6. 7 8. 5
0.5
1.0
8.7
20.3
2.0
3.6
^ 5.3
7. 0 8. 7
30.5
2.2
4.0
5.9
7. 8 9. 7
1.0
1.5
9.2
0.9
2.6
4.3
6.0
7. 8 9. 5
1.4
3.2
5.0
7.0
8. 9 40. 9
1.5
2.0
9.8
1.5
3.2
5.0
6.8
8.6 1 30.4
2.3
4.2
6.1
8.1
40. 2 2. 3
2.0
72.5
20.3
22.1
23.9
25.7
27.6
29.5 31.4
33.3
35.3
37.3
39.4
41. 5 43. 7
72.5
3.0
0.9
2.8
4.6
6.5
8.4
30.4 1 2.4
4.4
6.5
8.6
40.8
3. 0 5. 3
3.0
3.5
1.6
3.5
5.4
7.4
9.3
1.4 1 3.4
5.5
7.7
9.9
2.2
4.6
7.0
3.5
4.0
2.3
4.3
6.2
8.3
30.3
2. 5 1 4. 6
6.8
9.1
41.4
3.8
6.3
8.9
4.0
4.5
3.0
5.1
7.1
9.3
1.4
3.6 1 5.8
8.2
40.5
3.0
5.6
8.2
51.1
4.5
75.0
23.8
26.0
28.1
30.3
32.5
34.8
37.2
39.6
42.1
44.8
47.5
50.4
53.5
75.0
5.5
4.7
6.9
9.1
1.4
3.8
6.2
8.7
41.2
3.9
6.7
9.6
2.8
6.2
5.5
6.0
5.6
7.9
30.2
2.6
5.1
7.7
40.3
3.0
5.9
8.9
52.1
5.5
9.3
6.0
6.5
6.6
9.0
1.4
4.0
6.6
9.3
2.1
5.0
8.1
51.3
4.8
8.7
63.0
6.5
7.0
7.7
30.2
2.8
5.5
8.2
41.1
4.1
7.2
50.5
4.1 ' 8.0
62.4
7.6
7.0
'2US9—0S-
-37
Page 578]
TABLE 39.
Amplitudes.
Lati-
tude.
Declination.
Lati-
tude.
12°.0 1
12°. 6
18°.0
1S°.5
14°.0
14°. 5
15°.0
15°. 6
1«°.0
16°. 5
17°.0
17°, 5
18°.0
o
o
c
o
o
o
o o 1
o .
o
o
o
o
o
o
0
12.0
12.5
13.0
13.5
14.0
14.5
15.0
15.5
16.0
16.5
17.0
17.5
18.0
0
10
2.2
2.7
3.2
3.7
4.2
4.7
5.3
5.8
6.3
6.8
7.3
7.9
8.3
10
15
2.5
2.9<
► 3.5
4.0
4.5
5.0
5.6
6.1
6.6
7.1
7. 7
8.2
8.7
15
20
2.8
3.3
3.8
4.4
4.9
5.5
6.0
6.5
7.1
7.6
8.1
8.7
9.2
20
25
3.3
3.8
4.4
4.9
5.5
6.1
6.6
7.1
7.7
8.3
8.8
9.4
9.9
25
80
13.9
14.5
15.0
15.6
16.2
16.8
17.4
18.0
18.6
19.2
19.7
20.3
20.9
30
32
4.2
4.8
5.3
6.0
6.6
7.2
7.8
8.4
9.0
9.6
20.2
0.8
1.4
32
34
4.5
5.1
5.7
6.4
7.0
7.6
8.2
8.8
9.5
20.0
0.7
1.3
1.9
34
36
4.9
5.5
6.1
6.8
7.4
8.0
8.7
9.3
20.0
0.5
1.2
1.8
2.5
36
38
5.3
6.0
6.6
7.2
7.9
8.5
9.2
9.8
0.5
1.1
1.8
2.4
3.1
38
40
40
15.7
16.4
17.1
17.8
18.4
19.1
19.7
20.4
21.1
21.8
22.4
23.1
23.8
41
6.0
6.7
7.3
8.0
8.7
9.4
20.0
0.8
1.4
2.1
2.8
3.5
4.2
41
42
6.2
6.9
7.6
8.3
9.0
9.7
0.4
1.1
1.8
2.5
3.2
3.9
4.6
42
43
6.5
7.2
7.9
8.6
9.3
20.0
0.7
1.4
2.2
2.9
3.6
4.3
5.0
43
44
45
6.8
17.1
7.5
8.2
18.5
8.9
9.6
0.4
20.7
1.1
1.8
2.6
3.3
4.0
4.7
25. 2
5.4
44
17.8
19.3
20.0
21.5
22.2
23.0
23.7
24.4
25.9
45
46
7.4
8.2
8.9
9.6
0.4
1.1
1.9
2.6
3.4
4.1
4.9
5.7
6.4
46
47
7.7
8.5
9.3
20.0
0.8
1.5
2.3
3.1
3.8
4.6
5.4
6.2
6.9
47
48
8.1
8.9
9.7
0.4
1.2
2.0
2.8
3.6
4.3
5.1
5.9
6.7
7.5
48
49
8.5
9.3
20.1
0.8
1.6
2.4
3.2
4.1
4.9
5.7
6.5
7.3
8.1
28.7
49
50
18.9
19.7
20.5
21.3
22.1
22.9
23.7
24.6
25.4
26.2
27.0
27.9
50
51
9.3
20.1
0.9
1.8
2.6
3.5
4.3
5.1
6.0
6.8
7.6
8.5
9.4
51
52
9.7
0.6
1.4
2.3
3.1
4.0
4.9
5.7
6.6
7.5
8.3
9.2
30.1
52
53
20.2
1.1
1.9
2.8
3.7
4.6
5.5
6.4
7.3
8.2
9.0
30.0
0.9
53
54
0.7
1.6
2.5
3.4
4.3
5.2
6.1
7.1
8.0
8.9
9.8
0.8
1.7
54
55
21.2
22.2
23.1
24.0
24.9
25.9
26.8
27.8
28.7
29.7
30.6
31.6
32.6
55
56
1.8
2.8
3.7
4.7
5.6
6.6
7.6
8.6
9.5
30.5
1.5
2.5
3.6
56
57
2.4
3.4
4.4
5.4
6.4
7.4
8.4
9.4
30.4
1.4
2.5
3.5
4.6
57
58
3.1
4.1
5.1
6.1
7.2
8.2
9.2
30.3
1.3
2.4
3.5
4.6
5.7
58
59
3.8
4.8
5.9
6.9
8.0
9.1
30.2
1.3
2.3
3.5
4.6
5.7
6.9
59
60
24.6
25.6
26.7
27,8
28.9
30.1
31.2
32.3
33.4
34.6
35.8
36.9
38.2
60
61
5.4
6.5
7.6
8.8
9.9
1.1
2.2
3.5
4.6
5.8
7.1
8.3
9.6
61
62
6.3
7.5
8.6
9.8
31.0
2.2
3.4
4.7
5.9
7.2
8.5
9.8
41.2
62
63
7.2
8.5
9.7
31.0
2.2
3.5
4.7
6.1
7.4
8.7
40.1
41.5
2.9
63
64
8.3
9.6
30.9
2.2
3.5
4.8
6.2
7.6
9.0
40.4
1.8
3.3
4.8
64
65.0
29.5
30.8
32.2
33.5
34.9
36.3
37.8
39.2
40.7
42.2
43.8
45.4
47.0
65.0
5.5
30.1
1.5
2.9
4.3
5.7
7.1
8.6
40.1
1.6
3.2
4.8
6.5
8.2
5.5
6.0
0.7
2.2
3.6
5.0
6.5
8.0
9.5
1.1
2.7
4.3
5.9
7.7
9.4
6.0
6.5
1.4
2.9
4.3
5.8
7.3
8.9
40.5
2.1
3.8
5.4
7.1
8.9
50.8
6.5
7.0
2.1
3.6
5.1
6.7
8.2
9.8
1.5
3.2
4.9
6.6
8.4
50.3
2.3
7.0
67.5
32.9
34.4
36.0
37.6
39.2
,^.8
42.6
44.3
46.1
47.9
49.8
51.8
53.9
67.5
8.0
3.7
5.3
6.9
8.6
40.2
1.9
3.7
5.5
7.4
9.3
51.3
3.4
5.6
8.0
8.5
4.6
6.2
7.9
9.6
1.3
3.1
4.9
6.8
8.8
50.8
2.9
5.1
7.5
8.5
9.0
5.5
7.2
8.9
40.7
2.5
4.3
6.2
8.2
50.3
2.4
4.6
7.0
9.6
9.0
9.5
70.0
6.4 ! 8.2
40.0
1.8
43.0
3.7
5.6
7.6
9.7
1.9
4.2
6.5
9.1
61.9
9.5
37.4
39.3
41.1
45.0
47.0
49.2
51.4
53.7
56.1
58.7
61.5
64.6
70.0
0.5
8.5
40.4
2.4
4.4
6.4
8.6
50.8
3.2
5.7
8.3
61.1
4.3
7.8
0.5
1.0
9.7
1.7
3.7
5.8
8.0
50.3
2.6
5.2
7.9
60.7
3.9
7.5
71.7
1.0
1.5
40.9
3.0
5.1
7.4
9.7
2.1
4.6
7.4
60.3
3.5
7.1.
71.4
6.9
1.5
2.0
2.3
43. 7
4.4
6.7
9.1
! 51.5
4.1
6.9
9.9
3.1
6.8
71.1
6.7
90.0
2.0
72.5
46.0
48.4
50.9
53.6
56.4
59.4
62.7
66.4
70.9
76.5
90.0
72.5
3.0
5.3
7.7
50.3
3.0
5.9
8.9
62.2
6.1
70.6
6.3
90.0
3.0
3.5
7.0
9.6
2.3
5.3
8.4
61.8
5.6
70.3
6.1
90.0
3.5
4.0
8.9
51.7
4.7
7.9
61.4
5.3
9.8
75.9
90.0
4.0
4.5
51.1
4.1
7.3
60.9
; 4.9
9.5
75.5
90.0
4.5
TABLE
39.
[Page 579 |
Amplitudes.
Declination.
Lati-
tude.
Lati-
tude.
18°.0
18°. 5
19°.0
19°. 5
20°. 0
20°. 5
21°.0
21°. 6
22°.0
22°. 6
28°. 0
28°. 5
24°.0
o
Q
o
o
0
o
o
o
o
o
o
o
0
o
o
0
18.0
18.5
19.0
19.5
20.0
20.5
21.0
21.5
22.0
22.5
23.0
23.5
24.0
0
10
8.3
8.8
9.3
9.8
0.3
0.8
1.3
1.8
2.3
2.9
3.4
3.9
4.4
10
15
8.7
9.2
9.7
20.2
0.7
1.3
1.8
2.3
2.8
3.3
3.9
4.4
4.9
15
20
9.2
9.7
20.3
0.8
1.4
1.9
2.4
3.0
3.5
4.0
4.6
5.1
5.7
20
25
30
9.9
20.9
20.5
21.5
1.1
22.1
1.6
2.2
2.7 1 3.3
3.9
4.4
5.0
5.5
6.1
6.7
25
22.7
23.3
23.8
24.4
25.0
25.6
26.2
26.8
27.4
28.0
30
32
1.4
2.0
2.6
3.2
3.8
4.4
5.0v
5.6
6.2
6.8
7.4
8.0
8.7
32
34
1.9
2.5
3.1
3.8
4.4
5.0
5.6
6.2
6.9
7.5
8.1
8.7
9.4
34
36
2.5
3.1
3.7
4.4
5.0
5.7
6.3
6.9
7.6
8.2
8.9
9.5
30.2
36
38
3.1
3.8
4.4
5.1
5.7
6.4
7.0
7. 7
8.4
9.1
9.7
30.4
1.1
38
40
23.9
24.4
25.1
25.8
26.5
27.2
27.9
28.6
29.3
30.0
30.7
31.3
32.1
40
41
4.2
4.8
5.5
6.2
6.9
7.7
8.3
9.1
9.8
0.5
1.2
1.8
2.6
41
42
4.6
5.3
6.0
6.7
7.4
8.1
8.8
9.6
30.3
1.0
1.7
2.4
3.2
42
43
5.0
5.7
6.4
7.2
7.9
8.6
9.3
30.1
0.8
1.6
2.3
3.0
3.8
43
44
5.4
6.2
6.9
7.7
8.4
9.1
9.8
0.6
1.4
2.2
2.9
3.6
4.4
44
45
25.9
26.7
27.4
28.2
28.9
29.7
30.4
31.2
32.0
32.8
33.5
34.3
35.1
45
46
6.4
7.2
7.9
8.7
9.5
30.3
1.0
1.8
2.6
3.4
4.2
5.0
5.8
46
47
6.9
7.7
8.5
9.3
30.1
0.9
1.7
2.5
3.3
4.1
4.9
5.7
6.6
47
48
7.5
8.3
9.1
9.9
0.7
1.6
2.4
3.2
4.0
4.9
5.7
6.5
7.4
48
49
8.1
28.7
8.9
9.7
30.6
1.4
2.3
3.1
4.0
4.8
5.7
6.5
37.4
7.4
8.3
49
50
29.6
30.4
31.3
32.1
33.0
33.9
34.8
35.6
36.5
38.3
39.2
50 -
51
9.4
30.3
1.1
2.0
2.9
3.8
4.7
5.6
6.5
7.4
8.4
9.3
40.2
51
52
30.1
1.0
1.9
2.8
3.7
4.7
5.6
6.5
7.5
8.4
9.4
40.3
1.3
52
53
0.9
1.8
2.7
3.7
4.6
5.6
6.6
7.5
8.5
9.5
40.5
1.4
2.5
53
54
1.7
2.7
3.6
4.6
5.6
6.6
7.6
8.6
9.6
40.6
1.7
2.6
3.8
54
55
32.6
33.6
34.6
35.6
36.6
37.6
38.7
39.7
40.8
41.9
42.9
44.0
45.2
55
56
3.6
4.6
5.6
6.7
7.7
8.8
9.8
41.0
2.1
3.2
4.3
5.4
6.7
56
57
4.6
5.6
6.7
7.8
8.9
40.0
41.1
2.3
3.5
4.6
5.8
7.0
8.3
57
58
5.7
6.8
7.9
9.1
40.2
1.4
2.5
3.8
5.0
6.2
7.5
8.8
50.1
58
59
60.0
6.9
8.0
9.2
40.4.
1.6
2.8
4.1
5.4
6.7
8.0
9.3
50.7
2.2
59
38.2
39.4
40.6
41.9
43.2
44.5
45.8
47.2
48.6
49.9
51.4 i 52.9
54.4
60.0
0.5
8.9
40.1
1.4
2.7
4.0
5.4
6.7
8.1
9.6
51.0
2.5
4.1
5.7
0.5
1.0
9.6
0.9
2.2
3.5
4.9
6.3
7.7
9.1
50.6
2.1
3.7
5.3
7.0
1.0
1.5
40.4
1.7
3.0
4.4
5.8
7.3
8.7
50.2
1.7
3.3
5.0
6.7
8.5
1.5
2.0
62.5
1.2
2.5
3.9
5.3
6.8
8.3
9.8
1.3
2.9
4.6
6.3
8.1
60.0
2.0
42.0
43.4
44.9
46.3
47.8
49.4
51.0
52.6
54.2
56.0
57.8
59.7
61.7
62.5
3.0
2.9
4.3
5.9
7.4
8.9
50.5
2.2
3.9
5.6
7.5
9.4
61.4
3.6
3.0
3.5
3.8
5.3
6.9
8.5
50.1
1.7
3.5
5.3
7.1
9.1
61.1
3.4
5.7
3.5
4.0
4.8
6.4
8.0
9.7
1.3
3.0
4.9
6.7
8.7
60.7
3.0
5.5
8.1
4.0
4.5
65.0
5.9
7.5
9.2
50.9
2.6
4.5
6.4
8.4
60.5
62.5
2.8
5.2
7.8
70.9
74.4
4.5
47.0
48.7
50.4
52.2
54.0
56.0
58.0
60.2
64.9
67.6
70.6
65.0
5.5
8.2
50.0
1.8
3.6
5.6
7,6
9.8
2.2
4.7
7.3
70.4
4.1
8.9
5.5
6.0
9.4
1.3
3.2
5.1
7.3
9.4
61.8
4.4
7.1
70.2
3.8
8.6
90.0
6.0
6.5
50.8
2.7
4.7
6.8
9.1
61.4
4.0
6.8
70.0
3.7
8.4
90.0
6.5
7.0
2.3
4.3
6.4
8.7
61.1
3.7
6.5
9.8
3.5
8.3
90.0
7.0
67.5
53.9
56.0
58.3
60.7
63.4
66.2
69.5
73.3
78.2
90.0
67.5
8.0
5.6
7.9
60.3
3.0
5.9
9.2
73.0
8.1
90.0
8.0
8.5
7.5
60.0
2.6
5.6
8.9
72.8
7.9
90.0
8.5
9.0
9.6
2.3
5.3
8.7
72.7
7.7
90.0
9.0
9.5
61.9
5.0
8.4
72.4
7.6
90.0
9.5
70.0
64.6
69.1
72.2
77.4
90.0
70.0
0.5
7.8
71.9
7.2
90.0
0.5
1.0
71.7
7.1
90.0
1.0
1.5
6.9
90.0
1.5
2.0
90.0
2.0
Page 580]
TABLE
39.
Amplitudes.
Declination.
Lati-
tude.
Lati-
tude.
24°.0
24°. 5
25°.0
25°. 6
26°. 0
26°. 6
27°.0
27°.5
28°. 0
28°. 6
29°. 0
29°.5
80°. 0
o
o
o
o
o
o
o
o
o
o
o
o
o
o
o
0
24.0
24.5
25.0
25.5
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
30.0
0
4
4.1
4.6
5.1
5.6
6.1
6.6
7.1
7.6
8.1
8.6
9.1
9.6
0.1
4
8
4.3
4.8
t.3
5.8
6.3
6.8
7.3
7.8
8.3
8.8
9.3
9.8
0.3
8
12
4.6
5.1
5.6
6.1
6.6
7.1
7.6
8.1
8.7
9.2
9.7
30.2
0.7
12
16
5.0
5.6
6.1
6.6
7.1
7.6
8.2
8.7
9.2
9.8
30.3
0.8
1.3
32.1
16
20
25.7
26.2
26.7
27.3
27.8
28.3
28.9
29.4
30.0
30.5
31.1
31.6
20
22
6.0
6.6
7.1
7. 7 8. 2
8.8
9.3
9.9
0.4
1.0
1.5
2.1
2.6
22
24
6.4
7.0
7.6
8.1
8.7
9.2
9.8
30.4
0.9
1.5
2.0
2.6
3.2
24
26
6.9
7.5
8.1
8.6
9.2
9.7
30.3
0.9
1.5
2.1
2.6
3.2
3.8
26
28
7.4
8.0
8.6
9.2
9.8
30.3
0.9
1.5
2.1
2.7
3.3
3.9
4.5
28
30
28.0
28.6
29.2
29.8
30.4
31.0
31.6
32.2
32.8
33.4
34.0
34.7
35.3
30
31
8.3
8.9
9.5
30.1
0.8
1.4
2.0
2.6
3.2
3.8
4.5
5.1
5.7
31
32
8.7
9.3
9.9
0.5
1.1
1.7
2.4
3.0
3.6
4.2
4.9
5.5
6.1
32
33
9.0
9.6
30.2
0.9
1.5
2.1
2.8
3.4
4.0
4.7
5.3
6.0
6.6
33
34
35
9.4
29.8
30.0
0.6
31.3
1.9
32.3
2.6
33.0
3.2
3.8
4.5
5.1
5.8
6.4
7.1
34
30.4
31.1
31.7
33.6
34.3
35.0
35.6
36.3 ! 36.9
37.6
35
36
30.2
0.8
1.5
2.1
2.8
3.5
4.1
4.8
5.5
6.1
6.8
7.5
8.2
36
37
0.6
1.3
1.9
2.6
3.3
4.0
4.6
5.3
6.0
6.7
7.4
8.1
8.8
37
38
1.1
1.7
2.4
3.1
3.8
4.5
5.2
5.9
6.6
7.3
8.0
8.7
9.4
38
39
1.6
2.2
2.9
3.6
4.3
5.0
5.7
6.5
7.2
7.9
8.6
9.3
40.0
39
40
40
32.1
32.8
33.5
34.2
34.9
35.6
36.3
37.1
37.8
38.5
39.3
40.0
40.7
41
2.6
3.3
4.1
4.8
5.5
6.2
7.0
7.7
8.5
9.2
40.0
0.7
1.5
41
42
3.2
3.9
4.7
5.4
6.1
6.9
7.7
8.4
9.2
9.9
0.7
1.5
2.3
42
43
3.8
4.5
5.3
6.1
6.8
7.6
8.4
9.2
9.9
40.7
1.5
2.3
3.1
43
44
4.4
5.2
6.0
6.8
7.5
8.3
9.1
40.0
40.7
1.6
2.4
3.2
4.0
44
45
35.1
35.9
36.7
37.5
38.3
39.1
39.9
40.8
41.6
42.5
43.3
44.1
45.0
45
46
5.8
6.6
7.5
8.3
9.1
40.0
40.8
1.7
2.5
3.4
4.3
5.1
6.0
46
47
6.6
7.4
8.3
9.1
40.0
0.9
1.7
2.6
3.5
4.4
5.3
6.2
7.1
47
48
7.4
8.3
9.2
40.0
0.9
1.8
2.7
3.6
4.6
5.5
6.4
7.4
8.3
48
49
50
8.3
39.2
9.2
40.1
1.0
1.9
2.8
3.8
4.7
5.7
6.7
7.6
8.6
9.6
49
40.2
41.1
42.0
43.0
43.9
44.9
45.9
46.9
47.9
48.9
50.0
51.1
50
51
40.2
1.2
2.2
3.2
4.1
5.1
6.2
7.2
8.2
9.3
50.4
1.5
2.6
51
52
1.3
2.3
3.3
4.4
5.4
6.4
7.5
8.6
9.7
50.8
2.0
3.1
4.3
52
53
2.5
3.5
4.6
5.7
6.7
7.8
9.0
50.1
51.3
2.5
3.7
4.9
6.2
53
54
3.8
4.9
6.0
7.1
8.2
9.4
50.6
1.8
3.0
4.3
5.6
6.9
8.3
54
55.0
45.2
46.3
47.5
48.6
49.8
51.1
52.3
53.6
54.9
56.3
57.7
59.1
60.7
55.0
5.5
5.9
7.1
8.3
.9.5
50.7
2.0
3.3
4.6
6.0
7.4
8.9
60.4
2.0
5.5
6.0
6.7
7.9
9.1
50.4
1.6
2.9
4.3
5.7
7.1
8.6
60.1
1.7
3.4
6.0
6.5
7.5
8.8
50.0
1.3
2.6
3.9
5.4
6.8
8.3
9.9
1.5
3.2
5.0
6.5
7.0
8.3
9.6
0.9
2.2
3.6
5.0
6.5
8.0
9.5
61.2
2.9
4.7
6.6
7.0
57.5
49.2
50.5
51.9
53.2
54.7
56.2
57.7
59.3
60.9
62.6
64.5
66.4
68.5
57.v5
8.0
50.1
1.5
2.9
4.3
5.8
7.4
8.9
60.6
2.4
4.2
6.2
8.3
70.7
8.0
8.5
1.1
2.5
4.0
5.5
7.0
8.6
60.3
2.1
3.9
6.0
8.1
70.4
3.1
8.5
9.0
2.2
3.6
5.1
6.7
8.3
60.0
1.8
3.7
5.7
7.9
70.3
3.0
6.2
9.0
9.5
3.3
4.8
6.4
8.0
9.7
1.5
3.4
5.5
7.7
70.1
2.8 I 5.9
80.1
9.5
60.0
54.4
56.0
57.7
59.4
61.2
63.2
65.2
67.4
69.9
72.6
75.8
80.0
90.0
60.0
0.5
5.7
7.4
9.1
61.0
2.9
5.0
7.2
9.6
72.4
5.8
9.9
90.0
0.5
1.0
7.0
8.8
60.7
2.6
4.7
7.0
9.5
72.3
5.5
9.8
90.0
1.0
1.5
8.5
60.3
2.3
4.4
6.7
9.2
72.0
5.4
9.7
90.0
1.5
2.0
60.0
61.7
2.0
4.2
6.5
9.0
71,9
5.2
9.6
90.0
2.0
62.5
63.9
66.2
68.8
71.7
75.1
9.5
90.0
62.5
3.0
3.6
6.0
8.6
71.5
4.9
9.4
90.0
3.0
3.5
5.7
8.3
71.3
4.8
9.3
90.0
3.5
4.0
8.1
71.1
4.6
9.2
90.0
4.0
4.5
70.9
4.4
9.0
90.0
4.5
TABLE
40.
[Page
581
Correction of the Amplitude as observed on
the Apparent Horizon.
Declination. .
Lati-
tude.
Lati-
tude.
0°
5°
10°
12°
14°
16°
18°
20°
22°
24°
26°
28°
30°
0
0
0
0
o
0
o
o
o
o
0
o
0
o
0
0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0
5
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
5
10
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
.1
10
15
.2
.2
.2
.2
.2
.2
.2
.2
.2
.2
.2
. 2
.2
15
20
24
.2
.2
2
.2
.2
.2
.3
.3
.3
.3
.3
.3
.3
0.4
20
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
24
28
.3
.4
.4
.4
.4
.4
.4
.4
.4
.4
.4
.4
.4
28
32
.4
.4
.4
.4
.4
.4
.4
.5
.5
.5
.5
.5
. 0
32
36
.5
.5
.5
.5
.5
.5
.5
.5
.6
.6
.6
.6
.6
36
38
40
.5
.5
.5
.5
.6
.6
.6
.6
.6
.6
.6
.7
.7
38
40
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.7
0.7
0.7
0.7
42
.6
.6
.6
.6
.6
.7
.7
.7
.7
.7
.8
.8
.8
42
44
.6
.6
.7
.7
.7
.7
.7
.7
.8
.8
.8
.9
.9
44
46
.7
.7
.7
.7
. 7
.8
.8
.8
.8
.9
.9
.9
1.0
46
48
50
.7
0.8
.8
.8
.8
.8
.8
.8
.9
.9
1.0
1.0
1.0
.1
48
50
0.8
0.8
0.8
0.9
0.9
0.9
0.9
1.0
1.1
1.1
1.1
1.3
52
.8
.9
.9
.9
.9
1.0
1.0
1.0
.1
.2
.2
.3
.5
52
54
.9
.9
1.0
1.0
1.0
.1
.1
.1
.2
.3
.4
. .5
.8
54
56
1.0
1.0
.1
.1
.1
.2
.2
.2
.3
.5
.6
.8
2.2
56
58
.1
.1
.2
.2
.2
.3
.3
.4
.5
.7
.9
2.3
3.2
58
60
1.2
1.2
1.3
1.3
1.3
1.4
1.5
1.6
1.7
2.0
2.4
3.4
60
62
.3
.3
.4
.4
.4
.6
.7
.8
2.1
.5
3.5
62
64
.4
.4
.5
.5
.6
.8
.9
2.2
.6
3.7
64
66
.5
.5
.7
.7
.9
2.0
2.3
.8
3.8
66
68
.6
.7
.9
2.0
2.2
.4
.9
4.0
68
70
1.8
1.9
2.1
2.3
2.6
3.1
4.3
70
72
2.0
2.1
.5
.8
3.3
4.6
72
74
.2
.5
3.0
3.5
4.8
74
76
.6
3.0
.8
5.2
76
78
3.1
.6
5.7
78
80
3.8
4.4
80
Page 582]
TABLE 41.
Natural Sines and Cosines.
Prop.
0°
1
3
2°
8°
4
o
Prop.
parts
29
parts
8
M.
N. sine.
N.cos.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
99863
N. sine
N.,cos.
0
0
00000
100000
01745
99985
03490
99939
05234
06976
99756
60
2
0
1
00029
100000
01774
99984
03519
99938
05263
99861
07005
99754
59
2
1
2
00058
100000
01803
99984
03548
99937
05292
99860
07034
99752
58
2
1
3
00087
1(^)000
01832
99983
03577
99936
05321
99858
07063
99750
57
2
2
4
00116
lOOOiX)
01862
99983 .
03606
99935
05350
99857
07092
99748
56
2
2
5
00145
100000
01891
99982
03635
99934
05379
99855
07121
99746
55
2
3
6
00175
100000
01920
99982
036tM
99933
05408
99854
071.50
99744
.54
2
3
7
00204
100000
01949
99981
03693
99932
05437
99852
07179
99742
53
2
4
8
00233
100000
01978
99980
03723
99931
05466
99851
07208
99740
52
2
4
9
00262
100000
02007
99980
03752
99930
05495
99849
07237
997.38
51
2
5
10
00291
100000
02036
99979
03781
99929
05524
99847
07266
99736
50
2
5
11
00320
99999
02065
99979
03810
99927
05553
99846
07295
99734
49
2
6
12
13
00349
00378
99999
99999
02094
02123
99978
99977
03839
99926
05582
05611
99844
99842
07324
07353
99731
99729
48
2
6
03868
99925
47
2
7
14
00407
99999
02152
99977
03897
99924
05640
99841
07.382
99727
46
2
7
15
00436
99999
02181
99976
03926
99923
05669
998.39
07411
99725
45
2
8
16
00465
99999
02211
99976
0.3955
99922
05698
99838
07440
99723
44
8
17
00495
99999
02240
99975
03984
99921
05727
99836
07469
99721
43
9
18
19
00524
00553
99999
02269
02298
99974
99974
04013
04042
99919
057.36
05785
99834
99833
07498
99719
42
41
1 ,
9
99998
99918
07527
99716
10
20
00582
99998
02327
99973
04071
99917
0.5814
99831
07556
99714
40
10
21
00611
99998
02356
99972
04100
99916
05844
99829
07585
99712
.39
11
22
00640
99998
02385
99972
04129
99915
0,5873
99827
07614
99710
38
11
23
00669
99998
02414
99971
04159
99913
05902
99826
07643
99708
37
12
24
00698
99998
99997
02443
99970
99969
04188
04217
99912
99911
05931
05960
99824
99822
07672
07701
99705
99703
36
35
12
25
00727
02472
13
26
00756
99997
02501
99969
04246
99910
05989
99821
07730
99701
34
13
27
00785
99997
02530
99968
04275 ' 99909
06018
99819
07759
99699
33
14
28
00814
99997
02560
99967
04304 I 99907
06047
99817
07788
99696
32
14
29
00844
99996
02589
99966
04333 1 99906
06076
99815
07817
99694
31
15
15
30
31
00873
99996
02618
99966 04362 j 99905
06105
06134
99813
99812
07846
99692
30
29
00902
99996
02647
99965
04391
99904
07875
99689
15
32
00931
99996
02676
99964
04420
99902
06163
99810
07904
99687
28
16
33
00960
99995
02705
99963
04449
99901
06192
99808
07933
99685
27
16
34
00989
99995
02734
99963
04478
99900
06221
99806
07962
99683
26
17
35
01018
99995
02763
99962
04507
99898
06250
99804
07991
99680
25
17
36
01047
99995
02792
99961
04536
04565
99897
99896
06279
99803
99801
08020
99678
24
18
37
01076
99994
02821
99960
06308
08049
99676
23
18
38
01105
99994
02850
99959 04594 j 99894
06337
99799
08078
99673
22
19
39
01134
99994
02879
99959
04623 1 99893
06366
99797
08107
99671
21
1
19
40
01164
99993
02908
99958
04653
99892
06395
99795
08136
99668
20
20
41
01193
99993
02938
99957
04682
99890
06424
99793
08165
99666
19
20
42
01222
99993
02967
99956
99955
04711
99889
06453
06482'
99792
99790
08194
08223
99664
18
21
43
01251
99992
02996
04740
99888
99661
17
21
44
01280
99992
03025
99954
04769
99886
06511
99788
08252
99659
16
1
22
45
01309
99991
03054
99953
04798
99885
06540
99786
08281
99657
15
22
46
01338
99991
03083
99952
04827
99883
06569
99784
08310
99654
14
0
23
47
01367
99991
03112
99952
04856
99882
06598
99782
08339
99652
13
0
23
48
01396
99990
03141
99951
04885
99881
06627
06656
99780
99778
08368
99649
99647
12
U
0
0
24
49
01425
99990
03170
99950
04914
99879
08397
24
50
01454
99989
03199
99949
04943
99878
06685
99776
08426
99644
10
0
25
51
01483
99989
03228
99948
04972
99876
06714
99774
08455
99642
9
0
25
52
01513
99989
03257
99947
05001
99875
06743
99772
08484
99639
8
0
26
53
01542
99988
03286
99946
050.30
99873
06773
99770
08513
99637
7
0
26
27
54
55
01571
01600
99988
99987
03316
99945
99944
050-59
05088
99872
99870
06802
99768
99766
08542
08571
99635
99632
6
5
0
0
03345
06831
27
56
01629
99987
03374
99943
05117
99869
06860
99764
08600
99630
4
0
28
57
01658
99986
03403
99942
05146
99867
06889
99762
08629
99627
3
0
28
58
01687
99986
03432
99941
05175
99866
06918
99760
08658
99625
2
0
29
59
01716
99985
03461
99940
05205
99864
06947
99758
08687
99622
1
0
29
60
01745
99985
03490
99939
05234
99863
N. sine.
06976
99756
N. sine.
08716
99619
0
0
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. COS.
N. COS.
N. sine.
M.
89°
88°
87°
86°
8
j°
TABLE 41.
[Page 583
Natural Sines and Cosines.
Prop.
parts
29
5
o
6°
7
o
8
o
9°
Prop,
parts
4
M.
N. sine.
N. COS.
N. sine.
N. COS.
N.sine.
N.cos.
N. sine.
N. COS.
N. .sine. N. cos.
0
0
08716
99619
10453
99452
12187
99255
13917
99027
15643 98769
60
4
0
1
08745
99617
10482
99449
12216
99251
13946
99023
15672 1 98764
59
4
1
2
08774
99614
10511
99446
12245
99248
13975
99019
15701 98760
58
4
1
3
08803
99612
10540
99443
12274
99244
14004
99015
15730 ; 98755
57
4
2
4
08831
99609
10569
99440
12302
99240
14033
99011
15758
98751
56
4
2
5
08860
99607
10597
99437
12331
99237
14061
99006
15787
98746
55
4
3
6
7
08889
08918
99604
99602
10626
99434
12360
12389
99233
99230
14090
99002
15816
15845
98741
54
53
4
4
3
10655
99431
14119
98998
98737
4 8
08947
99599
10684
99428
12418
99226
14148
98994
15873
98732
52
3
4
9
08976
99596
10713
99424
12447
99222
14177
98990
15902
98728
51
3
5
10
09005
99594
10742
99421
12476
99219
14205
98986
15931
98723
50
3
5
11
09034
99591
10771
99418
12504
99215
14234
98982
15959
98718
49
3
6
12
09063
99588
10800
10829
99415
99412
12533
99211
14263
14292
98978
15988
98714
98709
48
47
3
3
6
13
09092
99586
12562
99208
98973
16017
7 14
09121
99583
10858
99409
12591
99204
14320
98969
16046
98704
46
3
7 1 15
09150
99580
10887
99406
12620
99200
14349
98965
16074
98700
45
3
8 1 16
09179
99578
10916
99402
12649
99197
14378
98961
16103 98695
44
3
8 1 17
09208
99575
10945
99399
12678
99193
14407
98957
16132
98690
43
3
9 18
9 19
09237
99572
99570
10973
11002
99396
99393
12706
99189
14436
14464
98953
16160
16189
98686
42
41
3
3
09266
12735
99186
98948
98681
10 i 20
09295
99567
11031
99390
12764
99182
14493
98944
16218
98676
40
3
10 ' 21
09324
99564
11060
99386
12793
99178
14522
98940
16246
98671
39
3
11 22
09353
99562
11089
99383
12822
99175
14551
98936
16275
98667
38
3
11 ! 23
09382
99559
11118
99380
12851
99171
14580
98931
16304
98662
37
2
12
24
09411
99556
11147
99377
12880
99167
14608
98927
16333
98657
36
35
2
2
12
25
09440
99553
11176
99374
12908
99163
14637
98923
16361
98652
13 26
09469
99551
11205
99370
12937
99160
14666
98919
16390
98648
34
2
13 27
09498
99548
11234
99367
12966
99156
14695
98914
16419 1 98ft43
33
9
14 28
09527
99545
11263
99364
12995
99152
14723
98910
16447 : 98638
32
2
14 29
09556
99542
11291
99360
13024
99148
14752
98906
16476 1 98633
31
2
15 30
15 31
09585
99540
11320
99357
13053
99144
14781
14810
98902
98897
16505
98629
30
29
2
09614
99537
11349
99354
13081
99141
16533
98624
2
15 32
09642
99534
11378
99351
13110
99137
14838
98893
16562
98619
28
2
16 33
09671
99531
11407
99347
13139
99133
14867
98889
16591
98614
27
2
16 i 34
09700
99528
11436
99344
13168
99129
14896
98884
16620
98609
26
2
17 35
09729
99526
11465
99341
13197
99125
14925
98880
16648
98604
25
2
17 36
18 ! 37
09758
09787
99523
11494
99337
99334
13226
99122
14954
14982
98876
98871
16677
16706
98600
24
2
99520
11523
13254
99118
98595
23
2
18 38
09816
99517
11552
99331
13283
99114
15011
98867
16734
98590
22
19 39
09845
99514
11580
99327
13312
99110
15040
98863
-16763 98585
21
19 • 40
09874
99511
11609
99324
13341
99106
15069
98858
16792 98580
20
20 41
09903
99508
11638
99320
13370
99102
15097
98854
16820 98575
19
20
42
43
09932
99506
11667
99317
13399
13427
99098
15126
98849
98845
16849 98570
18
17
21
09961
99503
11696
99314
99094
15155
16878 j 98565
21 44
09990
99500
11725
99310
13456
99091
15184
98841
16906 98561
16
22 45
10019
99497
11754
99307
13485
99087
15212
98836
16935 98556
15
22 46
10048
99494
11783
99303
13514
99083
15241
98832
16964 98551
14
23 i 47
10077
99491
11812
99300
13543
99079
15270
98827
16992 ! 98546
13
J
23 i 48
24 49
10106
99488
11840
99297
99293
13572
13600
99075
15299
98823
17021
17050
98541
12
10135
99485
11869
99071
15327
98818
98536
11
24 50
10164
99482
11898
99290
13629
99067
15356
98814
17078 ! 98531
10
25 j 51
10192
99479
11927
99286
13658
99063
15385
98809
17107
98526
9
25 52
10221
99476
11956
99283
13687
99059
15414
98805
17136
98521
8
26 53
10250
99473
11985
99279
13716
99055
15442
98800
17164
98516
7
0
26 54
27 55
10279
99470
12014
99276
13744
13773
99051
15471
98796
17193
98511
6
5
0
10308
99467
12043
99272
99047
15500
98791
17222 98506
0
27 i 56
10337
99464
12071
99269
13802
99043
15529
98787
17250 98501
4
0
28 ' 57
10366
99461
12100
99265
13831
99039
15557
98782
17279 98496
3
0
28 ; 58
10395
99458
12129
99262
13860
99035
15586
98778
17308 } 98491
2
0
29
59
10424
99455
12158
99258
13889
99031
15615
98773
17336 98486
1
0
29
60
10453
99452
12187
99255
13917
99027
15643
98769
17365 98481
0
0
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS. i N. sine.
M.
1
8
JO
88
o
8
2°
8
1°
80°
Page 584]
TABLE 41.
Natural Sines and Cosines.
Prop.
10° 1
11
o
12° 1
18° 1
14° 1
Prop.
parts
28
1
1
parte
6
M.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
0
0
17365
98481
19081
98163
20791
97815
22495
97437
24192
97030
60
6
0
1
17393
98476
19109
98157
20820
97809
22523
97430
24220 97023
59
6
1
2
17422
98471
19138
98152
20848
97803
22552
97424
24249 97015
58
6
1
3
17451
98466
19167
98146
20877
97797
22580
97417
24277 97008
57
6
2
4
17479
•98461
19195
98140
20905
97791
22608
97411
24305
97001
56
6
2
5
17508
98455
19224
98135
20933
97784
22637
97404
24333
96994
55
6
3
6
17537
98450
19252
98129
20962
97778
97772
22665
22693
97398
97391
24362
24390
96987
'96980'
54
5
3
7
17565
98445
19281
98124
20990
53
5
4
8
17594
98440
19309
98118
21019
97766
22722
97384
24418
96973
52
5
4
9
17623
98435
19338
98112
21047
97760
22750
97378
24446
96966
51
5
5
10
17651
98430
19366
98107
21076
97754
22778
97371
24474
96959
50
5
5
11
17680
98425
19395
98101
21104
97748
22807
97365
24503
96952
49
5
6
12
13
17708
98420
19423
98096
98090
21132
21161
97742
22835
97358
97351
24531
96945
48
47
5
6
17737
98414
19452
97735
22863
24559
96937
5
7
14
17766
98409
19481
98084
21189
97729
22892
97345
24587
96930
46
5
7
15
17794
98404
19509
98079
21218
97723
22920
97338
24615
96923
45
5
7
16
17823
98399
19538
98073
21246
97717
22948
97331
24644
96916
44
4
8
17
17852
98394
19566
98067
21275
97711
22977
97325
24672
96909
43
4
8 18 1
17880
98389
19595
98061
98056
21303
97705
23005
97318
24700
24728
96902
96894
42
41
4
9
19
17909
98383
19623
21331 97698
23033
97311
4
9
20
17937
98378
19652
98050
21360 97692
23062
97304
24756
96887
40
4
10
21
17966
98373
19680
98044
21388 1 97686
23090
97298
24784
96880
39
4
10
22
17995
98368
19709
98039
21417 ! 97680
23118
97291
24813
96873
38
4
11
23
18023
98362
19737
98033
21445 j 97673
23146
97284
24841
96866
37
4
11
12
24
25
18052
98357
19766
19794'
98027
98021
21474
97667
97661
23175
97278
24869
24897
96858
96851
36
35
4
18081
98352
21502
23203.
97271
4
12
26
18109
98347
19823
98016
21530 j 97655
23231
97264
24925
96844
34
3
13
27
18138
98341
19851
98010
21559 97648
23260
97257
24954
96837
33
3
13
28
18166
98336
19880
98004
21587 1 97642
23288
97251
24982
96829
32
3
14
29
18195
98331
19908
97998
21616 1 97636
23316
97244
25010
96822
31
3
14
14
30
31
18224
98325
19937
19965
97992
97987
21644
97630
97623
23345
23373
97237
97230
25038
25066
96815
96807
30
29
3
18252
98320
21672
3
15
32
18281
98315
19994
97981
21701 1 97617
23401
97223
25094
96800
28
3
15
33
18309
98310
20022
97975
21729 1 97611
2.3429
97217
25122
96793
27
3
16
34
18338
98304
20051
97969
21758 97604
23458
97210
25151
96786
26
3
16
35
18367
98299
20079
97963
21786 97598
23486
97203
25179 1 96778
25
3
17
17
36
37
18395
18424
98294
20108
97958
97952
21814 i 97592
21843 ; 97585
23514
23542
97196
97189
25207 96771
25235 1 96764
24
23
2
2
, 98288
20136
18
38
18452
1 98283
20165
97946
21871 97579
23571
97182
25263 ' 96756
22
2
18
39
18481
98277
20193
97940
21899 97573
23599
97176
25291 96749
21
2
19
40
18509
98272
20222
97934
21928 97566
2.3627
97169
25320 96742
20
2
19
41
18538
98267
20250
97928
21956 97560
23656
97162
25:348 96734
19
2
20
20
42
43
18567
18595
98261
20279
97922
97916
21985 \ 97553
23684
97155
97148'
25376 96727
25404 96719
18
17
2
98256
20307
1 22013
97547
23712
2
21
44
18624
[ 98250
20336
97910
22041
97541
23740
97141
25432 i 96712
16
2
21
45
18652
; 98245
20364
97905
22070
97534
23769
97134
25460 96705
15
2
21
46
18681
98240
20393
97899
22098
97528
23797
97127
25488 96697
14
22
47
18710
98234
20421
97893
22126
97521
23825
97120
25516 96690
13
22
23
48
49
18738
18767
98229
98223
20450
20478
97887
,'97881
22155
97515
97508
23853
23882
97113
97106
25545 96682
25573 : 96675
12
11
22183
23
50
18795
98218
20507
97875
22212
97502
23910
97100
25601 96667
10
24
51
18824
98212
20535
t 97869
22240
97496
23938
97093
25629 96660
9
24
52
18852
98207
20563
: 97863
22268
97489
23966
, 97086
25657 96653
8
25
53
18881
98201
20592
! 97857
22297
i 97483
23995
' 97079
25685 96645
/
25
26
54
55
18910
98196
20620
20649
i 97851
97845
22325
22353
97476
97470
24023
24051
1 97072
97065
25713 96638
6
5
18938
98190
25741
96630
26
56
18967
98185
20677
97839
22382
97463
24079
97058
25769
1 96623
4
0
27
57
18995
, 98179
20706
97833
22410
i 97457
24108
97051
25798 I 96615
3
1 0
27
58
19024
j 98174
20734
97827
22438
97450
24136
97044
25826 96608
2
0
28
59
19052
1 98168
20763
97821
22467
I 97444
24164
i 97037
25854
i 96600
1
0
28
60
19081
98163
20791
97815
22495
! 97437
24192
; 97030
25882
96593
0
0
N. CO.".
1 N. sine.
N. COS.
j N.sine.
N. COS.
j N. sine.
N. cos.
N. sine.
N. COS.
N. sine.
M.
7«°
7
s°
77°
7
fl°
75°
TABLE 41.
[Page 585
Natural Sines and Cosines.
Prop.
parts
27
1
5°
16
o
1'
o
18°
19°
Prop.
parts
9
M.
N. sine.
N. COS.
N. sine.
N. CCS.
N.siiie.
N.co.s.
N. sine.
N.cos.
N. sine.
N. COS.
0
0
25882
96593
27564
96126
29237
95630
30902
95106
32557
94552
60
9
0
1
25910
96585
27592
96118
29265
95622
30929
95097
32584
94542
59
9
1
2
25938
96578
27620
96110
29293
95613
30957
95088
32612
94533
58
9
1
3
25966
96570
27648
96102
29321
95605
30985
95079
32639 94523
57
9
2
4
25994
96562
27676
96094
29348
95596
31012
95070
32667 94514
56
8
2
5
26022
96555
27704
96086
29376
95588
31040
95061
32694 i 94504
55
8
3
6
26050
96547
96540
27731
96078
96070
29404
95579
95571
31068
31095
95052
95043"
32722
94495
94485
54
53
8
8
3
7
26079
27759
29432
32749
4
8
26107
96532
27787
96062
29460
95562
31123
95033
32777
94476
52
8
4
9
26135
96524
27815
96054
29487
95554
31151
95024
32804
94466
51
8
5
10
26163
96517
27843
96046
29515
95545
31178
95015
32832
94457
50
8
5
11
26191
96509
27871
96037
29543
95536
31206
95006
32859
94447
49
7
5
12
26219
96502
96494
27899
27927
96029
29571
95528
31233
31261
94997
32887
32914
94438
94428
48
47
7
7
6
13
26247
96021
29599
95519
94988
6
14
26275
96486
27955
96013
29626
95511
31289
94979
32942
94418
46
7
' 7
15
26303
96479
27983
96005
29654
95502
31316
94970
32969
94409
45
7
7
16
26331
96471
28011
95997
29682
95493
31344
94961
32997 94399
44
7
8
17
26359
96463
28039
95989
29710
95485
31372
94952
33024 i 94390
43
6
8
18
19
26387
96456
28067
95981
29737
95476
31399
31427
94943
94933
33051
33079"
94380
42
6
6
9
26415
96448
28095
95972
29765
95467
94370
41
9
20
26443
96440
28123
95964
29793
95459
31454
94924
33106 ( 94361
40
6
9
21
26471
96433
28150
95956
29821
95450
31482
94915
33134 ' 94351
39
6
10
22
26500
96425
28178
95948
29849
95441
31510
94906
33161 94342
38
6
10
23
26528
96417
28206
95940
29876
95433
31537
94897
33189 94332
37
6
11
24
26556
96410
28234
28262
95931
95923
29904
29932
95424
95415
31565
94888
94878
33216 94322
36
35
5
5
11
25
26584
96402
31593
33244 94313
12
26
26612
96394
28290
95915
29960
95407
31620
94869
33271 94303
34
5
12
27
26640
96386
28318
95907
29987
95398
31648
94860
33298 ; 94293
33
5
13
28
26668
96379
28346
95898
30015
95389
31675
94851
33326 , 94284
32
5
13
29
26696
96371
28374
95890
30043
95380
31703
94842
33353 94274
31
5
14
14
30
31
26724
96363
28402
95882
30071
95372
95363
31730
31758
94832
94823
33381 94264
33408 94254
30
29
5
26752
96355
28429
95874
30098
4
14
32
26780
96347
28457
95865
30126
95354
31786
94814
33436 ; 94245
28
4
15
33
26808
96340
28485
95857
30154
95345
31813
94805
33463 ; 94235
27
4
15
34
26836
96332
28513
95849
30182
95337
31841
94795
33490 i 94225
26
4
16
35
26864
96324
28541
95841
30209
95328
31868
94786
33518 , 94215
25
4
16
17
36
37
26892
96316
28569
28597
95832
95824
30237
30265
95319
95310
31896
31923
94777
33545 ; 94206
33573 1 94196
24
23"
4
26920
96308
94768
3
17
38
26948
96301
28625
95816
30292
95301
31951
94758
33600 , 94186
22
3
18
39
26976
96293
28652
95807
30320
95293
31979
94749
33627 94176
21
3
18
40
27004
96285
28680
95799
30348
95284
32006
94740
33655 94167
20
3
18
41
27032
96277
28708
95791
30376
95275
32034
94730
33682 94157
19
3
19
19
42
43
27060
96269
96261
28736
28764
95782
95774
30403
95266
95257
32061
94721
94712
33710
33737
94147
18
3
3
27088
30431
32089
94137
17
20
44
27116
96253
28792
95766
30459
95248
32116
94702
33764 ! 94127
16
2
20
45
27144
96246
28820
95757
30486
95240
32144
94693
33792
94118
15
2
21
46
27172
96238
28847
95749
30514
95231
32171
94684
33819
94108
14
2
21
47
27200
96230
28875
95740
30542
95222
32199
94674
33846
94098
13
2
22
48
27228
96222
28903
95732
95724
30570
95213
95204
32227
32254
94665
94656
33874
94088
12
2
22
49
27256
96214
28931
30597
33901
94078
11
2
23
50
27284
96206
28959
95715
30625
95195
32282
94646
33929
94068
10
23
51
27312
96198
28987
95707
30653
95186
32309
94637
33956
94058
9
23
52
27340
96190
29015
95698
30680
95177
32337
94627
33983
94049
8
24
53
27368
96182
29042
95690
30708
95168
32364
94618
34011
94039
7
24
25
54
55
27396
96174
96166
29070
29098
95681
95673
30736
95159
95150
32392
32419
94609
'94599
34038
94029
6
27424
30763
34065
94019
5
25
56
27452
96158
29126
95664
30791
95142
32447
94590
34093
94009
4
26
57
27480
96150
29154
95656
30819
95133
32474
94580
34120
93999
3
0
26
58
27508
96142
29182
95647
30846
95124
32502
94571
34147
93989
2
0
27
59
27536
96134
29209
95639
30874
95115
32529
94561
34175
93979
1
0
27
60
27564
96126
29237
95630
30902
95106
32557
94552
34202
93969
0
0
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
X. COS.
N. sine.
N. COS.
N. sine.
M.
7
t°
7S
t°
7
i°
71°
70°
Page 586] TABLE 41.
Natural Sines and Cosines.
Prop.
parts
87
M.
20'
21° 1
22°
28°
24°
Prop.
parts
11
N. sine. N. cos.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine. N. cos.
0
0
1
1
2
2
3
3
4
4
5
5
5
0
1
2
3
4
5
6
7
8
9
10
11
12
34202
34229
34257
34284
34311
34339
34366
34393
34421
34448
34475
34503
34530
93969
93959
93949
98939
93929
93919
93909
93899
93889
93879
93869
93859
93849
35837
35864
358^1
35918
35945
35973
36000
36027
36054
36081
36108
36135
36162
93358
93348
93337
93327
93316
93306
93295
37461
37488
37515
37542
37569
37595
37622
92718
92707
92697
92686
92675
926(>4
92653
92642
92631
92620
92609
92598
92587
39073
39100
39127
39153
39180
39207
39234
92050
92039
92028
92016
92005
91994
91982
40674
40700
40727
40753
40780
40806
40833
91355
9i:i43
91331
91319
91307
91295
91283
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
11
11
11
10
10
10
10
10
10
9
9
9
9
9
8
8
8
8
8
93285
93274
93264
93253
93243
93232
37649
37676
37703
37730
37757
37784
39260
39287
39314
39341
39367
39394
91971
91959
91948
91936
91925
91914
40860
40886
40913
40939
40966
40992
91272
91260
91248
91236
91224
91212
91200
91188
91176
91164
91152
91140
6
6
7
7
8
8
9
9
9
10
10
11
11
12
12
13
13
14
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55^
56
57
58
59
60
34557
34584
34612
34639
34666
34694
93839
93829
93819
93809
93799
93789
36190
36217
36244
36271
36298
36325
36352
36379
36406
36434
36461
36488
93222
93211
93201
93190
93180
93169
93159
93148
93137
93127
93116
93106
37811
37838
37865
37892
37919
37946
37973
37999
38026
38053
38080
38107
38134
38161
38188
38215
38241
38268
38295
38322
38349
38376
38403
38430
38456
38483
38510
38537
38564
38591
38617
38644
38671
38698
38725
38752
92576
92565
92554
92543
92532
92521
92510
92499
92488
92477
92466
92455
92444
92432
92421
92410
92399
92388
92377
92366
92355
92343
92332
92321
92310
92299
92287
92276
92265
92254
92243
92231
92220
92209
92198
92186
39421
39448
39474
39501
39528
39555
39581
39608
39635
39661
39688
39715
91902
91891
91879
91868
91856
91845
91833
91822
91810
91799
91787
91775
91764
91752
91741
91729
91718
91706
91694
91683
91671
91660
91648
91636
41019
41045
41072
41098
41125
41151
34721
34748
34775
34803
34830
34857
93779
93769
93759
93748
93738
93728
41178
41204
41231
41257
41284
41310
91128
91116
91104
91092
91080
91068
41 i 8
40 ! 7
39 ' 7
38 7
37 7
36 7
34884
34912
34939
34966
34993
35021
93718
93708
93698
93688
93677
93667
36515
36542
36569
36596
36623
36650
93095
93084
93074
93063
93052
93042
93031
93020
93010
92999
92988
92978
39741
39768
39795
39822
39848
39875
39902
39928
39955
39982
40008
40035
41337
41363
41390
41416
41443
41469
91056
91044
91032
91020
91008
90996
35
34
33
32
31
30
6
6
6
6
6
6
14
14
15
15
16
16
17
17
18
18
18
19
19
20
20
21
21
22
22
23
23
23
24
24
25
25
26
26
27
27
35048
35075
35102
35130
35157
35184
93657
93647
93637
93626
93616
93606
36677
36704
36731
36758
36785
36812
41496
41522
41549
41575
41602
41628
90984
90972
90960
90948
90936
90924
29
28
27
26
25
24
5
5
5
5
5
4
35211
35239
35266
35293
35320
35347
93596
93585
93575
93565
93555
93544
36839
36867
36894
36921
36948
36975
92967
92956
92945
92935
92924
92913
92902'
92892
92881
92870
92859
92849
92838
92827
92816
92805
92794
92784
40062
40088
40115
40141
40168
40195
40221
40248
40275
40301
40328
40355
40381
40408
40434
40461
40488
40514
40541'
40567
40594
40621
40647
40674
91625
91613
91601
91590
91578
91566
41655
41681
41707
41734
41760
41787
90911
90899
90887
90875
90863
90851
90839
90826
90814
90802
90790
90778
90766
90753
90741
90729
90717
90704
23
22
21
20
19
18
4
4
4
4
3
3
35375
35402
35429
35456
35484
35511
93534
93524
93514
93503
93493
93483
37002
37029
37056
37083
37110
37137
91555
91543
91531
91519
91508
91496
91484
91472
91461
91449
91437
91425
41813
41840
41866
41892
41919
41945
41972
41998
42024
42051
42077
42104
17
16
15
14
13
12
3
3
3
3
2
2
35538
35565
35592
35619
35647
35674
93472
93462
93452
93441
93431
93420
37164
37191
37218
37245
37272
37299
38778
38805
38832
38859
38886
38912
92175
92164
92152
92141
92130
92119
11
10
9
8
7
6
2
2
2
35701
35728
35755
35782
35810
35837
93410
93400
93389
93379
93368
93358
37326
37353
37380
37407
37434
37461
92773
92762
92751
92740
92729
92718
38939
38966
38993
39020
39046
39073
92107
92096
92085
92073
92062
92050
91414
91402
91390
91378
91366
91355
421.30
42156
42183
42209
42235
42262
90692
90680
90668
90655
90643
90631
5
4
3
2
1
0
0
0
0
—
N. coe.
N. sine.
N. cos.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
M.
09°
68°
67°
66°
65°
! 1
TABLE 41. [Page 587
Natural Sines and Cosines.
Prop. '
s
•5°
26°
27°
28°
29°
Prop.
parts
14
26 M.
N. sine.
N. COS.
N. sine.
N. COS.
X. sine. j. N. cos.
N. sine.
N. COS.
N. sine.
N. COS.
0 0
42262
90631
43837
89879
45399 89101
46947
88295
48481
87462
60
14
0 1
42288
90618
43863
89867
45425 1 89087
46973
88281
48506
87448
59
14
1 2
42315
90606
43889
89854
45451 i 89074
46999
88267
48532
87434
58
14
1 3
42341
90594
43916
89841
45477 ' 89061
47024
88254
48557
87420
57
13
2 1 4
42367
90582
43942
89828
45503 89048
47050
88240
48583
87406
56
13
2 i 5
42394
90569
43968
89816
45529 89035
47076
88226
48608
87391
55
13
3 j 6
3 ; 7
42420
90557
90545
43994
89803
45554 ! 89021
47101
88213
88199
48634
48659
87377
54
13
42446
44020
89790
45580 89008
47127
87363
53
12
3 i 8
42473
90532
44046
89777
45606 88995
47153
88185
48684
87349
52
12
4 9
42499
90520
44072
89764
45632 88981
47178
88172
48710
87335
51
12
4 10
42525
90507
44098
89752
45658 88968
47204
88158
48735
87321
50
12
5 1 n
42552
90495
44124
89739
45684 88955
47229
88144
48761
87306
49
11
5 12
42578
90483
44151
89726
45710 88942
47255
47281
88130
48786
87292
87278
48
11
6 1 13
42604
90470
44177
89713
45736 ( 88928
88117
48811
47
11
6 14
42631
90458
44203
89700
45762
88915
47306
88103
48837
87264
46
11
7 1 15
42657
90446
44229
89687
45787
88902
47332
88089
48862
87250
45
11
7 ' 16
42683
90433
44255
89674
45813
88888
47358
88075
48888
87235
44
10
7 ! 17
42709
90421
44281
89662
45839
88875
47383
88062
48913
87221
43
10
8 I 18
8 19
42736
90408
44307
89649
45865 1 88862
47409
88048
88034
48938
48964
87207
42
41
10
42762
90396
44333
89636
45891 i 88848
47434
87193
10
9 20
42788
90383
44359
89623
45917 ; 88835
47460
88020
48989
87178
40
9
9 j 21
42815
90371
44385
89610
45942 88822
47486
88006
49014
87164
39 9
10 22
42841
90358
44411
89597
45968 ' 88808
47511
87993
49040
87150
38 9
10 i 23
42867
90346
44437
89584
45994 88795
47537
87979
49065
87136
37 9
10
24
25
42894
90334
90321.
44464
89571
89558
46020 i 88782
46046 88768
47562
47588
87965
87951
49090
49116
87121
87107
36 8
35 ; 8
n
42920
44490
11
26
42946
90309
44516
89545
46072 88755
47614
87937
49141
87093
34 1 8
12
27
42972
90296
44542
89532
46097 88741
47639
87923
49166
87079
33 1 8
12 i 28
42999
90284
44568
89519
46123 88728
47665
87909
49192
87064
32 7
13 • 29
43025
90271
44594
89506
46149 88715
47690
87896
49217
87050
31 7
13 ! 30
43051
90259
44620
89493
46175 88701
47716
47741
87882
49242
87036
87021
30 7
29 7
13 1 31
43077
90246
44646
89480
46201 j 88688
87868
49268
14 ! 32
43104
90233
44672
89467
46226 ' 88674
47767
87854
49293
87007
28 ' 7
14 ! 33
43130
90221
44698
89454
46252 i 88661
47793
87840
49318
86993
27 1 6
15 ; 34
43156
90208
44724
89441
46278 ! 88647
47818
87826
49344
86978
26 6
15 35
43182
90196
44750
89428
46304 88634
47844
87812
49369
86964
25 6
16 36
43209
43235
90183
90171
44776
89415
89402
46330 88620
47869
87798
49394
49419
86949
24
23
6
16
37
44802
46355 i 88607
47895
87784=
86935
5
16
38
43261
90158
44828
89389
46381 88593
47920
87770'
49445
86921
22 5
17
39
43287
90146
44854
89376
46407 88580
47946
87756
49470
86906
21 5
17
40
43313
90133
44880
89363
46433 ; 88566
47971
87743
49495
86892
20 5
18
41
43340
90120
44906
89350
46458 1 88553
47997
87729
49521
86878
19 4
18
42
43366
43392
90108
44932
89337
89324
46484
46510
88539
48022
87715
87701
49546
49571
86863
18 . 4
17 4
19 43
90095
44958
88526
48048
86849
19 44
43418
90082
44984
89311
46536 88512
48073
87687
49596
86834
16 4
20 45
4:W45
90070
45010
89298
46561 88499
48099
87673
49622
86820
15 4
20 i 46
43471
90057
45036
89285
46587 ; 88485
48124
87659
49647
86805
14 3
20 ' 47
43497
90045
45062
89272
46613 88472
48150
87645
49672
86791
13 3
21 ' 48
21 49
43523
90032
45088
45114
89259
46639 i 88458
48175
87631
49697
49723
86777
12 3
43549
90019
89245
46664 88445
48201
87617
86762
11 3
22 50
43575
90007
45140
89232
46690
88431
48226
87603
49748
86748
10 2
22 51
43602
89994
45166
89219
46716
88417
48252
87589
49773
86733
-9 2
23 ; 52
43628
89981
45192
89206
46742
88404
48277
87575
49798
86719
8 2
23 53
43654
89968
45218
89193
46767
88390
48303
87561
49824
86704
7 2
23 1 54
24 i 55
43680
43706
89956
89943
45243
89180
46793
88377
88363
48328
48354
87546
87532
49849
49874
86690
86675
6 1
5 1
45269
89167
46819
24 56
43733
89930
45295
89153
46844 i 88349
48379
87518
49899
86661
4 1
25
57
43759
89918
45321
89140
46870 88336
48405
87504
49924
86646
3 j 1
25
58
43785
89905
45347
89127
46896
88322
48430
87490
49950
86632
2 0
26
59
43811
89892
45373
89114
46921
88308
48456
87476
49975
86617
1 ! 0
26
60
43837
89879
45399
89101
46947
88295
48481
87462
50000
86603
0
0
N. COS.
N. sine.
N. COS.
N. sine.
N. cos.
N. sine.
N. cos.
N. sine.
N. COS.
N. sine.
M.
64
1°
6
i°
62°
61°
60°
Page 588]
TABLE 41.
Natural Sines and Cosines.
Prop.
80° ■ 1
81° 1
82° 1
88° 1
3^
[°
!
Prop.
parts.
25
1
parts.
16
M.
N. sine.
N. COS.
N. sine.
N. COS.
N.*ine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
0
0
50000
86603
51504
85717
52992
84805
54464
83867
55919
82904
60
16
0
1
50025
86588
51529
85702
53017 ! 84789 |
54488
83851
55943
82887
59
16
1
2
50050
86573
51554
85687
53041
84774
54513
83835
55968
82871
58
15
1
3
50076
iS559
51579
85672
53066
84759
54537
83819
55992
82855
57
15
2
4
50101
86544
51604
85657
53091
84743
54561
83804
56016
82839
66
15
2
5
50126
86530
51628
85642
53115
84728
54586
83788
56040
82822
55
15
3
6
50151
86515
51653
85627
85612
53140
84712
54610
83772
83756
56064
82806
82790
54
53
14
14
3
7
50176
86501
51678
53164
84697
54635
56088
3
8
50201
86486
51703
85597
53189
84681
54659
83740
56112
82773
52
14
4
9
50227
86471
51728
85582
53214
84666
54683
83724
56136
82757
51
14
4
10
50252
86457
51753
85567
53238
84650
54708
83708
56160
82741
50
13
5
11
50277
86442
51778
85551
53263
84635
54732
83692
56184
82724
49
13
5
5
12
13
50302
50327
86427
51803
85536
85521
53288
53312
84619
84604
54756
'54781
83676
56208
82708
48
13
86413
51828
83660
56232
82692
47
13
6
14
50352
86398
51852
85506
53337
84588
54805
83645
56256
82675
46
12
6
15
50377
86384
51877
85491
53361 84573
54829
83629
56280
82659
45
12
7
16
50403
86369
51902
85476
53386 84557
54854
83613
56305
82643
44
12
7
17
50428
86354
51927
85461
53411 84542
54878
8.3597
56329
82626
43
11
8
8
18
19
50453
50478
86340
86325
51952
51977
85446
85431
53435
84526
84511
54902
83581
56353
82610
82593
42
11
53460
54927
83565
56377
41
11
8
20
50503
86310
52002
85416
53484 84495
54951
83549
56401
82577
40
11
9
21
50528
86295
52026
85401
53509
84480
54975
83533
56425
82561
39
10
9
22
50553
86281
52051
85385
53534
84464
54999
83517
56449
82544
38
10
10
23
50578
86266
52076
85370
53558
84448
55024
83501
56473
82528
37
10
10
24
50603
86251
52101
85355
53583
84433
84417
55048
83485
56497
56521
82511
36
35
10
9
10
25
50628
86237
52126
85340
53607
55072
■ 83469
82495
11
26
50654
86222
52151
85325
53632 84402
55097
83453
56545
82478
34
9
11
27
50679
86207
52175
85310
53656 84386
55121
83437
56569
82462
33
9
12
28
50704
86192
52200
85294
53681 84370
55145
83421
56593
82446
32
9
12
29
50729
86178
52225
85279
53705 ! 84355
55169 i 8.3405
56617
82429
31
8
13
30
50754
86163
52250
85264
53730
84339
55194 ! 83389
56641
82413
30
29
8
8
13
31
50779 .
86148
52275
85249
53754
84324
55218
83373
56665
82396
13
32
50804
86133
52299
85234
53779
84308
55242
83356
56689
82380
28
7
14
33
50829
86119
52324
85218
53804
84292
55266
83340
56713
82363
27
7
14
34
50854
86104
52349
85203
53828 "
• 84277
55291
83324
56736
82347
26
/
15
35
50879
86089
52374
85188
53853
84261
55315
83308
56760
82330
25
(
15
15
36
37
50904
' 50929
86074
86059
52399
85173
53877
84245
84230'
55339
83292
83276
56784
82314
24
23
6
6
52423
85157
53902
55363
56808
82297
16
38
50954
86045
52448
85142
53926
84214
55388
83260
56832
82281
22
6
16
39
50979
86030
52473
85127
53951
84198
55412
83244
56856
82264
21
6
17
40
51004
86015
52498
85112
53975
84182
55436
83228
56880
82248
20
o
17
41
51029
86000
52522
85096
54000
84167
55460
83212
56904
82231
19
0
18
42
43
51054
51079
85985
85970
52547
85081
54024
54049
84151
55484
83195
56928
82214
18
17
o
5~
18
52572
85066
84135
55509
83179
56952
82198
18
44
51104
85956
52597
85051
54073
84120
55533
83163
56976
82181
16
4
19
45
51129
85941
52621
85035
54097
84104
55557
83147
57000
82165
15
4
19
46
51154
85926
52646
85020
54122
84088
55581
83131
57024
82148
14
4
20
47
51179
85911
52671
85005
54146
84072
55605
83115
57047
82132
13
3
20
48
51204
85896
52696
84989
54171
84057
84041
55630
8.3098
57071
82115
12
11
3
3
20
49
51229
85881
52720
84974
54195
55654
83082
57095
82098
21
50
51254
85866
52745
84959
54220 i 84025
55678
83066
57119
82082
10
3
21
51
51279
85851
52770
84943
54244 , 84009
55702 j 83050
57143
82065
9
2
22
52
51304
85836
52794
84928
54260 ! 83994
55726 i 83034
57167
82048
8
2
22
53
51329
85821
52819
84913
54293
83978
55750 i 8.3017
57191
82032
7
2
23
23
54
55
51354
85806
52644
52869
84897
54317
54342
83962
83946
55775
55799'
83001
57215
57238
82015
6
5
2
1
51379
85792
84882
82985
81999
23
56
51404
85777
52893
84866
54366
83930
55823
82969
57262
81982
4
1
24
57
51429
85762
52918
84851
54391
83915
55847
82953
57286
81965
3
1
24
58
51454
85747
52943
84836
54415
83899
55871
829.36
57310
81949
2
1
25
59
51479
85732
52967
84820
54440
83883
55895
82920
57334
81932
1
0
25
60
51504
85717
52992
84805
54464
. 83867
55919
82904
57358
81915
0
0
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
M.
59°
5
*°
67°
56°
5
6°
TABLE 41.
[Page 589 [
Natural Sines and Cosines.
Prop.
85° 1
86° 1
S',
°
38°
89°
Prop.
parts
23
t
parts
18
M.
N. sine.
N. COS.
X. sine. ]
N. COS.
X. .sine.
N. COS.
X. sine.
N. COS.
N. sine.
N. cos.
0
0
57358
81915
58779
80902
60182
79864
61566
78801
62932
77715
60
18
0
1
57381
81899
58802
80885
60205
79846
61589
78783
62955
77696
59
18
1
9
57405
81882
58826
80867
60228
79829
61612
78765
62977
77678
58
17
1
3
57429
81865
58849
80850
60251
79811
61635
78747
63000
77660
57
17
2
4
57453
81848
58873
80833
60274
79793
61658
78729
63022
77641
56
17
2
o
57477
81832
58896
80816
60298
79776
61681
78711
63045
77623
55
17
2
3
6
7
57501
81815
58920
80799
60321
60344
79758
61704
78694
78676
63068
63090
77605
77586
54
16
57524
81798
58943
80782
79741
61726
53
16
3
8
57548
81782
58967
80765
60367
79723
61749
78658
63113
77568
52
16
3
9
57572
81765
58990
80748
60390
79706
61772
78640
63135
77550
51
15
4
10
57596
81748
59014
80730
60414
79688
61795
78622
63158
77531
50
15
4
11
57619
81731
59037
80713
60437
79671
61818
78604
63180
77513
49
15
5
12
57643
81714
59061
80696
80679
60460
60483
79653
61841
78586
63203
63225
77494
48
47
14
5
13
57667
81698
59084
79635
61864
78568
77476
14
5
14
57691
81681
59108
80662
60506
79618
61887
78550
63248
77458
46
14
6
15
57715
81664
59131
80644
60529
79600
61909
78532
63271
77439
45
14
6
16
57738
81647
59154
80627
60553
79583
61932
78514
63293
77421
44
13
7
17
57762
81631
59178
80610
60576
79565
61955
78496
63316
77402
43
13
7
7
18
19
57786
81614
59201
80593
80576
60599
79547
61978
62001
78478
63338
77384
42-
13
57810
81597
59225
60622
79530
78460
63361
77366
41
12
8
20
57833
81580
59248
80558
60645
79512
62024
78442
63383
77347
40
12
8
21
57857
81563
59272
80541
60668
79494
62046
78424
63406
77329
39
12
8
22
57881
81546
59295
80524
60691
79477
62069
78405
63428
77310
38
11
9
23
57904
81530
59318
80507
60714
79459
62092
78387
63451
77292
37
11
9
24
57928
81513
59342
59365
80489
80472
60738
79441
62115
62138
78369
78351
63473
77273
36
11
10
25
57952
81496
60761
79424
6:3496
77255
35
11
10
26
57976
81479
59389
80455
60784
79406
62160
78333
63518
77236
34
10
10
27
57999
81462
59412
80438
60807
79388
62183
78315
6;?540
77218
33
10
11
28
58023
81445
59436
80420
60830
79371
62206
78297
63563
77199
32
10
11
29
58047
81428
59459
80403
60853
79353
62229
78279
63585
77181
31
9
12
30
58070
81412
. 59482
59506
80386
80368
60876
60899
79335
79318
62251
62274
78261
63608
63630
77162
30
29
9
9
12
31
58094
81395
78243
77144
12
32
58118
81378
59529
80351
60922
79300
62297
78225
63653
77125
28
8
13
33
58141
81361
59552
80334
60945
79282
62320
78206
63675
77107
27
8
13
34
58165
81344
59576
80316
60968
79264
62342
78188
63698
77088
26
8
13
35
58189
81327
59599
80299
60991
79247
62365
78170
63720
77070
25
8
14
36
58212
81310
59622
80282
61015
61038
79229
62388
62411
78152
63742
77051
77033
24
23
7
7
14
37
58236
81293
59646
80264
79211
78134
63765
15
38
58260
81276
59669
80247
61061
79193
62433
78116
63787
77014
22
7
15
39
58283
81259
59693
80230
61084
79176
62456
78098
63810
76996
21
6
15
40
58307
81242
59716
80212
61107
79158
62479
78079
63832
76977
20
6
16
41
58330
81225
59739
80195
61130
79140
62502
78061
63854
76959
19
6
16
42
58354
81208
59763
80178
61153
79122
79105
62524
62547
78043
78025
63877
76940
76921
18
17
5
5
16
43
58378
81191
59786
80160
61176
63899
17
44
58401
81174
59809
80143
61199
79087
62570
78007
63922
76903
16
5
17
45
58425
81157
59832
80125
61222
79069
62592
77988
63944
76884
15
5
18
46
58449
81140
59856
80108
61245
79051
62615
77970
63966
76866
14
4
18
47
58472
81123
59879
80091
61268
79033
62638
77952
63989
76847
13
4
18
19
48
49
58496
81106
59902
80073
61291
79016
62660
77934
64011'
76828
76810
12
11
4
58519
81089
59926
80056
61314
78998
62683
77916
64033
3
19
50
58543
81072
59949
80038
61337
78980
62706
77897
64056
76791
10
3
20
51
58567
81055
59972
80021
61360
78962
62728
77879
64078
76772
9
3
20
52
58590
81038
59995
80003
61383
78944
62751
77861
64100
76754
8
2
20
53
58614
81021
60019
79986
61406
78926
62774
77843
64123
76735
7
2
21
21
54
55'
58637
58661
81004
60042
79968
61429
"61451
78908
62796
62819
77824
77806'
64145
76717
6
2
80987
60065
79951
78891
64167
76698
5
2
21
56
58684
80970
60089
79934
61474
78873
62842
77788
64190
76679
4
1
22
57
58708
80953
60112
79916
61497
78855
62864
77769
64212
76661
3
1
22
58
58731
80936
60135
79899
61520
78837
62887
77751
64234
76642
2
1
23
59
58755
80919
60158
79881
61543
78819
62909
77733
64256
76623
1
0
23
60
58779
80902
60182
79864
61566
78801
62932
77715
64279
76604
0
0
N. COS.
N. sine.
K. COS.
N. sine.
K. COS.
N. sine.
N. COS.
N. sine.
N. cos.
X. sine.
M.
5
1°
bS
°
5
>o
5
1°
Q<
0°
Page 590]
TABLE 41.
Natural Sines and Cosines.
Prop.
40° 1
41° 1
42° 1
48
o
44
o
Prop.
parts
22
1
parts
19
19
M.
N. sine.
N.cos.
N. sine.
65606
N. COS.
N.sine.
N. COS.
N.sine.
N. COS.
N. sine.
N. COS.
0
0
64279
76604
75471
66913
74314
68200
73135
69466
71934
60
0
1
64301
76586
65628
75452
66935
74295
68221
73116
69487
71914
59
19
1
2
64323
7fi567
65650
75433
66956
74276
68242
73096
69508
71894
58
18
1
3
64346
76548
65672
75414
66978
74256
68264
73076
69529
71873
57
18
1
4
64368
76530
65694
75395
66999
74237
68285
73056
69549
71853
56
18
2
5
64390
76511
65716
75375
67021
74217
68306
73036
69570
71833
55
17
2
3
6
64412
76492
76473
65738
75356
75337
67043
74198
74178
68327
73016
69591
71813
71792
54
53
17
7
64435
65759
67064
68349
72996
69612
17
3
8
64457
76455
65781
75318
67086
74159
68370
72976
69633
71772
52
16
3
9
64479
76436
65803
75299
67107
74139
68391
72957
69654
71752
51
16
4
10
64501
76417
65825
75280
67129
74120
68412
72937
69675
71732
50
16
4
11
64524
76398
65847
75261
67151
74100
68434
72917
69696
71711
49
16
4
5
12
13
64546
64568
76380
65869
75241
75222
67172
67194
74080
68455
72897
69717
69737
71691
71671
48
47
15
15
76361
65891
74061
68476
72877
5
14
64590
76342
65913
75203
67215
74041
68497
72857
69758
71650
46
15
6
15
64612
76323
65935
75184
67237
74022
68518
72837
69779
71630
45
14
6
16
64635
76304
65956
75165
67258
74002
68539
72817
69800
71610
44
14
6
17
64657
76286
65978
75146
67280
73983
68561
72797
69821
71590
43
14
7
7
18
19
64679
64701
76267
76248
66000
66022
75126
75107
67301
73963
68582
72777
72757
69842
69862
71569
71549
42
41
13
67323
73944
68603
13
7
20
64723
76229
66044
75088
67344
73924
68624
72737
69883
71529
40
13
8
21
64746
76210
66066
75069
67366
73904
68645
72717
69904
71508
39
12
8
22
64768
76192
66088
75050
67387
73885
68666
72697
69925
71488
38
12
8
23
64790
76173
66109
75030
67409
73865
68688
72677
69946
71468
37
12
9
24
64812
76154
66131
75011
67430
73846
68709
68730
72657
72637
69966
69987
71447
36
11
11
9
25
64834
76135
66153
74992
67452
73826
71427
35
10
26
64856
76116
66175
74973
67473
73806
68751
72617
70008
71407
34
11
10
27
64878
76097
66197
74953
67495
73787
68772
72597
70029
71386
33
10
10
28
64901
76078
66218
74934
67516
73767
68793
72577
70049
71366
32
10
11
29
64923
76059
66240
74915
67538
73747
68814
72557
70070
71.345
31
10
11
11
30
31
64945
64967
76041
76022
66262
74896
74876
67559
73728
73708
68835
72537
72517
70091
70112
71325
30
29
10
9
66284
67580
68857
71305
12
32
64989
76003
66306
74857
67602
73688
68878
72497
70132
71284
28
9
12
33
65011
75984
66327
74838
67623
73669
68899
72477
70153
71264
27
9
12
34
65033
75965
66349
74818
67645
73649
68920
72457
70174
71243
26
8
13
35
65055
75946
66371
74799
67666
73629
68941
72437
70195
71223
25
8
13
14
36
37
65077
75927
66393
74780
67688
67709
73610
68962
72417
72397
70215
71203
24
23
8
7
65100
75908
66414
74760
73590
68983
70236
71182
14
38
65122
75889
66436
74741
67730
73570
69004
72377
70257
71162
22
7
14
39
65144
75870
66458
74722
67752
73551
69025
72357
70277
71141
21
7
15
40
65166
75851
66480
74703
67773
73531
69046
72337
70298
71121
20
6
15
41
65188
75832
66501
74683
67795
73511
69067
72317
70319
71100
19
6
15
16
42
65210
75813
66523
66545
74664
67816
67837
73491
69088
72297
70339
71080
71059
18
17
6
43
65232
75794
74644
73472
69109
72277
70360
0
16
44
65254
75775
66566
74625
67859
73452
69130
72257
70381
71039
16
5
17
45
65276
75756
66588
74606
67880
73432
69151
72236
70401
71019
15
5
17
46
65298
75738
66610
74586
67901
73413
69172
72216
70422
70998
14
4
17
47
65320
75719
66632
74567
67923
73393
69193
72196
70443
70978
13
4
18
18
48
49
65342
65364
75700
66653
74548
67944
73373
69214
69235
72176
72156
70463
70484
70957
12
4
75680
66675
74528
67965
73353
70937
11
3
18
50
65386
75661
66697
74509
67987
73333
69256
72136
70505
70916
10
3
19
51
65408
75642
66718
74489
68008
73314
69277
72116
70525
70896
9
3
19
52
65430
75623
66740
74470
68029
73294
69298
72095
70546
70875
8
3
19
53
65452
75604
66762
74451
68051
73274
69319
72075
70567
70855
/
2
20
20
54
55
65474
75585
66783
66805
74431
68072
73254
73234
69340
72055
72035
70587
70608
70834
70813"
6
5
2
2
65496
75566
74412
68093
69361
21
56
65518
75547
66827
74392
68115
73215
69382
72015
70628
70793
4
I
21
57
65540
75528
66848
74373
68136
73195
69403
71995
70649
70772
3
1
21
58
65562
75509
66870
74353
68157
73175
69424
71974
70670
70752
2
1
22
59
65584
75490
66891
74334
68179
73155
69445
71954
70690
70731
1
0
22
60
65606
75471
66913
74314
68200
73135
69466
71934
70711
70711
0
0
—
N.cos.
i N.slne.
N. COS.
N.sine.
N. COS.
N. sine.
N. COS.
N. sine.
N.COS.
N. sine.
M.
49°
48°
47°
46°
46°
TABLE 42.
Page 591
Logarithms of Numbers.
No.
1 100.
Log. 0.00000 ^2.00000. 1
No.
Log.
No.
Log.
No.
Log.
No.
Log.
No.
Log.
1
0.00000
21
1. 32222
41
1.61278
61
1. 78533
81
1. 90849
2
0. 30103
22
1. 34242
42
1. 62325
62
1. 79239
82
1.91381
3
0.47712
23
1.36173
43
1. 63347
63
1. 79934
83
1. 91908
4
0. 60206
24
1. 38021
44
1. 64345
64
1.80618
84
1. 92428
5
6
0. 69897
25
"26
1.39794
45
46
1. 65321
65
1. 81291
85
1. 92942
0. 77815
1. 41497
1. 66276
66
1. 81954
86
1. 93450
7
0. 84510
27
1.43136
47
1. 67210
67
1. 82607
87
1. 93952
8
0. 90309
28
1.44716
48
1. 68124
68
1. 83251
88
1.94448
9
0. 95424
29
1. 46240
49
1. 69020
69
1. 83885
89
1.94939
10
1. 00000
30
1.47712
50
1. 69897
70
1. 84510
90
1. 95424
11
1. 04139
31
1. 49136
51
1. 70757
71
1. 85126
91
1. 95904
12
1.07918
32
1.50515
52-
1. 71600
72
1. 85733
92
1. 96379
13
1.11394
33
1. 51851
53
1. 72428
73
1. 86332
93
1. 96848
14
1. 14613
34
1. 53148
54
1. 73239
74
1. 86923
94
1. 97313
15
1. 17609
35
1. 54407
55
1. 74036
75
1. 87506
95
1.97772
16
1. 20412
36
1. 55630
56
1. 74819
76
1. 88081
96
1. 98227
17
1. 23045
37
1.56820
57
1. 75587
77
1. 88649
97
1. 98677
18
1. 25527
38
1.57978
58
1. 76343
78
1. 89209
98
1. 99123
19
1. 27875
39
1.59106
59
1. 77085
79
1. 89763
99
1. 99564
20
1. 30103
40
1. 60206
60
1. 77815
80
1. 90309
100
2. 00000
Page 592]
TABLE 42.
Logarithms of Numbers.
No.
100 1600
Log. 00000-
—20412.
No.
0
1
'■ i
8
00130
00561
00988
01410
01828
02243
02653
03060
03463
03862
04258
04650
05038
05423
05805
4
5 0
7
8
9
100
101
102
103
104
105
106
107
108
109
OOOOO
00432
008t)0
01284
01703
00043
00475
00903
0132^
01745
02160
02572
02979
03383
03782
04179
04571
04961
05346
05729
00087
00518
00945
01368
01787
02202
02612
03019
03423
03822
04218
04610
04999
05385
05767
00173
00604
01030
01452
01870
02284
02694
03100
03503
03902
04297
04689
05077
05461
05843
00217 ' 00260
00647 00689
00303
00732
01157
01578
01995
02407
02816
03222
03623
04021
04415
04805
05192
05576
05956
06333
06707
07078
07445
07809
00346
00775
01199
01620
02036
02449
02857
03262
03663
04060
00389
00817
01242
01662 ,
02078
02490
02898 1
03302
03703
04100
4S ! 42
01072
01494
01912
02325
02735
03141
03543
03941
01115
01536
01953
1
2
3
4
5
6
7
8
9
4
9
13
17
22
26
30
34
39
4
8
13
17
21
25
29
34
38
02119
02531
02938
03:342
03743
02366
02776
03181
03583
03981
110
111
112
113
114
115
116
117
118
119
04139
04532
04922
05308
05690
06070
06446
06819
07188
07555
04336
04727
05115
05500
05881
06258
06633
07004
07372
07737
08099
08458
08814
09167
09517
09864
10209
10551
10890
11227
11561
11893
12222
12548
12872
04376
04766
05154
05538
05918
06296'
06670
07041
07408
07773
08135
08493
08849
09202
09552
04454
04844
05231
05614
05994
04493
04883
05269
05652
06032
T
2
3
4
5
6
7
8
9
41
4
8
12
16
21-
25
29
33
37
40
4
8
12
16 •
20
24
28
32
36
06108
06483
06856
07225
07591
07954
08314
08672
09026
09377
06145
06521
06893
07262
07628
06183
06558
06930
07298
07664
08027
08386
08743
09096
09447
06221
06595
06967
07335
07700
08063
08422
08778
09132
09482
06371
06744
07115
07482
07846
06408
06781
07151
07518
07882
120
121
122
123
124
125
126
127
128
129
07918
08279
08636
08991
09342
09691
10037
10380
10721
11059
11394
11727
12057
12385
12710
13033
13354
13672
13988
14301
07990
08350
08707
09061
09412
08171
08529
08884
09237
09587
08207
08565
08920
09272
09621
08243
08600
08955
09307
09656
10003
10346
10687
11025
11361
2
3
4
5
6
7
8
9
89
4
8
12
16
20
23
27
31
35
88
4
8
11
15
19
23
27
30
34
09726
10072
10415
10755
11093
11428
11760
12090
12418
12743
09760
10106
10449
10789
11126
09795
10140
10483
10823
11160
09830
10175
10517
10857
11193
09899
10243
10585
10924
11261
09934
10278
10619
10958
11294
09968
10312-
10653
10992
11327
11661
11992
12320
12646
12969
130
131
132
133
134
135
136
137
138
139
11461
11793
12123
12450
12775
11494
11826
12156
12483
12808
11528
11860
12189
12516
12840
13162
13481
13799
14114
14426
14737
15045
15351
15655
15957
11594
11926
12254
12581
12905
11628
11959
12287
12613
12937
11694
12024
12352
12678
13001
87
36
1
2
3
4
5
6
7
8
9
4
7
11
15
19
22
26
30
33
4
7
11
14
18
22
25
29
32
13066
13386
13704
14019
14333
13098
13418
13735
14051
14364
13130
13450
13767
14082
14395
13194
13513
13830
14145
14457
14768
15076
15381
15685
15987
13226
13545
13862
14176
14489
13258
13577
13893
14208
14520
13290
13609
13925
14239
14551
13322
13640
13956
14270
14582
14891
15198
15503
15806
16107
16406
16702
16997
17289
17580
17869
18156
18441
18724
19005
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
14613
14922
15229
15534
15836
16137
16435
16732
17026
17319
14644
14953
15259
15564
15866
14675
14983
15290
15594
15897
14706
15014
15320
15625
15927
16227
16524
16820
17114
17406
14799
15106
15412
15715
16017
14829
15137
15442
15746
16047
16346
16643
16938
17231
17522
17811
18099
18384
18667
18949
19229
19507
19783
20058
20330
14860
15168
15473
15776
16077
16376
16673
16967
17260
17551
1~
2
3
4
5
6
7
8
9
85
"4"
7
11
14
18
21
25
28
32
84
3
7
10
14
17
20
24
27
31
16167
16465
16761
17056
17348
17638
17926
18213
18498
18780
16197
16495
16791
17085
17377
16256
16554
16850
17143
17435
16286
16584
16879
17173
17464
17754
18041
18327
18611
18893
19173
19451
19728
20003
20276
16316
16613
16909
17202
17493
17609
17898
18184
18469
18752
17667
17955
18241
18526
18808
17696
17984
18270
18554
18837
17725
18013
18298
18583
18865
17782
18070
18355
18639
18921
19201'
19479
19756
20030
20303.
17840
18127
18412
18696
18977
2
3
4
5
'6
7
8
88
32
3
7
10
13
17
20
23
26
30
3
6
10
13
16
19
22
26
29
19033
19312
19590
19866
20140
19061
19340
19618
19893
20167
19089
19368
19645
19921
20194
19117
19396
19673
19948
20222
19145
19424
19700
19976
20249
19257
19535
19811
20085
20358
8
19285
19562
19838
20112.
20385
No.
0
1
2
s
4
5 1 6
7
0
^
TABLE 4:2.
Logarithms of Nximbers.
[Page 593
N(
-2200
Log. 20412
-34242. 1
No.
0
1
2
8
4
5
6
7
«
9
160
161
162
163
164
165
166
167
168
169
20412
20683
20952
21219
21484
20439
20710
20978
21245
21511
20466
20737
21005
21272
21537
20493
20763
21032
21299
21564
21827
22089
22350
22608
22866
20520
20790
21059
21325
21590
21854
22115
22376
22634
22891
20548
20817
21085
21352
21617
21880
22141
22401
22660
22917
23172
23426
23679
23930
24180
20575
20844
21112
21378
21643
21906
22167
22427
22686
22943
23198
23452
23704
23955
24204
24452
24699
24944
25188
25431
25672
25912
26150
26387
26623
26858
27091
27323
27554
27784
28012
28240
28466
28691
28914
29137
29358
29579
29798
30016
30233
30449
30664
30878
31091
31302
31513
31723
31931
32139
20602
20871
21139
^405
21669
21932
22194
22453
22712
22968
23223
23477
23729
23980
24229
20629
20898
21165
21431
21696
21958
22220
22479
22737
22994
23249
23502
23754
24005
24254
20656
20925
21192
21458
21722
1
2
3
4
5
6
7
8
9
31
3
6
9
12
16
19
22
25
28
30
3
6
9
12
15
18
21
24
27
21748
22011
22272
22531
22789
21775
22037
22298
22557
22814
21801
22063
22324
22583
22840
21985
22246
22505
22763
23019
23274
23528
23779
24030
24279
170
171
172
173
174
175
176
177
178
179
23045
23300
23553
23805
24055
24304
24551
24797
25042
25285
23070
23325
23578
23830
24080
24329
24576
24822
25066
25310
23096
23350
23603
23855
24105
24353
24601
24846
25091
25334
23121 23147
23376 23401
29
28
23629
23880
24130
24378
24625
24871
25115
25358
23654
23905
24155
1
2
3
4
5
6
7
8
9
3
6
9
12
15
17
20
23
26
3
6
8
11
14
17
20
22
25
24403
24650
24895
25139
25382
24428
24674
24920
25164
25406
25648
25888
24477
24724
24969
25212
25455
25696
25935
26174
26411
26647
26881
27114
27346
27577
27807
28035
28262
28488
28713
28937
29159
29380
29601
29820
30038
30255
30471
30685
30899
31112
31323
31534
31744
31952
32160
32366
32572
32777
32980
33183
33385
33586
33786
33985
34183
24502
24748
24993
25237
25479
25720
25959
26198
2frl35
26670
26905
27138
27370
27600
27830
28058
28285
28511
28735
28959
29181
29403
29623
29842
30060
30276
30492
30707
30920
31133
31345
31555
31765
31973
32181
32387
32593
32797
33001
33203
33405
33606
33806
34005
34203
24527
24773
25018
25261
25503
180
181
182
183
184
25527
25768
26007
26245
26482
25551
25792
26031
26269
26505
25575
25816
26055
26293
26529
25600 25624
25840 25864
25744
25983
26221
26458
26694
1
2
3
4
5
6
7
8
9
27
3
5
8
11
14
16
19
22
24
26
26316 26M0 26364
26553 26576 | 26600
26788 26811 26834
27021 27045 1 27068
27254 27277 27300
27485 27508 ; 27531
27715 27738 27761
3
5
8
10
13
16
18
21
23
185
186
187
188
189
26717
26951
27184
27416
27646
26741
26975
27207
27439
27669
27898
28126
28353
28578
28803
29026
29248
29469
29688
29907
30125
30341
30557
30771
30984
26764
26998
27231
27462
27692
27921
28149
28375
28601
28825
29048
29270
29491
29710
29929
30146
30363
30578
30792
31006
26928
27161
27393
27623
27852
28081
28307
28533
28758
28981
29203
29425
29645
29863
30081
190
191
192
193
194
27»75
28103
28330
28556
28780
27944 27967
28171 28194
28398 1 28421
28623 28646
28847 ' 28870
29070 29092
29292 29314
29513 29535
29732 29754
29951 29973
30168 30190
30384 30406
30600 30621
30814 30835
31027 31048
31239 31260
31450 ' 31471
31660 31681
31869 31890
32077 i 32098
27989
28217
28443
28668
28892
29115
29336
29557
29776
29994
30211
30428
30&43
30856
31069
31281
31492
31702
31911
32118
25
24
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
3
5
8
10
13
15
18
20
23
2
5
7
10
12
14
17
19
22
195
196
197
198
199
29003
29226
29447
29667
29885
200
201
202
203
204
30103
30320
30535
30750
30963
30298
30514
30728
30942
31154
23
~2"
5
7
9
12
14
16
18
21
22
2
4
7
9
11
13
15
18
20
205
206
207
208
209
210
211
212
213
214
31175
31387
31597
31806
32015
31197
31408
31618
31827
32035
31218
31429
31639
31848
32056
31366
31576
31785
31994
32201
32408
32613
32818
33021
33224
33425
33626
33826
34025
34223
32222
32428
32634
32838
33041
32243
32449
32654
32858
33062
33264
33465
33666
33866
34064
32263
32469
32675
32879
33082
33284
33486
33686
33885
34084
32284 ' 32305 \ 32325
32490 1 32510 32531
32346
32552
32756
32960
33163
32695 32715
32899 32919
33102 33122
32736
32940
33143
1
2
3
4
5
6
7
8
9
21
"2~
4
20
2
4
215
216
217
218
219
33244
33445
33646
33846
34044
33304
33506
33706
33905
34104
33325
33526
33726
33925
34124
33345
33546
33746
33945
34143
33365
33566
33766
33965
34163
6 6
8 ! 8
11 ! 10
13 12
15 14
17 16
No.
0
1
2
3 ' 4
5
6
7
«
9
19
18
22489—03-
-38
Page 594]
TABLE 42.
Logarithms (
3f Numbers.
Xo. 2200 280C
.
Log. 34242-
— M716.
Ko.
« 1
1 i
2
3
4
5 1
34341
0 1
7
8
9
220
34242
34262
34282
34301
34321
34361
34380
34400
34420
221
34439
34459
34479
34498
34518
34537
34557
34577
34596
34616
20
222
34635
34655
34674
34694
34713
34733
34753
34772
34792
34811
1
2
223
34830
348o0
;34869
34889
34908
34928
34947
34967
34986
35005
2
4
224
35025
35044 1
35064
35083
35102
35295
35122
35315
35141
35334
35160
35353
35180
35199
35392
3
4
6
8
225
35218
35238
35257
35276
35372
226
35411
35430
35449
35468
35488
35507
35526
35545
35564
35583
5
10
227
35603
35622
35641
35660
35679
35698
35717
35736
35755
35774
6
12
228
35793
35813
35832
35851
35870
35889
35908
35927
35946
35965
V
14
229
35984
36003
36192
36021
36040
36059
36078
36097
36116
36135
36154
8
9
16
18
230
36173
36211
36229
36248
36267
36286
36305
36324
Sfi.^l9
231
36361
36380
36399
36418
36436
36455
36474
36493
36511 ! 36530
19
232
36549
36568
36586
36605
36624
36642
36661
36680
36698 36717
1
2
233
36736
36754
36773
36791
36810
36829
36847
36866
36884 36903
9
4
234
36922
36940
36959
36977
36996
37014
37033
37051
37070 37088
3
4
6
8
235
37107
37125
37144
37162
37181
37199
37218
37236
37254
37273
236
37291
37310
37328
37346
37365
37383
37401
37420
37438
37457
5
10
237
37475
37493
37511
37530
37548
37566
37585
37603
37621
37639
6
11
238
37658
37676
37694
37712
37731
37749
37767
37785
37803
37822
7
13
239
37840
37858
37876
37894
37912
37931
37949
37967
37985 38003
8
9
15
17
240
241
38021
38202
38039
38220
38057
38238
38075
38256
38093
38274
38112
38292
38130
38310
38148
38328
38166 ; 38184
38346 1 38364
18
242
38382
38399
38417
38435
38453
38471
38489
38507
38525
38543
1
2
3
4
2
4
5
7
243
38561
38578
38596
38614
38632
38650.
38668
38686
38703
38721
244
38739
38757
38775
38792
38810
38828
38846 ,
38863
38881
38899
245
38917
38934
38952
38970
38987
39005
39023
39041
39058
39076
246
39094
39111
39129
39146
39164
39182
39199
39217
39235 39252
5
Q
247
39270
39287
39305
39322
39340
39358
39375
39393
39410
39428
6
11
248
39445
39463
39480
39498
39515
39533
39550
39568
39585
39602
7
13
249
39620
39637
39655
39672
39690
39707 .
39724
39742
39759
39933
39777
8
9
It
250
39794
39811
39829
39846
39863
39881
39898
39915
39950
251
39967
39985
40002
40019
40037
40054
40071
40088
40106
40123
252
40140
40157
40175
40192
40209
40226
40243
40261
40278
40295
253
40312
40329
40346
40364
40381
40398
40415
40432
40449
40466
1
2
254
40483
40500
40518
40688
40535
40705
40552
40722
40569
40586
40603
40773
40620
40637
2
3
3
5
255
40654
40671
40739
40756
40790
40807
256
, 40824
40841
40858
40875
40892
40909
40926
40943
40960
40976
4
7
257
40993
41010
41027
41044
41061
41078
41095
41111
41128
41145
5
9
258
41162
41179
41196
41212
41229
41246
41263
41280
41296
41313
6
10
259
41330
41347
41363
41380
41397
41414
41430
41447
41464
41481
7
8
9
12
14
15
260
41497
41514
41531
41547
41564
41581
41597
41614
41631
41647
261
262
41664
41830
41681
41847
41697
41863
41714
41880
41731
41896
41747
41913
41764
41780
41 797
41814
41929
41946
41963
41979
16
263
41996
42012
42029
42045
42062
42078
42095
42111
42127
42144
1
2
264
42160
42177
42193
42210
42226
42243
42259
42423
42275
42292
42308
2
3
3
5
265
42325
42341
42357
42374
42390
42406
42439
42455
42472
266
42488
42504
42521
42537
42553
42570
42586
42602
42619
42635
4
6
267
42651
42667
42684
42700
42716
42732
42749
42765
42781
42797
5
8
268
42813
42830
42846
42862
42878
42894
42911
42927
42943
42959
6
10
269
42975
42991
43008
43024
43040
43056
43217
43072
43233
43088
43249
43104
43120
7
8
11
13
270
43136
43152
43169
43185
43201
43265
43281
271
272
43297
43457
43313
43473
43329
43489
43345
43505
43361
43521
43377
43537
43393
43553
43409
43569
43425
43584
43441
43600
9
14
15
273
43616
43632
43648
43664
43680
43696
43712
43727
43743
43759
1
2
274
43775
43791
43807
43823
43838
43854
44012
43870
44028
43886
44044
43902
43917
2
3
3
5
275
43933
43949
i 43965
43981
i 43996
44059
i 44075
276
44091
44107
44122
44138
! 44154
44170
44185
44201 ,
44217
44^32
4
6
277
44248
44264
44279
i 44295
44311
44326
44342
44358
44373
44389
5
8
278
44404
44420
44436
44451
44467
44483
44498
44514
44529
44545
6
9
279
44560
44576
44592
44607
44623
i
, 44638
44654
44669
44685
44700
8
9
11
12
,14
No.
0
1
2
3
4
5
6
7
8
9
TABLE 42.
Logarithms of Numbers.
[Page 595
No. 2800 3400.
Log. 44716 53148.
No.
0
1
2
3
4
5
6
7
8
»
1
280
281
282
283
284
285
286
287
288
289
44716
44871
45025
45179
45332
44731
44886
45040
45194
45347
44747
44902
45056
45209
45362
45515
45667
45818
45969
46120
44762
44917
45071
45225
45378
44778
44932
45086 1
45240 !
45393 1
45545
45697
45849
46000
46150
44793
44948
45102
45255
45408
45561
45712
45864
46015
46165
44809
44963
45117
45271
45423
44824
44979
45133
45286
45439
45591
45743
45894
46045
46195
44840 44855
44994 45010
45148 45163
45301 45317
45454 1 45469
16
1
2
3
4
5
6
7
8
9
2
3
5
6
8
10
11
13
14
45484
45637
45788
45939
46090
45500
45a52
45803
45954
46105
45530
45682
45834
45984
46135
45576
45728
45879
46030
46180
45606
45758 1
45909
46060
46210
46359"
46509
46657
46805
46953
45621
45773
45924
46075
46225
290
291
292
293
294
295
296
297
298
299
46240
46389
46538
46687
46835
46255
46404
46553
46702
46850
46270
46419
46568
46716
46864
47012
47159
47305
47451
47596
46285
46434
46583
46731
46879
47026
47173
47319
47465
47611
46300
46449
46598
46746
. 46894
47041
47188
47334
47480
47625
46315
46464
46613
46761
46909
47056
47202
47349
47494
47640
46330
46479
46627
46776
46923
56345
46494
46642
46790
46938
46374
46523
46672
46820
46967
47114
47261
47407
47553
47698
1
15
1
2
3
4
5
6
7
8
9
2
3
5
6
8
9
11
12
14
46982
47129
47276
47422
47567
46997
47144
47290
47436
47582
47070
47217
47363
47509
47654
47085
47232
47378
47524
47669
47100
47246
47392
47538
47683
300
301
302
303
304
47712
47857
48001
48144
48287
47727
47871
48015
48159
48302
47741
47885
48029
48173
48316
47756
47900
48044
48187
48330
47770
47914
48058
48202
48344
47784
47929
48073
48216
48359
47799
47943
48087
48230
48373
47813
47958
48101
48244
48387
47828 47842
47972 47986
48116 48130
48259 48273
48401 i 48416
1
305
306
307
308
309
48430
48572
48714
48855
48996
48444
48586
48728
48869
49010
48458
48601
48742
48883
49024
48473
48615
48756
48897
49038
48487
48629
48770
48911
49052
48501
48643
48785
48926
49066
48515
48657
48799
48940
49080
48530
48671
48813
48954
49094
49234
49374
49513
49651
49790
49927
50065
50202
50338
50474
50610
50745
50880
51014
51148
48544 1 48558
14
48827
48968
49108
49248
49388
49527
49665
49803
49941
50079
50215
50352
50488
50623
50759
50893
51028
51162
51295
51428
51561
51693
51825
51957
52088
52218
52349
52479
52608
52737
52866
52994
53122
48841
48982
49122
492(32
49402
49541
49679
49817
49955
50092
50229
50365
50501
50637
50772
50907
51041
51175
51308
51441
51574
51706
51838
51970
52101
52231
52362
52492
52621
52750
52879
53007
53135
1
2
3
4
5
6
7
8
9
1
3
4
6
7
8
10
11
13
310
311
312
313
314
49136
49276
49415
49554
49693
49150
49290
49429
49568
49707
49164
49304
49443
49582
49721
49859
49996
50133
50270
50406
49178
49318
49457
49596
49734
49872
50010
50147
50284
50420
49192
49332
49471
49610
49748
49206
49346
49485
49624
49762
49220
49360
49499
49638
49776
315
316
317
318
319
49831
49969
50106
50243
50379
49845
49982
50120
50256
50393
50529
50664
50799
50934
51068
49886
50024
50161
50297
50433
50569
50705
50840
50974
51108
49900
50037
50174
50311
50447
49914
50051
50188
50325
50461
1
18
1
2
3
4
5
6
7
8
9
1
3
4
5
7
8
9
10
12
320
321
322
323
324
50515
50651
50786
50920
51055
50542
50678
50813
50947
51081
50556
50691
50826
50961
51095
50583
50718
50853
50987
51121
50596
50732
50866
51001
51135
51268'
51402
51534
51667
51799
325
326
327
328
329
51188
51322
51455
51587
51720
51202
51335
51468
51601
51733
51215
51348
51481
51614
51746
51228
51362
51495
51627
51759
51891
52022
52153
52284
52414
51242
51375
51508
51640
51772
51255
51388
51521
51654
51786
51282
51415
51548
51680
51812
51943
52075
52205
52336
52466
1
330
331
332
333
334
51851
51983
52114
52244
52375
51865
51996
52127
52257
52388
51878
52009
52140
52270
52401
51904
52035
52166
52297
52427
51917
52048
52179
52310
52440
51930
52061
52192
52323
52453
1
2
3
4
5
6
7
8
9
12
1
2
4
5
6
7
8
10
11
335
336
337
338
339
52504
52634
52763
52892
53020
52517
52647
52776
52905
53033
52530
52660
52789
52917
53046
52543
52673
52802
52930
53058
52556
52686
52815
52943
53071
52569
52699
52827
52956
53084
52582
52711
52840
52969
53097
52595
52724
52853
52982
53110
No.
0
1
2
3
4
5
6
7
8
9
Page 596]
TABLE 42.
Logarithms of Numbers.
No.
S400 lOOC
.
Log. 53148 60206. 1
No.
0
1
2
3
4
5
G
7
8
9
1
340
:^i
342
343
344
345
346
347
348
349
350
351
352
353
354
53148
53275 1
53403
53529
53^56
53782 1
53908 '
54033 !
54158 '
54283
. 54407
54531
54654
54777
54900
53161
53288
53415
535*
53668
53794
53920
54045
54170
54295
54419
54543
54667
54790
54913
53173
53301
53428
53555
53681
53807"
53933
54058
54183
54307
54432
54555
54679
54802
54925
53186
53314
53441
53567
53694 '
53820 1
53945 :
54070
54195
54320
53199
53326
53453
53580
53706
5.3832
53958
54083
54208
54332
53212
53339
5;i466
53593
53719
53845
5.3970
54095
54220
54345
53224
53352
53479
5.3605
53732
53857
53983
54108
54233
.54357
53237
53364
5,3491
53618
53744
53870
5,3995
54120
54245
54370
54494
54617
5-^741
54864
54986
55108
55230
55352
5,5473
55594
53250
53377
53504
53631
53757
53882
,54008
,54133
54258
54382
54506
54630
54753
54876
54998
55121
55242
55364
55485
55606
53263
53390
,5.3517
53643
53769
53895
54020
,54145
54270
54394
54518
54642
54765
54888
55011
Vi
1
2
3
4
5
/
8
9
1
3
4
5
7
8
9
10
12
54444
54568
54691
54814
54937 :
54456
54580
54704
54827
54949
54469
54593
54716
548.39
.54962.
55084
55206
55328
55449
55570
54481
54605
54728
54851
54974
55096
55218
55;i40
55461
55582
355
356
357
358
359
55023
,55145
55267
55388
55509
550;i5
55157
55279
55400
55522
55047
55169
55291
55413
55534
55060
55182
55303
55425
55546
55072
55194
55315
55437
55558
55133
55255
55376
55497
55618
55739
55859
55979
56098
56217^
1
2
3
4
5
6
7
8
9
12
1
2
4
5
6
7
8
10
11
360
361
362
363
364
55630
55751 1
55871
55991 '
56110 i
55642
55763
55883
56003
56122
55654
55775
55895
56015
56134
55666
55787
55907 i
56027
56146
55678
55799
55919
56038
56158
55691
55811
55931
56050
56170
55703
55823
55943
56062
56182
55715
55835
55955
56074
56194
56312
5&431
56549
56667
56785
55727
,55847
55967
56086
56205
365
366
367
368
369
56229 ,
56348
56467
56585
56703 '
56241
56360
56478
56597
56714
56832
56949
57066
57183
57299
56253
56372
56490
56608
56726
56844
56961
57078
57194
57310
56265
56384
56502
56620
56738
56277
56396
56514
56632
56750
56289
56407
56526
56644
56761
56301
56419
56538
56656
56773
56324
56443
56561
56679
56797
56914
57031
57148
57264
57380
57496
57611
57726
57841
57955
56336
56455
56573
56691
56808
370
371
372
373
374
56820
56937
57054
57171
57287
56855
56972
57089
57206
57322
56867
56984
57101
57217
57334
56879
56996
57113
57229
57345
56891
57008
57124
57241
57357
56902
57019
57136
57252
57368
56926
57043
57159
57276
57392
57507
57623
57738
57852
57967
11
1
2
3
4
5
6
7
8
9
1
2
3
4
6
7
8
9
10
375
376
377
378
379
57403
57519
57634
57749
57864
57415
57530
57646
57761
57875
57426
57542
57657
57772
57887
57438
57553
57669
57784
57898
57449
57565
57680
57795
57910
57461
57576
57692
57807
57921
57473
57588
57703
.57818
579,33
57484
57600
,57715
57830
57944
380
381
382
383
384
57978
58092
58206
58320
58433
57990
58104
58218
58331
58444
58001
58115
58229
58343
58456
58013
58127
58240
58354
58467
58024
581.38
58252
58365
58478
58035
58149
58263
58377
58490
58047
58161
58274
58388
58501
58058
58172
58286
58399
.58512
58070
58184
58297
,58410
58524
58081
58195
58309
58422
58535
5864?
58760
58872
58984
59095
385
386
387
388
389
58546
58659
58771
58883
58995
58557
58670
58782
58894
59006
58569
58681
58794
58906
59017
58580
58692
58805
58917
59028
58591
58704
58816
58928
59040
58602
58715
58827
58939
59051
58614
58726
58838
58950
59062
58625
58737
58850
58961
59073
58636
58749
58861
58973
59084
10
390
391
392
393
394
59106
59218
59329
59439
59550
59660"
59770
59879
59988
60097
0
59118
59229
59340
59450
59561
59671
59780
59890
59999
60108
1
59129
59240
59351
59461
59572
59682
59791
59901
60010
60119
59140
59251
59362
59472
59583
59693'
59802
59912
60021
60130
59151
59262
59373
59483
59594
59704'
59813
59923
60032
60141
59162
59273
59384
59494
59605
i 59715
59824
59934
60043
60152
59173
59284
59.395
.59506
,59616
"59726
59835
59945
60054
60163
59184
59295
59406
59517
59627
59737
59846
59956
60065
60173
59195
59306
59417
59528
59638
59207
,59318
59428
59539
59649
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
395
396
397
398
399
59748
59857
59966
60076
60184
59759
59868
59977
60086
60195
No.
2
S
4
o
G
7
8
! »
1
No.
TABLE 42.
Logarithms of Numbers.
[Page 597
4000 1600.
Log. 60206 66276. 1
No.
0
1
2
3
4
5
6
7
8
9
1
400
401
402
403
404
60206
60314
60423
60531
60638
60746
60853
60959
61066
61172
6f278
61384
61490
61595
61700
60217
60325
60433
60541
60649
60756
60863
60970
61077
61183
60228
60336
60444
60552
60660
60239
60347
60455
60563
60670
60249
60358
60466
60574
60681
60260
60369
60477
60584
60692
60271
60379
60487
60595
60703
60282
60390
60498
60606
60713
60293
60401
60509
60617
60724
60304
60412
60520
60627
60735
60842"
60949
61055
61162
61268
61374
61479
61584
61690
61794
61899
62003
62107
62211
62315
11
1
2
3
4
5
6
7
8
9
1
2
3
4
6
7
8
9
10
405
406
407
408
409
60767
60874
60981
61087
61194
60778
60885
60991
61098
61204
60788
60895
61002
61109
61215
60799
60906
61013
61119
61225
60810
60917
61023
61130
61236
60821
60927
61034
61140
61247
60831
60938
61045
61151
61257
410
411
412
413
414
61289
61395
61500
61606
61711
61300
61405
61511
61616
61721
61310
61416
61521
61627
61731
61321
61426
61532
61637
61742
61331
61437
61542
61648
61752
61342
61448
61553
61658
61763
61868
61972
62076
62180
62284
62387
62490
62593
62696
62798
61352
61458
61563
61669
61773
61878
61982
62086
62190
62294
62397
62500
62603
62706
62808
62910
63012
63114
63215
63317
61363
61469
61574
61679
61784
61888
61993
62097
62201
62304
62408
62511
62613
62716
62818
62921
63022
63124
63225
63327
63428
63528
63629
63729
63829
63929
64028
64128
64227
64326
415
416
417
418
419
420
421
422
423
424
61805
61909
62014
62118
62221
62325
62428
62531
62634
62737
61815
61920
62024
62128
62232
62335
62439
62542
62644
62747
61826
61930
62034
62138
62242
62346
62449
62552
62655
62757
62859
62961
63063
63165
63266
63367
63468
63568
63669
63769
61836
61941
62045
62149
62252
62356
62459
62562
62665
62767
62870
62972
63073
63175
63276
61847
61951
62055
62159
62263
62366
62469
62572
62675
62778
62880
62982
63083
63185
63286
61857
61962
62066
62170
62273
62377
62480
62583
62685
62788
62418
62521
62624
62726
62829
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
425
4^6
427
428
429
430
431
432
433
434
62839
62941
63043
63144
63246
62849
62951
63053
63155
63256
63357'
63458
63558
63659
63759
62890
62992
63094
63195
63296
62900
63002
63104
63205
63306
62931
63033
63134
63236
63337
63438
63538
63639
63739
63839
63347
63448
63548
63649
63749
63377
63478
63579
63679
63779
63387
63488
63589
63689
63789
63397
63498
63599
63699
63799
63899
63998
64098
64197
64296
63407
63508
63609
63709
63809
63909
64008
64108
64207
64306
63417
63518
63619
63719
63819
63919
64018
64118
64217
64316
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
63849
63949
64048
64147
64246 .
63859
63959
64058
64157
64256
63869
63969
64068
64167
64266
63879
63979
64078
64177
64276
63889
63988
64088
64187
64286
63939
64038
64137
64237
64335
64345
64444
64542
64640
64738
64355
64454
64552
64650
64748
64365
64464
64562
64660
64758
64375
64473
64572
64670
64768
64865
64963
65060
&5157
65254
64385
64483
64582
64680
64777
64875
64972
65070
65167
65263
64395
64493
64591
64689
64787
64404
64503
64601
64699
64797
64414
64513
64611
64709
64807
64424
64523
64621
64719
64816
64914
65011
65108
65205
65302
65398
65495
65591
65686
65782
64434
64532
64631
64729
64826
64924"
65021
65118
65215
65312
65408
65504
65600
65696
65792
64836
64933
65031
65128
65225
64846
64943
65040
65137
65234
64856
64953
65050
65147
65244
64885
64982
65079
65176
65273
6t895
64992
65089
65186
65283
6^904
65002
65099
65196
65292
1
2
3
4
5
6
7
8
9
9
450
451
452
453
454
65321
65418
65514
65610
65706
65331
65427
65523
65619
65715
65341
65437
65533
65629
65725
65350
65447
65543
65639
65734
65360
65456
65552
65648
65744
65369
65466
65562
65658
65753
65379
65475
65571
65667
65763
65389
65485
65581
65677
65772
1
2
3
4
5
5
6
7
8
455
456
457
458
459
65801
65896
65992
66087
66181
65811
65906
66001
66096
66191
65820
65916
66011
66106
66200
65830
65925
66020
66115
66210
65839
65935
66030
66124
66219
65849
65944
66039
66134
66229
65858
65954
66049
66143
66238
65868
65963
66058
66153
66247
65877
65973
66068
66162
66257
65887
65982
66077
66172
66266
No.
0
1
2
3
4
5
6
7
8
9
1
Page 598]
TABLE 42.
Logarithms
of Numbers.
No.
4600 5200.
«
Log. 66276-
^71600.
No. .
0
1
2
8
4
fi
7
8
9
460
461
66276
66370
66285
66380
6()295
66389
66304
66398
66314
66408
66323
66417
66332
66427
66342
66436
66351
66445
66361
66455
•10
1
1
2
462
66464
66474
66483
66492
66502
66511
66521
66530
66539
66549
1
463
66558
6659r
66577
66586
66596
66605
66614
66624
66633
66642
2
464
66652
66661
66755^
66671
66764
66680
66773"
66689
66783
66699
66792
66708
66801
66717
66727
66820
66736
66829
3
4
5
6
3
4
5
465
66745
66811
466
66839
66848
66857
66867
66876
66885
66894
66904
(>6913
66922
467
66932
66941
66950
66960
66969
66978
(56987
66997
67006
67015
1^
468
67025
67034
67043
67052
67062
67071
67080
67089
67099
67108
8
9
1
469
67117
67127
67136
67145
67237
67330
67154
67164
67173
67182
67274
67191
67284
67201
67293
8
9
470
67210
67219
67228
67247
67339
67256
67265
471
67302
6731 1
67321
67348
67357
67367
67376
67385
472
67394
{)7403
67413
67422
67431
67440
67449
67459
67468
67477
473
67486
67495
67504
67514
67523
67532
67541
67550
67560
67569
474
475
67578
67669^
67587
67679
67596
67688
67605
67697
67614
67706
67624
67715
67633
67724'
67642
677^3
67651
67742
67660
67752
476
67761
67770
67779
67788
67797
67806
67815
67825
67834
67843
477
67852
67861
67870
67879
67888
67897
67906
67916
67925
67934
478
67943
67952
67961
67970
67979
67988
67997
68006
68015
68024
479
68034
68124
68043
68133
68052
68142
68061
68151
68070
68160
68079
68169"
68088
68178
68097
68187
68106
68196
68115
68205
480
481
68215
68224
68233
68242
68251
68260
68269
68278
68287
68296
482
68m5
68314
68323
68332
68341
68350
68:^59
68368
68377
68386
483
484
485
486
68395
68485
68574
68664
68404
68494
68583'
68673
68413
68502
68592
68681
68422
68511
68431
68520
68440
68529
68449
68538
68628
68717
68458
68547
68467
68556
68476
68565
9
68601
68690
68610
68699
68619
68708
68637
68726
68646
68735
68655
68744
1
1
487
68753
68762
68771
68780
68789
68797
68806
68815
68824
68833
9
2
488
68842
68851
68860
68869
68878
68886
68895
68904
68913
68922
;]
o
489
490
68931
68940
69028
68949
69037
68958
69046
68966
69055
68975
69064
68984
69073
68993
69082
69002
69090
69011
4
5
4
5
69020
69099
491
69108
69117
69126
69135
69144
69152
69161
69170
69179
69188
6
5
492
69197
69205
69214
69223
69232
69241
69249
69258
69267
69276
7
6
493
69285
69294
69302
69311
69320
69329
69338
69346
69355
69364
8
7
494
69373
69381
69390
69399
69408
69417
69425
69434
69443
69452
9
8
495
496
69461
69548
69469
69557
69478
69566
69487
69574
69496
69583
69504
69592
69513
69601
69522
69609
69531
69618
69539
69627
497
69636
69644
69653
69662
69671
69679
69688
69697
69705
69714
498
69723
69732
69740
69749
69758
69767
69775
69784
69793
69801
499
69810
69897
69819
69827
69836
69845
69854
69940
69862
69949
69871
69958
69880
69966
69888
69975
500
69906
69914
69923
69932
501
69984
69992
70001
70010
70018
70027
70036
70044
70053
70062
502
70070
70079
70088
70096
70105
70114
70122
70131
70140
70148
503
70157
70165
70174
70183
70191
70200
70209
70217
70226
70234
504
70243
70252
70260
70269
70278
70286
70295
70381'
70303
70389
70312
70398
70321
505
70329
70338
70346
70355
70364
70372
70406
506
70415
70424
70432
70441
70449
70458
70467
70475
70484
70492
507
70501
70509
70518
70526
70535
70544
70552
70561
70569
70578
508
509
70586
70672
70595
70680
70603
70689
70612
70697
70621
70706
70629
70714
70800
70638
70723
70808
70646
70731
70817
70655
70740
70825
70663
70749
„
8
510
70757
70766
70774
70783
70791
70834
511
70842
70851
70859
70868
70876
70885
70893
70902
70910
70919
1
1
512
70927
70935
70944
70952
70961
70969
70978
70986
70995
71003
?.
2
513
71012
71020
71029
71037
71046
71054
71063
71071
71079
71088
3
2
514
71096
71105
71113
71122
71130
71139
71147
71155
71240
71164
71248
71172
71257
4
5
3
4
515
71181
71189
71198
71206
71214
71223
71231
516
71265
71273
71282
71290
71299
71307
71315
71.324
71332
71341
6
5
517
71349
71357
71366
71374
71383
71391
71399
71408
71416
71425
7
6
518
71433
71441
71450
71458
71466
71475
71483
71492
71500
71508
8
6
519
71517
71525
71533
71542
71550
71559
71567
71575
71584
71592
9
7
No.
0
1
2
«
4
5
6
7
8
9
1
TABLE 42.
Logarithms of Numbers.
[Page 699
No
5200 5800.
Log. 71600 76343.
No.
0
1
2
3
4
5
6
7
8
9
1
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
71600
71684
71767
71850
71933
71609
71692
71775
71858
71941
71617
71700
71784
71867
71950
71625
71709
71792
71875
71958
71634
71717
71800
71883
71966
71642
71725
71809
71892
71975
71650
71734
71817
71900
71983
71659
71742
71825
71908
71991
71667
71750
71834
71917
71999
72082
72165
72247
72329
72411
72493
72575
72656
72738
72819
72900
72981
73062
73143
73223
71675
71759
71842
71925
72008
72090
72173
72255
72337
72419
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
5
6
7
8
72016
72099
72181
72263
72346
72428
72509
72591
72673
72754
~ 72835
72916
72997
73078
73159
72024
72107
72189
72272
72354
72032
72115
72198
72280
72362
72041
72123
72206
72288
72370
72049
72132
72214
72296
72378
72057
72140
72222
72304
72387
72066
72148
72230
72313
72395
72074
72156
72239
72321
72403
72436
72518
72599
72681
72762
72444
72526
72607
72689
72770
72452
72534
72616
72697
72779
72460
72542
72624
72705
72787
72469
72550
72632
72713
72795
72477
72558
72640
72722
72803
72485
72567
72648
72730
72811
72501
72583
72665
72746
72827
72908
72989
73070
73151
73231
72843
72925
73006
73086
73167
72852
72933
73014
73094
73175
7^860
72941
73022
73102
73183
72868
72949
73030
73111
73191
73272
73352
73432
73512
73592
72876
72957
73038
73119
73199
73280
73360
73440
73520
73600
73679
73759
73838
73918
73997
72884
72965
73046
73127
73207
73288
73368
73448
73528
73608
72892
72973
73054
73135
73215
73296
73376
73456
73536
73616
73239
73320
73400
73480
73560
73247
73328
73408
73488
73568
73255
73336
73416
73496
73576
73263
73344
73424
73504
73584
73304
73384
73464
73544
73624
73312
73392
73472
73552
73632
8
73640
73719
73799
73878
73957.
74036
74115
74194
74273
74351
73648
73727
73807
73886
73965
73656
73735
73815
73894
73973
73664
73743
73823
73902
73981
73672
73751
73830
73910
73989
73687
73767
73846
73926
74005
73695
73775
73854
73933
74013
73703
73783
7.3862
73941
74020
74099
74178
74257
74335
74414
74492
74570
74648
74726
74803
73711
73791
73870
73949
74028
74107
74186
74265
74343
74421
1
2
3
4
5
6
7
8
9
1
2
2
3
4
5
6
6
7
74044
74123
74202
74280
74359
74052
74131
74210
74288
74367
74060
74139
74218
74296
74374
74068
74147
74225
74304
74382
74076
74155
74233
74312
74390
74084
74162
74241
74320
74398
74092
74170
74249
74327
74406
74429
74507
74586
74663
74741
74437
74515
74593
74671
74749
74445
74523
74601
74679
74757
74453
74531
74609
74687
74764
74461
74539
74617
74695
74772
74468
74547
74624
74702
74780
74476
74554
74632
74710
74788
74484
74562
74640
74718
74796
74500
74578
74656
74733
74811
74889
74966
75043
75120
75197
75274
75351
75427
75504
75580
74819
74896
74974
75051
75128
74827
74904
74981
75059
75136
74834
74912
74989
75066
75143
74842
74920
74997
75074
75151
74850
74927
75005
75082
75159
74858
74935
75012
75089
75166
74865
74943
75020
75097
75174
74873
74950
75028
75105
75182
74881
74958
75035
75113
75189
75266
75343
75420
75496
75572
'75648
75724
75800
75876
75952
75205
75282
75358
75435
75511
75587
75664
75740
75815
75891
75213
75289
75366
75442
75519
75595
75671
75747
75823
75899
75220
75297
75374
75450
75526
75603
75679
75755
75831
75906
75228
75305
75381
75458
75534
75610
75686
75762
75838
75914
75236
75312
75389
75465
75542
75618
75694
75770
75846
75921
75243
75320
75397
75473
75549
75626
75702
75778
75853
75929
75251
75328
75404
75481
75557
75633
75709
75785
75861
75937
75259
75335
75412
75488
75565
75641
75717
75793
75868
75944
7
570
571
572
573
574
75656
757.32
75808
75884
75959
1
2
3
4
5
6
7
8
9
1
1
2
3
4
4
5
6
6
575
576
577
578
579
75967
76042
76118
76193
76268
75974
76050
76125
76200
76275
75982
76057
76133
76208
76283
75989
76065
76140
76215
76290
75997
76072
76148
76223
76298
76005
76080
76155
76230
76305
76012
76087
76163
762.38
76313
76020
76095
76170
76245
76320
76027
76103
76178
76253
76328
76035
76110
76185
76260
76335
No.
0
1
8
»
4
5
«
7
8
9
1
Page 600J
TABLE 42.
Logarithms of Numbers.
No.
5800 WOO.
Log. 76343 80618. 1
No.
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
0
1 •
i
3
4
5
6
7
76395
76470
76545
76619
76693
"76768
76842
76916
76989
77063
77137
77210
77283
77357
77430
8
0
1
76343
76418
76492
76567
76641
76716
76790
76864
76938
77012
"77085"
77159
77232
77305
77379
1
76360
76425
76500
765y
76649
; 76723
' 76797
76871
7«>945
77019
" 77093"
■ 77166
77240
77313
77386
76358
76433
76507
76582
7(5656
"76730"
76805
76879
76953
77026
"77100"
77173
77247
77320
77393
76365
76440
76515
76589
76664
76373
76448
76522
76597
76671
76380
76455
76530
76604
76678
76388
76462
76537
76612
76686
76403
76477
76552
76626
76701
76775
76849
76923
76997
77070
77144
77217
77291
77364
77437
76410
76485
76559
76634
76708
8
1
2
3
4
6
6
7
8
9
1
2
2
3
4
6
6
6
7
76738
76812
76886
76960
77034
76745
76819
76893
76967
77041
76753
76827
76901
76975
77048
76760
76834
76908
76982
77056
77129
77203
77276
77349
77422
76782
76856
76930
77004
77078
77151
77225
77298
77371
77444
77107
77181
77254
77327
77401
77115
77188
77262
77335
77408
77122
77195
77269
77342
77415
595
596
597
598
599
77452
77525
77597
77670
77743
77459
77532
77605
77677
77750
77466
77539
77612
77685
77757
77474
77546
77619
77692
77764
77481
77554
77627
77699
77772
77488
77561
77634
77706
77779
77495
77568
77641
77714
77786
77503
77576
77648
77721
77793
77866"
77938
78010
78082
78154
77510
77583
77656
77728
77801
77873"
77945
78017
78089
78161
78233
78305
78376
78447
78519
77517
77590
77J563
77735
77808
77880
77952
78025
78097
78168
600
601
602
603
604
77815
77887
77960
78032
78104
77822
77895
77967
78039
78111
78183"
78254
78326
78398
78469
77830
77902
77974
78046
78118
78190
78262
78333
78405
78476
78547
78618
78689
78760
78831
77837-
77909
77981
78053
78125
77844
77916
77988
78061
78132
77851
77924
77996
78068
78140
78211
78283
78355
78426
78497
77859.
77931
78003
78075
78147
7
605
606
607
608
609
78176
78247
78319
78390
78462
78197
78269
78340
78412
78483
78204
78276
78347
78419
78490
78219
78290
78362
78433
78504
^ 78226
78297
78369
78440
78512
78240
78312
78383
78455
78526
1
2
3
4
5
6
-7
8
9
1
1
2
3
4
4
5
6
6
610
611
612
613
614
615
616
617
618
619
78533
78604
78675
78746
78817
78888
78958
79029
79099
79169
78540
78611
78682
78753
78824
78554
78625
78696
78767
78838
78909
78979
79050
79120
79190
78561
78633
78704
78774
78845
78569
78640
78711
78781
78852
78923
78993
79064
79134
79204
78576
78647
78718
78789
78859
78930
79000
79071
79141
79211
78583
78654
78725
78796
78866
78937
79007
79078
79148
79218
78590
78661
78732
78803
78873
78944
79014
79085
79155
79225
78597
78668
78739
78810
78880
78951
79021
79092
79162
79232
78895
78965
79036
79106
79176
78902
78972
79043
79113
79183
78916
78986
79057
79127
79197
620
621
622
623
624
625
62(5
627
628
629
79239
79309
79379
79449
79518
79246
79316
79386
79456
• 79525
79253
79323
79393
79463
79532
79260
79330
79400
79470
79539
79267
79337
79407
79477
79546
79274
79344
79414
79484
79553
79281
79351
79421
79491
79560
79288
79358
79428
79498
79567
79295
79365
79435
79505
79574
79644
79713
79782
79851
79920
79989
80058
80127
80195
80264
80332
80400
80468
80536
80604
79302
79372
79442
79511
79581
79588
79657
79727
79796
79865
799;?4
80003
80072
80140
80209
8d277
80346
80414
80482
80550
79595
79664
79734
79803
79872
79602
79671
79741
79810
79879
79609
79678
79748
79817
79886
79616
79685
79754
79824
79893
79623
79692
79761
79831
79900
79630
79699
79768
79837
79906
79637
79706
79775
79844
79913
79982
80051
80120
80188
80257
80325
80393
80462
80530
80598
79650
79720
79789
79868
79927
6
630
631
632
633
634
635
636
637
638
639
79941
80010
80079
80147
80216
80284
80353
80421
80489
80557
79948
80017
80085
80154
80223
80291
80359
80428
80496
805^4
79955
80024
80092
80161
80229
79962
80030
80099
80168
80236
79969
80037
80106
80175
80243
80312"
80380
80448
80516
80584
79975
80044
80113
80182
80250
80318
80387
80455
80523
80691
79996
80065
80134
80202
80271
80339"
80407
80475
80543
80611
1
2
3
4
5
6
7
8
9
1
1
2
2
3
4
4
5
5
80298
80366
80434
80502
80570
80305
80373
80441
80509
80577
No.
0
1
2
3
4
o
6
7
8
9
1
TABLE 42.
[Page 601
Logarithms
of Numbers.
No
. 6400 7000.
Log. 80G18 84510. 1
No.
0
1
2
3
4
5
6
7
8
9
640
641
80618
80686
80625
80693
80632
80699
80638
80706
80645
80713k
80652
80720
80659
80726
80665
80733
80672
80740
80679
80747
1 '
1
642
80754
80760
80767
80774
80781
80787
80794
80801
80808
80814
1 1 1
643
80821
80828
80835
80841
80848
80855
80862
80868
80875
80882
2 i 1
644
645
80889
80895
80902
80909
80916
80922
80929
80936
80943
80949
3 ; 2
4 i 3
5 4
6 1 4
7 i 5
8 ; 6
9 6
■ 80956
80963
80969
80976
80983
80990
80996
81003
81010
81017
646
81023
81030
81037
81043
81050
81057
81064
81070
81077
81084
647
81090
81097
81104
81111
81117
81124
81131
81137
81144
81151
648
81158
81164
81171
81178
81184
81191
81198
81204
81211
81218
649
81224
81231
81238
81245
81251
81258
81265
81271
81278
81285
650
81291
81298
81305
81311
81318
81325
81331
81338
81345
81351
651
81358
81365
81371
81378
81385
81391
81398
81405
81411
81418
652
81425
81431
81438
81445
81451
81458
81465
81471
81478
81485
653
81491
81498
81505
81511
81518
81525
81531
81538
81544
81551
654
81558
81564
81571
81578
81584
81591
81598
81604
'81671
81611
81677
81617
655
81624
81631
81637
81644
81651
81657
81664
81684
656
81690
81697
81704
81710
81717
81723
81730
81737
81743
81750
657
81757
81763
81770
81776
81783
81790
81796
81803
81809
81816
658
81823
81829
81836
81842
81849
81856
81862
81869
81875
81882
659
81889
81895
81902
81968
81908
81974
81915
81981
81921
81987
81928
81935
81941
82007'
81948
82014
660
81954
81961
81994
82000
661
82020
82027
82033
82040
82046
82053
82060
82066
82073
82079
662
82086
82092
82099
82105
82112
82119
82125
82132
82138
82145
663
82151
82158
82164
82171
82178
82184
82191
82197
82204
82210
664
665
82217
82223
82230
82236
82243
82249
82256
82263
82269
82334
82276
82282
82289
8229"5
82302
82308
82315
82321
82328
82341
666
82347
82354
82360
82367
82373
82380
82387
82393
82400
82406
667
82413
82419
82426
82432
82439
82445
82452
82458
82465
82471
668
82478
82484
82491
82497
82504
82510
82517
82523
82530
82536
669
82543
82549
82556
82562
82569
82575
82582
82588
82595
82601
670
82607
82614
82620
82627
82633
82640
82646
82653
82659
82666
671
82672
82679
82685
82692
82698
82705
82711
82718
82724
82730
672
- 82737
82743
82750
82756
82763
82769
82776
82782
82789
82795
673
82802
82808
82814
82821
82827
82834
82840
82847
82853
82860
674
82866
82872
82879
82885
82892
82898
82905
82911
82918
82982
82924
675
82930
82937
82943
82950
82956
82963
82969
82975
82988
676
82995
83001
83008
83014
83020
83027
83033
83040
83046
83052
677
83059
83065
83072
83078
83085
83091
83097
83104
83110
83117
678
83123
83129
83136
83142
83149
83155
83161
83168
83174
83181
679
680
83187
83193
83200
83206
83213
83219
83225'
83289
83232
83296
83238
83302
83245
83308
83251
83257
83264
83270
83276
83283
681
83315
83321
83327
83334
83340
83347
83353
83359
83366
83372
682
83378
83385
83391
83398
83404
83410
83417
83423
83429
83436
683
83442
83448
83455
83461
83467
8.3474
83480
8.3487
83493
83499
684
685
83506
83569
83512
83575
83518
83525
83531
83537
83601
83544
83607
83550
83613
83556
83620
83563
83626
83582
83588
83594
686
83632
83639
83645
83651
83658
83664
83670
83677
83683
83689
687
83696
83702
83708
83715
83721
83727
83734
83740
83746
83753
688
689
83759
83822
83765
83828
83771
83835
83778
83841
83784
83847
83790
83853
83797
83860
83803
83866
83809
83872
83816
83879
! 6
690
83885
83891
83897
83904
83910
83916
83923
83929
83935
83942
691
83948
83954
83960
83967
83973
83979
83985
83992
83998
84004
1 1
692
84011
84017
84023
84029
84036
84042
84048
84055
84061
84067
2 1
693
84073
84080
84086
84092
84098
84105
84111
84117
84123
84130
3 2
694
84136
84142
84148
84155.
84161
84167
84173
84180
84186
84248
84192
84255
4 2
5 3
695
84198
84205
84211
84217
84223
84230
84236
84242
696
84261
84267
84273
84280
84286
84292
84298
84305
84311
84317
6 , 4
697
84323
84330
84336
84342
84348
84354
84361
84367
84373
84379
7 ! 4
698
84386
84392
84398
84404
84410
84417
84423
84429
84435
84442
8 5
699
84448
84454
84460
84466
84473
84479
84485
84491
84497
84504
9 ; 5
No.
0
1
2
3
4
5
6
7
8
9
Pag
e602]
TABLE 42.
IjOgarithms of Numbers.
No. 7000 7600.
Log. 84510 88081. 1
No.
0
1
i
8 1
4
6 1
6
7 1
8
1
700
701
702
703
704
84510
84572
84634
84696
84757
84516
84578
84640
84796
84763
84522
84584
84646
84708
84770
84528
84590
84652
84714
84776
84535
84597-
84658 1
84720
84782
84541
84603
84665
84726
84788
84547 84553
84609 84615
84671 84677
84733 84739
84794 ! 84800
84559
84566
1
1
7
84621 !
84683 i
84745 !
84807 ;
84628
84689
84751
84813
1
2 i
3 I
.4
5 !
6 i
7 -i
8
9
1
1
2
3
4
4
5
6
6
705
706
707
708
709
710
711
712
713
714
84819
84880
■ 84942
85003
85065
84825 {
84887
84948
85009
85071 '
84831
84893
84954
85016
85077
85138
85199
85260
85321
85382
84837
84899
84960
• 85022
85083
84844
84905
84967
85028
85089
84850 1
84911 '
84973 '
85034 <
85095 i
85156
85217
85278
85339
85400
84856 i 84862
84917 ! 84924
84979 84985
85040 85046
85101 ! 85107
85163 85169
84868 :
84930 i
84991
85052
85114
84874
84936
84997
85058
85120
85126
85187
85248
85309
85370
85132
85193
85254
85315
85376
85144
85205
85266
85327
85388
85150
85211
85272
85333
85394
85175
85236
85297
85358
85418
85181
85242
85303
85364
85425
85224 '
85285
85345
85406
85291
85352
85412
715
716
717
718
719
85431
85491
85552
85612
85673
85437
85497
85558
85618
85679
85443
85503
85564
85625
85685
85449
85509
85570
85631
85691
85455
85516
85576
85637
85697
85461
85522
85582
85643
85703
85467 85473
85528 85534
85588 85594
85649 1 85655
85709 i 85715
85479 1
85540
85600
85661
85721
85485
85546
85606
85667
85727
720
721
722
723
724
725
726
727
728
729
85733
85794
85854
85914
85974
85739
85800
85860
85920
85980
85745
85806
85866
85926
85986
85751
85812
85872
85932
85992
86052
86112
86171
86231
86291
85757
85818
85878
85938
85998
85763
85824
85884
85944
86004
86064
86124
86183
86243
86303
85769 : 85775
85830 1 85836
85890 1 85896
85950 85956
85781
85842
85902
85962
86022
85788
85848
85908
85968
86028
86088
86147
86207
86267
86326
86386
86445
86504
86564
86623
86010
86070 ■'
86130
86189
86249
86308
86016
1
2
3
4
5
6
7
8
9
6
1
1
2
2
3
4
4
5
5
86034
86094
86153
86213
86273
86040
86100
86159
86219
86279
86046
86106
86165
86225
86285
86058
86118
86177
86237
86297
86076
86136
86195
86255
86314
86082
86141
86201
86261
86320
730
. 731
732
733
734
86332
86392
86451
86510
86570
86338
86398
86457
86516
86576
86635
86694
86753
86812
86870
86344
86404
86463
86522
86581
86641
86700
86759
86817
86876
86935
86994
87052
87111
87169
86350
86410
86469
86528
86587
86646
86705
86764
86823
86882
86356
86415
86475
86534
86593
86362
86421
86481
86540
86599
86368 i 86374
86427 ■ 86433
86487 86493
8a546 86552
86605 86611'
86380
86439
86499
86558
86617
735
736
737
738
739
86629
86688
86747
86806
86864
86652
86711
86770
86829
86888
86658
86717
86776
86835
86894
86664 86670 i 86676
86682
86741
86800
86859
86917
86723
86782
.86841
86900
86729 86735
86788 86794
86847 1 86853
86906 1 86911
740
741
742
743
744
86923
86982
87040
87099
87157
86929
86988
87046
87105
87163
86941
86999
87058
87116
87175
86947
87005
87064
87122
87181
86953
87011
87070
87128
87186
86958
87017
87075
87134
87192
86964
87023
87081
87140
87198
1 86970
87029
1 87087
87146
87204
86976
87035
87093
87151
87210
87268
87326
87384
87442
87500
745
746
747
748
749
87216
87274
87332
87390
87448
87221
87280
87338
87-396
87454
87227
87286
87344
87402
87460
87233
87291
87349
87408
87466
87239
87297
87355
87413
87471
87245
87303
87361
87419
87477
87251
87309
87367
87425
87483
87256
87315
87373
87431
87489
87262
87320
87379
87437
87495
1
2
3
4
5
6
7
8
9
5
750
751
752
753
754
87506
87564
87622
87679
87737
87512
87570
87628
1 87685
87743
87518
87576
87633
87691
87749
87523
87581
87639
87697
87754
87529
87587
87645
87703
87760
87535
87593
87651
87708
87766
87541
87599
87656
87714
87772
87547
87604
87662
87720
87777
87552
87610
87668
87726
87783
875"58
87616
87674
87731
87789
1
1
2
2
3
3
4
4
5
755
756
757
758
759
87795
87852
87910
87967
88024
87800
87858
87915
87973
88030
87806
87864
; 87921
! 87978
88036
87812
87869
87927
87984
88041
87818
87875
87933
87990
88047
87823
87881
87938
87996
88053
87829
87887
87944
88001
88058
87835
87892
87950
88007
88064
87841
87898
87955
88013
88070
87846
87904
87961
88018
88076
No.
0
1
1 ^
8
4
5
6
'
8
»
1
TABLE 42.
[Page 603
Logarithms of Numbers.
No.
7600 8200.
Log. 88081 91381. 1
No.
0
1
2
8
*
5
6
7
8
9
760
761
88081
88138
88087
88144
88093
88150
88098
88156
88104
88161
88110
88167
88116
88173
88121
88178
88127
88184
88133
88190
1 6
762
88195
88201
88207
88213
88218
88224
88230
88235
88241
88247
1 1
763
88252
88258
88264
88270
88275
88281
88287
88292
88298
88304
2 1
764
765
88309
"88366
88315
88"372
88321
88326
88332
88338
88343
88349
88406
88355
88412
88360
88417
3 i 2
A O
88377
88383
88389
88:395
88400
5
6
7
3
4
4
766
88423
88429
88434
88440
•88446
88451
88457
88463
88468
88474
767
88480
88485
88491
88497
88502
88508
88513
88519
88525
88530
768
88536
88542
88547
88553
88559
88564
88570
88576
88581
88587
769
88593
88598
88604
88610
88615
88672
88621
88677
88627
88683
88632
88689
88638
88694
88643
88700
9 1 5
770
88649
88655
88660
88666
771
88705
88711
88717
88722
88728
88734
88739
88745
88750
88756
772
88762
88767
88773
88779
88784
88790
88795
88801
88807
88812
773
88818
88824
88829
88835
88840
88846
88852
88857
88863
88868
774
775
88874
88930
88880
88885
88891
88897
88902
88908
88913
88919
88975
88925
88936
88941
88947
88953
88958
88964
88969
88981
776
88986
88992
88997
89003
89009
89014
89020
89025
89031
89037
777
89042
89048
89053
89059
89064
89070
89076
89081
89087
89092
778
89098
89104
89109
89115
89120
89126
89131
89137
89143
89148
779
89154
89159
89165
89170
89176
89182
89237
89187
89193
89198
89204
89260
780
89209
89215
89221
89226
89232
89243
89248
89254
781
89265
89271
89276
89282
89287
89293
89298
89304
89310
89315
782
89321
89326
89332
89337
89343
89348
89354
89360
89365
89371
783
89376
89382
89387
- 89393
89398
89404
89409
89415
89421
89426
784
89432
89437
89443
89448
89454
89459
89515
89465
89520
89470
89526
89476
89531
89481
89537
785
89487
89492
89498
89504
89509
786
89542
89548
89553
89559
89564
89570
89575
89581
89586
89592
787
89597
89603
89609
89614
89620
89625
89631
89636
89642
89647
788
89653
89658
89664
89669
89675
89680
89686
89691
89697
89702
789
790
89708
89713
89719
89724
89730
89735
89741
89746
89752
89757
89763
89768
89774
89779
89785
89790
89796
89801
89807
89812
791
89818
89823
89829
898^4
89840
89845
89851
89856
89862
89867
792
89873
89878
89883
89889
89894
89900
89905
89911
89916
89922
793
89927
89933
89938
89944
89949
89955
89960
89966
89971
89977
794
89982
89988
89993
89998
90004
90009
90015
90069
90020
90075
90026
90080
90031
90086
795
90037
90042
90048
90053
90059
90064
796
90091
90097
90102
90108
90113
90119
90124
90129
90135
90140
797
90146
90151
90157
90162
90168
90173
90179
90184
90189
90195
798
90200
90206
90211
90217
90222
90227
90233
90238
90244
90249
799
800
90255
90309
90260
90266
90271
90325
90276
90282
90287
90293
90:347
90298
90352
90;304
90358
90314
90320
90331
90336
90342
801
90363
90369
90374
90380
90385
90390
90396
90401
90407
90412
802
90417
90423
90428
90434
90439
90445
90450
90455
90461
9046()
803
90472
90477
90482
90488
90493
90499
90504
90509
90515
90520
804
90526
90531
90536
90542
90547
90553
90558
90563
90617
90569
90623"
90574
90628
805
90580
90585
90590
90596
90601
90607
90612
806
90634
90639
90644
90650
90655
90660
90666
90671
90677
90682
807
90687
90693
90698
90703
90709
90714
90720
90725
90730
907:36
808
809
90741
90795
90747
90800
90752
90806
90757
90811
90763
90816
90768
90822
90773
90827
90779
90832
90886
90784
90838
90891
90789
90843
5
810
90849
90854
90859
90865
90870
90875
90881
90897
811
90902
90907
90913
90918
90924
90929
90934
90940
90945
90950
1
1
812
90956
90961
90966
90972
90977
90982
90988
90993
90998
91004
2
1
813
91009
91014
91020
91025
91030
91036
91041
91046
91052
91057
3
2
814
91062
91068
91073
91078
91132^
91084
91137
91089
91142
91094
91148
91100
91153
91105
91110
4
5
2
3
815
91116
91121
91126
91158
91164
816
91169
91174
91180
91185
91190
91196
91201
91206
91212
91217
6
3
817
91222
91228
91233
91238
91243
91249
91254
91259
91265
91270
7
4
818
91275
91281
91286
91291
91297
91302
91307
91312
91318
91323
8
4
819
91328
91334
91339
91344
91350
91355
91360
91365
91371
91376
9
5
No.
0
1
2
3
4
5
«
7
8
9
1
Page 604]
TABLE 42.
Logarithms
of Numbers.
No.
8200 8800.
Log. 91381 94448
No.
0
1
2
S
4
5
6
7
8
9
1
820
821
91381
91434
91387
91440
91392
91445
91397
91450
91403
91466
91408
91461
91413
91466
91418 91424
91429
91482
6
91471
91477
822
91487
91492
91498
91503
91608
91514
91619
91524
91629
91535
1
1
823
91540
9154»
91551
91556
91561
91566
91572
91577
91682
91687
1
824
91593
91598
91603
91609
91614
91619
91624
91630 91635
91640
3
4
2
3
4
4
6
5
825
91645
91661
91656
91661
91666
91672
91677
91682 91687
91693
826
91698
91703
91709
91714
91719
91724
91730
91735 91740
91745
6
827
91751
91756
91761
91766
91772
91777
91782
91787 91793
91798
828
91803
91808
91814
91819
91824
91829
91834
91840 91845
91850
8
9
829
91855
91861
91866
91871
91876
91882
91887
91892 91897
91903
830
91908
91913
91918
91924
91929
91934
91939
91944 91950
91955
831
91960
91965
91971
91976
91981
91986
91991
91997 92002
92007
832
92012
92018
92023
92028
92033
92038
92044
92049 92054
92059
833
92065
92070
92075
92080
92085
92091
92096
92101 92106
92111
834
92117
92122
92127
92132
92137
92143
92148
92153 92158
92205' 92210
92163
835
92169
92174
92179
92184
92189
92195
92200
92215
836
92221
92226
92231
92236
92241
92247
92252
92257 92262
92267
837
92273
92278
92283
92288
92293
92298
92304
92309 92314
92319
838
92324
92330
92335
92340
92345
92360
92355
92361 92366
92371
839
92376
92381
92387
92392
92397
92402
92454
92407
92459
92412 92418
92464 92469
92423
92474
840
92428
92433
92438
92443
92449
841
92480
92485
92490
92495
92500
92505
92511
92616 92521
92526
842
92531
92536
92542
92547
92552
92557
92562
92567 92572
92578
843
844
92583
92634
92588
92639
92593
92645
92598
92650
92603
92655
92609
92660
92614 J
92665
92619 92624
92670 92676
92722 92727
92629
92681
5
845
92686
92691
92696
92701
92706
92711
92716
92732
846
92737
92742
92747
92752
92758
92763
92768
92773 92778
92783
1
2
1
1
9
847
92788
92793
92799
92804
92809
92814
92819
92824 92829
92834'
848
92840
92845
92860
92855
92860
92865
92870
92876 92881
92886
849
92891
92896
92901
92906
92911
92916
92921
92927
92932
92983
92937
4
5
2
3
850
92942
92947
92952
92967
92962
92967
92973
92978
92988
851
92993
92998
93003
93008
93013
93018
93024
93029 93034
93039
6
3
852
93044
93049
93054
~ 93059
93064
93069
93075
93080 93085
93090
7
4
853
93095
93100
93106
93110
93115
93120
93125
93131 93136
93141
8
4
854
93146
93151
93156
93161
93166
93217
93268
93171
93222
93273
93176
93181 93186
93192
9
5
855
856
93197
93247
93202
93252
93207
93258
93212
93263
93227
93278
93232 93237
93283 93288
93242
93293
857
93298
93303
93308
93313
93318
93323
93328
93334 93339
93344
858
93349
93354
93359
93364
93369
93374
93379
93384 93389
93394
859
93399
93404
93409
93414
93420
93425
93430
93435
93440
93490
93445
860
93450
93455
93460
93465
93470
93475
93480
93486
93495
861
93500
93505
93510
93515
93520
93526
93631
93536 : 93541
93546
862
93551
93556
93561
93566
93571
93576
93581
93586 93591
93596
863
93601
93606
93611
93616
93621
93626
93631
93636 93641
93646
864
865
93651
93702
93656
93707
93661
93712
93666
93717
93671
93722
93676
93727
93682
93687 93692
93737 93742
93697
93747
93732
866
93752
93757
93762
93767
93772
93777
93782
93787 93792
93797
867
93802
93807
93812
93817
93822
93827
93832
93837 93842
93847
868
869
93852
93902
93857
93907
93862
93912
93962
93867
93917
93967
93872
93922
93877
93927
93882
93932
93982
93887 93892
93937 93942
9398; "93992
93897
93947
4
870
93952
93957
93972
93977
93997
871
94002
94007
94012
94017
94022
94027
94032
94037 i 94042
94047
1
0
872
94052
94057
94062
94067
94072
94077
94082
94086 94091
94096
2
1
873
94101
94106
94111
94116
94121
94126
94131
94136 1 94141
94146
3
1
874
94151
94156
94161
94166
94171
94176
94181
94186
94191
94240
94196
94245
4
5
2
2
875
94201
94206
94211
94216
94221
94226
94231
94236
876
94250
94255
94260
94265
94270
94275
94280
94285
94290
94295
6
2
877
94300
94305
94310
94316
94320
94325
94330
94335
94340
94345
7
3
878
94349
94354
94359
94364
94369
94374
94379
94384
94389
94394
8
3
879
94399
94404
94409
94414
94419
94424
94429
6
94433
94438
94443
9
4
No.
0
1 ■
2
3
4
5
i '
' 8
9
1
TABLE 42.
[Page 605
Logarithms
of Numbers.
No.
8800 9400.
L
og. 94448 97313
No.
0
94448
94498
1
2
3
4
9
6
7
8
9
1
880
881
94453
94503
94458
94507
94463
94512
94468
94517
94473
94522
94478
94527
94483
94532
94488
94537
94493
94542
5
882
94547
94552
94557
94562
94567
94571
94576
94581
94586
94591
1
1
883
94596
94601
94606
94611
94616
94621
94626
94630
94635
94640
2
1
884
8'85
94645
94694
94650
94699
94655
94704
94660
94709
94665
94670
94675
94724
94680
94729
94685
94734
94689
94738
3
4
5
6
7
8
9
2
2
3
3
4
4
5
94714
94719
886
94743
94748
94753
94758
94763
94768
94773
94778
94783
94787
887
94792
94797
94802
94807
94812
94817
94822
94827
94832
94836
888
94841
94846
94851
94856
94861
94866
94871
94876
94880
94885
889
890
94890
94939
94895
94900
94905
94910
94915
94919
94924
94929
94934
94983
94944
94949
94954
94959
94963
94968
94973
94978
891
94988
94993
94998
95002
95007
95012
95017
95022
95027
95032
892
95036
95041
95046
95051
95056
95061
95066
95071
95075
95080
893
95085
95090
95095
95100
95105
95109
95114
95119
95124
95129
894
95134
95139
95143
95148
95153
95158
95163
95168
95173
95221
95177
95226
895
95182
95'187
95192
95197
95202
95207
95211
95216
896
95231
95236
95240
95245
95250
95255
95260
95265
95270
95274
897
95279
95284
95289
95294
95299
95303
95308
95313
95318
95323
898
95328
95332
95337
95342
95347
95352
95357
95361
95366
95371
899
900
95376
95381
95386
95390
95395
95400
95405
95410
95415
95419
95424
95429
95434
95439
95444
95448
95453
95458 95463
95468
901
95472
95477
95482
95487
95492
95497
95501
95506 95511
95516
902
95521
95525
95530
95535
95540
95545
95550
95554 95559
95564
903
95569
95574
95578
95583
95588
95593
95598
95602 , 95607
95612
904
95617
95622
95626
95631
95636
95641
95646
95650
95655
95703
95660
95708
905
95665
95670
95674
95679
95684
95689
95694
95698
906
95713
95718
95722
95727
95732
95737
95742
95746 i 95751
95756
907
95761
95766
95770
95775
95780
95785
95789
95794 1 95799
95804
908
95809
95813
95818
95823
95828
95832
95837
95842 1 95847
95852
909
' 95856
95861
95866
95914
95871
95918
95875
95923
95880
95885
95890 ! 95895
95938 95942
95899
95947
910
95904
95909
95928
95933
911
95952
95957
95961
95966
95971
95976
95980
95985 I 95990
95995
912
95999
96004
96009
96014
96019
96023
96028
96033
96038
96042
913
96047
96052
96057
96061
96066
96071
96076
96080
96085
96090
914
96095
96099
96104
96109
96114
96118
96123
96128
96133
96137
915
96142
96147
96152
96156
96161
96166
96171
96175
96180
96185
916
96190
96194
96199
96204
96209
96213
96218
96223 t 96227
96232
917
96237
96242
96246
96251
96256
96261
96265
96270
96275
96280
918
96284
96289
96294
96298
96303
96308
96313
96317
96322
9(i327
919
96332
96336
96341
96388
96346
96393
96350
96398
96355
96402
96360
96407
96365
96369
96374
920
96379
96384
96412
96417
96421
921
96426
96431
96435
96440
96445
96450
96454
96459 ! 96464
96468
922
96473
96478
96483
96487
96492
96497
96501
96506
96511
96515
923
96520
96525
96530
96534
96539
96544
96548
96553
96558
96562
924
925
96567
96572
96577
96581
96586
96591
96595
96600
96605
96609
96614
96619
96624
96628
96633
96638
96642
96647
96652
96(556
926
96661
96666
96670
96675
96680
96685
96689
96694
96699
96703
927
96708
96713
96717
96722
96727
96731
96736
96741
96745
96750
928
929
930
96755
96802
96759
96806
96853
96764
96811
96858
96769
96816
96862
96774
96820
96778
96825
96783
96830
96788
96834
96881
96792
96839
96886
96797
96844
4
96848
96867
96872
96876
96890
931
96895
96900
96904
96909
96914
96918
96923
96928
96932
96937
1 : 0
932
96942
96946
96951
96956
96960
96965
96970
96974
96979
96984
2 1
933
96988
96993
96997
97002
97007
97011
97016
97021
97025
97030
3 1
934
935
97035
970.39
97044
97049
97053
97058
97063
97067
97072
97118
97077
97123"
4
5
2
• 2
97081
97086
97090
97095
97100
97104
97109
97114
936
97128
97132
97137
97142
97146
97151
97155
97160
97165
97169
6
2
937
97174
97179
97183
97188
97192
97197
97202
97206
97211
97216
7
3
938
97220
97225
97230
97234
97239
97243
97248
97253
97257
97262
8
3
939
No.
97267
97271
97276
97280
97285
97290
97294
97299
97304
97308
^
4
0 1
o
3
4
5
6
7
8
9
1
Page 606]
TABLE 42.
Logarithms
of Numbers.
No.
9400 10000.
Log. 97313-
99996.
No.
0
1
i
8
4
5
*
1
8 1 »
940
97313
97317
97322
97327
97331
97336
97340
97345
1
97350 97354
5
941
97359
97364
97368
97373
97377
97382
97387
97391
97396 97400
942
97405
97410
97414
97419
97424
97428
97433
97437
97442 97447
1 1
943
97451
97456
97460
97465
97470
97474
97479
97483
97488 97493
2 1
944
945
97497
97502
97506
97511
97516
97520
97525
97529
97534
97539
97585
3 ! 2
4 1 2
97543
97548
97552
97557
97562
97566
97571
97575
97580
946
97589
97594
97598
97603
97607
97612
97617
97621
97626 \ 97630
5 1 3
947
97635
97640
97644
97649
97653
97658
97663
97667
97672 97676
6 i 3
948
97681
97685
97690
97695
97699
97704
97708
97713
97717 ! 97722
7 ! 4
949
950'
97727
97731
, 97736
97740
97745
97791
97749
97795
97754
97800
97759
97804
97763 i 97768
97809^ 97813
8 ; 4
9 i 5
97772
97777
97782
97786
951
97818
97823
97827
97832
97836
97841
97845
97850
97855 ' 97859
952
97864
97868
97873
97877
97882
97886
97891
97896
97900 97905
953
97909
97914
97918
97923
97928
97932
97937
97941
97946 i 97950
954
97955
97959
97964
97968
97973
97978
97982
98028
97987
98032
97991 1 97996
955
98000
98005
98009
98014
98019
98023
9803.7 1 98041
956
98046
98050
98055
98059
98064
98068
98073
98078
98082 ! 98087
957
98091
98096
98100
98105
98109
98114
98118
98123
98127 1 98132
958
98137
98141
98146
98150
98155
98159
98164
98168
98173 1 98177
959
98182
98227
98186
98191
98195
98200
98245
98204
98209
98214
98218 ! 98223
98263 98268
960
98232
98236
98241
98250
98254
98259
961
98272
98277
98281
98286
98290
98295
98299
98304
98308 98313
962
98318
98322
98327
98331
98336
98340
98345
98349
98354 98358
963
98363
98367
98372
98376
98381
98385
98390
98394
98399 98403
964
965
98408
98453
98412
98457
98417
98421
98426
98430
98435
98439
98444 , 98448
98462
98466
98471
98475
98480
98484
98489 98493.
966
98498
98502
98507
98511
98516
98520
98525
98529
98534 98538
967
98543
98547
98552
98556
98561
98565
98570
98574
98579 1 98583
968
98588
98592
98597
98601
98605
98610
98614
98619
98623 98628
969
970
98632
98637
98641
98646
98650
98655
98659
98664
98709
98668 : 98673
98713 98717
98677
98682
98686
98691
98695
98700
98704
971
98722
98726
98731
98735
98740
98744
98749
98753
98758 98762
972
98767
98771
98776
98780
98784
98789
98793
98798
98802 98807
973
98811
98816
98820
98825
98829
98834
98838
98843
98847 : 98851
974
98856
98860
98865
98869
98874
98878
98883
98887
98892
98896
98941
975
9890'0
98905
98909
98914
98918
98923
98927
98932
98936
976
98945
98949
98954
98958
98963
98967
98972
98976
98981 98985
977
98989
98994
98998
99003
99007
99012
99016
99021
99025
99029
978
99034
99038
99043
99047
99052
99056
99061
99065
99069
99074
979
99078
99083
99127
99087
99092
99096
99140
99100
99145
99105
99149
99109
99154
99114
99118
99162
980
99123
99131
99136
99158
981
99167
99171
99176
99180
99185
99189
99193
99198
99202
99207
982
99211
99216
99220
99224
99229
99233
99238
99242
99247
99251
983
99255
99260
99264
99269
99273
99277
99282
99286
99291
99295
984
99300
99304
99308
99313
99317
99322
99326
99330
99335
99339
985
99344
99348
99352
99357
99361
99366
99370
99374
99379
99383
986
99388
99392
99396
99401
99405
99410
99414
99419
99423
99427
987
99432
99436
99441
99445
99449
99454
99458
99463
99467
99471
988
989
990
99476
99520
99480
99524
99484
99528
99489
99533
99493
99537
99498
99542
99502
99546
99506
99550
99511 1 99515
99555
99559
99603
4
99564
99568
99572
99577
99581
99585
99590
99594
99599
991
99607
99612
99616
99621
99625
99629
99634
99638
99642
99647
1 ' 0
992
99651
99656
99660
99664
99669
99673
99677
99682
99686
99691
2 1
993
99695
99699
99704
99708
99712
99717
99721
99726
99730
99734
3 1
994
995
99739
99782'
99743
99787
99747
99791
99752
99795
99756
99760
99804~
99765
99808
99769
99813
99774
99817
99778
99822
4 2
5 i 2
99800
996
99826
99830
99835
99839
99843
99848
99852
99856
99861 99865
6 2
997
99870
99874
99878
99883
99887
99891
99896
99900
99904 99909
7 3
998
99913
99917
99922
99926
99930
99935
99939
99944
99948 99952
n !
999
99957
99961
99965
99970
99974
99978
99983
99987
99991
99996
0
9 ; 4
No.
0
1
2
8
4
5
a
7
8
TABLE 43. [Page 607
Logarithmic Sines, Tangents, and Secants to every Point and Quarter Point of the Compass.
Points.
Sine. 1 Cosine. 1 Tangent.
Cotangent.
Secant.
Cosecant.
0
1
Inf. neg. 10. 00000 Inf. neg.
8.69080 9.99948 j 8.69132
8.99130 i 9.99790 8.99340
9.16652 9.99527 i 9.17125
infinite.
11. 30868
11.00660
10. 82875
10.00000
10.00052
10. 00210
10. 00473
Infinite.
11. 30920
11. 00870
10. 83348
8
71
1
u
9. 29024
9. 38557
9. 46282
9. 52749
9. 99157
9. 98679
9. 98088
9. 97384
9. 29866
9. 39879
9. 48194
9. 55365
10. 70134
10. 60121
10. 51806
10. 44635
10. 00843
10. 01321
10. 01912
10. 02616
10. 70976
10. 61443
10. 53718
10. 47251
7
6|
6J
6i
2
2i
21
9. 58284
9. 63099
9. 67339
9. 71105
9. 96562
9. 95616
9. 94543
9. 93335
9. 61722
9. 67483
9. 72796
9. 77770
10. 38278
10. 32517
10. -27204
10. 22230
10. 03438
10. 04384
10. 05457
10. 06665
10.41716
10. 36901
10. 32661
10. 28895
6
5^
5i
3
3i
31
9.74474
9. 77503
9. 80236
9. 82708
9. 91985
9. 90483
9. 88819
9. 86979
9. 82489
9. 87020
9.91417
9. 95729
10. 17511
10. 12980
10. 08583
10. 04271
10. 08015
10. 09517
10. 11181
10. 13021
10. 25526
10.22497
10. 19764
10. 17292
5
4|
^
4i
4
9. 84949
9. 84949
10.00000
10. 00000 10. 15051
10. 15051
4
Cosine.
Sine.
Cotangent.
Tangent. Cosecant.
Secant.
Points.
Page 608j
TABLE U.
Log. Sines, Tangents, and Secants.
0"
179°
M.
Hour A. M.
Hour p. M.
Sine.
Diff. 1'.
Cosecant.
Tangent.
Diff. 1'.
Cotangent.
Secant.
Cosine.
M.
0
12 0 0
0 0 0
Inf. neg.
lniinit«.
Inf. neg.
Infinite.
10. 00000
10.00000
60
1
11 59 52
0 8
6.46373 30103
13. 53627
6. 46373
30103
13.53627
00000
00000
59
2
59 44
0 16
76476 17609
23524
76476 17609
23524
00000
00000
58
3
59 3t5
0 24
94085 12494
05915
94085 12494
05915
00000
00000
57
4
59 28
0 3?
0 0 40
7.06579 j 9691
7. 16270 7918
12. 93421
7. 06579
9691
12. 93421
12. 83730
00000
00000
56
55
5
11 59 20
12. 83730
7. 16270
7918
10.00000
10. 00000
6
59 12
0 48
24188 6694
75812
24188
6694
75812
00000
00000
54
7
59 4
0 56
30882 1 5800
69118
.30882
5800
69118
00000
00000
53
8
58 56
1 4
36682 5115
63318
36682
5115
63318
00000
00000
52
9
10
58 48
11 58 40
1 12
41797 4576
58203
41797
4576
58203
00000
00000
51
50
0 1 20
7. 46373
4139
12. 53627
7. 46373
4139
12. 53627
10. 00000
10. 00000
11
58 32
1 28
50512
3779
49488
50512
3779
49488
00000
00000
49
12
58 24
1 36
54291
3476
45709
54291
3476
45709
00000
00000
48
13
58 16
1 44
57767
3218
42233
57767
3219
42233
00000
00000
47
14
15
58 8
1 52
60985
2997
39015
60986
2996
39014
00000
00000
10. 00000
46
45
11 58 0
0 2 0
7. 63982
2802
12. 36018
7. 63982
2803
12. 36018
10. 00000
16
57 52
2 8
66784
2633
33216
66785
2633
33215
00000
00000
44
17
57 44
2 16
69417
2483
30583
69418
2482
30582
00001
9. 99999
43
18
57 36
2 24
71900
2348
28100
71900
2348
28100
00001
99999
42
19
20
57 28
11 57 20
2 32
0 2 40
74248
7. 76475
2227
2119
25752
12. 23525
74248
7. 76476
2228
25752
00001
99999
41
'40
2119
12. 23524
10. 00001
9. 99999
21
57 12
2 48
78594
2021
21406
78595
2020
21405
00001
99999
39
22
57 4
2 56
80615
1930
19385
80615
1931
19385
00001
99999
38
23
56 56
3 4
82545
1848
17455
82546
1848
17454
00001
99999
37
24
56 48
3 12
0 3 20
84393
1773
15607
12. 13834
84.394
1773
1704
15606
00001
99999
36
35
25
11 56 40
7.86166 1 1704
7. 86167
12. 13833
10. 00001
9. 99999
26
56 32
3 28
87870 1 1639
12130
87871
1639
12129
00001
99999
34
27
56 24
3 36
89509 ! 1579
10491
89510
1579
10490
00001
99999
33
28
56 16
3 44
91088
1524
08912
91089
1524
08911
00001
99999
32
29
56 8
3 52
92612
1472
07388
92613 1473
07387
00002
99998
31
30
11 56 0
0 4 0
7. 94084
1424
12. 05916
7. 94086
1424
12. 05914
10. 00002
9. 99998
30
31
55 52
4 8
95508
137£i
04492
95510
1379
04490
00002
99998
29
32
55 44
4 16
96887
1336
03113
96889
1336
03111
00002
99998
28
33
55 36
4 24
98223
1297
01777
98225
1297
01775
00002
99998
27
34
55 28
4 32
99520
1259
00480
99522
1259
00478
00002
99998
9. 99998
26
25
35
11 55 20
0 4 40
8.00779 1 1223
11. 99221
8. 00781
1223
11.99219
10. 00002
36
55 12
4 48
02002
-1190
97998
02004
1190
97996
00002
99998
24
37
55 4
4 56
03192
1158
96808
03194
1159
96806
00003
99997
23
38
54 56
5 4
04350
1128
95650
04353
1128
95647
00003
. 99997
22
39
54 48
5 12,
0 5 20
05478
1100
94522
05481
1100
94519
00003
99997
21
40
11 54 40
8. 06578
1072
11. 93422
8. 06581
1072
11. 93419
10. 00003
9. 99997
20
41
54 32
5 28
07650
1046
92350
07653
1047
92347
00003
99967
19
42
54 24
5 36
08696
1022
91.304
08700
1022
91300
00003
99997
18
43
54 16
5 44
09718
999
90282
09722
998
90278
00003
99997
17
44
45
54 8
5 52
10717
976
89283
10720
976
89280
00004
99996
16
11 54 0
0 6 0
8. 11693
954
11. 88307
8. 11696
955
11. 88304
10. 00004
9. 99996
15
46
53 52
6 8
12647
934
87353
12651
934
87349
00004
99996
14
47
53 44
6 16
13581
914
86419
13585
915
86415
00004
99996
13
48
53 36
6 24
14495
896
85505
14500
895
85500
00004
99996
12
49
53 28
6 32
15391
877
84609
15395
878
84605
00004
99996
11
10
50
11 53 20
0 6 40
8. 16268
860
11. 83732
8. 16273
860
11. 83727
10. 00005
9. 99995
51
53 12
6 48
17128
843
82872
17133
843
82867
00005
99995
9
52
53 4
6 56
17971
827
82029
17976
828
82024
00005
99995
8
53
52 56
7 4
18798
812
81202
18804
812
81196
00005
99995
/
54
55
52 48
7 12
19610
797
80390
19616
797
80384
00005
99995
6
11 52 40
0 7 20
8. 20407
782
11. 79593
8. 20413
782
11. 79587
10. 00006
9. 99994
5
56
52 32
7 28
21189
769
78811
21195
769
78805
00006
99994
4
57
52 24
7 36
21958
755
78042
21964
756
78036
00006
99994
3
58
52 16
7 44
22713
743
77287
22720
742
77280
00006
99994
2
59
52 8
7 52
23456
730
76544
23462
730
76538
00006
99994
1
60
M.
52 0
8 0
24186
. 717
75814
24192
718
75808
00007
99993
0
Hour p. M.
Hour A. M.
Cosine.
Dlff.l'.
Secant.
Cotangent. Diflf.l'.
Tangent.
Cosecant.
Sine.
M.
90°
89°
-
TABLE 44.
[Page 609
1°
l,og. Sines, Tangents, and Secants
178°
M.
0
Hour A. M.
Hour p. M.
Sine.
Dia. 1'.
Cosecant.
Tangent.
Diff. 1'.
Cotangent.
Secant.
Cosine.
M.
11 52 0
0 8 0
8.24186
717
11. 75814
8. 24192
718
11. 75808
10. 00007
9. 99993
60
1
51 52
8 8
24903
706
75097
24910
706
75090
00007
99993
59
2
51 44
8 16
25609
695
74391
25616
696
74384
00007
99993
58
3
51 36
8 24
26304
684
73696
26312
684
73688
00007
99993
57
4
5
51 28
8 32
26988
673
73012
26996
673
73004
00008
10. 00008
99992
56
55
11 51 20
0 8 40
8. 27661
663
11. 72339
8. 27669
663
11. 72331
9. 99992
6
51 12
8 48
28324
653
71676
28332
654
71668
00008
99992
54
7
51 4
8 56
28977
644
71023
28986
643
71014
00008
99992
53
8
50 56
9 4
29621
634
70379
29629
634
70371
00008
99992
52
9
10
50 48
9 12
30255
624
69745
30263
625
69737
00009
99991
51
11 50 40
0 9 20
8. 30879
616
11. 69121
8. 30888
617
11.69112
10. 00009
9. 99991
50
11
50 32
9 28
31495
608
68505
31505
607
68495
00009
99991
49
12
50 24
9 36
32103
599
67897
32112
599
67888
00010
99990
48
13
50 16
9 44
32702
590
67298
32711
591
67289
00010
99990
47
14
50 8
9 52
33292
583
66708
33302
584
66698
00010
99990
46
45
15
11 50 0
0 10 0
8. 33875
575
11. 66125
8. 33886
575
11.66114
10. 00010
9. 99990
16
49 52
10 8
34450
568
65550
34461
568
65539
00011
99989
44
17
49 44
10 16
35018
560
64982
35029
561
64971
00011
99989
43
18
49 36
10 24
35578
553
64422
35590
553
64410
00011
99989
42
19
20
49 28
11 49 20'
10 32
0 10 40
36131
547
63869
36143
546
63857
00011
99989
41
8. 36678
539
11. 63322
8. 36689
540
11. 63311
10. 00012
9. 99988
40
21
49 12
10 48
37217
533
62783
37229
533
62771
00012
99988
39
22
49 4
10 56
37750
526
62250
37762
527
62238
00012
99988
38
23
48 56
11 4
38276
520
61724
38289
520
61711
00013
99987
37
24
48 48
11 12
38796
514
61204
38809
514
61191
00013
99987
36
25
11 48 40
0 11 20
8. 39310
508
11. 60690
8. 39323
509
11. 60677
10.00013
9. 99987
35
26
48 32
11 28
39818
502
60182
39832
502
60168
00014
99986
34
27
48 24
11 36
40320
496
59680
40334
496
59666
00014
99986
33
28
48 16
11 44
40816
491
59184
40830
491
59170
00014
99986
32
29
48 8
11 52
41307
485
58693
41321
486
58679
00015
99985
31
30
11 48 0
0 12 0
8. 41792
480
11. 58208
8. 41807
480
11. 58193
10. 00015
9. 99985
30
31
47 52
12 8
42272
474
57728
42287
475
57713
00015
99985
29
32
47 44
12 16
42746
470
57254
42762
470
57238
00016
99984
28
33
47 36
12 24
4.3216
464
56784
43232
464
567()8
00016
99984
27
34
35
47 28
12 32
43680
459
56320
43696
460
56304
00016
99984
26
11 47 20
0 12 40
8.44139
455
11. 55861
8. 44156
455
11. 55844
10. 00017
9. 99983
25
36
47 12
12 48
44594
450
55406
44611
450
55389
00017
99983
24
37
47 4
12 56
45044
445
54956
45061
446
54939
00017
99983
23
38
46 56
13 4
45489
441
54511
45507
. 441
54493
00018
99982
22
39
40
46 48
13 12
45930
436
54070
45948
437
54052
00018
To. 00018
99982
9. 99982
21
20
11 46 40
0 13 20
8. 46366
433
11, 53634
8. 46385
432
11. 53615
41
46 32
13 28
46799
427
5.3201
46817
428
53183
00019
99981
19
42
46 24
13 36
47226
424
52774
47245
424
52755
00019
99981
18
43
46 16
13 44
47650
419
52350
47669
420
52.331
00019
99981
17
44
46 8
13 52
48069
416
51931
48089
416
51911
00020
99980
16
15
45
11 46 0
0 14 0
8. 48485
411
11.51515
8. 48505
412
11. 51495
10. 00020
9. 99980
46
45 52
14 8
48896
408
51104
48917
408
51083
oa)2i
99979
14
47
45 44
14 16
49304
404
50696
49325
404
50675
00021
99979
13
48
45 36
14 24
49708
400
50292
49729
401
50271
00021
99979
12
49
45 28
14 32
50108
396
49892
50130
397
49870
00022
99978
11
10
50
11 45 20
0 14 40
8. 50504
393
11. 49496
8. 50527
393
11. 49473
10. 00022
9. 99978
51
45 12
14 48
50897
390
49103
50920
390
49080
00023
99977
9
52
45 4
14 56
51287
386
48713
51310
386
48690
00023
99977
8
/53
44 56
15 4
51673
382
48327
51696
383
48304
00023
99977
/
54
44 48
15 12
52055
379
47945
52079
380
47921
00024
99976
6
55
11 44 40
0 15 20
8. 52434
376
11. 47566
8. 52459
376
11. 47541
10. 00024
9. 99976
5
56
44 32
15 28
52810
373
47190
52835
373
47165
00025
99975
4
57
44 24
15 36
53183
369
46817
53208
370
46792
00025
99975
3
58
44 16
15 44
53552
367
46448
53578
367
46422
00026
99974
2
59
44 8
15 52
53919
363
46081
53945
363
46055
0002(1
99974
1
60
44 0
16 0
54282
360
45718
54308
361
45692
00026
99974
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff. 1'.
Secant.
Cotangent.
Diff. 1'.
Tangent.
Cosecant.
Sine.
M.
91°
88° 1
22489—03-
-39
Page 610]
TABLE 44.
2°
Log. Sines, Tangents, and Secants
177°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.l'.
Cosecant.
Tangent.
Diff. 1'.
Cotangent.
Secant.
Co.slne.
M.
0
11 44 0
0 16 0
8. 54282
360
11. 45718
8. 54308
361
11.45692
10. 00026
9. 99974
60
1
43 52
16 8
54642
357
45358
54669
358
45331
00027
99973
59
2
43 44
16 16
54999
355
45001
55027
355
44973
00027
99973
58
3
43 36
16 24
55354
351
44646
55382
352
44618
00028
99972
57
4
5
43 28
16 32
55705
349
44295
55734
349
44266
00028
99972
56
11 43 20
0 16 40
8. 56054
346
11. 43946
8. 56083
346
11.43917
10. 00029
9. 99971
55
6
43 12
16 48
56400
343
43600
5t>429
344
. 43571
00029
99971
54
1
43 4
16 56
56743
341
43257
56773
341
43227
00030
99970
53
8
42 56
17 4
57084
337
42916
57114
338
42886
00030
99970
52
9
10
42 48
17 12
57421
336
42579
57452
336
42548
00031
99969
51
11 42 40
0 17 20
8. 57757
332
11. 42243
8. 57788
333
11.42212
10. 00031
9. 99969
50
11
42 32
17 28
58089
330
41911
58121
330
41879
00032
99968
49
12
42 24
17 36
58419
328
41581
58451
328
41549
00032
99968
48
13
42 16
17 44
58747
325
41253
58779
326
41221
00033
99967
47
14
42 8
17 52
59072
323
40928
59105
323
40895
00033
99967
46
45
15
11 42 0
0 18 0
8. 59395
320
11. 40605
8. 59428
321
11. 40572
10. 00033
9. 99967
16
41 52
18 8
59715
318
40285
59749
319
40251
00034
99966
44
17
41 44
18 16
60033
316
39967
60068
316
39932
00034
99966
43
18
41 36
18 24
60349
313
39651
60384
314
39616
00035
99965
42
19
20
41 28
18 32
60662
311
39338
60698
311
39302
00036
99964
41
40
11 41 20
0 18 40
8. 60973
309
11. 39027
8. 61009
310
11. 38991
10. 00036
9. 99964
21
41 12
18 48
61282
307
38718
61319
307
38681
00037
99963
39
22
41 4
18 56
61589
305
38411
61626
305
38374
00037
99963
38
23
40 56
19 4
61894
302
38106
61931
303
38069
00038
99962
37
24
25
40 48
19 12
62196
301
37804
62234
301
37766
00038
99962
36
35~
11 40 40
0 19 20
8. 62497
298
11. 37503
8. 62535
299
11. 37465
10. 00039
9. 99961
26
40 32
19 28
62795
296
37205
62834
297
37166
00039
99961
34
27
40 24
19 36
63091
294
36909
63131
295
36869
00040
99960
33
28
40 16
19 44
63385
293
36615
63426
292
36574
00040
99960
32
29
30
40 8
19 52
63678
290
36322
63718
291
36282
00041
99959
31
11 40 0
0 20 0
8. 63968
288
11. 36032
8. 64009
289
11. 35991
10. 00041
9. 99959
30
31
39 52
20 8
64256
287
35744
64298
287
35702
00042
99958
29
32
39 44
20 16
64543
284
35457
64585
285
35415
00042
99958
28
33
39 36
20 24
64827
283
35173
64870
284
35130
00043
99957
27
34
39 28
20 32
65110
281
34890
65154
281
34846
00044
99956
26
35
11 39 20
0 20 40
8. 65391
279
11. 34609
8. 65435
280
11. 34565
10. 00044
9. 99956
25
36
3i^ 12
20 48
65670
277
34330
65715
278
34285
00045
99955
24
37
39 4
20 56
65947
276
34053
65993
276
34007
00045
99955
23
38
38 56
21 4
66223
274
33777
66269
274
33731
00046
99954
22
39
38 48
21 12
66497
272
33503
66543
273
33457
00046
99954
9. 99953
21
20
40
11 38 40
0 21 20
8. 66769
270
11. 33231
8. 66816
271
11. 33184
10. 00047
41
38 32
21 28
67039
269
32961
67087
269
32913
00048
99952
19
42
38 24
21 36
67308
267
32692
67356
268
32644
00048
99952
18
43
38 16
21 44
67575
266
32425
67624
266
32376
00049
99951
17
44
38 8
21 52
67841
263
32159
67890
264
32110
00049
99951
16
45
11 38 0
0 22 0
8. 68104
263
11. 31896
8. 68154
263
11. 31846
10. 00050
9. 99950
15
46
37 52
22 8
68367
260
31633
68417
261
31583
00051
99949
14
47
37 44
22 16
68627
259
31373
68678
260
31322
00051
99949
13
48
37 36
22 24
68886
258
31114
68938
258
31062
00052
99948
12
49
37 28
22 32
69144
256
30856
69196
257
30804
00052
99948
9. 99947
11
10
50
11 37 20
0 22 40
8. 69400
254
11. 30600
8. 69453
255
11. 30547
10. 00053
51
37 12
22 48
69654
253
30.346
69708
254
30292
00054
99946
9
52
37 4
22 56
69907
252
30093
69962
252
30038
00054
99946
8
53
36 56
23 4
70159
250
29841
70214
251
29786
00055
99945
7
54
36 48
23 12
0 23 20
70409
249
29591
70465
249
29535
00056
99944
6
55
11 36 40
8. 70658
247
11. 29342
8. 70714
248
11. 29286
10.00056
9. 99944
5
56
36 32
23 28
70905
246
29095
70962
246
29038
00057
99943
4
57
36 24
23 36
71151
244
28849
71208
245
28792
00058
99942
3
58
36 16
23 44
71395
243
28605
71453
244
28547
00058
99942
2
59
36 8
23 52
71638
242
28362
71697
243
28303
00059
99941
1
60
36 0
24 0
71880
240
28120
71940
241
28060
00060
99940
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff. 1'.
Secant.
Cotangent.
Diff.l'.
Tangent.
Cosecant.
Sine.
M.
92°
87°
TABLE 44.
[Page 611
3°
Log. Sines, Tangents, and Secants
176°
M.
Hour *. M.
Hour P. M.
Sine.
Difl. 1'.
Cosecant.
Tangent.
Diff. 1'.
Cotangent.
Secant.
Cosine.
M.
0
11 36 0
0 24 0
8. 71880
240
11. 28120
8. 71940
241
11. 28060
10. 00060
9. 99940
60
1
35 52
24 8
72120
239
27880
72181
239
27819
00060
99940
59
?.
35 44
24 16
72359
238
27641
72420
239
27580
00061
99939
58
8
35 36
24 24
72597
237
27403
72659
237
27341
00062
99938
0/
4
35 28
24 32
72884
235
27166
72896
236
27104
00062
99938
56
55
5
11 35 20
0 24 40
8. 73069
234
11. 26981
8. 73132
234
11. 26868
10. 00068
9. 99937
6
35 12
24 48
73303
232
26697
73366
234
26634
000«)4
99986
54
7
35 4
24 56
73535
232
26465
73600
232
26400
000(>1
99936
53
8
34 56
25 4
73767
230
26233
73832
231
26168
00065
99935
52
9
34 48
25 12
73997
229
26003
74063
229
25937
11. 25708
00066
10. 00066
99934
51
50
10
11 34 40
0 25 20
8. 74226
228
11. 25774
8. 74292
229
9. 99934
11
34 32
25 28
74454
226
25546
74521
227
25479
00067
99933
49
12
34 24
25 36
74680
226
25320
74748
226
25252
00068
99982
48
13
34 16
25 44
74906
224
25094
74974
225
25026
00068
99932
47
14
34 8
25 52
75130
223
24870
75199
224
24801
00069
99931
'9. 99930
46
45
15
11 34 0
0 26 0
8. 75353
222
11.24647
8. 75423
222
11. 24577 ! 10. 00070
18
33 52
26 8
75575
220
24425
75645
222
24355
00071
99929
44
17
33 44
26 16
75795
220
24205
75867
220
24183
00071
99929
43
18
33 36
26 24
76015
219
23985
76087
219
23913
00072
99928
42
19
33 28
26 82
76234
217
23766
76306
219
23694
00073
99927
41
40
?.o
11 33 20
0 26 40
8. 76451
216
11. 23549
8. 76525
217
11. 23475
10. 00074
9. 99926
21
33 12
26 48
76667
216
23333
76742
216
23258
00074
99926
39
22
33 4
26 56
76883
211
23117
76958
215
23042
00075
99925
38
28
82 56
27 4
77097
213
22903
77173
214
22827
00076
99924
37
24
32 48
27 12
77310
212
22690
77387
213
22613
00077
99923
36
35
2o
11 82 40
0 27 20
8. 77522
211
11. 22478
8. 77600
211
11. 22406
10. 00077
9. 99923
26
32 32
27 28
77733
210
22267
77811
211
22189
00078
99922
34
27
32 24
27 36
77943
209
22057
78022
210
21978
00079
99921
33
28
32 16
27 44
78152
208
21848
78232
209
21768
00080
99920
32
29
32 8
27 52
78360
208
21640
78441
208
21559
00080
99920
31
30
80
11 32 0
0 28 0
8. 78568
206
11. 21432
8. 78649
206
11.21351 1 10. 00081
9. 99919
81
31 52
28 8
78774
205
21226
78855
206
21145
00082
99918
29
82
31 44
28 16
78979
204
21021
79061
205
20989
00088
99917
28
88
31 36
28 24
79188
203
20817
79266
204
20784
00083
99917
27
84
31 28
28 82
79386
202
20614
79470
203
20580 i 00084
99916
9. 99915
26
25
85
11 31 20
0 28 40
8. 79588
201
11.20412
8. 79673
202
11.20827110.00085
8fi
31 12
28 48
79789
201
20211
79875
201
20125; 00086
99914
24
87
31 4
28 56
79990
199
20010
80076
201
19924
00087
99918
23
88
30 56
29 4
80189
199
19811
80277
199
19728
00087
99913
22
89
30 48
29 12
80388
197
19612
80476
198
19524
00088
99912
21
40
11 30 40
0 2v^ 20
8. 80585
197
11.19415
8. 80674
198
11.19326 10.00089
9.99911
20
41
30 32
29 28
80782
196
19218
80872
196
19128
00090
99910
19
42
30 24
29 36
80978
195
19022
81068
196
18982
00091
99909
18
48
30 16
29 44
81173
194
18827
81264
195
18736
00091
9<>909
17
44
30 8
29 52
0 30 0
81367
8.81560'
193
18633
81459
194
18541
00092
99908
16
45
11 30 0
192
11. 18440
8. 816.53
193
11.18847 10.00098
9. 99907
15
46
29 52
30 8
81752
192
18248
81846
192
18154
00094
99906
14
47
29 44
30 m
81944
190
18056
82038
192
17962
00095
99905
18
48
29 36
30 24
82134
190
1 7866
82280
190
17770
00096
99904
12
49
50
29 28
11 29 20
80 82
0 80 40
82824
8.82513
189
17676
82420
190
17580
00096
99904
11
188
11.17487
8. 82610
189
11. 173V.0
10. 00097
9. 99903
10
51
29 12
- 80 48
82701
187
17299
82799
188
17201
00098
99902
9
52
29 4
30 56
82888
187
17112
82987
188
17013
00099
99901
8
58
28 56
31 4
83075
186
16925
83175
186
16825
00100
99900
/
54
55
28 48
11 28 40
31 12
0 31 20
83261
185
16739
88361
186
16689
00101
99899
6
5
8. 88446
184
11.16554
8. 83547
185
11.16458
10.00102
9. 99898
56
28 32
81 28
83680
188
16370
88732
184
16268
00102
99898
4
57
28 24
31 m
83813
183
16187
83916
184
16084
00108
99897
3
58
28 16
31 44
88996
181
16004
84100
182
15900
00104
99896
2
59
28 8
31 52
84177
181
15828
84282
182
15718
00105
99895
1
60
M.
28 0
32 0
S4:ioS
181
15642
84464
182
15536
00106
99894
0
Hour p. M.
Hour A. M.
Cosine.
Diff. 1'.
Secant.
Cotangent.
Diff. 1'.
Tangent. Cosecant.
Sine.
M.
93°
86° 1
Page 612]
TABLE 44.
4°
Log. Sines, Tangents, and Secants
175°
M.
Hour A. M.
Hour p. K.
Sine.
Diff.l'.
Cosecant.
Tangent.
Diff.l'.
1
Cotangent.
Secant.
Cosine.
M.
0
11 28 0
0 32 0
8. 84358
181
11. 15642
8.84464
182
11. 15536
10. 00106
9. 99894
60
1
27 52
32 8
84539
179
15461
84646
180
15354
00107
99893
59
2
27 44
32 16
84718
179
15282
84826
180
15174
00108
99892
58
3
27 36
32 24
84897
178
15103
85006
179
14994
00109
99891
57
4
27 28
32 3f
85075
177
14925
85185
. 178
14815
00109
99891
56
55
5
11 27 20
0 32 40
8. 85252
177
11. 14748
8. 85363
177
11. 14637
10. 00110
9. 99890
6
27 12
32 48
85429
176
14571
85540
177
14460
00111
99889
54
7
27 4
32 56
85605
175
14395
8.5717
176
14283
00112
99888
53
8
26 56
33 4
85780
175
14220
85893
176
14107
00113
99887
52
9
10
26 48
11 26 40
33 12
85955
173
14045
86069
174
13931
00114
99886
51
50
0 33 20
8. 86128
173
11. 13872
8. 86243
174
11. 1.3757
10. 00115
9. 99885
11
26 32
33 28
86301
173
13699
86417
174
13583
00116
99884
49
12
26 24
33 36
86474
171
13526
86591
172
13409
00117
99883
48
13
26 16
33 44
86645
171
13355
86763
172
13237
00118
99882
47
14
26 8
33 52
86816
171
13184
86935
171
13065
00119
99881
46
45
15
11 26 0
0 34 0
8. 86987
169
11. 13013
8. 87106
171
11. 12894
10. 00120
9. 99880
16
25 52
34 8
87156
169
12844
87277
170
12723
00121
99879
44
17
25 44
34 16
87325
169
12675
87447
169
12553
00121
99879
43
18
25 36
34 24
87494
167
12506
87616
169
12384
00122
99878
42
19
20
25 28
11 25 20
34 32
87661
168
12339
87785
168
12215
00123
99877
41
40
0 34 40
8. 87829
166
11.12171
8. 87953
167
11. 12047
10. 00124
9. 99876
21
25 12
34 48
87995
166
12005
88120
167
11880
00125
99875
39
22
25 4
34 56
88161
165
11839
88287
166
11713
00126
99874
38
23
24 56
35 4
88326
164
11674
88453
165
11547
00127
99873
37
24
24 48
35 12
88490
164
11510
88618
165
11382
00128
99872
36
35
25
11 24 40
0 35 20
8. 88654
163
11. 11346
8. 88783
165
11. 11217
10. 00129
9. 99871
26
24 32
35 28
88817
163
11183
88948
163
11052
00130
99870
34
27
24 24
35 36
88980
162
11020
89111
163
10889
00131
99869
33
28
24 16
35 44
89142
162
• 10858
89274
163
10726
00132
99868
32
29
24 8
35 52
89304
160
10696
89437
161
10563
00133
99867
31
30
11 24 0
0 36 0
8. 89464
161
11. 10536
8. 89598
162
11. 10402
10. 00i;34
9. 99866
30
31
23 52
36 8
89625
159
10375
89760
160
10240
00135
99865
29
32
23 44
36 16
89784
159
10216
89920
160
10080
00136
99864
28
33
23 36
36 24
89943
159
10057
90080
160
09920
00137
99863
27
34
35
23 28
36 32
90102
158
09898
90240
159
09760
001.38
99862
26
11 23 20
0 36 40
8. 90260
157
11. 09740
8. 90399
158
11. 09601
10. 00139
9. 99861
25
36
23 12
36 48
90417
157
09583
90557
158
09443
00140
99860
24
37
23 4
36 56
90574
156
09426
90715
157
09285
00141
99859
23
38
22 56
37 4
90730
155
09270
90872
157
09128
00142
99858
22
39
22 48
37 12
90885
155
09115
91029
156
08971
00143
99857
21
40
11 22 40
0 37 20
8. 91040
155
11. 08960
8. 91185
155
11. 08815
10. 00144
9. 99856
20
41
22 32
37 28
91195
154
08805
91340
155
08660
00145
99855
19
42
22 24
37 36
91349
153
08651
91495
155
08505
00146
99854
18
43
22 16
37 44
91502
153
08498
91650
153
083.50
00147
99853
17
44
22 8
37 52
91655
152
08345
91803
154
08197
00148
99852
16
15
45
11 22 0
0 38 0
8.91807
152
11.08193
8. 91957
153
11.08043
10. 00149
9. 99851
46
21 52
38 8
91959
151
08041
92110
152
07890
00150
99850
14
47
21 44
38 16
92110
151
07890
92262
152
07738
00152
99848
13
48
21 36
38 24
92261
150
07739
92414
151
07586
00153
99847
12
49
21 28
38 32
92411
150
07589
92565
151
07435
00154
99846
11
50
11 21 20
0 38 40
8. 92561
149
11.074.39
8. 92716
150
11. 07284
10. 001.55
9. 99845
JO
51
21 12
38 48
92710
149
07290
92866
150
07134
00156
99844
9
52
21 4
38 56
92859
148
07141
93016
149
06984
00157
99843
8
53
20 56
39 4
93007
147
06993
93165
148
0683.5
00158
99842
7
54
20 48
39 12
93154
147
06846
93313
149
06687
00159
99841
6
55
11 20 40
0 39 20
8. 93301
147
11. 06699
8. 93462
147
11.06538
10. 00160
9. 99840
5
56
20 32
39 28
93448
146
06552
93609
147
06.391
00161
99839
4
57
20 24
39 36
93594
146
06406
93756
147
06244
00162
99838
3
58
20 16
39 44
93740
145
06260
93903
146
06097
00163
99837
2
59
20 8
39 52
93885
145
06115
94049
146
05951
00164
998.36
1
60
20 0
40 0
94030
144
05970
94195
145
05805
00166
99834
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.l'.
Secant.
Cotangent.
Diff.l'.
Tangent.
Cosecant.
Sine.
M.
94°
85° 1
TABLE 44.
[Page 613
Log.
Sines, Tangents, and Secants.
6°
A
A B
B
C
C 174°
M.
0
Hour A. M.
Hour p. M.
Sine.
Difl.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
11 20 00
0 40 00
8. 94030
0
11.05970
8. 94195
0
11. 05805
10. 00166
0
9. 99834
60
1
19 52
40 08
94174
2
05826
94340
2
05660
00167
0 99833 1
59
">,
19 44
40 16
94317
4
05683
94485
4
05515
00168
0
99832
58
w
19 36
40 24
94461
7
05539
94630
7
05370
00169
0
99831
57
4
5
19 28
11 19 20
40 32
94603
9
05397
94773
9
05227
00170
0
93830
56
0 40 40
8. 94746
11
11. 05254
8. 94917
11
11. 05088
10.00171
0
9. 99829
55
(\
19 12
40 48
94887
13
05113
95060
13
04940
00172
0
99828
54
7
19 04
40 56
95029
15
04971
95202
15
04798
00173
0
99827
53
8
18 56
41 04
95170
18
04830
95344
18
04656
00175
0
99825
52
9
18 48
41 12
95310
20
04690
95486
8.95627
20
22
04514
11.04873
00176
0 99824
51
50"
10
11 18 40
0 41 20
8. 95450
22
11.04550
10.00177
0 i 9. 99823
n
18 82
41 28
95589
24
04411
95767
24
04233
00178
0 99822
49
1^
18 24
41 36
95728
26
04272
95908
27
04092
00179
0 99821
48
ia
18 16
41 44
95867
29
041.33
96047
29
03953
00180
0 99820
47
14
15
18 08
41 52
96005
31
03995
96187
31
03813
00181
10.00183
0 99819
0 19.99817
46
45
11 18 00
0 42 00
8. 96143
33
11.03857
8. 96325
83
11.08675
18
17 52
42 08
96280
35
03720
96464
35
08536
00184
0
99816
44
17
17 44
42 16
96417
37
03583
96602
38
03398
00185
0
99815
48
IS
17 36
42 24
96553
89
03447
96739
40
03261
00186
0
99814
42
19
17 28
42 82
96689
42
44
08311
11.03175
96877
42
44
03123
00187
0
99813
41
90
11 17 20
0 42 40
8. 96825
8. 97013
11.02987
10. 00188
0
9. 99812
40
?A
17 12
42 48
96960
46
03040
97150
46
02850
00190
0
99810
39
22
17 04
42 56
97095
48
02905
97285
49
02715
00191
0
99809
38
28
16 56
43 04
97229
50
02771
97421
51
02579
00192
0
99808
37
24
16 48
43 12
97368
53
55
02637
97556
53
02444
00193
0
99807
36
35
2ft
11 16 40
0 43 20
8. 97496
11.02504
8. 97691
55
11. 02309
10.00194
1 9.99806
26
16 32
43 28
97629
57
02371
97825
58
02175
00196
1 99804
34
27
16 24
43 36
97762
59
02238
97959
60
02041
00197
1 99803
88
28
16 16
43 44
97894
61
02106
98092
62
01908
00198
99802
32
29
80
16 08
43 52
98026
64
01974
11. 01843
98225
&4
01775
00199
99801
31
30
11 16 00
0 44 00
8. 98157
66
8. 98358
66
11.01642
10. 00200
9. 99800
81
15 52
44 08
98288
68
01712
98490
69
01510
00202
99798
29
82
15 44
44 16
98419
70
01581
98622
71
01378
00203
99797
28
88
15 36
44 24
98549
72
01451
98753
73
01247
00204
99796
27
34
15 28
44 82
98679
75
01321
98884
75
01116
11.00985
00205
99795
26
25
85
11 15 20
0 44 40
8. 98808
77
11.01192
8. 99015
77
10. 00207
9. 99793
86
15 12
44 48
98937
79
01068
99145
80
00855
00208
99792
24
87
15 04
44 56
99066
81
00934
99275
82
00725
00209
99791
23
88
14 56
45 04
99194
83
00806
99405
84
00595
00210
99790
22
39
14 48
45 12
99322
86
00678
99534
86
89
00466
00212
99788
21
20
40
11 14 40
0 45 20
8. 99450
88
11.00550
8. 99662
11.00888
10. 00213
9. 99787
41
14 32
45 28
99577
90
00423
99791
91
00209
00214
99786
19
42
14 24
45 36
99704
92
00296
99919
93
00081
00215
99785
18
48
14 16
45 44
99880
94
00170
9.00046
95
10. 999,54
00217
99783
17
44
45
14 08
45 52
99956
96
00044
10. 99918
00174
9.00301
97
100
99826
00218
To. 00219
1 1 99782
1 9.99781
16
15
11 14 00
0 46 00
9. 00082
99
10.99699
46
18 52
46 08
00207
101
99793
00427
102
99573
00220
1 1 99780
14
47
18 44
46 16
00332
108
99668
00553
104
99447
00222
1 i 99778
13
48
13 36
46 24
00456
105
99544
00670
106
99321
00223
99777
12
49
50
13 28
11 18 20
46 32
0 46 40
00581
9.00704
107
110
99419
10. 99296
00805
9. 00930
108
111
99195
00224
10. 00225
99776
9. 99775
11
10
10. 99070
51
13 12
46 48
00828
112
99172
01055
113
98945
00227
99773
9
52
13 04
46 56
00951
114
99049
01179
115
98821
00228
99772
8
58
12 56
47 04
01074
116
98926
• 01303
117
98697
00229
99771
7
54
55
12 48
47 12
0 47 20
01196
9.01318
118
121
98804
10. 98682
01427
120
122
98578
10.98450
00231
99769
99768
6
5
11 12 40
9. 01550
10. 00232
56
12 32
47 28
01440
123
98560
01673
124
98827
00233
99767
4
57
12 24
47 36
01561
125
98439
01796
126
98204
00235
1 j 99765
3
58
12 16
47 44
01682
127
98318
01918
128
98082
00236
99764
2
59
12 08
47 52
01808
129
98197
02040
131
97960
00237
99763
1
60
12 00
48 00
01923
132
98077
02162
133
97838
00239
99761
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
96°
A
A B
B
C
C 84° 1
Seconds of time
1»
•.'= j 8b
4'
5- i C 7. 1
Prop, parts of cols. -; B
(c
16
17
0
33 49 66
33 50 66
0 0 1
82
83
1
99
100
1
115
116
1
Page 614]
TABLE U.
Log. Sines, Tangents, and Secants.
6°
A A
B B
C
C
178°
M.
Hour A. M. Hour p. m.
Sine.
Diflf.
Cosecant.
Tangent. Diff. 1 Cotangent.
Secant.
10. 00239
Diff.
0
Cosine.
M.
60
0
11 12 00
0 48 00
9.01923
0
10. 98077
9.02162 0 10.97838
9. 99761
1
11 52
48 08
02043 i 2
97957
02283 1 2 97717
00240
0
99760
59
2
11 44 1 48 16
02163 : 4
97837
02404 j 4 97596
00241
0
99759
58
3
11 36
48 24
02283 ! 6
97717
02525 1 6
97475
00243
0
99757
57
4
11 28
48 321
02402
7
9
97598
02645
8
9
97355
10^97234
00244
10. 00245
0
0
99756
9. 99755
56
55
5
11 11 20
0 48 40
9. 02520
10. 97480
9. 02766
6
11 12
48 48
02639 1 11
97361
02885 1 11
97115
00247
0
99753
.54
7
11 04
48 56
02757 ! 13
97243
03005 13 96995
00248
0
99752
53
8
10 56
49 04
02874
15
97126
03124 15 96876
00249
0
9975]
52
9
10
10 48
49 12
049 20
02992
17
97008
03242
9. 03361
17
19
96758
10. 96639
00251
10. 00252
0
0"
99749
51
11 10 40
9. 03109
19
10. 96891
9. 99748
50
11
10 32
49 28
03226
20
96774
03479
21
96521
00253
0
99747
49
12
10 24
49 36
03342
22
96658
03597 23 96403
00255
0
99745
48
13
10 16
49 44
03458
24
96542
03714 i 24
96286
00256
0
99744
47
14
15
10 08
49 52
03574
26
96426
03832 1 26
96168
00258
10. 00259
0
0
99742
46
45
11 10 00
0 50 00
9. 03690
28
10. 96310
9.03948 28
10. 96052
9. 99741
16
9 52
50 08
03805
30
96195
04065 1 30
95935
00260
0
99740
44
17
9 44
50 16
03920
31
96080
04181 1 32
95819
00262
0
99738
43
18
9 36
50 24
04034
33
95966
04297 1 34
95703
00263
0
99737
42
19
9 28
50 32
0 50 40
04149
35
95851
04413 36
95587
00264
0
99736
41
40
20
11 9 20
9. 04262
37
10. 95738
9.04528 ! 38
10. 95472
10. 00266
0
9. 99734
21
9 12
50 48
04376
39
95624
04643 39
95357
00267
99733
39
22
9 04
50 56
04490
41
95510
04758 41
95242
00269
99731
38
23
8 56
51 04
04603
43
95397
04873 43 95127
00270
99730
37
24
8 48
51 12
04715 44
95285
04987 i 45
95013
00272
99728
36
35
25
11 8 40 1 0 51 20
9.04828 1 46
10.95172
9.05101 1 47
10. 94899
10. 00273
9. 99727
26
8 32 51 28
04940 48
95060
05214 i 49
94786
00274
99726
34
27
8 24 51 36
05052
50
94948
05328 1 51
94672
00276
99724
33
28
8 16 1 51 44
05164
52
94836
05441 ! 53
94559
00277
99723
32
29
8 08 i 51 52
05275
9. 05386
54
56
94725
05553 54
94447
00279
99721
9. 99720
31
30
30
11 8 00
0 52 00
10. 94614
9.05666 56 10.94334
10. 00280
31
7 52
52 08
05497
57
94503
05778 1 58 1 94222
00282
99718
29
32
7 44
52 16
05607
59 94393
05890 1 60 94110
00283
99717
28
33
7 36
52 24
05717
61 94283
06002 62 93998
00284
99716
27
34
7 28
52 32
05827
63 94173
06113 64 93887
00286
99714
26
35
11 7 20
0 52 40
9.05937 65 10.94063
9.06224 66 10.93776
10. 00287
9. 99713
25
36
7 12
52 48
06046 67
93954
06335 68 93665
00289
99711
24
37
7 04
52 56
06155 69
93845
06445
69
93555
00290
99710
23
38
6 56
53 04
06264 70
93736
06556
71
93444
00292
99708
22
39
40"
6 48
53 12
06372
9. 06481"
72
93628
06666
73
93334
00293
99707
21
20
11 6 40
0 53 20
74 10.93519
9. 06775
75
10. 93225
10. 00295
9. 99705
41
6 32
53 28
06589 i 76
93411
06885
77
93115
00296
99704
19
42
6 24
53 36
06696
78
93304
06994
79
93006
00298
99702
18
43
6 16
53 44
06804
80
93196
07103
81
92897
00299
99701
17
44
45
6 08
53 52
06911
81
93089
07211
83
84
92789
00301
99699
9. 99698
16
15
11 6 00
0 54 00
9. 07018
83
10. 92982
9. 07320
10. 92680
fo. oote'
46
5 52
54 08
07124
85
92876
07428
86
92572
00304
99696
14
47
5 44
54 16
07231
87
92769
07536
88
92464
00305
99695
13
48
5 36
54 24
07337
89
92663
07643
90
92357
00307
99693
12
49
. 5 28
54 32
07442
91
92558
07751
92
92249
10. 92142
00308
99692
9. 99690
11
10
50
11 5 20
0 54 40
9. 07548
93
10. 92452
9. 07858
94
10. 00310
51
5 12
54 48
07653
94
92347
07964
96
92036
00311
99689
9
52
5 04
54 56
07758
96
92242
08071
98
91929
. 00313
99687
8
53
4 56
55 04
07863
98
92137
08177
99
91823
00314
99686
7
54
4 48
55 12
07968
100
92032
08283
101
91717
00316
99684
6
5
55
11 4 40
0 55 20
9. 08072
102
10. 91928
9. 08389
103
10.91611
10. 00317
1
9. 99683
56
4 32
55 28
08176
104
91824
08495
105
91505
00319
99681
4
57
4 24
55 36
08280
106
91720
08600
107
91400
00320
99680
3
58
4 16
55 44
08383
107
91617
08705
109
91295
00322
99678
2
59
4 08
55 52
08486
109
91514
08810
111
91190
00323
99677
1
60
4 00
56 00
08589
111
91411
08914
113
91086
00325
99675
0
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Diflf.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
96°
A A
B B
c
C
88°
Seconds of time
Prop, parts
of cols. <
2»
28
28
0
6'
83
84
1
TABLE U.
[Page 615
Log. Sines, Tangents, and Secants.
7°
A A
B
B
C
C 172°
M.
Hour A. M.
Hour P. M.
0 56 0
Sine.
DiflF.
Cosecant.
Tangent. DiS.
i Cotangent.
Seeant.
Diff.
Cosine.
M.
60
0
n 4 0
9. 08589
0
10.91411
9. 08914
0
10. 91086
10. 00325
0
9. 99675
1
3 52
56 8
08692
2
91308
09019
2
90981
00326
0
99674
59
2
3 44
56 16
08795
3
91205
09123
3
i 90877
00328
0
99672
58
8
3 36
56 24
08897
5
91103
09227
5
1 90773
00330
0
99670
57
4
5
3 28
56 32
08999
6
8
91001
rd."90899
09330
9.09434
7
8
i 90670
00331
0
99669
56
11 3 20
0 56 40
9. 09101
[10. 90566
10. 00333
0
9. 99667
55
6
3 12
56 48
09202
10
90798
09537
10
90463
00334
0
99666
54
7
3 4
56 56
09304
11
90696
09640
11
90360
00336
0
99664
53
8
2 56
57 4
09405
13
90595
09742
13
90258
00337
0
99663
52
9
10
2 48
11 2 40
57 12
0 57 20
09506
9. 09606
14
16"
90494
10. 90394
09845
9. 09947
15
16
90155
10. 90053
00339
0
99661
51
10. 00341
0
9. 99659
50
11
2 32
57 28
09707
18
90293
10049
18
89951
00342
0
99658
49
12
2 24
57 36
09807
19
90193
10150
20
89850
00344
0
99656
48
13
2 16
57 44
09907
21
90093
10252
21
89748
00345
0
99655
47
14
2 8
57 52
10006
22
89994
10353
23
89647
00347
0
99653
9. 99651"
46
45
15
11 2 0
0 58 0
9. 10106
24
10. 89894
9. 10454
24
10. 89546
10. 00349
0
16
1 52
58 8
10205
26
89795
10555
26
89445
00350
0
99650
44
17
1 44
58 16
10304
27
89696
10656
28
89344
00352
0
99648
43
18
1 36
58 24
10402
29
89598
10756
29
89244
00353
99647
42
19
1 28
58 32
0 58 40
10501
9. 10599
30
89499
10856
31
89144
00355
99645
41
20
11 1 20
32 110.89401
9. 10956
33
10. 89044
10. 00357
9. 99643
40
21
1 12
58 48
10697
34 89303
11056
34
88944
00358
99642
39
22
1 4
58 56
10795
35 89205
11155
36
88845
00360
99640
38
23
0 56
59 4
10893
37 89107
11254
37
88746
00362
99638
37
24
25'
0 48
59 12
10990
38 1 89010
lia53
39
88647
00363
10. 00365
99637
9. 99635
36
35
11 0 40
0 59 20
9. 11087
40 [10.88913
9. 11452
41
10. 88548
26
0 32
59 28
11184
42 ! 88816
11551
42
88449
00367
1
99633
34
27
0 24
59 36
11281
43
88719
11649
44
88351
00368
99632
33
28
0 16
59 44
11377
45
88623
11747
46
88253
00370
99630
32
29
0 8
59 52
11474
46
88526
11845
47
88155
10. 88057
00371
10. 00373
99629
9. 99627
31
30
30
11 0 0
1 0 0
9. 11570
48 110.88430
9.11943
49
31
10 59 52
0 8
11666 i 50 88334
12040
51
87960
00375
99625
29
32
59 44
0 16
11761
51 88239
12138
52
87862
00376
99624
28
33
59 36
0 24
11857
53 1 88143
12235
54
87765
00378
99622
27
34
35
59 28
0 32
11952
54 ! 88048
12332
9. 12428
55
57
87668
00380
10. 00382
99620
26
10 59 20
1 0 40
9. 12047
56 10.87953
10. 87572
9. 99618
25
36
59 12
0 48
12142
58 87858
12525
59
87475
00383
99617
24
37
59 4
0 56
12236
59 87764
12621
60
87379
00385
99615
23
38
58 56
1 4
12331
61 87669
12717
62
87283
8/187
00387
99613
22
39
58 48
1 12
12425
62 i 87575
12813
64
00388
99612
21
20
40
10 58 40
1 1 20
9. 12519
64 (10.87481
9. 12909
65
10. 87091
10.00390
9.99610
41
58 32
1 28
12612
66 ! 87388
13004
67
86996
00392
99608
19
42
58 24
1 36
12706
67 87294
13099
68
86901
00393
99607
18
43
58 16
1 44
12799
69 • 87201
13194
70
86806
00395
99(W5
17
44
45
58 8
1 52
12892
70 1 87108
13289
72
86711
00397
99603
16
15
10 58 0
1 2 0
9. 12985
72 10.87015
9. 13384
73
10. 86616
10. 00.399
9. 99()01
46
57 52
2 8
13078
74 86922
13478
to
86522
00400
99(i00
14
47
57 44
2 16
13171
75
86829
13573
77
86427
00402
99598
13
48
57 36
2 24
13263
77
86737
13667
78
• 86333
00404
99596
12
49
50
57 28
10 57 20
2 32
1 2 40
13355
9. 13447
78
80
86645
10. 86553
13761
9. 13854
80
81
86239
10. 86146
00405
99595
9. 99593
11
10
10. 00407
51
57 12
2 48
13539
82
8<>461
13948 i 83
86052
00409
99591
9
52
57 4
2 56
13630
83
86370
14041 85
85959
00411
99589
8
53
56 56
3 4
13722 85 : 86278 |
14134 86
85866
00412
99588
7
54
55
56 48
3 12
13813
87 : 86187
88 110.86096
14227 1 88
9.14320 1 90
85773
10. 85680
00414
10. 00416
2
2
99586
9. 99584
6
5
10 56 40
1 3 20
9. 13904
56
56 32
3 28
13994
90 8600(i
14412 91
85588
00418
2
99582
4
57
56 24
3 36
14085
91
85915
14.504 i 93
85496
00419
2
9958 1
3
58
56 16
3 44
14175
93
85825
14597
95
85403
00421
2
99579
2
59
56 8
3 52
14266
95
85734
14688
96
85312
00423
2
99577
1
60
56 0
4 0
14356 96 85644
14780
98
85220
00425
2
99575
0
M.
Hour p. M.
Hour AHU.
Cosine. Diff. Secant, i
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
97^
A A
B
B
C
C 82° 1
Seconds of time
1'
2' -8'
4'
b>
6^ 1 7.
Prop, parts of cols. < B
12
12
0
24 36
24 37
0 1
48
49
1
60
61
1
72 84
73 86
1 1
Page 616]
TABLE 44.
Log. Sines, Tangente, and Secants.
8°
A A
B B
C
C
I'iV
M.
Hour A. M. Hour p. M.
Sine. JDifl. Cosecant.
Tangent. Dili.
Cotangent.
Secant.
Difif.
Cosine.
M.
0
10 56 0 14 0
9.14356 1 0 10.85644
9. 14780 0
10. 85220
10. 00425
0
9. 99575
60
1
55 52 4 8
14445 : 1 1 85555
14872 1
85128
00426
0
99574
59
9
55 44 ■ 4 16
14535 3 i 85465
14963 1 3 85037
00428
0
99572
58
3
55 36 I 4 24
14624 4 85376
15054 4 84946
00430
0
99570
57
4
5
55 28 1 4 32
10 55 20 I 1 4 40
14714 i 6 85286
9.14803 7 10,85197
15145 6 84855
9.15236 ! 7 10.84764
00432
10.00434
0
99568
56
55
0
9. 99566
6
55 12 : 4 48
14891 1 8 85109
15327 9 1 84673
00435
0 99565
54
7
55 4 4 56
14980 1 10
85020
15417 10 i 84583
00437
0 99563
53
8
54 56 ! 5 4
15069 11
84931
15508 12 84492
00439
0 ; 99561
52
9
54 48 1 5 12
15157 13
84843
15598 , 13 84402
00441
0
99559
51
50
10
10 54 40 1 1 5 20
9.15245 14 10.84755
9.15688 14 10.84312
10.00443
0
9. 99557
11
54 32 ' 5 28
15333 16 84667
15777 16 84223
00444
0
99556
49
12
54 24 5 36
15421 17 84579
15867 1 17 ! 84133
00446
0
99554
48
13
54 16 5 44
15508 \ 18 84492
15956 19 ! 84044
00448
0
99552
47
14
54 8 1 5 52
15596 20 84404
16046 20 ' 83954
00450
0
99550
46
15
10 54 0 1 6 0
9. 15683 21 10. 84317
9.1613.5 i 22 10.83865
10. 00452
0
9. 99548
45
16
53 52 6 8
15770 23 84230
16224 [ 23 83776
00454
99546
44
17
53 44 6 16
15857 X 24 84143
15944"^ 25 84056
16312 25 I "83688
00455
99545
48
18
53 36 6 24
16401 26 ' 83599
00457
99543
42
19
20
53 28 1 6 32
16030
27
83970
16489
27
83511
10. 83423
00459
1
99541
41
40
10 53 20 1 6 40
9. 16116
28
10. 83884
9. 16577
29
10. 00461
9. 99539
21
53 12 6 48
16203
30 83797
16665
30 83335
00463
99537
39
22
53 4 6 56
16289
31 83711
16753
32 83247
00465
99535
38
23
52 56 7 4
16374 1 32 j 83626
16841
33
83159
00467
1 99533
37
24
52 48 1 7 12
16460 1 34 1 83540
16928
35
83072
00468
1 99532
36
25
10 52 40 1 7 20
9. 16545 , 35 ilO. 83455
9. 17016
36 10.82984
10. 00470
1 9.99530
35
26
52 32
7 28
16631
37
83369
17103
37
82897
00472
99528
34
27
52 24
7 36
16716
38
83284
17190
39
82810
00474
99526
33
28
52 16
7 44
16801
39
83199
17277
40
82723
00476
99524
32
29
30
52 8
10 52 0
7 52
18 0
16886
41
83114
17363
42
82637
00478
99522
9. 99520
31
30
9. 16970
42
10. 83030
9. 17450
43
10. 82550
10. 00480
31
51 52 i 8 8
17055 1 44 82945
17536
45
82464
00482
99518
29
32
51 44
8 16
17139 45 82861
17622
46
82378
00483
99517
28
33
51 36
8 24
17223 i 47 82777
17708
48
82292
00485
99515
27
34
35
51 28
8 32
17307 48
82693
10. 82609
17794
49
82206
00487-
99513
26
25
10 51 20 1 8 40
9. 17391 49
9.17880
50
10. 82120
10. 00489
9.99511
36
51 12 8 48
17474
51
82526
17965
52
82035
00491
. 99509
24
37
51 4 { 8 56
17558
52
82442
18051
53
81949
00493
99507
23
38
50 56 9 4
17641
54
82359
18136
55
81864
00495
99505
22
39
40
50 48 1 9 12
17724
55
82276
18221
56
81779
00497
99503
21
10 50 40 1 9 20
9. 17807
56 10.82193
9. 18306
58 10.81694
10. 00499
1 9.99501
20
41
50 32 I 9 28
17890 58 82110
18391
59 81609
00501
1 99499
19
42
50 24 ! 9 36
17973 i 59 82027
18475
61
81525
00503
1 99497
18
43
50 16 9 44
18055 61 81945
18560
62
. 81440
00505
1 ! 99495
17
44
50 8
9 52
1 10 0
18137 62 81863
9.18220 i 63 10.81780
18644
63
81356
00506
1 i 99494
16
15
45
10 50 0
9. 18728
65 10.81272
10. 00508
1 19.99492
46
49 52 : 10 8
18302 i 65 ! 81698
18812
66
81188
00510
99490
14
47
49 44 10 16
18383 66 81617
18896 1 68
81104
00512
1
99488
13
48
49 36 I 10 24
18465 68 81535
18979 i 69
81021
00514
2
99486
12
49
50
49 28 1 10 32
18547 1 69 81453
9.18628 71 ;iO. 81372
19063
9.19146
71 80937
72 10780854
00516
10. 00518
2
2
99484
9. 99482
11
10
10 49 20 i 1 10 40
51
49 12 10 48
18709 1 72 81291
19229
74 80771
00520
2 99480
9
52
49 4 10 56
18790 73 ; 81210
19312
75 • 80688
■ 00522
2 1 99478
8
53
48 56 11 4
18871 75 81129
19395
76 80605
00524
2 i 99476
7
54
55
48 48 11 12
18952 76 ■ 81048
19478 i 78 1 80522
00526
2 j 99474
6
10 48 40 i 1 11 20
9.19033 i 78 10.80967
9.19561 ' 79 10.80439
10. 00528
2 9. 99472
5
56
48 32 11 28
19113 79 ! 80887
19643 1 81 1 80357
00530
2 \ 99470
4
57
48 24 11 36
19193
80 i 80807
19725
82 j 80275
00532
2 99468
3
58
48 16 11 44
19273
82 I 80727
19807
84
80193
00534
2 i 99466
2
59
48 8 i 11 52
19353
83
80647
19889
85
80111
00536
2
99464
1
60
M.
48 0 12 0
19433
85
80567
19971
87
80029
00538
2
99462
0
M.
Hour p. M. j Hoxir a. m.
Cosine. Dlfif.
Secant.
Cotangent. ^ Diff.
Tangent.
Cosecant.
DiflE.
Sine.
98°
A A
. B B
C
C
81°
Seconds of time 1"
2»
8- j 4«
o'
«•
<•
fA 11
Prop, parts of cols. -JB 11
[C 1 0
21
22
0
32 42
32 43
1 [ 1
53
54
1
63
65
1
74
76
2
TABLE U.
[Page 617
Log.
Sines, Tangents, and Secants.
9°
A
A
B
B
C
C 170°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff. 1 Cosine.
M.
0
10 48 0
1 12 0
9. 19433
0
10. 80567
9. 19971
0
10. 80029
10. 00538
0 9.99462
60
1
47 52
12 8
19513
1
80487
20053
1
79947
00540
0
99460
59
2
47 44
12 16
19592
3
80408
20134
3
79865
00542
0
99458
58
3
47 36
12 24
19672
4
80328
20216
4
79784
00544
0
99456
57
4
47 28
12 32
19751
5
80249
10.80170
20297
5
79703
10. 79622
00546
10. 00548
0
99454
56
55
5
10 47 20
1 12 40
9. 19830
6
9. 20378 6
0
9. 99452
H
47 12
12 48
19909
8
80091
20459
8
79541
00550
0
99450
54
7
47 4
12 56
19988
9
80012
20540
9
79460
00552
0
99448
53
8
46 56
13 4
20067
10
79933
20621 10
79379
00554
0
99446
52
9
10
46 48
10 46 40
13 12
1 13 20
20145
9. 20223
11
13
79855
20701
12
13
79299
00556
0
99444
51
50
10. 79777
9. 20782 '
10. 79218
10. 00558
0 9.99442
11
46 32
13 28
20302
14
79698
20862 1 14
79138
00560
0
99440
49
12
46 24
13 36
20380
15
79620
20942 16
79058
00562
0
99438
48
13
46 16
13 44
20458
16
79.542
21022
17
78978
00564
0
99436
47
14
46 8
13 52
20535
18
79465
21102
18
78898
00566
0
99434
46
45
15
10 46 0
1 14 0
9. 20613
19
10. 79387
9.21182
19
10. 78818
10. 00568
9. 99432
K)
45 52
14 8
20691
20
79309
21261
21
78739
00571
. 99429
44
17
45 44
14 16
20768
21
79232
21341
22
78659
00573
99427
43
18
45 36
14 24
20845
23
79155
21420
23
78580
00575
99425
42
19
45 28
14 32
20922
24
79078
21499
25
78501
00577
99423
41
20
10 45 20
1 14 40
9. 20999
25
10. 79001
9. 21578
26
10. 78422
10. 00579
9. 99421
40
21
45 12
14 48
21076
26
> 78924
21657
27
78343
00581
99419
39
22
45 4
14 56
21153
28
78847
21736
28
78264
00583
99417
38
23
44 56
15 4
21229
29
78771
21814
30
78186
00585
99415
37
24
44 48
15 12
21306
9. 21382
30
78694
21893
31
78107
00587
99413
36
25
10 44 40
1 15 20
31
10. 78618
9. 21971
32
10. 78029
10. 00589
9.99411
35
26
44 32
15 28
21458
33
78542
22049
34
77951
00591
99409
34
27
44 24
15 36
21534
34
78466
22127
35
77873
00593
99407
33
28
44 16
15 44
21610
35
78390
22205
36
77795
00596
99404
32
29
30
44 8
15 52
21685
37
78315
10. 78239
22283
38
77717
10. 77639
00598
99402
31
10 44 0
1 16 0
9. 21761
38
9. 22361
39
10.00600
9.99400
30
31
43 52
16 8
21836
39
78164
22438
40
77562
00602
99398
29
32
43 44
16 16
21912
40
78088
22516
41
77484
00604
99396
28
33
43 36
16 24
21987
42
78013
22593
43
77407
00606
99394
27
34
35
43 28
16 32
22062
43
77938
22670
44
77330
00608
99392
26
10 43 20
1 16 40
9. 22137
44
10. 77863
9. 22747
45
10. 77253
10. 00610
9. 99390
25
36
43 12
16 48
22211
45
77789
22824
47
77176
00612
99388
24
37
43 4
16 56
22286
47
77714
22901
48
77099
00615
99385
23
38
42 56
17 4
22361
48
77639
22977
49
77023
00617
99383
22
39
42 48
17 12
22435
9. 22509
49
50
77565
10. 77491
23054
9. 23130
50
52
76946
00619
99381
21
40
10 42 40
1 17 20
10. 76870
10. 00621
9. 99379
20
41
42 32
17 28
22583
52
77417
23206
53
76794
00623
99377
19
42
42 24
17 36
22657
53
77343
23283
54
76717
00625
99375
18
43
42 16
17 44
22731
54
77269
23359
56
76641
00628
2
99372
17
44
45
42 8
17 52
22805
55
57
77195
10. 77122
23435
57
76565
00630
2
99370
16
15
10 42 0
1 18 0
9. 22878
9. 23510
58
10. 76490
10. 00632
2
9. 99368
46
41 52
18 8
22952
58
77048
23586
60
76414
00634
2
99366
14
47
41 44
18 16
23025
59
76975
23661
61
76339
00(i36
2
99364
13
48
41 36
18 24
23098
60
76902
23737
62
76263
00638
2
99362
12
49
41 28
18 32
23171
9. 23244
62
63
76829
23812
63
65
76188
00641
2
99359
11
10
50
10 41 20
1 18 40
10. 76756
9. 23887
10.76113
10. 00643
2 9,99357
51
41 12
18 48
23317
64
76683
23962
66
76038
00645
2
99355
9
52
41 4
18 56
23390
65
76610
24037
67
75963
00(>47
2
99353
8
53
40 56
19 4
23462
67
76538
24112
69
75888
00649
2
99351
i
54
55
40 48
10 40 40
19 12
23535
9. 23607
68
76465
24186
70
75814
00652
2
99348
6
1 19 20
69
10. 76393
9. 24261
71
10. 75739
10. 00654
2
9. 99346
5
56
40 32
19 28
23679
71
76321
24335
73
75665
00656
2
99344
4
57
40 24
19 36
23752
72
76248
24410
74
75590
00658
2
99342
3
58
40 16
19 44
23823
73
76177
24484
75
75516
00660
2
99340
2
59
40 8
19 52
23895
74
76105
24558
76
75442
00663
2
99337
1
60
M.
40 0
20 0
23967
76
76033
24632
78
75368
00665
2
99335
0
-M.
Hour p. M.
Hour A. M.
Co.sine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff. } Sine.
99°
A
A
B
B
C
C 80° 1
Seconds of time
1« 2» 3^
4.
5'
6»
7»
Prop, parts of cols. •! B
Ic
9 19 28
10 19 29
0 1 i 1
38
39
1
47
49
1
57
58
2
66
68
2
Page 618]
TABLE 44.
Log. Sines, Tangents, and Secants.
10°
A A
B
B
C
C 169°
M.
Hour A. M.
Hour p. M.
Sine. Diff. 1 Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
10 40 0
1 20 0
9.23967 0 10.76033
9. 24632
0
10.75368
10.00665
0
9. 99335
60
1
39 52
20 8
24039 1 i 75961
24706
1 1
75294
00667
0 99333
59
2
39 44
20 16
24110 2 1 75890
24779 2
75221
00669
0 99331
58
:^
39 36
20 24
24181 3
75819
24853 4
75147
00672
0 99328
57
4
39 28
20 3i
24253
5
75747
10. 75676
24926
5
6
75074
10. 75000
00674
0 i 99326
0 i 9. 99324
56
55
5
10 39 20
1 20 40
9. 24324
6
9. 25000
10. 00676
6
39 12
20 48
24395
7
75605
25073
7
74927
00678
0 99322
54
7
39 4
20 56
24466
8
75534
25146
8
74854
00681
0 99319
53
8
38 56
21 4
24536
9
75464
25219
9
74781
00683
0 99317
52
9
10
38 48
21 12
24607
10
75393
25292
11
12
74708
00685
0 99315
51
10 38 40
1 21 20
9. 24677
11
10. 75323
9. 25365
10. 74635
10. 00687
0 9.99313
50
11
38 32
21 28
24748
13
75252
25437 13
74563
00690
0 99310
49
12
38 24
21 36
24818
14
75182
. 25510 i 14
74490
00692
0 i 99308
48
13
38 16
21 44
24888
15
75112
25582
15
74418
00694
99306
47
14
38 8
21 52
24958
16
75042
25655
16
74345
00696
99304
46
15
10 38 0
1 22 0
9. 25028
17
10. 74972
9. 25727
18
10. 74273
10. 00699
9. 99301
45
1(1
37 52
22 8
25098
18
74902
25799
19
74201
00701
99299
44
17
37 44
22 16
25168
19
74832
25871
20
74129
00703
99297
43
18
37 36
22 24
25237
20
74763
25943
21
74057
00706
99294
42
19
37 28
22 32
25307
22
74693
26015
22
73985
00708
99292
41
20
10 37 20
1 22 40
9. 25376
23
10. 74624
9. 26086
24
10. 73914
10. 00710
9. 99290
40
21
37 12
22 48
25445
24
74555
26158
25,
73842
00712
99288
39
22
37 4
22 56
25514
25
74486
26229
26
73771
00715
99285
38
23
36 56
23 4
25583
26
74417
26301
27
73699
00717
99283
37
24
25
36 48
23 12
25652
27
74348
26372
28
73628
00719
99281
9. 99278
36
35
10 36 40
1 23 20
9. 25721
28
10. 74279
9. 26443
29
10. 73557
10. 00722
26
36 32
23 28
25790
30
74210
26514 31
73486
00724
99276
34
27
36 24
23 36
25858
31
74142
26585
32
73415
00726
99274
33
28
36 16
23 44
25927
32
74073
26655
33
73345
00729
99271
32
29
30
36 8
23 52
25995
33
34
74005
26726
34
35
73274
00731
99269
31
30
10 36 0
1 24 0
9. 26063
10. 73937
9. 26797
10. 73203
10. 00733
9. 99267
31
35 52
24 8
26131
35
73869
26867
36
73133
00736
99264
29
32
35 44
24 16
26199
36
73801
26937
38
73063
00738
99262
28
33
35 36
24 24
26267
38
73733
27008
39
72992
00740
99260
27
34
35 28
24 32
26335
39
73665
27078
40
72922
00743
99257
26
35
10 35 20
1 24 40
9. 26403
40
10. 73597
9. 27148
41
10. 72852
10. 00745
9. 99255
25
3H
35 12
24 48
26470
41
73530
27218
42
72782
00748
99252
24
37
35 4
24 56
26538
42
73462
27288
44
72712
00750
99250
23
38
34 56
25 4
26605
43
73395
27357
45
72643
00752
99248
22
39
34 48
25 12
26672
44
73328
27427
46
72573
00755
2
99245
21
40
10 34 40
1 25 20
9. 26739
45
10. 73261
9. 27496
47
10. 72504
10. 00757
2
9. 99243
20
41
34 32
25 28
26806
47
73194
27566
48
72434
00759
2
99241
19
42
34 24
25 36
26873
48
73127
27635
49
72365
00762
2
99238
18
43
34 16
25 44
26940
49
73060
27704
51
72296
00764
2
99236
17
44
34 8
25 52
27007
50
72993
27773
52
72227
00767
2
99233
16
15
45
10 34 0
1 26 0
9. 27073
51
10. 72927
9. 27842
53
10. 72158
10. 00769
2
9. 99231
46
33 52
26 8
27140
52
72860
27911
54
72089
00771
2
99229
14
47
33 44
26 16
27206
53
72794
27980
55
72020
00774
2
99226
13
48
33 36
26 24
27273
55
72727
28049 1 56
71951
00776
2
99224
12
49
33 28
26 32
27339
56
72661
28117 ! 58
71883
00779
2
99221
11
10
50
10 33 20
1 26 40
9. 27405
57
10. 72595
9. 28186
59
10. 71814
10. 00781
2
9. 99219
51
33 12
26 48
27471
58
72529
28254
60
71746
00783
2
99217
9
52
33 4
26 56
27537
59
72463
28323
61
71677
00786
2
99214
8
53
32 56
27 4
27602
60
72398
28391
62
71609
00788
2
99212
7
54
32 48
27 12
27668
61
72332
28459
63
71541
00791
2
2
99209
9. 99207
5'
55
10 32 40
1 27 20
9. 27734
63
10. 72266
9. 28527
65
10. 71473
10. 00793
56
32 32
27 28
27799
64
72201
28595
66
71405
00796
2
99204
4
57
32 24
27 36
27864
65
72136
28662 \ 67
71338
00798
2
99202
3
58
32 16
27 44
27930
66
72070
28730 68
71270
00800
2
99200
2
59
32 8
27 52
27995
67
72005
28798
69
71202
00803
2
99197
1
60
32 0
28 0
28060
68
71940
28865
71
71135
00805
2
Diff.
99195
0
M.
Hour P.M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent. Diff.
Tangent.
Cosecant.
Sine.
M.
100^
A A
B
B
C
C 79° 1
Seconds of time
1.
2-
8"
4"
5»
6»
7'
Prop, parts of cols, i B
9
9
0
17
18
1
26
26
1
34
35
1
43
44
1
51
53
2
60
62
2
TABLE U.
[Page 619
Log.
Sines, Tangents, and Secants.
11°
A
A
B
B
C
C 168°
M.
Hour A. M.
Hour p. M.
Sine.
Difl.
Cosecant.
Tangent.
Diflf.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
10 32 0
1 28 0
9. 28060
0
10. 71940
9. 28865
0
10.71135
10. 00805
0
9. 99195
60
1
31 52
28 8
28125
1
71875
28933
1
71067
00808
0
99192
59
2
31 44
28 16
28190
2
71810
29000
2
71000
00810
0
99190
58
8
31 36
28 24
28254
3
71746
29067
3
70933
00818
0
99187
57
4
81 28
28 32
28319
4
71681
29184
4
70866
00815
0
99185
9. 99182
56
55
5
10 31 20
1 28 40
9. 28384
5
10. 71616
9. 29201
5
10. 70799
10. 00818
0
6
31 12
28 48
28448
6
71552
29268
6
70732
00820
0
99180
54
7
31 4
28 56
28512
7
71488
29335
8
70665
00823
0
99177
58
8
30 56
29 4
28577
8
71423
29402
9
70598
00825
0
99175
52
9
10
30 48
29 12
28641
9
71359
29468
10
70532
00828
0
99172
51
50
10 80 40
1 29 20
9. 28705
10
10. 71295
9. 29585
11
10. 70465
10. 00830
0
9.99170
n
30 82
29 28
28769
11
71281
29601
12
70399
00833
0
99167
49
12
30 24
29 36
28833 1 12
71167
29668
13
70332
00835
99165
48
18
30 16
29 44
28896
13
71104
29734
14
70266
00838
99162
47
14
30 8
29 52
28960
14
71040
29800
15
16
70200
00840
99160
9. 99157
46
45
15
10 30 0
1 30 0
9. 29024
16
10. 70976
9. 29866
10. 70134
10. 00843
IB
29 52
30 8
29087
17
70913
29932
17
70068
00845
99155
44
17
29 44
30 16
29150
18
70850
29998
18
70002
00848
99152
43
18
29 36
30 24
29214
19
70786
30064
19
69936
00850
99150
42
19
29 28
30 32
29277
20
70723
30130
20
69870
00853
99147
9. 99145
41
40
20
10 29 20
1 80 40
9. 29340
21
10. 70660
9. 30195
22
10. 69805
10. 00855
21
29 12
80 48
29403
22
70597
30261
23
69739
00858
99142
39
22
29 4
80 56
29466
23
70534
30326
24
69674
00860
99140
38
28
28 56
31 4
29529
24
70471
30.391
25
69609
00863
99137
87
24
28 48
31 12
1 31 20
29591
25
70409
30457
26
69543
10. 69478
00865
99135
36
35
25
10 28 40
9. 29654
26
10. 70346
9. 30522
27
10. 00868
9. 99182
26
28 32
81 28
29716
27
70284
30587
28
69413
00870
99130
34
27
28 24
31 36
29779
28
70221
30652
29
69.348
00873
99127
38
28
28 16
31 44
29841
29
70159
30717
30
69283
00876
99124
32
29
80
28 8
31 52
29903
30
70097
30782
31
32
69218
10. 69154
00878
99122
9. 99119
31
30
10 28 0
1 82 0
9. 29966
31
10. 70034
9. 30846
10. 00881
81
27 52
82 8
30028
32
69972
30911
33
69089
00883
99117
29
82
27 44
32 16
30090
33
69910
30975
35
69025
00886
99114
28
88
27 36
82 24
80151
34
69849
31040
36
68960
00888
99112
27
34
85
27 28
32 32
30213
35
69787
81104.
37
68896
00891
1
99109
9. 99106
26
25
10 27 20
1 32 40
9. 30275
36
10. 69725
9. 31168
38
10. 68832
10. 00894
2
86
27 12
32 48
30336
37
69664
31233
39
68767
005?&6
2
99104
24
87
27 4
32 56
80898
38
69602
31297
40
68703
00899
2
99101
23
88
26 56
33 4
30459
89
69541
31361
41
68689
00901
2
99099
22
39
26 48
83 12
30521
40
69479
31425
42
68575
00904
2
2
99096
9. 99093
21
20
40
10 26 40
1 33 20
9. 30582
41
10. 69418
9. 31489
43
10.68511
10. 00907
41
26 32
83 28
30643
42
69357
31552
44
68448
00909
2
99091
19
42
26 24
33 36
30704
43
69296
31616
45
68384
00912
2
99088
18
48
26 16
33 44
80765
45
69235
31679
46
68321
00914
2
99086
17
44
45
26 8
33 52
30826
46
47
69174
31743
47
68257
00917
2
2
99083
16
15
10 26 0
1 34 0
9. 30887
10.69113
9. 81806
49
10. 68194
10. 00920
9. 99080
46
25 52
34 8
30947
48
69053
31870
50
68130
00922
2
99078
14
47
25 44
34 16
31008
49
68992
31933
51
68067
00925
2
99075
13
48
25 86
34 24
31068
50
68932
31996
52
68004
00928
2
99072
12
49
25 28
34 82
31129
51
68871
32059
53
67941
00980
2
99070
11
10
50
10 25 20
1 34 40
9. 31189
52
10. 68811
9. 32122
54
10. 67878
10. 00938
2
9. 99067
51
25 12
34 48
31250
53
68750
32185
55
67815
00936
2
99064
9
52
25 4
34 56
31310
54
68690
82248
56
67752
00938
2
99062
8
58
24 56
35 4
31370
55
68630
32311
57
67689
00941
2
99059
7
54
55
24 48
35 12
31480
56
68570
32373
58
67627
00944
2
2
99056
6
10 24 40
1 35 20
9. 31490
57
10. 68510
9. 32436
59
10. 67564
10. 00946
9. 99054
5
56
24 32
35 28
31549
58
68451
32498
60
67502
00949
2
99051
4
57
24 24
35 36
31609
69
68391
32561
61
67439
00952
2
99048
3
58
24 16
35 44
81669
60
68331
32628
63
67877
00954
2 99046
2
59
24 8
35 52
81728
61
68272
32685
64
67315
00957
3 99043
1
60
24 0
36 0
31788
62
68212
32747
65
67253
00960
3
99040
0
M.
Hour p. M.
Hour A. M.
Cosine. Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
101°
A
A
B
B
C
C 78° 1
Seconds of time ■ 1*
2'
3»
4'
5» 1 6»
7'
Prop, parts of cols. •{B
ic
8
a
0
16
16
1
23
24
1
31
32
1
39 1 47
40 1 49
2 ! 2
54
57
2
Page 620]
TABLE U.
Log. Sines, Tangents, and Secants.
129
A A
B B
C
C 167°
M.
Hour A. M.
Hour p, M.
Sine.
Difl.
Cosecant.
Tangent.
DiS.
Cotangent.
Secant. •
Difl. j Cosine.
M.
60
0
10 24 0
1 36 0
9. 31788
0
10. 68212
9. 32747
0
10. 67253
10. 00960
0 9.99040
1
23 52
36 8
31847
1
68153
32810 1
67190
00962
0 99088
59
2
23 44
36 16
31907
2
68093
32872
2
67128
00965
0 : 99085
58
8
23 36
36 24
31966
3
68034
32933
3
67067
00968
0 99082
57
4
5
23 28
10 23 20
36 3t
1 36 40
82025 j 4
67975
10. 67916
32995
9.33057
4
5
67005
00970
10. 0097'3
0 '• 99080
0 9.99027
56
55
9. 32084
5
10. 66943
B
23 12 1
36 48
32143
6
67857
33119
6
66881
00976
0 99024
54
7
23 4 1
36 56
82202
7
67798
33180
7
66820
00978
0 99022
53
8
22 56
37 4
82261
8
67739
33242
8
66758
00981
0 99019
52
9
22 48
37 12
82319
9
67681
33803
9
66697
00984
10. 00987
0 ; 99016
0 9. 99013
51
50
10
10 22 40
1 37 20
9.32378 1 10
10. 67622
9. 88365
10 10.66635 1
11
22 32
37 28
82437 10
67563
33426 11
66574
00989
1 99011
49
12
22 24
37 36
82495
11
67505
33487
12
66513
00992
1 99008
48
18
22 16
37 44
32553
12
67447
33548
13
66452
00995
1 99005
47
14
22 8
37 52
32612
13
14
67388
38609
14 66391
00998
1 99002
46
45
15
10 22 0
1 38 0
9. 32670
10. 67880
9. 33670
15 10.66380
10. 01000
1 9.99000
16
21 52
38 8
32728
15
67272
38731
16
66269
01003
1 98997
44
17
21 44
38 16
82786
16
67214
33792
17
66208
01006
1 98994
43
18
21 36
38 24
32844
17
67156
33853
18
66147
01009
1 i 98991
42
19
20
21 28
38 32
32902
18
67098
33913
19
66087
01011
10.01014
1 98989
1 9.98986
41
40
10 21 20
1 38 40
9. 32960
19
10. 67040
9. 38974
20 10.66026
21
21 12
38 48
33018
20
66982
34034
21 65966
01017
1 98983
.39
22
21 4
38 56
38075 21
66925
34095
22 65905
01020
1 98980
38
28
20 56
39 4
33133
22
66867
34155
28 65845
01022
1 98978
37
24
20 48
39 12
88190
28
66810
34215
24
65785
10. 65724
01025
10.01028
1 98975
36
35
25
10 20 40
1 39 20
9. 33248
24
10. 66752
9. 34276
25
1 9.98972
26-
20 32
39 28
38805
25
66695
34336
26 I 6o664
01031
1 98969
34
27
20 24
39 36
33362
26
66638
34396
27 1 65604
01033
1 98967
83
28
20 16
39 44
83420
27
66580
34456
28
65544
01086
1 ' 98964
32
29
20 8
39 52
33477 ! 28
66523
84516
29
65484
01089
1 98961
31
80
10 20 0
1 40 0
9.33534 29
10. 66466
9. 34576
30
10. 65424
10. 01042
1 9.98958
80
81
19 52
40 8
33591 29
66409
34635
31
65365
01045
1 98955
29
82
19 44
40 16
88647
30
66358
84695
32 ! 65305
01047
1 98958
28
38
19 36
40 24
83704
31
66296
84755
83 65245
01050
2 98950
27
34
85
19 28
40 32
33761
32
66239
34814
34 65186
01053
2 98947
26
25
10 19 20
1 40 40
9.33818
33
10. 66182
9. 34874
35 10.65126
10. 01056
2 9.98944
36
19 12
40 4^
33874
34
66126
.34933
36 65067
01059
2 98941
24
87
19 4
40 56
38931
35
66069
34992
37 i 65008
01062
2 98988
23
88
18 56
41 4
33987
36
66013
35051
38 64949
01064
2 98936
22
39
18 48
41 12
34043 i 87
65957
8.5111
39 64889
01067
2
98933
9. 98930
21
20
40
10 18 40
1 41 20
9. 34100
38
10. 65900
9. 35170
40 10.64830
10.01070
2
41
18 32
41 28
34156
39
65844
85229
41 ! 64771
01073
2
98927
19
42
18 24
41 36
34212
40
65788
85288
42
64712
01076
2
98924
18
48
18 16
41 44
34268 1 41
65782
35347
43
64653
01079
2
98921
17
44
45
18 8
41 52
34324 ; 42
65676
85405
44
45
64595
01081
2
98919
9. 98916
16
15
10 18 0
1 42 0
9. 34380
43
10. 65620
9. 35464
10. 64536
10. 01084
2
46
17 52
42 8
34436
44
65564
35523
46 64477
01087
2
98913
14
47
17 44
42 16
34491
45
65509
35581
47 64419
01090
2
98910
13
48
17 36
42 24
34547
46
65453
35640
48 64360
01093
2
98907
12
49
17 28
42 32
34602
47
65398
35698
49 64302
01096
2
98904
11
50
10 17 20
1 42 40
9.84658 1 48
10. 65342
9. 35757
50 110.64243
10. 01099
2
9. 98901
10
51
17 12
42 48
34713
48
65287
35815
51
641^5
01102
2
98898
9
52
17 4
42 56
34769
49
65231
85873
52
64127
01104
2
98896
8
53
16 56
43 4
34824
50
65176
35981
53
64069
01107
2
98893
7
54
16 48
43 12
34879
51
65121
85989
64
64011
OHIO
3
3'
98890
9. 98887
6
5
55
10 16 40
1 43 20
9. 34934
52
10. 65066
9. 36047
55 10.63953
10.01113
56
16 32
43 28
34989
53
65011
36105
56
63895
01116
3
98884
4
57
16 24
43 36
35044
54
64956
36163
57
63837
01119
3
98881
3
58
16 16
43 44
35099
55
64901
36221
58
63779
01122
8
98878
2
59
16 8
43 52
35154
56
64846
36279
59
63721
01125
3
98875
1
60
16 0
44 0
35209
57
64791
36836
60
63664
01128
3
Difl.
98872
0
M.
Hour p. M.
Hour A. M.
Cosine, j Diflf.
Secant.
Cotangent.
Difif.
Tangent.
Cosecant.
Sine.
M.
102
o
A A
B B
C
C 77° 1
Seconds of time
Prop, parts of cols. -{B
C
TABLE U.
[Page 621
I
Mg. Sines, Tangents, and Secants.
13°
A
A
B
B
C
C 166°
M.
Hour A.M.
Hour P. M.
Sine.
9. 35209
Diff.
Cosecant.
Tangent. Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
60
0
10 16 0
1 44 0
0
10. 64791
9. 36336
0
10. 63664
10.01128
0
9. 98872
1
15 52
44 8
35268
1
64737
36394
1
63606
01181
0 ! 98869 1
59
?<
15 44
44 16
35818
2
64682
86452
2
68548
01183
0
98867
58
8
15 86
44 24
85373
3
&4627
36509
3
63491
01186
0
98864
57
4
15 28
44 32
35427
4
64578
10. 64519
36566
4
5
63484
10. 63876
01189
0
98861
56
55
5
10 15 20
1 44 40
9. 85481
4
9. 36624
10. 01142
0
9. 98858
fi
15 12
44 48
35536
5
64464
86681
6
68319
01145
0
98855
54
7
15 4
44 56
35590
6
64410
36738
6
63262
01148
0
98852
53
8
14 56
45 4
85644
7
64356
36795
7
63205
01151
0
98849
52
9
14 48
45 12
35698
8
64302
36852
8
63148
01154
0
98846
51
10
10 14 40
1 45 20
9. ;^752
9
10. 64248
9. 36909
9
10. 63091
10.01157
9. 98848
50
n
14 82
45 28
35806
10
64194
36966
10
63034
01160
98840
49
12
14 24
45 86
35860
11
64140
37023
11
62977
01163
98887
48
i;s
14 16
45 44
85914
11
64086
37080
12
62920
01166
98834
47
14
14 8
45 52
85968
12
64082
37137
13
62868
01169
98831
46
45
15
10 14 0
1 46 0
9. 86022
13
10. 63978
9. 37193
14
10. 62807
10.01172
9. 98828
ifi
18 52
46 8
36075
14
63925
87250
15
62750
01175
98825
44
17
18 44
46 16
36129
15
68871
87306
16
62694
01178
98822
43
18
18 86
46 24
36182
16
68818
37363
17
62637
01181
98819
42
19
18 28
46 32
86236
17
63764
37419
18
62581
01184
98816
41
20
10 18 20
1 46 40
9. 36289
18
10. 63711
9. 37476
19
10. 62524
10.01187
9. 98813
40
21
13 12
46 48
36842
18
63658
37532
19
62468
01190
98810
39
22
13 4
46 56
36895
19
68605
37588
20
62412
01193
98807
88
28
12 56
47 4
36449
20
63551
37644
21
62356
01196
98804
37
24
25
12 48
47 12
36502
21
6,3498
37700
22
62300
01199
98801
36
35
10 12 40
1 47 20
9. 36555
22 !l0.6;i445
9. 37756
23
10. 62244
10. 01202
9. 98798
2rt
12 82
47 28
36608
23
68392
37812
24
62188
01205
98795
34
27
12 24
47 86
36660
24
68340
37868
25
62182
01208
98792
38
28
12 16
47 44
36713
25
63287
37924
26
62076
01211
98789
32
29
30
12 8
47 52
36766
25
63284
37980
27
62020
01214
10. 01217
2
98786
31
10 12 0
1 48 0
9. 86819
26 110.63181
9. 38035
28
10. 61965
9. 98788
30
81
11 52
48 8
36871
27 68129
38091
29
61909
01220
2
98780
29
82
11 44
48 16
36924
28 68076
38147
30
61858
01223
2
98777
28
88
11 86
48 24
36976
29
6.8024
38202
31
61798
01226
2
98774
27
84
85
11 28
48 32
37028
30
62972
38257
32
61743
10. 61687
01229
10. 01232
2
2
98771
26
25
10 11 20
1 48 40
9. 37081
31
10. 62919
9. 38813
32
9. 98768
m
11 12
48 48
87183
32
62867
38868 ! 33
61632
01235
2
98765
24
87
11 4
48 56
37185
32
62815
88423 1 34
61577
012.38
2
98762
23
88
10 56
49 4
87237
33
62763
38479 i a5
61521
t)1241
2
98759
22
89
10 48
49 12
87289
34
62711
38534 36
61466
01244
2
98756
21
40
10 10 40
1 49 20
9. 87841
35
10. 62659
9. 38589 37
10. 61411
10.01247
2
9. 98758
20
41
10 32
49 28
87893
36
62607
88644 88
61856
01250
2
98750
19
42
10 24
49 86
87445
37
62555
88699
39
61301
01254
2
98746
18
48
10 16
49 44
37497
38
62503
88754
40
61246
01257
2
98748
17
44
45
10 8
49 52
37549
9. 37600
39
62451
88808
42
61192
10. 61137
01260
10. 01263
2
2
98740
16
15
10 10 0
1 50 0
39 10.62400
9. 38863
9. 98787
46
9 52
50 8
37652
40
62348
38918
43
61082
01266
2
98784
14
47
9 44
50 16
37703
41
62297
38972
44
61028
01269
2
98731
13
48
9 36
50 24
37755
42
62245
39027
45
60973
01272
2
98728
12
49
50
9 28
50 32
37806
9.37858
43
44
62194
10. 62142
39082
45
60918
01275
2
98725
11
10
10 9 20
1 50 40
9. 39136
46
10. e0864
10. 01278
3
9. 98722
51
9 12
50 48
37909
45
62091
39190
47
60810
01281
3
98719
9
52
9 4
50 56
37960
46
62040
39245
48
60755
01285
3
98715
8
58
8 56
51 4
38011
47
61989
39299
49
60701
01288
3
98712
7
54
8 48
51 12
38062
47
61988
39353
50
60647
01291
3
98709
6
55
10 8 40
1 51 20
9.88113
48
10. 61887
9. 39407
51
10. 60593
10. 01294
3
9. 98706
5
56
8 32
51 28
88164
49
61836
39461
52
60589
01297
3
98703
4
57
8 24
51 86
38215
50
61785
39515
53
60485
01300
3
98700
3
58
8 16
51 44
38266
51
61784
39569
54
60431
01303
3
98697
2
59
8 8
51 52
38817
52
61683
39623
55
60377
01306
3
98694
1
60
M.
8 0
52 0
38368
53
61682
39677
56
Diff.
60323
Tangent.
01310
3
98690
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Cosecant.
Diff.
Sine.
103°
A
A
B
B
C
C 76° 1
Seconds of time
1« i 2'
3s ^ 4, ^ 5» j 6'
7»
Prop, parts of cols. < B
Ic
7
7
0
13
14
1
20 26
21 28
1 2
33 39
8.5 42
2 2
46
49
3
Page 622]
TABLE 44.
Log. Sines, Tangents, and Secants.
14°
A
A
B B
C
C
16o°
M.
0
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
10. 60323
Secant.
Diff.
Cosine.
10 8 0
1 52 0
9. 38368
0
10. 61632
9. 39677
0
10. 01310
0
9. 98690
60
1
7 52
52 8
3S418
1 ! 61582
39731
1
60269
01313
0
98687
59
2
7 44
52 16
38469
2
61531
39785
9
60215
01316
0
98684
58
3
7 36
52 24
38519
2
61481
39838
3
60162
01319
0
98681
57
4
7 28
52 32*
38570
3
61430
39892
3
60108
01322
0
98(>78
56
55
5
10 7 20
1 52 40
38620
4
10. 61380
9. 39945
4
10. 60055
10. 01325
0
9. 98675
6
7 12
52 48
38670
5
61330
39999
5
60001
01329
0
98671
54
7
7 4
52 56
38721
6
61279
40052
6
599t8
01332
0
98668
53
8
6 56
53 4
38771
7
61229
40106
7
59894
01335
0
98665
52
9
6 48
53 12
38821
7
61179
40159
8
59841
01338
0
98662
51
10
10 6 40
1 53 20
9. 38871
8
10. 61129
9.40212 i 9
10. 59788
10. 01341
9. 98659
50
11
6 32
53 28
38921
9
61079
40266 10
59734
01344
98656
49
12
6 24
53 36
38971
10
61029
40319 1 10
59681
01348
98652
48
13
6 16
53 44
39021
11
60979
40372 j 11
59628
01351
98649
47
14
6 8
53 52
39071
11
60929
40425 1 12
59575
01354
98646
46
15
15
10 6 0
1 54 0
9. 39121
12 ilO. 60879
9.40478 i 13
10. 59522
10. 01357
9. 98643
16
5 52
54 8
39170
13 60830
40531 14
59469
01360
98640
44
17
5 44
54 16
39220
14
60780
40584 15
59416
01364
98636
43
18
5 36
54 24
39270
15
60730
40636 16
59364
01367
98633
42
19
20
5 28
10 5 20
54 32
39319
15
60681
10. 60631
40689 17
59311
01370
— J-
98630
9. 98627
41
40
1 54 40
9. 39369
16
9.40742 : 17
10. 59258
10. 01373
21
5 12
54 48
39418
17
60582
40795 1 18
59205
01377
98623
39
22
5 4
54 56
39467
18
60533
40847 19
59153
01380
98620
38
23
4 56
55 4
■ 39517
19
60483
40900 20
59100
01383
98617
37
24
4 48.
55 12
1 55 20
39566
S. 39615
20
60434
40952 ! 21
59048
01386
98614
36
25
10 4 40
20 10.60385
9.41005 22 10.58995
10. 01390
9. 98610
35
26
4 32
55 28
39664
21 60336
41057 ! 23
58943
01393
98607
34
27
4 24
55 36
39713
22 60287
41109 23
58891
01396
98604
33
28
4 16
55 44
39762
23 60238
41161 24
58839
01399
2
98601
32
29
4 8
55 52
39811
24 60189
41214 25
58786
01403
2
98597
31
30
10 4 0
1 56 0
9. 39860
24 10.60140
9.41266 26 10.58734
10. 01406
2
9. 98594
30
31
3 52
56 8
39909
25
60091
41318 27
58682
01409
2
98591
29
32
3 44
56 16
39958
26
60042
41370 28
58630
01412
2
98588
28
33
3 36
56 24
40006
27
59994
41422 29
58578
01416
2
98584
27
34
3 28
56 32
40055
28 59945
41474 30
58526
01419
2
2
98581
9. 98578
26
25
35
10 3 20
1 56 40
9. 40103
29 10.59897
9.41526 30
10. 58474
01422
36
3 12
56 48
40152
29
59848
41578 31
58422
01426
2
98574
24
37
3 4
56 56
40200
30
59800
41629 32
58371
01429
2
98571
23
38
2 56
57 4
40249
31
59751
41681 1 33
58319
01432
2
98568
22
39
2 48
57 12
40297
32 59703
41733 1 34
58267
01435
2
98565
21
40
10 2 40
1 57 20
9. 40346
33
10. 59654
9.41784 35 110.58216
10. 01439
2
9. 98561
20
41
2 32
57 28
40394
33
59606
41836 36
58164
01442
2
98558
19
42
2 24
57 36
40442
34
59558
41887 ! 36
58113
01445
2
98555
18
43
2 16
57 44
40490
36
59510
41939 i 37
58061
01449
2
98551
17
44
2 8
57 52
40538
36
59462
41990
38
58010
01452
2
985^8
16
15
45
10 2 0
1 58 0
9. 40586
37
10. 59414
9. 42041
39
10. 57959
10. 01455
2
9. 98545
46
1 52
58 8
40634
37
59366
42093 40 i 57907
01459
3
98541
14
47
1 44
58 16
40682
38
59318
42144 41
57856
01462
3
98538
13
48
1 36
58 24
40730
39
59270
42195 42
57805
01465
3
98535
12
49
1 28
58 32
40778
40
59222
42246 43
57754
01469
3
3
98531
9. 98528
11
10
50
10 1 20
1 58 40
9. 40825
41 :i0. 59175
9.42297 : 43
10. 57703
10. 01472
51
1 12
58 48
40873
42
59127
42348 i 44
57652
01475
3
98525
9
52
1 4
58 56
40921
42
59079
42399 i 45
57601
01479
3
98521
8
53
0 56
59 4
40968
43
59032
42450
46
57550
01482
3
98518
7
54
0 48
59 12
41016
44
58984
42501
47
48
57499
01485
3
98515
9.98511
6
5
55
10 0 40
1 59 20
9. 41063
45 10.58937
9. 42552
10. 57448
10. 01489
3
56
0 32
59 28
41111
46
58889
42603
49
57397
01492
3
98508
4
57
0 24
59 36
41158
46
58842
42653
50
57347
01495
3
98505
3
58
0 16
59 44
41205
47
58795
42704
50
57296
01499
3
98501
2
59
0 8
59 52
41252
48
58748
42755
51
57245
01502
3
98498
1
60
0 0
2 0 0
41300
49
58700
42805
52
57195
01506
3
98494
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
104°
A
A
B B
C
c
76°
Seconds of time
1«
2«
3»
4»
5>
«•
7»
fA
Prop, parts of cols, i B
IC
6
7
0
12
13
1
18
20
1
24
26
2
31
83
2
37
39
2
43
40
3
TABLE 44.
[Page 623
Log.
Sines, Tangents, and Secants.
15°
A
A
B
B
C
C 164°
M.
0
Hour A.M.
10 0 0
Hour P.M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff. Cosine.
M.
2 0 0
9.41300
0
10. 58700
9. 42805
0
10. 57195
10. 01506
0 ! 9. 98494
60
1
9 59 52 0 8
41347
1
58653
42856
1
57144
01509
0 98491
59
2
59 44 0 16
41394
2
5860(5
42906
2
57094
01512
0 1 98488 1 58 1
8
59 36 1 0 24
41441
2
58559
42957
2
57043
01516
0 98484 ! 57 I
4
59 28 0 32
41488
3
58512
43007
3
56993
01519
0
98481 56
5
9 59 20 2 0 40
9. 41535
4
10. 58465
9. 43057
4
10. 56943
10. 01523
0
9.98477 55
6
59 12 0 48
41582
5
58418
43108
5
56892
01526
0 1 98474
54
7
59 4 0 56
41628
5
58372
43158
6
56842
01529
0 1 98471
53
8
58 56 ; 14'
41675
6
58325
43208
7
56792
01533
0 ; 98467
52
9
10
58 48 ! 1 12
41722
7
58278
43258
7
56742
01536
98464
9. 98460
51
50
9 58 40 2 1 20
9. 41768
8
10. 58232
9. 43308
8
10. 56692
10. 01540
1
n
58 32 1 28
41815
8
58185
43358
9
56642
01543
98457
49
12
58 24 1 36
41861
9
58139
43408
10
56592
01547
98453
48
13
58 16 , 1 44
41908
10
58092
43458
11
56542
01550
98450
47
14
15
58 8
9 58 0
1 52
41954
9. 42001
11
11
58046
43508
11
56492
01553
10. 01557
98447
9. 9844;^
46
45
2 2 0
10. 57999
9. 43558
12 110.56442
16
57 52 i 2 8
42047
12
57953
43607
13
56393
01560
98440
44
17
57 44
2 16
42093
13
57907
43657
14
56343
01564
98436
43
18
57 36
2 24
42140
14
57860
43707
15
56293
01567
98433
42
19
57 28
2 32
42186
14
57814
43756
9. 43806
16
56244
01571
10. 01574
98429
41
20
9 57 20 i 2 2 40
9. 42232
15
10. 57768
16
10. 56194
1 9. 98426 1 40 |
21
57 12 j 2 48
42278
16
57722
43855
17
56145
01578
1 98422
39
22
57 4 2 56
42324
17
57676
43905
18
56095
01581
1 98419
38
23
56 56
3 4
42370
17
576.30
43954
19 i 56046
01585
1 , 98415
37
24
25
56 48
3 12
42416
18
57584
44004
20
55996
01588
1 98412 1 36
9 56 40 i 2 3 20
9. 42461
19
10. 57539
9. 44053
20
10. 55947
10. 01591
1 9.98409 1 35
26
56 32 3 28
42507
20
57493
44102
21
55898
01595
2 98405
34
27
56 24 3 36
42553
21
57447
44151
2-2
55849
01598
2 98402
33
28
56 16 3 44
42599
21
57401
44201
23
55799
01602
2 98398
32
29
30
56 8 3 52
42644
9. 42690
22
23
57356
10.57310
44250
24
55750
01605
2 98395
31
9 56 0
2 4 0
9. 44299
25 ilO. 55701
10. 01609
2 9.98391 i 30
31
55 52
4 8
42735
24
57265
44.348
25
55652
01612
2 98388 t 29
32
55 44 4 16
42781
24
57219
44397
26
55603
01616
2 ' 98384 28
33
55 36 1 4 24
42826
25
57174
44446
27
55554
01619
2 i 98381
27
34
55 28 i 4 32
42872
26
57128
10. 57083
44495
9. 44544
28
55505
01623
2 98377
26
25
35
9 55 20
2 4 40
9.42917
27
29
10. 55456
10. 01627
2 9.98373
36
55 12
4 48
42962
27
57038
44592
29
55408
016.30
2 98370
24
37
55 4
4 56
43008
28
56992
44641
30
55359
01634
2 98366
23
38
54 56
5 4
43053
29
56947
44690
.31
55310
01637
2 98363
22
39
40
54 48
9 54 iO'
5 12
43098
30
30
56902
44738
9. 44787
32
33
55262
10. 55213
01641
10. 01644
2 98359 1 21
2 9. 98356 i 20
2 5 20
9. 43143
10. 56857
41
54 32
5 28
43188
31
56812
44836
34
55164
01648
2
98352 19
42
54 24
5 36
43233
32
56767
44884
34
55116
01651
2
98349 18
43
54 16
5 44
43278
33
56722
44933
35
55067
01655
3
98345 17
44
54 8
5 52
43323
9. 43367
33
34
56677
44981
9. 45029
36
37
55019
10. 54971
01658
10. 01662
3
98342 t 16
45
9 54 0
2 6 0
10. 56633
3 9. 98338 15 1
46
53 52
6 8
4.3412
35
56588
45078
38
54922
01666
3 98.334 14 I
47
53 44 6 16
43457
36
56543
45126
38
54874
01669
3 98331
13
48
53 36 i 6 24
43502
36
56498
45174
39
54826
01673
3 98327
12
49
50
53 28
6 32
2 6 40
43546
37
56454
45222
9. 45271
40
41
54778
10. 54729
01676
10. 01680
3
3
98324
11
10
9 53 20
9. 43591
38
10. 56409
9. 98320
51
53 12 i 6 48.
43635
39
56365
45319
42
54681
01683
3
98317
9
52
53 4 ■ 6 56
43680
39
56320
45367
43
54633
01687
3
98313
8
53
52 56
7 4
43724
40
56276
45415
43
54585
01691
3
98309
7
54
55
52 48
9 52 40
7 12
2 7 20
43769
9743813
41
42
56231
45463
9.45511
44
45
54537
01694
10.01698
3
3
98306
9. 98302
6
5
10. 56187
10. 54489
56
52 32
7 28
43857
43
56143
45559
46
54441
01701
3
98299
4
57
52 24
7 36
43901
43
56099
45606
47-
54394
01705
3
98295
3
58
52 16
7 44
43946
44
56054
45654
47
54.346
01709
3
98291
2
59
52 8
7 52
43990
45
56010
45702
48
54298
01712
3
98288
1
60
52 0
8 0
440.34
46
55966
45750
49
54250
01716
4
98284
0
M.
Hour p. M.
Hour A. x.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
105°
A
A
B
B
C
C 74° 1
.Seconds of time ; 1» '2' \ 3'
4» 5»
6' 1'
A 6
Prop, parts of cols. B 6
Ic 0
11
12
1
17
18
1
23 28
25 31
2 2
34 40
37 43
3 3
Page 624]
TABLE 44.
Log. Sines, Tangents, and Secants.
1S°
A A
B
B
C
C
163°
M.
Hour A. M
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
9 52 0
2 8 0
9. 44034
0
10. 55966
9. 45750
0
10. 542.50
10.01716
0
9. 98284
60
1
51 52
8 8
44078
1
55922
45797
1
54203
01719
0
98281
59
2
51 44
8 16
44122 1
55878
45845
2
541.55
01723
0
98277
58
8
51 36
8 24
44166 2
55834
45892
2
54108
01727
0
98273
57
4
51 28
8 ^2
44210 3
9. 44253 4
557f;0
10. 55747
45940
9. 45987'
3
4
54060
10. 54013
01730
10. 61734
0 98270
0 9.98266
56
55
5
9 51 20
2 8 40
6
51 12
8 48
44297
4
55703
46035
5
53965
01738
0 98262
54
7
51 4
8 56
44341
5
55659
46082
5
53918
01741
0 ' 98259
53
8
50 56
9 4
44385
6
55615
46130
6
53870
01745
0 98255
52
9
10
50 48
9 12
44428
6
55572
10. 5.5528
46177
9. 46224
7
8
53823
10. 53776
01749
1 98251
1 9.98248
51
,50
9 50 40
2 9 20
9. 44472
7
10.01752
11
50 32
9 28
44516 8
55484
46271
9
53729
017.56
98244
49
12
50 24
9 36
44559 9
55441
46319
9
53681
01760
98240
48
13
50 16
9 44
44602 9
55398
46366
10
53634
01763
98237
47
14
15
50 8
9 50 0
9 52
44646 10
9.44689 1 11
553.54
10.5.5311
46413
9. 46460
11
12
5.3587
01767
98233
9. 98229
46
45
2 10 0
10. ,53540
10.01771
16
4 ) 52
10 8
447.33 1 11
55267
46507
12
53493
01774
98226
44
17
49 44
10 16
44776 12
55224
46554
13
53446
01778
98222
43
18
4 J 36
10 24
44819 13
55181
46601
14
53399
01782
98218
42
19
20
49 28
9 49 20
10 32
2 10 40
44862
14
14
55138
10. 55095
46648
9.46694
15
15
53352
10. 53306
01785
10.01'78'9
98215
41
9. 44905
9.98211
40
21
49 12
10 48
44948 1 15
5.5052
46741
16
53259
01793
98207
39
22 49 4
10 56
44992 16
55008
46788
17
53212
01796
98204
38
23 48 56
11 4
45035 16
54965
46835
18
,53165
01800
1
98200
37
24 48 48
11 12
46077 17
54923
46881
19
53119
01804
98196
36
25 9 48 40
2 11 20
9.45120 18
10. .54880
9. 46928
19
10. 53072
10.01808
2
9.98192
35
26 48 32
11 28 ^
45163 18
54837
46975
20
53025
01811
2
98189
34
27 48 24
11 36 '
45206 19
54794
47021
21
52979
01815
2
98185
33
28 48 16
11 44
45249 20
54751
47068
22
52932
01819
2
98181
32
29
30
48 8
11 52
2 12 0
45292 21
9.453.34 21
54708
47114
22
52886
01823
2
98177
31
30
9 48 0
10.54666
9. 47160
23
10. 52840
10. 01826
2
9.98174
31
47 52
12 8
45377 i 22
54623
47207
24
52793
01830
2
98170
29
32
47 44
12 16 '
45419 23
54581
47253
25
52747
01834
2
98166
28
33
47 36
12 24
45462 : 23
54538
47299
26
52701
01838
2
98162
27
34
47 28
12 32
2 12 40
45504 : 24
9.4.5547 25
54496
10. 54453
47346
9. 47392
26
27
52654
10. 52608
01841
2
98159
26
25
35
9 47 20
10.01845
2
9.981.55
36
47 12
12 48
4.5589 26
54411
47438
28
52562
01849
2
98151
24
37
47 4
12 56
45632 26
54368
47484
29
52516
018,53
2
98147
23
38 46 56
13 4
45674 27
54326
47.530
29
52470
01856
2
98144
22
39 46 48
40 9 46 40
13 12
2 13 20
45716
28
28'
54284
10. .54242
47576
9. 47622
30
31
52424
01860
10.01864
2
2
98140
9»98136
21
20
9. 45758
10. 52378
41 46 32
13 28
45801 29
54199
47668
32
52.332
01868
3
98132
19
42 46 24
13 36
45843 30
54157
47714
32
52286
01871
3
98129
18
43 46 16
13 44
45885 31
54115
47760
33
52240
01875
3
98125
17
44 46 8
45 9 46 0
13 52
2 14 0
4,5927
31
54073
10. .54031
47806
9. 47852
34
35
.52194
10. ,52148
01879
10. 01883
3
3
98121
9.98117
16
15
9. 45969
32
46 45 52
14 8
46011
33
53989
47897
36
52103
01887
3
98113
14
47 45 44
14 16
46053
33
53947
47943
36
52057
01890
3
98110
13
48 ■ 45 36
14 24
46095 i 34
53905
47989
37
52011
01894
3
98106
12
49 45 28
14 32
461.36 1 35
53864
48035
38
51965
01898
3
98102
11
50 i 9 45 20
2 14 40
9.46178 .36
10. 53822
9. 48080
39
10.51920
10.01902
3
9. 98098
10
51 45 12
14 48
46220 i 36
53780
48126
39
51874
01906
3
98094
9
52 j 45 4
14 56
46262 37
53738
48171
40
51829
01910
3
98090
8
53 I 44 56
15 4
46303 38
53697
48217
41
51783
01913
3
98087
7
54
44 48
15 12
46.345 38
53655
10.53614
48262
9. 48.307
42
43
51738
01917
3
3
98083
6
5
55
9 44 40
2 15 20
9.46386 39
10. 51693
10. 01921
9. 98079
56
44 32
15 28
46428 40
53572
48353
43
5ia47
01925
3
98075
4
57
44 24
15 36
46469 41
• 53531
48398
44
51602
01929
4
98071
3
58
44 16
15 44
46511 ! 41
53489
48443
45
51.5-57
01933
4
98067
2
59
44 8
15 52
46552 1 42
5.3448
48489
46
51511
01937
4
98063
1
60
M.
44 0
16 0
46594
43
53406
Secant.
48534
46
51466
01940
4
Diff
98060
0
M.
Hour p. M.
Hour A. M.
Casine.
Diff.
Cotangent
Diff.
Tangent.
Cosecant.
Sine.
106°
A A
B
B
C
C
73°
Seconds of time
1"
«•
3«
4'
&>
6<
7"
Prop, parts of cols.
(1
5
6
0
11
12
1
16
17
1
21
•23
2
27
29
2
32
35
3
37
41
3
TABLE 44.
[Page 625
Log. Sines, Tangents, and Secants.
17°
A A
B B
C
C 162°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Difl. Cosine.
M.
0
9 44 0
2 16 0
9. 46594
0
10. 53406
9. 48584
0
10. 51466
10. 01940
0 9.98060
60
1
48 52
16 8
46685
1
53365
48579
1
51421
01944
0 98056
59
2
48 44
16 16
46676
1
53324
48624
1
51376
01948
0 98052
58
8
48 86
16 24
46717
2
53283
48669
2
51331
019.52
0 98048
57
4
5
43 28
16 32
46758
3
54242
48714
3
51286
01956
0 98044
56
55
9 43 20
2 16 40
9. 46800
3
10. 53200
9.48759
4
10. 51241
10. 01960
0 9.98040
6
43 12
16 48
4()S41
4
53159
48804
4
51196
01964
0
98036
54
1
43 4
16 56
4(i8S2
5
53118
48849
5
51151
01968
0
98032
58
8
42 56
17 4
46923
5
53077
48894
6
51106
01971
98029
52
9
10
42 48
17 12
46964
6
7
53036
10. 52995
48939
7
51061
01975
98025
51
9 42 40
2 17 20
9. 47005
9. 48984
7
10. 51016
10. 01979
9. 98021
50
11
42 32
17 28
47045
7
52955
49029
8
50971
01983
1 1 98017
49
12
42 24
17 36
47086
8
52914
49073
9
50927
01987
1 1 98013
48
13
42 16
17 44
47127
9
52873
49118 i 10
50882
01991
1 1 98009
47
14
15
42 8
17 52
2 18 0
47168
9
52832
10. 52791
49163
10
50837
01995
1 1 98005
1 9.98001
46
45
9 42 0
9. 47209
10
9. 49207
11 110.50793
10. 01999
16
41 52
18 8
47249
11
52751
49252
12
50748
02008
97997
44
17
41 44
18 16
47290
11
52710
49296
12
50704
02007
97998
43
18
41 36
18 24
47830
12
52670
49341
13
50659
02011
97989
42
19
41 28
18 32
47371
13
52629
49385
14
50615
02014
1 ' 97986
41
20
9 41 20
2 18 40
9.47411
13
10. 52589
9. 49430
15
10. 50570
10.02018
1 9.97982
40
21
41 12
18 48
47452
14
52548
49474
15
50526
02022
1 I 979.78
39
22
41 4
18 56
47492
15
52508
49519
16
50481
02026
1 97974
38
28
40 56
19 4
47533
15
52467
49563
17
50487
02080
2 97970
37
24
40 48
19 12
47573
16
52427
49607
18
50393
02084
10. 02038
2 97966
2 9.97962
36
35
25
9 40 40
2 19 20
9. 47613
17
10. 52387
9. 49652
18
10. 50848
2(5
40 32
19 28
47654
17
52346
49696
19
50304
02042
2
97958
34
27
40 24
19 36
47694
18
52306
49740
20
50260
02046
2
97954
33
28
40 16
19 44
47734
19
52266
49784
21
50216
02050
2
97950
32
29
40 8
19 52
47774
19
20
52226
49828
21
22
50172
02054
2
2
97946
31
30
80
9 40 0
2 20 0
9.47814
10.52186
9. 49872
10. 50128
10. 02058
9. 97942
81
39 52
20 8
47854
21
52146
49916
23
50084
02062
2
97938
29
82
39 44
20 16
47894
21
52106
49960
24
50040
02066
2
97934
28
88
39 36
20 24
47934
22
52066
50004
24
49996
02070
2
97930
27
34
85
39 28
20 32
47974 j 23
52026
50048
9. 50092
25
26
49952
10. 49908
02074
2
97926
26
25
9 39 20
2 20 40
9. 48014
23
10. 51986
10. 02078
2 9.97922
36
39 12
20 48
48054
24
51946
50136
26
49864
02082
2
97918
24
37
39 4
20 56
48094
25
51906
50180
27
49820
02086
2
97914
23
38
38 56
21 4
48133
25
51867
50223
28
49777
02090
3
97910
22
39
40
38 48
21 12
2 21 20
48173
26
51827
50267
29
49733
02094
3 i 97906
3 9.97902
21
20
9 38 40
9. 48213
27
10. 51787
9.50311
29 ilO. 49689
10. 02098
41
38 32
21 28
48252
27
51748
50.355
30 1 49645
02102
3 j 97898
19
42
38 24
21 86
48292
28
51708
50398
31 49602
02106
3 ; 97894
18
43
38 16
21 44
48332
29
51668
50442
32 49558
02110
3 97890
17
44
45
38 8
21 52
2 22 0
48371
29
30
51629
10. 51589
50485
32 49515
02114
3
3
97886
9. 97882
16
15
9 38 0
9.48411
9. 50529
33 10.49471
10.02118
46
87 52
22 8
48450
31
51550
50572
34
49428
02122
3
97878
14
47
37 44
22 16
48490
31
51510
50616
35
49884
02126
3
97874
13
48
37 36
22 24
48529
32
51471
50659
35
49341
02130
3
97870
12
49
50
37 28
9 37 20
22 32
2 22 40
48568
33
33
51432
10. 51393
50703
9. 50746^
36
49297
02134
3 97866
11
10
9. 48607
37
10. 49254
10. 02139
3 9.97861
51
37 12
22 48
48647
'34
51353
50789
37
49211
02143
3 97857
9
52
37 4
22 56
48686
35
51314
50833
38
49167
02147
3
97853
8
58
36 56
23 4
48725
35
51275
50876
39
49124
02151
4
97849
t
54
55
36 48
9 36 40
23 12
2 23 20
48764
36
51236
50919
9. 50962
40
40
49081
02155
4
97845
6
5
9. 48803
37
10.51197
10. 49038
10. 02159
4
9. 97841
56
36 32
23 28
48842
37
51158
51005 41
48995
02163
4
97887
4
57
36 24
23 36
48881
38
51119
51048
42
48952
02167
4
97888
3
58
36 16
23 44
48920
39
51080
51092
43
48908
02171
4
97829
2
59
36 8
23 52
48959
39
51041
511.35
43
48865
02175
4
97825
1
60
36 0
24 0
48998
40
51002
51178
44
48822
02179
4
97821
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.] Diflf.
Tangent.
Cosecant.
Diff.
Sine.
M.
107°
A A
B B
C
C 72° 1
Seconds of time
Prop, parts of cols. -{B
C
10
11'
\
30
33
L3
22489-03-
40
Page 626]
TABLE U.
Log.
Sines, Tangents, and Secants.
18°
A
A
B B
C
C 161°
M.
0
Hour A.M.
9 36 0
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent. Diff.
Cotangent.
Secant.
Diff.
Cosine. 1
M.
2 24 0
9. 48998
0
10. 51002
9.51178
0
10. 48822
10. 02179
0 I 9. 97821 1
60
1
35 52
24 8
49037
1
50963
51221
1
48779
02183
0
97817
59
2
85 44
24 16
49076
1
50924
51264
1
48736
02188
0
97812
58
8
35 36
24 24
49115
2
50885
51806
2
48694
02192
0
97808
57
4
5
35 28
24«82
49158
3
50847
51349
8
48651
02196
0
0
97804
56
55
9 35 20
2 24 40
9. 49192
8
10. 50808
9. 51392
3
10. 48608
10. 02200
9. 97800
6
85 12
24 48
49281
4
50769
51435
4
48565
02204
0
97796
54
7
35 4
24 56
49269
4
50731
51478
5
48522
02208
0
97792
53
8
34 56
25 4
49308
5
50692
51520
6
48480
02212
97788
52
9
34 48
25 12
49347
6
50653
51563
6
48437
02216
97784
51
50
10
9 34 40
2 25 20
9. 49385
6
10. 50615
9. 51606
7
10. 48394
10. 02221
9. 97779
11
84 32
25 28
49424
7
50576
51648
8
48352
02225
97775
49
12
34 24
25 86
49462
8
50538
51691
8
48309
02229
97771
48
18
34 16
25 44
49500
8
50500
51784
9
48266
02233
97767
47
14
84 8
25 52
49539
9
50461
51776
10
48224
02237
97763
46
45
15
9 34 0
2 26 0
9. 49577
9
10. 50428
9. 51819
10 10.48181
10. 02241
9. 97759
1«
38 52
26 8
49615
10
50385
51861
11
48139
02246
97754
44
17
83 44
26 16
49654
11
50346
51903
12
48097
02250
97750
43
18
33 36
26 24
49692
11
50308
51946
18
48054
02254
97746
42
19
33 28
26 32
49730
9. 49768
12
13
50270
10. 50232
51988
9. 52031
18
48012
02258
97742
41
40
20
9 88 20
2 26 40
14
10. 47969
10. 02262
9. 97738
21
. 33 12
26 48
49806
13
50194
52073
15
47927
02266
97734
39
22
83 4
26 56
49844
14
50156
52115
15
47885
02271
2
97729
38
23
82 56
27 4
49882
14
50118
52157
16
47843
02275
2
97725
37
24
32 48
27 12
49920
15
50080
52200
17
17
47800
02279
2
97721
36
25
9 32 40
2 27 20
9. 49958
16
10. 50042
9. 52242
10. 47758
10. 02283
2
9. 97717
85
26
32 82
27 28
49996
16
50004
52284
18
47716
02287
2
97713
84
27
82 24
27 86
50084
17
49966
52326
19
47674
02292
2
97708
33
28
32 16
27 44
50072
18
49928
52368
20
47632
02296
2
97704
32
29
82 8
27 52
50110
18
49890
52410
20
47590
02300
2
97700
81
30
9 82 0
2 28 0
9. 50148
19
10. 49852
9. 52452
21
10. 47548
10. 02304
2
9. 97696
30
31
31 52
28 8
50185
20
49815
52494
22
47506
02309
2
97691
29
82
31 44
28 16
50228
20
49777
52536
22
47464
02313
2
97687
28
83
31 36
28 24
50261
21
49739
52578
28
47422
02317
2
> 97688
27
34
81 28
28 82
50298
21
49702
52620
24
47380
02321
2
97679
26
25
85
9 81 20
2 28 40
9. 50336
22
10. 49664
9. 52661
24
10. 47389
10. 02326
2
9. 97674
86
31 12
28 48
50374
23
49626
52708
25
47297
02880
3
97670
24
37
81 4
28 56
50411
23
49589
52745
26
47255
02334
3
97666
23
88
30 56
29 4
50449
24
49551
52787
27
47213
02838
3
97662
22
39
40
30 48
29 12
50486
25
49514
52829
27
47171
10. 47130
02848
3
97657
21
20
9 30 40
2 29 20
9. 50523
25
10. 49477
9. 52870
28
10. 02847
3
9. 97653
41
30 32
29 28
50561
26
49489
52912
29
47088
02351
3
97649
19
42
30 24
29 86
50598
26
49402
52953
29
47047
02355
3
97645
18
43
30 16
29 44
50635
27
49865
52995
80
47005
02360
3
97640
17
44
30 8
29 62
50673
28
49327
58087
31
46963
02864
3
97636
16
45
9 30 0
2 30 0
9. 50710
28
10. 49290
9. 58078
31
10. 46922
10. 02868
8
9. 97682
15
46
29 52
30 8
50747
29
49253
53120
82
46880
02372
8
97628
14
47
29 44
30 16
50784
80
49216
53161
83
46889
02377
3
97623
18
48
29 36
30 24
50821
30
49179
53202
34
46798
02381
3
97619
12
49
29 28
30 32
50858
31
49142
58244
84
46756
02385
8
4
97615
9. 97610
11
10
50
9 29 20
2 30 40
9. 50896
31
10. 49104
9. 58285
35
10. 46715
10.02390
51
29 12
30 48
50988
82
49067
53327
36
46673
02394
4
97606
9
52
29 4
30 56
50970
38
49030
53368
36
46632
02398
4
97602
8
53
28 56
31 4
r^007
88
48998
53409
37
46591
02408
4
97597
/
54
55
28 48
9 28 40
31 12
2 31 20
51043
84
85
48957
10. 48920
58450
9. 53492
38
88
46550
10. 46508
02407
10. 02411
4
4
97593
9. 97589
6
5
9. 51080
56
28 82
31 28
51117
85
48888
53533
89
46467
02416
4
97584
4
57
28 24
81 36
51154
36
48846
53574
40
46426
02420
4
97580
3
58
28 16
31 44
51191
37
48809
53615
41
46385
02424
4
97576
2
59
28 8
31 52
51227
87
48773
53656
41
46344
02429
4
97571
i
60
28 0
82 0
51264
88
48736
53697
42
46303
02488
4
97567
0
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
108
3
A
A
B B
C
C 71°|
Seconds of time
1»
2«
8»
4'
5>
6»
T
Prop, parts of cols. <B
5
5
1
9
10
1
14
16
2
19
21
2
24
26
3
28
31
3
38
37
4
TABLE U.
[Page 627
Log. Sines, Tangents, and Secants.
10°
A A
B
B
C
C 106°
M.
Hour A. M.
Hour P.M.
Sine.
Dlff.
Cosecant.
Tangent.
Diflf.
Cotangent.
Secant.
Diflf.
Cosine.
M.
0
9 28 0
2 32 0
9. 51264
0
10. 48736
9. 53697
0
10. 46303
10. 02433
0
9. 97567
60
1
27 52
32 8
51301
1
48699
53738
1 i 46262
02437
0
97563
59
2
27 44
32 16
51338
1
48662
53779
1 1 46221
02442
0
97558
58
?,
27 36
32 24
51374
2
48626
53820
2 I 46180
02446
0
97554
57
4
5
27 28
9 27 20
32 32
2 32 40'
51411
2
48589
53861
3 ! 46139
02450
0
0
97550
56
55
9. 51447
3 10.48553
9. 53902
3 i 10. 46098
10. 02455
9.97545
(i
27 12
32 48
51484
4
48516
53943
4 I 46057
02459
0
97541
54
I
27 4
32 56
51520
4
48480
53984
5 1 46016
02464
97536
53
8
26 56
33 4
51557
5
48443
54025
5 'i 45975
02468
1 97532
52
9
26 48
33 12
51593
5 ! 48407
54065
9. 54106
6
7
45935
02472
97528
51
50
10
9 26 40
2 33 20
9. 51629
6 10.48371
10. 45894
10. 02477
9. 97523
11
26 32
33 28
51666
7
48334
54147
7 i 45853
02481
97519
49
12
26 24
33 36
51702
7
48298
54187
8 4.5813
02485
97515
48
18
26 16
33 44
51738
8
48262
54228
9 45772
02490
97510
47
14
26 8
33 52
51774
8
48226
54269
9 ! 45731
02494
97506
46
45
15
9 26 0
2 34 0
9.51811
9
10. 48189
9. 54309
10 10.45691
10. 02499
9. 97501
16
25 52
34 8
51847
10
48153
54350
11 45650
02503
97497
44
17
25 44
34 16
51883
10
48117
54390
11 45610
02508
97492
43
18
25 36
34 24
51919
11
48081
54431
12 45569
02512
97488
42
19
25 28
34 32
51955
11
48045
54471
13 45529
02516
97484
41
40
20
9 25 20
2 34 40
9. 51991
12
10. 48009
9.54512
13 10.45488
10. 02521
9. 97479
21
25 12
34 48
52027 ! 12
47973
54552
14 , 45448
02525
2
97475
39
22
25 4
34 56
52063
13
47937
54593
15 45407
02530
2
97470
38
23
24 56
35 4
52099
14
47901
54633
15 45367
02534
2
97466
37
24
25
24 48
35 12
52135
14
47865
54673
16
45327
10. 45286
02539
2
97461
36
35
9 24 40
2 35 20
9.52171
15
10. 47829
9. 54714
17
10. 02543
2
9. 97457
26
24 32
35 28
52207
15
47793
54754
17 45246
02547
2
97453
34
27
24 24
35 36
52242
16
47758
54794
18 45206
02552
2
97448
33
28
24 16
35 44
52278
17
47722
54835
19 , 45165
02556
2
97444
32
29
24 8
35 52
52314
17
47686
54875
19 ! 45125
02561
2
97439
31
30
30
9 24 0
2 36 0
9.52350
18
10. 47650
9. 54915
20 10.45085
10. 02565
2
9. 97435
31
23 52
36 8
52385
18
47615
54955
21 i 45045
02570
2
97430
29
32
23 44
36 16
52421
19
47579
54995
21
45005
02574
2
97426
28
33
23 36
36 24
52456
20
47544
55035
22
44965
02579
2
97421
27
34
23 28
36 32
52492
20
47508
55075
23
44925
02583
3
97417
26
35
9 23 20
2 36 40
9. 52527
21
10.47473
9.55115
23
10. 44885
10. 02588
3
9. 97412
25
36
23 12
36 48
52563
21
47437
55155
24
44845
02592
3
97408
24
37
23 4
36 56
52598
22
47402
55195
25
44805
02597
3
97403
23
38
22 56
37 4
52634
23
47366
55235
25
44765
02601
3
97399
22
39
22 48
37 12
52669
23
47331
55275
26
27
44725
02606
3
97394
9. 97390
21
20
40
9 22 40
2 37 20
9. 52705
24
10. 47295
9. 55315
10. 44685
10. 02610
3
41
22 32
37 28
52740
24
47260
55355
27
44645
02615
3
97385
19
42
22 24
37 36
52775
25
47225
55395
28
44605
02619
3
97381
18
43
22 16
37 44
52811
26
47189
55434
29
44566
02624
3
97376
17
44
45
22 8
9 22 0
37 52
52846
9. 52881
26
27
47154
55474
29
44526
02628
3
97372
16
15
2 38 0
10.47119
9. 55514
30 ; 10. 44486
10. 02633
3
9. 97367
46
21 52
38 8
52916
27
47084
55554
31
44446
02637
3
97363
14
47
21 44
38 16
52951
28
47049
55593
31
44407-
02642
3
97358
13
48
21 36
38 24
52986
29
47014
55633
32
44367
02647
4
97353
12
49
50
21 28
38 32
53021
29
46979
55673
33
44327
02651
4
97349
11
9 21 20
2 38 40
9. 53056
30
10. 46944
9.55712
33
10. 44288
10. 02656
4
9. 97344
10
51
21 12
38 48
53092
30
46908
55752
34
44248
02660
4
97340
9
52
21 4
38 56
53126
31
46874
55791
35
44209
02665
4
97335
8
53
20 56
39 4
53161
32
46839
55831
35
44169
02669
4
97331
t
54
55
20 48
39 12
53196
32
46804
55870
36
441.30
02674
4
97326
6
5
9 20 40
2 39 20
9. 53231
33
10. 46769
9. 55910
37 !10. 44090
10. 02678
4
9. 97322
56
20 32
39 28
53266
33
46734
55949
37
44051
02683
4
97317
4
n{
20 24
39 36
53301
34
46699
55989
38
44011
02(588
4
97312
3
58
20 16
39 44
53336
34
46664
56028
39,
4.3972
02692
4
97308
2
59
20 8
39 52
53370
35
46630
56067
39
43933
02697
4
97303
1
60
20 0
40 0
53406
36
46595
56107
40
43893
02701
4
97299
0
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant. *
Cotangent.
Difif.
Tangent.
Cosecant.
Diff.
Sine.
109=
A A
B
B
C
C 70° 1
Seconds of time.
Prop, parts
of cols.!
I'
Page 628]
TABLE U,
Log. Sines, Tangents, and Secants.
20°
A A
B
B
C
C
159°
M.
0
Hour A.M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Difl.
Co.sine.
M.
60
9 20 0
2 40 0
9. 58405
0
10. 46595
9. 56107
0
10. 43898
10. 02701
0
9. 97299
1
19 52
40 8
53440
1
46560
56146
1
48854
0270(5
0
97294
59
•)
19 44
40 16
58475
1
46525
56185
1
43815
02711
0
97289
58
8
19 36
40 24
5:^09
2
46491
56224
2
43776
02715
0
97285
57
4
5
19 28
40 3t
2 40 40
53544
9. 53578
2
3
46456
10. 46422
56264
3
3
43736
10. 43697
02720
10.02724
0
0
97280
56
9 19 20
9. 56303
9. 97276
55
6
19 12
40 48
53613
3
46387
56342
4
43658
02729
0
97271
54
7
19 4
40 56
53647 4
46353
56381
4
43619
02734
9726()
53
8
18 56
41 4
58682
5
46318
56420
5
43580
02738
972()2
52
9
10
18 48
41 12
53716
5
6
46284
56459
6
43541
10. 43502
. 02743
10. 02748
97257
9. 97252
51
50
9 18 40
2 41 20
9. 53751
10. 46249
9. 56498
6
11
18 32
41 28
53785 .
6
46215
5a537
/
43463
02752
97248
49
12
18 24
41 36
58819
7
46181
56576
8
43424
02757
97243
48
13
18 16
41 44
53854
7
46146
56615
8
43385
02762
97238
47
14
18 8
41 52
53888 8
46112
56654
9 43846
02766
97234
46
15
9 18 0
2 42 0
9. 58922 8
10. 46078
9. 56693
10 110.43307
10.02771
J
9. 97229
45
16
17 52
42 8
53957 9
46043
56732
10
43268
02776
97224
44
17
17 44
42 16
53991
10
46009
56771
11
43229
02780
97220
43
18
17 36
42 24
54025
10
45975
56810
12 43190
02785
97215
42
19
20"
17 28
42 32
54059
9. 54093 '
11
11
45941
10. 45907
56849
9.56887
12 1 43151
13 10.43113
02790
2
97210
9. 97206
41
40
9 17 20
2 42 40
10. 02794
21
17 12
42 48
54127
12
45878
56926
13 43074
02799
2
97201
39
22
17 4
42 56
54161
12
45839
56965
14 ! 43085
02804
2
97196
88
28
16 56
43 4
54195
13
45805
57004
15 ! 42996
02808
2
97192
37
24
16 48
43 12
54229
14
14
45771
10. 45737
57042
15
42958
10. 42919
02813
2
97187
36
25
9 16 40
2 43 20
9. 54263
9. 57081
16
10. 02818
2
9. 97182
35
26
16 32
43 28
54297
15
45703
57120
17 42880
02822
2
97178
34
27
16 24
43 36
54831
15
45669
57158
17 i 42842
02827.
2
97173
88
28
16 16
43 44
54365
16
45635
57197
18 i 42803
02832
2
97168
82
29
16 8
43 52
54399
16
45601
57235
19 42765
19 10.42726
02837
2
97163
31
80
30
9 16 0
2 44 0
9. 54488
17
10. 45567
9. 57274
10. 02841
2
9. 97159
81
15 52
44 8
54466
17
45534
57312
20 i 42688
02846
2
97154
29
82
15 44
44 16
54500
18
' 45500
57351
21 42649
02851
3
97149
28
88
15 36
44 24
54534
19
45466
57389
21 42611
02855
3
97145
27
84
85
15 28
44 32
•54567
19
45433
57428
22 42572
02860
3
97140
26
9 15 20
2 44 40
9.54601 i 20 '10.45399
9. 57466
22 10.42534
10. 02865
8
9.97135
25
86
15 12
44 48
54635 20 1 45365
57504
23 42496
02870
3
97180
24
87
15 4
44 56
54668 1 21 i 45332
57543
24 42457
02874
3
97126
23
88
14 56
45 4
54702 1 21 1 45298
57581
24 i 42419
02879
3
97121
22
39
40
14 48
9 14 40
45 12
2 45 20
54735
22 1 45265
23 10.45231
57619
9. 57658
25
26
42381
02884
3
97116
9.97111
21
201
9. 54769
10. 42342
10. 02889
3
41
14 32
45 28
54802 ' 23 i 45198
57696
26 42304
02898
3
97107
19'
42
14 24
45 36
54886 1 24
45164
57734
27 42266
02898
3
. 97102
18
48
14 16
45 44
54869 1 24
45131
57772
28 : 42228
02903
3
97097
17
44
14 8
45 52
54908 1 25
45097
57810
28 42190
02908
3
97092
16
15
45
9 14 0
2 46 0
9.54986 i 25
10. 45064
9. 57849
29 10.42151
10. 02913
4
9. 97087
46
13 52
46 8
54969 ' 26
45031
57887
30 42113
02917
4
97083
14
47
13 44
46 16
55003 26
44997
57925
30 42075
02922
4
97078
13
48
13 36
46 24
55036
27
44964
57963
t 31 42037
02927
4
97073
12
49
50
13 28
46 32
55069
28
44931
58001
, 31 i 41999
02932
4
4
97068
9. 97068
11
10
9 13 20
2 46 40
9. 55102
28
10. 44898
9. 58039
32 10.41961
10. 02937
51
13 12
46 48
55136
29
44864
58077
33 41923
02941
4
97059
9
52
13 4
46 56
55169
29
44831
58115
33 1 41885
02946
4
97054
8
58
12 56
47 4
55202
30
44798
58153
34
41847
02951
4
97049
• 7
54
12 48
47 12
2 47 20
55235
30
44765
10. 44732
58191
35
41809
02956
10. 02961
4
4
97044
9. 97039
6
5
55
9 12 40
9.55268 31
9. 58229
1 35
10. 41771
56
12 32
47 28
55301 i 32
44699
58267
i 36
41733
02965
4
97085
4
57
12 24
47 36
55334 I 32
44666
58304
1 37
41696
02970
4
97030
8
58
12 16
47 44
55367 33
44633
58342
! 37
41658
02975
5
97025
2
59
12 8
47 52
55400 33
44600
58380
1 38 1 41620
02980
5
97020
1
60
12 0
48 0
55433 34
44567
58418
39 ! 41582
02985
5
97015
0
M.
(5»°
M.
Hour p. M.
Hour A. M.
Cosine. | Difl.
Secant.
Cotangent.
Diff. Tangent.
Cosecant.
Diff.
Sine.
110°
A A
B
1?
c
r
Seconds of time
!•
2»
8-
4»
b'
6*
J»
Prop, parts of cols. •; B
4
5
1
8
10
1
13
14
2
17
19
2
21
24
3
25
29
4 .
30
84
4
TABLE 44.
[Page 629
Log. Sines, Tangents, and Secants.
21°
A A
B
B
C
C 158°
M.
Hour A.M.
Hour P.M.
Sine.
Did.
Cosecant.
Tangent.
Difif.
Cotangent.
Secant.
Difif.
Cosine.
M.
0
9 12 0
2 48 0
9.55433
0
10. 44567
9. 58418
0
10. 41582
10. 02985
0
9. 97015
60
1
11 52
48 8
55466
1
44534
58455
1
41545
02990
0
97010
59
2
11 44
48 16
55499
1
44501
58493
1
41507
02995
0
97005
58
3
11 36
48 24
55532
2
44468
58531
2
41469
02999
0
97001
57
4
11 28
48 32
55564
2
44436
58569
2
41431
03004
0
0
96996
56
"55
5
9 11 20
2 48 40
9. 55597
3
10. 44403
9. 58606
3
10. 41394
10. 03009
9. 96991
6
11 12 48 48
55630
3
^4370
58644
4
41356
03014
0
96986
54
7
11 4 ! 48 56
55663
4
44337
58681
4
41319
03019
1
96981
53
8
10 56 49 4
55695
4
44305
58719
5
41281
03024
1
96976
52
9
10
10 48 49 12
9 10 40 2 49 20
55728
9. 55764
5
44272
58757
9. 58794
6
6
41243
03029
1
96971
51
50
5
10. 44239
10.41206
10. 03034
1
9. 96966
11
10 32 49 28
55793
6
44207
58832
7
41168
03038
1
96962
49
12
10 24 49 36
55826
6
44174
58869
7
41131
03043
1
96957
48
13
10 16 i 49 44
55858
7
44142
58907
8
41093
03048
1
96952
47
14
10 8
49 52
55891
7
44109
58944
9
41056
03053
1
96947
46
15 ; 9 10 0
2 50 0
9. 55923
8 ilO. 44077
9. 58981
9
10. 41019
10. 03058
1
9. 96942
45
16 1 9 52 ! 50 8
55956
9
44044
59019
10
40981
03063
1
96937
44
17
9 44
50 16
55988
9
44012
59056
10
40944
03068
1
96932
43
18
9 36
50 24
56021
10
43979
59094
11
40906
03073
1
96927
42
19
9 28
50 32
56053
9.56085
10
11
43947
10. 43915
59131
12
40869
10. 40832
03078
10. 03083
2
2
96922
41
40
20
9 9 20 i 2 50 40
9. 59168
12
9.96917
21
9 12 1 50 48
56118
11
43882
59205
13
40795
03088
2
96912
39
22
9 4 50 56
56150
12 1 43850
59243
14
40757
03093
2
96907
38
23
8 56 1 51 4
56182
12 1 43818
59280
14
40720
03097
2
96903
37
24
25
8 48 1 51 12
56215
9. 56247
13
13
43785
59317
9.59354
15
15
40683
10. 40646
03102
10.03107
2
2
96898
36
35
9 8 40 I 2 51 20
10. 43753
9.96893
26
8 32 1 51 28
56279 1 14 43721
59391 i 16
40609
03112
2
96888
U
27
8 24 b\ 36
56311
14 43689
59429
17
40571
03117
2
96883
33
28
8 16 51 44
56343
15 43657
59466
17
40534
03122
2
96878
32
29
8 8
51 52
2 52 0
56375
16 43625
59503
18
19
40497
10. 40460
03127
10. 03132
2
2
96873
31
30
9 8 0
9. 56408
16 10.43592
9. 59540
9. 96868
30
31
7 52 i 52 8
56440
17 43560
59577
19
40423
03137
3
96863
29
32
7 44 1 52 16
56472
17 43528
59614
20
40386
03142
3
96858
28
33
7 36 ' 52 24
56504 : 18 43496
59651
20
40349
03147
3
96853
27
34
7 28 52 32
56536 18 43464
9.56568 1 19 10.43432
59688
9. 59725
21
22
40312
10. 40275
03152
10.03157
3
96848
26
25
35
9 7 20 2 52 40
3
9. 96843
36 1 7 12 52 48
• 56599 19 43401
59762
22
40238
03162
3 i 96838
24
37 ! 7 4 52 50
56631 20 43369
59799 23
40201
03167
3
96833
23
38 ! 6 56 53 4
56663 20 43337
59835 i 23
40165
03172
3
96828
22
39 1 6 48 53 12
56695 i 21
43305
10. 43273
59872
24
25
40128
10. 40091
03177
3
96823
21
20
40
9 6 40 2 53 20
9.56727 21
9. 59909
10. 03182
3 19.96818
41
6 32 53 28
56759 22 43241
59946
25
40054
03187
3 96813
19
42
6 24 53 36
56790 22 43210
59983
26
40017
03192
3 j 96808
18
43
6 16 53 44
56822 23 43178
60019 27
39981
03197
4 96803
17
44
6 8
53 52
2 '54 0
56854 24 '] 43146
9.56886 24 10.43114
60056 1 27
9.60093 1 28
39944
03202
4 1 96798
16
45
9 6 0
10. 39907
10. 03207
4 19.96793
15
46 5 52 54 8
56917 25 43083
60130 1 28
39870
03212
4 1 96788
14
47
5 44 54 16
56949 25 43051
60166 29
39834
03217
4 96783
13
48
5 36 54 24
56980 26 43020
60203 30
39797
03222
4 1 96778
12
49
50
5 28 54 32
9 5 20 2 54 40
57012
'9. 57044
26 1 42988
60240 1 30
9. 60276 31
39760
10. 39724
03228
10. 03233
4 96772
4 9.96767
11
10
27 10.42956
51 i 5 12 : 54 48
57075 27
42925
60313 31
39687
03238
4 96762
9
52
5 4: 54 56
57107 28
42893
60349 32
39651
03243
4 1 96757
8
53
4 56 1 55 4
57138 28
42862
60386 33
39614
03248
4 i 96752
7
54
55"
4 48
9 4 40
55 12
57169
29
42831
60422
33
34
39578
10. 39541
03253
10.03258
4
5
96747
6
5
2 55 20
9. 57201
29
10. 42799
9. 60459
9. 96742
56
4 32
55 28
57232
30
42768
60495 35
39505
03263
5 96737
4
57
4 24
55 36
57264
30
42736
60532 35
39468
03268
5 96732
3
58
4 16 55 44
57295
31
42705
60568 36
39432
03273
5 I 96727
•>
59
4 8 1 55 52
57326
32 ; 42674
60605 ; 36
39395
03278
5 I 96722
1
60
4 0
56 0
57358
32
42642
60641 1 37
39359
03283
5 1 96717
i
0
M.
Hour P.M.
Hour A. M.
Cosine.
Difl.
Secant.
Cotangent. Biff.
Tangent.
Cosecant.
Difif. 1 Sine.
M.
111°
A A
B
B
C
C 68° 1
Second of time
1'
2'
3»
4«
5»
6»
7»
Prop, parts of cols.
t
4
5
1
8
9
1
12
14
16
19
2 ■
20
23
3
24
28
4
28
32
4
1 Page 630]
TABLE 44.
Log. Sines, Tangents, and Secants.
22°
A
A
B
B
C
c
157°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
60
0
9 4 0
2 56 0
9. 57358
0
10. 42642
9. 60&41
0
10. 39359
10. 03283
0
9. 96717
1
3 52
56 8
57389
1 42611
60677
1
39323
03289
0
96711
59
2
3 44
56 16
57420
1 i 42580
60714
1
39286
03294
0
96706
58
3
3 36
56 24
57451
2 ! 42549
60750
2
39250
03299
0
96701
57
4
3 28
56 32*
57482
2 ' 42518
60786
2
.3
39214
10.39177
03304
10. 03309
0
0'
96696
9. 96691
56
55
5
9 3 20
2 56 40
9. 57514
3 |lO. 42486
9. 60823
6
3 12
56 48
57545
3 1 42455
60859
4
39141
03314
96686
54
t
3 4
56 56
57576
4 ! 42424
60895
4
39105
03319
96681
53
8
2 56
57 4
57607
4 42393
60931
5
39069
03324
96676
52
9
2 48
57 12
57638
5 42362
60967
5
39033
03330
10.03335
96670
51
50
10
9 2 40
2 57 20
9. 57669
5 ilO. 42331
9. 61004
6
10. 38996
9. 96665
11
2 32
57 28
57700
6 42300
61040
1
38960
03340
96660
49
12
2 24
57 36
57731
6 42269
61076
/
38924
03345
96655
48
13
2 16
57 44
57762
7 42238
61112
8
38888
03350
96650
47
14
15
2 8
57 52
57793
7 i 42207
61148
8
9
38852
03355
96645
9. 96640
46
45
9 2 0
2 58 0
9. 57824
8 110.42176
9.61184
10. 38816
10. 03360
16
1 52
58 8
57855
8 i 42145
61220
10
• 38780
03366
96634
44
17
1 44
58 16
57885
9 42115
61256
10
38744
03371
96629
43
18
1 36
58 24
57916
9 42084
61292
11
38708
03376
2
96624
42
19
1 28
58 32
57947
10 42053
61328
11
38672
03381
2
96619
9.96614
41
40
20
9 1 20
2 58 40
9. 57978
10 ilO. 42022
9. 61364
12
10. 38636
10. 03386
2
21
1 12
58 48
58008
11 ! 41992
61400
13
38600
03392
2
96608
39
22
1 4
58 56
58039
11
41961
61436
13
38564
03397
2
96603
38
23
0 56
59 4
58070
12
41930
61472
14
38528
03402
2
96598
37
24
0 48
59 12
58101
12
41899
61508
14
38492
10. 38456
03407
2
2
96593
9. 96588
36
35
25
9 0 40
2 59 20
9. 58131
13 10.41869
9. 61544
15
10. 03412
2(j
0 32
59 28
58162
13 41838
61579
15
38421
o:^i8
2
96582
34
27
0 24
59 36
58192
14 ! 41808
61615
16
38385
03423*
2
96577
33
28
0 16
59 44
58223
14
41777
61651
17
38349
03428
2
96572
32
29
0 8
59 52
58253
15
41747
61687
17
38313
10. 38278
03433
3
96567
31
30
80
9 0 0
3 0 0
9. 58284
15
10.41716
9. 61722
18
10. 03438
3
9. 96562
31
8 59 52
0 8
58314
16
41686
61758
18
38242
03444
3
96556
29
32
59 44
0 16
58345
16
41655
61794
19
38206
03449
3
96551
28
33
59 36
0 24
58375
17
41625
61830
20
38170
03454
3
96546
27
34
59 28
0 32
58406
17 1 41594
61865
20
21
38135
03459
10. 03465
3
3
96541
9. 96535
26
25
35
8 59 20
3 0 40
9. 58436
18 jlO. 41564
9. 61901
10. 38099
36
59 12
0 48
58467
18 1 41533
61936
21
38064
03470
3
96530
24
37
59 4
0 56
58497
19
41503
61972
22
38028
03475
3
96525
23
38
58 56
1 4
58527
19
41473
62008
23
37992
03480
3
96520
22
39
40
58 48
1 12
58557
20 ! 41443
62043
23
37957
03486
3
96514
21
20
8 58 40
3 1 20
9. 58588
20 ilO. 41412
9. 62079
24
10. 37921
10. 03491
3
9. 96509
41
58 32
1 28
58618
21 i 41382
62114
24
37886
03496
4
96504
19
42
58 24
1 36
58648
21 1 41352
62150
25
37850
03502
4
96498
18
43
58 16
1 44
58678
22
41322
62185
26
37815
03507
4
96493
17
44
58 8
1 52
58709
22
41291
62221
26
27
37779
03512
4
4
96488
16
15
4o
8 58 0
3 2 0
9. 58739
23
10. 41261
9. 62256
10. 37744
10.03517
9. 96483
46
57 52
2 8
58769
23
41231
62292
27
37708
03523
4
96477
14
47
57 44
2 16
58799
24
41201
62327
28
37673
03528
4
96472
13
48
57 36
2 24
58829
24
41171
62362
29
37638
03533
4
96467
12
49
57 28
2 32
58859
25
41141
62398
29
37602
03539
4
96461
9. 96456
11
10'
50
8 57 20
3 2 40
9. 58889
25
10.41111
9. 62433
30
10. 37567
10. 03544
4
51
57 12
2 48
58919
26
41081
62468
30
37532
03549
4
96451
9
52
57 4
2 56
58949
26
41051
62504
31
37496
03555
5
96445
8
53
56 56
3 4
58979
27
41021
62539
32
37461
03560
5
96440
7
54
56 48
3 12
59009
27
40991
62574
32
33
37426
03565
5
96435
6
5
55
8 56 40
3 3 20
9. 59039
28
10. 40961
9. 62609
10. 37391
10. 03571
5
9. 96429
56
56 32
3 28
59069
28
40931
62645
33
37355
03576
5
96424
4
57
56 24
3 36
59098
29
40902
62680
34
37320
03581
5
96419
3
58
56 16
3 44
59128
29 ! 40872
62715
35
37285
03587
5
96413
2
59
56 8
3 52
59158
30
40842
62750
35
37250
03592
5
96408
1
60
56 0
4 0
59188
31
4081.2
62785
36
37215
03597
5
96403
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
11 2°
A
A
B
B
C
C
67°
Seconds of time
1»
2»
3*
4'
5-
6-
?•
fA
Prop, parts of cols, i B
Ic
4
4
1
8
9
1
11
13
2
15
18
3
19
22
8
23
27
4
27
81
5
TABLE 44.
[Page 631
Log. Sines, Tangents, and Secants.
•23°
A
A
B B C
C 156°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
. Tangent.
Diff.
Cotangent: Secant.
Difl.
Cosine.
M.
0
8 56 0
3 4 0
9. 59188
0
10. 40812
9. 62785
0
10. 87215
10. 08597
0
9. 96403
60
1
55 52
4 8
59218
0
40782
62820
1
37180
03608
0
96.397
59
2
55 44
4 16
59247
1
40758
62855
1
37145
03608
0
96392
58
S
55 86
4 24
59277
1
40723
62890
2
37110
03613
0
96387
57
4
5
55 28
"8 55 20
4 32
59307
9. 59836
2
2
40698
10. 40664
62926
9. 62961
2
37074
03619
0
0
96381
9. 96376
56
55
3 4 40
3
10. 37039
10. 03624
«
55 12
4 48
59866
3
40634
62996
3
37004
03680
96370
54
7
55 4
4 56
59896
3
40604
63081
4'
36969
03635
96365
58
8
54 56
5 4
59425
4
40575
68066
5
36934
03640
96360
52
9
54 48
5 12
59455
4
40545
63101
5
.36899
03646
96854
9. 96849
51
50
10
8 54 40
8 5 20
9. 59484
5
10. 40516
9. 63135
6
10. 36865
10. 08651
11
54 82
5 28
59514
5
40486
68170
6
36880
08657
96843
49
1^
54 24
5 36
59543
6
40457
68205
7
36795
03662
96388
48
1H
54 16
5 44
59573
6
40427
63240
7
36760
03667
96833
47
14
15
54 8
5 52
59602
7
7
40398
10. 40368
68275
8
86725
03673
96327
46
45
8 54 0
3 6 0
9. 59632
9. 68310
9
10. 36690
10. 03678
9. 96822
16
53 52
6 8
59661
8
40389
63345
9
86655
03684
96316
44
17
58 44
6 16
59690
8
40810
63879
10
36621
03689
2
96.311
48
18
58 36
6 24
59720
9
40280
63414
10
36586
03695
2
96805
42
19
20
53 28
6 32
59749
9
40251
63449
11 I 36551
03700
2
96300
41
8 53 20
3 6 40
9. 59778
10
10. 40222
9. 63484
12 10.36.516
10. 03706
2
9. 96294
40
21
53 12
6 48
59808
10
40192
63519
12 1 86481
03711
2
96289
39
22
53 4
6 56
59837
11
40163
63.553
13 36447
03716
2
96284
38
2S
52 56
7 4
59866
11
40134
6;i588
13 36412
03722
2
96278
37
24
25
52 48
8 52 40
7 12
59895
12
40105
63623
14
.36377
03727
10. 087.33
2
2
. 96273
36
35
3 7 20
9. 59924
12
10. 40076
9. 63657
14
10, 36843
9. 96267
26
52 32
7 28
59954
13
40046
63692
15
36308
087.38
2
96262
84
27
52 24
7 86
59983
13
40017
63726
16
36274
03744
2
96256
83
28
52 16
7 44
60012
14
89988
63761
16
86239
03749
3
96251
32
29
52 8
7 52
60041
14
39959
10. 39930
68796
17
36204
03755
3
96245
31
30
80
8 52 0
3 8 0
9. 60070
15
9. 63880
17
10.36170
10. 03760
3
9. 96240
81
51 52
8 8
60099
15
39901
63865
18 i 361.35
03766
3
96234
29
82
51 44
8 16
60128
15
89872
6.3899 1 18 86101
03771
3
■ 96229
28
88
51 36
8 24
60157
16
89848
68934 19 36066
03777
3
96228
27
34
85
51 28
8 32
60186
9. 60215
16
17
39814
63968
20 36032
03782
10. 03788
3
3
96218
26
8 51 20
3 8 40
10. 39785
9.64003
20 |10. 3.5997
9. 96212
25
86
51 12
8 48
60244
17
39756
64037
21 1 35968
03798
3
96207
24
87
51 4
8 56
60273
18
89727
64072 ! 21 i .35928
03799
3
96201
23
88
50 56
9 4
60302
18
89698
64106
22 .85894
03804
3
96196
22
39
40
50 48
9 12
60331
19 ! 39669
64140
22 35860
0.3810
4
4
96190
9. 96185
21
20
8 50 40
3 9 20
9. 60359
19 [10.39641
9. 64175
23 10.35825
10. 03815
41
50 32
9 28
60888
20
89612
64209
24 j a5791
03821
4
96179
19
42
50 24
9 36
60417
20
89583
64243
24 .35757
03826
4
96174
18
48
50 16
9 44
60446
21
39554
64278
25 35722
03832
4
96168
17
44
"45
50 8
9 52
60474
21 39526
64812
25 35688
03838
4
96162
16
8 50 0
3 10 0
9. 60503
22 10.89497
9.64346 1 26 10.3.56.54
10. 08843
4
9.961.57
15
46
49 52
10 8
60582
22
89468
64381
26
3.5619
03849
4
96151
14
47
49 44
10 16
60561
28
89489
64415
27
.35585
08854
4
96146
18
48
49 86
10 24
60589
28
89411
64449
28
85.551
08860
4
96140
12
49
50
49 28
8 49 20
10 32
3 10 40
60618
24
39882
64483
28
3.5517
08865
10. 03871
4
5
96135
9.96129
11
10
9. 60646
! 24
10. 39:^4
9.64517
29
10. 35483
51
49 12
10 48
60675
i 25
89325
64552
29 1 35448
03877
5
96128
9
52
49 4
10 56
60704
i 25
39296
(M586
30
35414
03882
5
96118
8
58
48 56
11 4
60782
26
39268
64620
81
35380
03888
5
96112
/
54
55"
48 48
8 48 40
11 12
60761
9. 60789
26
27
39239
10.39211
64654
9. 64688
31
32
.35.346
10. .8.5812
08893
10.03899
5
5
/96107
9.96101
6
5
8 11 20
56
48 32
11 28
60818
27
39182
64722
32
35278
08905
5
96095
4
57
48 24
11 36
60846
28
89154
64756
38
.35244
03910
5
96090
8
58
48 16
11 44
60875
28
89125
64790
38
.35210
03916
5
96084
2
59
48 8
11 52
60903
29
39097
64824
.34
.35176
03921
5
96079
1
60
M.
48 0
12 0
60981
29
39069
64858
35
35142
03927
6
96073
0
Hour p. M.
Hour A.M.
Cosine.
Diff.
Secant.
Cotangent.
Diff
Tangent.
.;Cosecant.
Diff.
Sine.
M.
113^
A
A
B B C
C 66° 1
Seconds of time
Prop, parts
of cols. -< B
p
age 632j
TABLE 41.
Log. Sines, Tangents, and Secants.
24°
A A
B B
C
C
165°
M.
60
M.
Hour A. M.
Hour p. 3C.
Sine. 1 Diff. j Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
0
8 48 0
3 12 0
9.60931 i 0 10.39069
9.64858
0
10. 35142
10. 03927
0
9. 96073
1
47 52
12 8
60960
0 39040
64892
1
35108
03933
0
96067
59
2
47 44
12 16
60988
1 1 39012
64926
1
35074
03938
0
96062
58
3
47 36
12 24
61016
1 i 38984
64960
2
35040
03944
0
96056
57
4
5
47 28
12 3g
61045
9. 61073
2
2
38955
64994
2
35006
03950
0
0
96050
56
55
8 47 20
3 12 40
10. 38927
9. 65028
3 10.34972
10. 03955
9. 96045
6
47 12
12 48
61101
3 ! 38899
65062
3
34938
03961
96039
54
7
47 4
12 56
61129
3 38871
65096
4
34904
03966
96034
53
8
46 56
13 4
61158
4 38842
65130
4
34870
03972
96028
52
9
10
46 48
13 12
61186
4 38814
65164
5
34836
03978
96022
51
50
8 46 40
3 13 20
9. 61214
5 10.38786
9. 65197
6
10. 34803
10. 03983
9.96017
11
46 32
13 28
61242-
5 , 38758
65231
6
34769
03989
96011
49
12
46 24
13 36
61270
6
38730
' 65265
7
34735
03995
96005
48
13
46 16
13 44
61298
6
38702
65299
7
34701
04000
96000
47
14
46 8
13 52
61326
6
38674
65333
8
34667
04006
95994
46
45
15
8 46 0
3 14 0
9. 6i;i54
/
10. 38646
9. 65366
8
10. 34634
10. 04012
9. 95988
16
45 52
14 8
61382
7
38618
65400
9
34600
04018
2
95982
44
17
45 44
14 16
61411
8
38589
65434
9
34566
04023
2
95977
43
18
45 36
14 24
61438
8
38562
65467
10
34533
04029
2
95971
42
19
20
45 28
8 45 20
14 32
3 14 40
61466
9 38534
9 10.38506
65501 1 11
9.65535 i 11
34499
04035
2
2
95965
41
40
9. 61494
10. 34465
10. 04040
9. 95960
21
45 12
14 48
61522
10 i 38478
65568 12 i 34432
04046
2
95954
39
22
45 4
14 56
61550
10
38450
65602 1 12
34398
04052
2
95948
38
23
44 56
15 4
61578
11
38422
65636
13
34364
04058
2
95942
37
24
44 48
15 12
61606
11
38394
65669
13 i 34331
04063
2
95937
36
35
25
8 44 40
3 15 20
9. 61634
12
10. 38366
9. 65703
14 ilO. 34297
10. 04069
2
9. 95931
26
44 32
15 28
61662
12
38338
65736
15
34264
04075
2
95925
34
27
44 24
15 36
61689
12
38311
65770
15
34230
04080
3
95920
33
28
44 16
15 44
61717
13
38283
65803
16
34197
04086
3
95914
32
29
30
44 8
15 52
61745
13
38255
65837 16
34163
04092
3
95908
31
8 44 0
3 16 0
9. 61773
14
10. 38227
9.65870 17 ,10.34130
10. 04098
3
9. 95902
30
31
43 52
16 8
61800
14
38200
65904 17
34096
04103
3
95897
29
32
43 44
16 16
61828
15
38172
65937 18
34063
04109
3
95891
28
33
43 36
16 24
61856 : 15
38144
65971 18
34029
04115
3
95885
27
34
35
43 28
16 32
61883 \ 16 ! 38117
66004
19 ! 33996
04121
3
95879
26
25"
8 43 20
3 16 40
9. 61911
16 ilO. 38089
9. 66038
20
10. 33962
10. 04127
3
9. 95873
36
43 12
16 48
61939
17
38061
66071
20
33929
04132
3
95868
24
37
43 4
16 56
61966
17
38034
66104
21
33896
04138
4
95862
23
38
42 56
17 4
61994
18
38006
66138
21
33862
04144
4
95856
22
39
42 48
17 12
62021
18
37979
66171
22
33829
04150
4
95850
21
20
40
8 42 40
3 17 20
9.62049 1 18 10.37951
9.66204 22 10.33796
10. 04156
4
9. 95844
41
42 32
17 28
62076 i 19
37924
66238 1 23
33762
04161
4
95839
19
42
42 24
17 36
62104
19
37896
66271 23
33729
04167
4
95833
18
43
42 16
17 44
62131
20
37869
66304 1 24
33696
04173
4
95827
17
44
42 8
17 52
62159
20
37841
66337
25
33663
04179
4
95821
9. 95815
16
15
45
8 42 0
3 18 0
9. 62186
21
10. 37814
9. 66371
25
10. 33629
10. 04185
4
46
41 52
18 8
62214
21
37786
66404
26
33596
04190
4
95810
14
47
41 44
18 16
62241
22
37759
66437
26
33563
04196
5
95804
13
48
41 36
18 24
62268
22
37732
66470
27
33530
04202
5
95798
12
49
50
41 28
8 41 20
18 32
62296
23
37704
66503
9. 66537
27
28
33497
04208
5
95792
11
10
3 18 40
9. 62323 1 23 10. 37677
10. 33463
10. 04214
5
9. 95786
51
41 12
18 48
62350 ; 24
37650
66570
28
33430
04220
5
95780
9
52
41 4
18 56
62377 24
37623
66603
29
33397
04225
5
95775
8
53
40 56
19 4
62405 ! 24
37595
66636
30
33364
04231
5
95769
7
54
55
40 48
8 40 40
19 12
3 19 20
62432 25 37568
9.62459 1 25 10.37541
66669
9. 66702
30
31
33331
04237
5
5
95763
6
5
10. 33298
10. 04243
9. 95757
56
40 32
19 28
62486 ■ 26 37514
66735
31
33265
04249
5
95751
4
57
40 24
19 36
62513 ; 26
37487
66768
32
33232
04255
5
95745
3
58
40 16
19 44
62541 27
37459
66801
32
33199
04261
6
95739
9
59
40 8
19 52
62568
27
37432
66834
33
33166
04267
6
95733
1
60
40 0
20 0
'62595
28
37405
66867
33
Diff.
33133
04272
6
95728
0
M.
M.
Hour p. M.
Hour A.M
Cosine. Diff.
Secant.
Cotangent.
Tangent.
Cosecant.
Diff.
Sine.
114°
A A
B B
C
C
65°
.Seconds of time
1»
i'
){•
4'
5*
17
21
4
C
21
2.'i
4
7«
24
29
Prop, parts of colp.-fE
5
1
7
8
1
10
13
2
14
17
3
TABLE 44.
Page 633
Log. Sines, Tangents, and Secants.
25°
A
A
B
B
C
C 154°
M.
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
8 40 0
3 20 0
9. 62595
0
10. 87405
9. 66867
0
10. 33133
10. 04272
0
9. 95728
60
1
39 52
20 8
62622
0
87378
66900
1
38100
04278
0
95722
59
9,
39 44
20 16
62649
1
37351
66933
1
38067
04284
0
95716
58
8
39 36
20 24
62676
1
37824
66966
2
33034
04290
0
95710
57
4
5
39 28
20 32
62703
2
87297
66999
2
33001
04296
0
95704
56
55
8 39 20
3 20 40
9. 62730
2
10. 37270
9. 67032
3
10. 32968
10.04302
9. 95698
6
39 12
20 48
62757
3
37243
67065
3
32935
04308
95692
54
7
39 4
20 56
62784
3
37216
67098
4
32902
04314
95686
53
H
38 56
21 4
62811
4
87189
67131
4
32869
04320
95680
52
9
10
38 48
21 12
62838
4
87162
67163
5
5
32837
04326
95674
51
8 38 40
3 21 20
9. 62865
4 10.37135
9. 67196
10. 32804
10. 04332
9. 95668
50
11
38 32
21 28
62892
5 37108
67229
6
32771
04337
95663
49
12
38 24
21 36
62918
5 87082
67262
7
32738
04343
95657
48
18
38 16
21 44
62945
6 87055
67295
7
32705
04349
95651
47
14
38 8
21 52
62972
6 37028
67327
8
.32673
04355
95645
46
15
8 38 0
3 22 0
9. 62999
7 10.37001
9. 67860
8
10. 32640
10. 64361
2
9. 95639
45
16
37 52
22 8
63026
7
36974
67393
9
32607
04367
2
95683
44
17
37 44
22 16
63052
8
36948
67426
9
32574
04373
2
95627
43
18
37 36
22 24
63079
8
36921
67458
10
32542
04379
2
95621
42
19
37 28
22 32
63106
8
36894
67491
10
32509
04385
2
95615
41
40
20
8 37 20
3 22 40
9. 63133
9 10.36867
9. 67524
11
10. 32476
10. 04391
2
9. 95609
21
37 12
22 48
63159
9 i 36841
67556
11
32444
04397
2 95603
39
22
37 4
22 56
63186
10 ! 36814
67589
12
32411
04403
2 95597
38
28
36 56
23 4
63213
10 36787
67622
12
32378
04409
2 95591
37
24
36 48
23 12
63239
11 36761
67654
13
32346
04415
2 955a5
36
25
8 36 40
3 23 20
9. 63266
11 10.36734
9. 67687
14 10.32813
10. 04421
3
9. 95579
35
26
36 32
23 28
63292
11
36708
67719
14 32281
04427
3
95.573
34
27
36 24
23 36
63319
12
36681
67752
15 32248
04433
3
95567
83
28
36 16
23 44
63345
12
36655
67785
15 32215
04439
3
95561
32
29
80
36 8
23 52
63372
9. 63398
13
36628
67817
16 32183
04445
3
95555
31
30
8 36 0
3 24 0
13
10. 36602
9. 67850
16 :10. 32150
10. 04451
3 19.95549
81
35 52
24 8
63425
14 36575
67882
17
32118
04457
3
95543
29
82
35 44
24 16
63451
14 36549
67915
17
32085
04463
3
95537
28
88
35 36
24 24
63478
15 86522
67947
18
32053
04469
3
95531
27
34
35 28
24 32
63504
15 36496
67980
18
32020
04475
3
95525
26
25
85
8 35 20
3 24 40
9. 63531
15 10.36469
9. 68012
19
10. 31988
10. 04481
4
9. 95519
86
35 12
24 48
63557
16 .36443
68044
20
31956
04487
4
95513
24
87
35 4
24 56
68583
16 86417
68077
20
31928
04493
4
95507
23
88
34 56
25 4
63610
17 1 36390
68109
21
31891
04500
4
95500
22
39
34 48
25 12
63636
17 1 36364
68142
21
31858
04506
4
95494
21
20
40
8 34 40
3 25 20
9. 63662
18 ;iO. 36338
9. 68174
22
10. 31826
10. 04512
4
9. 95488
41
34 32
25 28
63689
18
36311
68206
22
31794
04518
4
95482
19
42
34 24
25 36
63715
19
36285
68239
23
31761
04524
4
95476
18
43
34 16
25 44
63741
19
36259
68271
23
31729
04530
4
95470
17
44
34 8
25 52
63767
19
36233
68303
24
31697
04536
4
95464
16
45
8 34 0
3 26 0
9. 68794
.20 10.36206
9. 68336
24 10.31664
10. 04542
5
9. 95458
15
46
33 52
26 8
68820
20
36180
68368
25
31632
04548
5
95452
14
47
33 44
26 16
63846
21
36154
68400
25
31600
04554
5
95446
13
48
33 36
26 24
63872
21
86128
68432
26
31568
04560
0
95440
12
49
33 28
26 32
68898
22
36102
68465
27
31535
04566
5
95434
11
10
50
8 33 20
3 26 40
9. 63924
22 10.36076
9. 68497
27 ilO. 31503
10. 04573
5
9. 95427
51
33 12
26 48
63950
23
36050
68529
28
31471
04579
5
95461
9
52
33 4
26 56
63976
23
36024
68.561
28
31489
04585
5
95415
8
53
32 56
27 4
64002
23
35998
68593
29
31407
04591
5
95409
7
54
32 48
27 12
64028
24
35972
68626
29
30
31374
10. 31342
04597
5
95403
6
5
55
8 32 40
3 27 20
9. 64054
24
10. 35946
9. 68658
10. 04603
6
9. 95397
56
32 32
27 28
64080
25
35920
68690
30
31310
04609
6
95391
4
57
32 24
27 36
64106
25
85894
68722
31
31278
04616
6
95384
3
58
32 16
27 44
64132
26 1 85868
68754
31 1 31246
04622
6
95378
2
59
32 8
27 52
64158
26
85842
68786
32
31214
04628
6
95372
1
60
32 0
28 0
64184
26
85816
68818
33
31182
04634
6
95366
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diflf.
Sine.
M.
115°
A
A
B
B
C
C 64° 1
Seconds of time ! 1»
2. 1 3.
4"
5« 1 6»
7«
f A 1 3
Prop, parts of cols, -j B ] 4
vC 1
7
8
2
10
12
2
13
16
3
17 20
20 24
4 5
23
28
5
Page 634]
TABLE U.
Log.
Sines, Tangents, and Secants.
26°
M.
A
A
B
B
C
c
153°
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff. Cosine.
M.
0
8 32 0
3 28 0
9.64184
0
10. 35816
9. 68818
0
10.31182
10. 04634
0 9.95366
60
1
31 52 ! 28 8
64210
0
35790
68850
1
31150
04640
0 95360
59
2
31 44
28 16
64236
1
35764
68882
1
31118
04646
0 95354
58
8
31 36
28 24
64262
1
35738
68914
2
31086
04652
0 95348
57
4
5
31 28
28 32<
64288
9.64313
2
~2'
35712
10735687
68946
9. 68978
2
3
31054
10.31022
04659
10. 04665
0 . 95341
1 9.95335
56
55
8 31 20
3 28 40
6
31 12 ' 28 48
64;«9
3
:i5661
69010
3
30990
04671
1 i 95329
54
7
31 4 i 28 56
64365
3
35635
69042
4
30958
04677
1 ! 95323
53
8
30 56 29 4
64391
3
35609
69074
4
3092f)
04683
1 1 95317
52
9
10
30 48
29 12
3 29 20
64417
4
4
35583
10. 35558
69106
5
5
30894
10. 30862
04690
10. 04696
1 95310
1 9.95304
51
50
8 30 40
9.64442
9. 69138
11
30 32 1 29 28
64468
5
35532
69170
6
30830
04702
1 I 95298
49
12
30 24 29 36
64494
5
35506
69202
6
30798
04708
1 95292
48
13
30 16 29 44
64519
5
35481
69234
7 '
30766
04714
1 1 95286
47
14
30 8 29 52
64545
6
35455
69266
8
30734
10. 30702
04721
1 1 95279
46
45"
15
8 30 0 ! 3 30 0
9. 64571
6
10. 35429
9. 69298
10. 04727
2 i 9. 95273
16
29 52 30 8
64596
7
35404
69329
8
30671
04733
2 1 95267
44
17
29 44 1 30 16
64622
7
35378
69361
9
30639
04739
2 ' 95261
43
18
29 36
30 24
64647
8
35353
69393
9
30607
04746
2 ; 95254
42
19
20
29 28
30 32
64673
9.64698
8
35327
69425
10
30575
04752
10. 04758
2
2
95248
41
40
8 29 20
3 30 40
8
10. 35302
9. 69457
11
10. 30543
9. 95242
21
29 12 30 48
64724
9
35276
69488
11
30512
04764
2 95236
39
22
29 4 1 30 56
64749
9
35251
69520
12
30480
04771
2 95229
38
23
28 56
31 4
64775
10
35225
69552
12
30448
04777
2 1 95223
37
24
28 48
31 12
64800
10
11
35200
10. 35174
69584
13
13
30416
10. 30385
04783
10.04789
3 1 95217
36
35
25
8 28 40
3 31 20
9. 64826
9. 69615
3
9.95211
26
28 32
31 28
64851
11
35149
69647
14
30353
04796
3
95204
34
27
28 24
31 36
64877
11
35123
69679
•14
30321
04802
3
95198
33
28
28 16
31 44
64902
12
35098
69710
15
30290
04808
3
95192
32
29
30
28 8 31 52
64927
12
35073
10. 35047
69742
15
16
30258
10. 30226
04815
3 ' 95185
31
30
8 28 0 i 3 32 0
9. 64953
13
9. 69774
10. 04821
3 9.95179
31
27 52 32 8
64978
13
35022
69805
16
30195
04827
3 95173
29
32
27 44 32 16
65003
14
34997
69837
17
30163
04833
3
95167
28
33
27 36 i 32 24
65029
14
34971
69868
17
30132
04840
3
95160
27
34
"35"
27 28 32 32
65054
14
15
•34946
10. 34921
69900
18
30100
10. 30068
04846
4
95154
26
25
8 27 20
3 32 40
9. 65079
9. 69932
18
10.04852
4
9.95148
36
27 12
32 48
65104
15
34896
69963
19
30037
04859
4 95141
24
37
27 4 ! 32 56
65130
16
34870
69995
20
30005
04865
4 95135
23
38
26 56 33 4
65155
16
34845
70026
20
29974
04871
4 95129
22
39
26 48 33 12
65180
16
34820
70058
21
29942
04878
4 1 95122
21
40
8 26 40 ! 3 33 20
9. 65205
17
10. 34795
9.70089 ! 21
10.29911
10. 04884
4 9.95116
20
41
26 32 33 28
65230
17
34770
70121
22
29879
04890
4 95110
19
42
26 24
33 36
65255
18
34745
70152
22
29848
04897
4 95103
18
43
26 16
33 44
65281
18
34719
70184
23
29816
04903
5 95097
17
44
26 8
33 52
65306
19
34694
70215
23
29785
04910
5 95090
16
45
8 26 0
3 34 0
9. 65331
19
10. 34669
9. 70247
24
10. 29753
10. 04916
5 9.95084
15
46
25 52 : 34 8
65356
19
34644
70278
24
29722
04922
5 95078
14
47
25 44 34 16
65381
20
34619
70309
25
29691
04929
5 95071
13
48
25 36 34 24
65406
20
34594
70341
25
29659
04935
5 9.5065
12
49
50'
25 28 34 32
8 25 20 3 M 40
65431
"9.65456
21
"21
34569
10. 34544
70372
26
26
29628
10. 29596
04941
10.04948
5 95059
5 9.95052
11
10
9. 70404
51
25 12 i M 48
65481
22
34519
70435
27
29565
04954
5 95046
9
52
25 4 I M 56
65506
22
34494
70466
27
29534
04961
5 95039
8
53
24 56 : 35 4
65531
22
34469
70498
28
29502
04967
6 95033-
7
54
24 48 1 35 12
65556
23
34444
70529
28
29471
04973
6 ! 95027
6
00
8 24 40 i 3 35 20
9. 65580
23
10. 34420
9. 70560
29
10. 29440
10. 04980
6 9.95020
5
56
24 32 35 28
65605
24
34395
70592
30
29408
04986
6 95014
4
57
24 24 35 36
65630
24
34370
70623
30
29377
04993
6 95007
3
58
24 16 35 44
65655
25
34345
70654
31
29346
04999
6 95001
2
59
24 8 35 52
65680
25
34320
70685
31
29315
05005
6 i 94995
1
60
M.
24 0 36 0
65705
25
Difl.
34295
70717
32
29283
05012
6 94988
0
Hour p. M. 1 Hour a. m.
Cosine.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Difl. j Sine.
M.
116°
A
A
B
B
C
C
68°
Seconds of time
!•• 2«
8*
4«
&• 6>
7«
(A
Prop, parts of cols. < B
(C
8 6
4 8
1 2
10
12
2
13
16
3
16 19
20 24
4 6
22
28
6
TABLE 44.
[Page 635
Log.
Sines, Tangents, and Secants.
27°
A
A
B
B
C
C 152°
M.
•Hour A.M.
Hour P. M.
Sine. i Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff. Cosine.
M.
60
0
8 24 0
3 36 0
9.65705 i 0
10. 34295
9. 70717i
0
10. 29283
10. 05012
0
9. 94988
1
23 52
36 8
65729 0
34271
70748
1
29252
05018
0 94982
59
?,
23 44
36 16
65754
1
34246
70779
1
29221
05025
0 1 94975
58
n
23 36
36 24
65779
1
34221
70810
2
29190
05081
0
94969
57
4
23 28
36 32
65804
2
34196
70841
9. 70873
2
3
29159
10. 29127
05088
0
94962
56
55
5
8 23 20
3 36 40
9.65828 i 2
10. 34172
10.05044
9. 94956
H
23 12
36 48
65853 i 2
34147
70904
3
29096
05051
94949
54
7
23 4
36 56
65878 3
34122
70935
4
29065
05057
94948
58
8
22 56
37 4
65902 i 3
34098
70966
4
29034
05064
94986
52
9
To
22 48
37 12
3 37 2b
65927
9.65952
4
34073
70997
5
29008
05070
94980
9. 94928
51
50
8 22 40
4
10. 34048
9. 71028
5
10. 28972
10. 05077
n
22 32
37 28
65976 4
34024
71059
6
28941
05083
94917
49
1!^
22 24
37 36
66001 , 5
33999
71090
6
28910
05089
1 94911
48
18
22 16
37 44
66025 5
33975
71121
/
28879
05096
1 • 94904
47
u
22 8
37 52
66050 6
33950
71153
/
28847
10. 28816
05102
10. 05109
2
2
94898
46
45
15
8 22 0
3 38 0
9.66075 1 6
10. 33925
9. 71184
8
9. 94891
IH
21 52
38 8
66099 6
33901
71215
8
28785
05115
2
94885
44
17
21 44
38 16
66124 ! 7
38876
71246
9
28754
05122
2
94878
43
18
21 36
38 24
66148 7
33852
71277
9
28723
05129
2
94871
42
19
21 28
38 32
66173 8
33827
71308
10
10
28692
05135
10. 05142
2
2
94865
9. 94858
41
40
20
8 21 20
3 38 40
9. 66197 8
10. 33803
9. 71339
10.28661
21
21 12
38 48
66221 8
33779
71370
11
28630
05148
2
94852
39
9.2
21 4
38 56
66246 9
33754
71401
11
28599
05155
2
94845
88
23
20 56
39 4
66270 9
33730
71431
12
28569
05161
3
94839
87
24
2o
20 48
8 20 40
39 12
3 39 20
66295 I 10
9.66319 10
33705
10. 33681
71462
12
13
28538
10. 28507
05168
3
94832
36
9. 71493
10. 05174
3
9. 94826
.35
2<5
20 32
39 28
66348 11
33657
71524
13
28476
05181
3
94819
.84
27
20 24
39 36
66368 11
33632
71555
14
28445
05187
3 94813
33
28
20 16
39 44
66392 11
33608
71586
14
28414
05194
3 94806
32
29
20 8
89 52
66416 12
33584
71617
15
28883
05201
3
94799
31
80
8 20 0
3 40 0
9. 66441 12
10. 83559
9. 71648
15
10. 28852
10. 05207
3
9. 94793
30
81
19 52
40 8
66465 13
33535
71679
16
28321
05214
3
94786
29
82
19 44
40 16
66489 13
33511
71709
16
28291
05220
4
94780
28
88
19 36
'40 24
66513 13
83487
71740
17
28260
05227
4
94773
27
34
85
19 28
8 19 20
40 32
3 40 40
66537 14
9. 66562 14
33463
71771
17
28229
10. 28198
05233
10. 05240
4
4
94767
9. 94760
26
25
10. 33438
9. 71802
18
86
19 12
40 48
66586 15
33414
71833
19
28167
05247
4
94753
24
87
19 4
40 56
66610 15
83390
71863
19
28137
05253
JL
94747
23
88
18 56
41 4
66634 15
83366
71894
20
28106
05260
4
94740
22
89
40"
18 48
8 18 40
41 12
66658
16
16
33342
10. 83318
71925
9. 71955
20
21
28075
05266
4
4
947.34
21
20
3 41 ao
41 f8
9. 66682
10. 28045
10. 05273
9. 94727
41
18 32
66706 17
33294
71986
21
28014
05280
4
94720
19
42
18 24
41 36
66731 17
88269
72017
22
27988
05286
5
94714
18
48
18 16
41 44
66755 17
33245
72048
22
27952
05293
5
94707
17
44
18 8
41 52
66779 18
83221
72078
23
27922
05300
5
94700
9. 94694
16
15
45
8 18 0
8 42 0
9.66803 ; 18
10. 88197
9. 72109
23
10. 27891
10. 05306
5
4H
17 52
42 8
66827 19
33173
72140
24
27860
05313
5 : 94687
14
47
17 44
42 16
66851 19
83149
72170
24
27830
05320
5
94680
13
48
17 36
42 24
66875 19
33125
72201
25
27799
05326
5
94674
12
49
50
17 28
42 32
66899
20
20
33101
10. 33078
72231
9. 72262
25
26
27769
10727738
05333
10. 05;340
5
5
94667
11
8 17 20
3 42 40
9. 66922
9. 94660
10
51
17 12
42 48
66946 ' 21
33054
72293
26
27707
05346
6
94654
9
52
17 4
42 56
66970 21
33030
72323
27
27677
05353
6
94647
8
58
16 56
43 4
66994 21
33006
72354
27
27646
05360
6
94640
7
54
55
16 48
8 16 40
43 12
67018 22
9. 67042 22
32982
10. 32958
72384
9. 72415
28
28
27616
10. 27585
05366
6 94634
6
5
3 48 20
10. 05373
6 9.94627
5(>
16 32
43 28
67066 23
329:^
72445
29
27555
05380
6 94620
4
57
16 24
43 36
67090 i 23
32910
72476
29
27524
05386
6
94614
8
58
16 16
43 44
67118 i 23
32887
72506
30
27494
05393
6
94607
2
59
16 8
43 52
67137 I 24
32863
72537
30
27463
05400
6
94600
1
60
M.
16 0
44 0
67161 24
32839
72567
31
27433
05407
/
94593
0
Hour p. M.
Hour A.M.
Cosine. ' Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff. Sine.
M.
117°
A
A
B
B
C
C 62° j
Seconds of time
1» 2«
3«
4»
5'
6'
7'
Prop, parts of cols. -(B
Ic
3 6
4 8
1 2
9
12
2
12
15
3
15
19
4
18
23
5
21
27
6
Page 636]
TABLE 44.
Log.
Sines, Tangents, and Secants.
28°
A
A
B B
C
C 151°
M.
Hour A. M.
Hour p. M.
Sine.
DiS.
Cosecant.
Tangent. Diflf. ! Cotangent.
Secant.
Diff.
Cosine.
M.
60
0
8 16 0
3 44 0
9. 67161
0
10. 32839
9.72567 1 0 10.27438
10. 05407
0
9. 94593
1
15 52
44 8
67185
0
32815
72598 1 1 27402
05413
0
94587
59
2
15 44
44 16
67208
1
32792
72628
1 27372 1
05420
0
94580
58
8
15 36
44 24
67232
1
32768
72659
2
27341
05427
0
94573
57
4
5^
15 28
8 15 20
44 32^
3 44 40
67256
9.67280
2
2
32744
72689
2
3
27311
05433
0
94567
56
55
10. 32720
9. 72720
10. 27280
10. 05440
9. 94560
H
15 12
44 48
67303
2
32697
72750
3
27250
05447
94553
54
7
15 4
44 56
67327
3
32678
72780
4
27220
05454
94546
58
S
14 56
45 4
67350
3
32650
72811
4
27189
05460
94540
52
9
10
14 48
45 12
67374
9. 67398
3
4
32626
10. 32602
72841
5
27159
05467
94533
51
50
8 14 40
3 45 20
9.72872
5
10. 27128
10. 05474
9. 94526
11
14 32
45 28
67421
4
32579
72902
6
27098
05481
94519
49
12
14 24
45 36
67445
5
32555
72932
6
27068
05487
94513
48
18
14 16
45 44
67468
5
32532
72963
7
27037
05494
94506
47
14
14 8
45 52
67492
5
32508
72993
7
27007
05501
2
94499
46
45
15
8 14 0
3 46 0
9. 67515
6
10. 32485
9. 73023
8
10. 26977
10. 05508
2
9. 94492
16
13 52
46 8
67539
6
32461
73054
8
26946
05515
2
94485
44
17
13 44
46 16
67562
7
32438
78084
9
26916
05521
2
94479
43
18
13 36
46 24
67586
7
32414
73114
9
26886
05528
2
94472
42
19
13 28
46 32
67609
7
32391
73144
10
26856
05535
2
94465
41
40
20
8 13 20
3 46 40
9. 67633
8
10. 32367
9. 73175
10
10. 26825
10. 05542
2
9. 94458
21
13 12
46 48
67656
8
32344
73205
11
26795
05549
2
94451
39
22
13 4
46 56
67680
9
32320
73235
11
26765
05555
3
94445
38
28
12 56
47 4
67703
9
32297
73265
12
26735
05562
3
94438
37
24
12 48
47 12
67726
9
32274
73295
12
26705
05569
8
94431
36
35
25
8 12 40
3 47 20
9. 67750
10
10. 32250
9. 73326
18
10. 26674
10. 05576
8
9.94^4
26
12 32
47 28
67773
10
32227
73356
18
26644
05583
3
94417
34
27
12 24
47 36
67796
10
32204
73386
14
26614
05590
8
94410
88
28
12 16
47 44
67820
11
32180
73416
14
26584
05596
3
94404
32
29
12 8
47 52
67848
11
32157
78446
9. 73476
15
26554
05603
3
94397
81
30
80
8 12 0
3 48 0
9. 67866
12
10. 32134
15
10. 26524
10. 05610
3
9. 94390
81
11 52
48 8
67890
12
32110
73507
16
26493
05617
4
94383
29
82
11 44
48 16
67913
12
32087
73537
16
26463
05624
4
94376
28
88
11 36
48 24
67936
13
32064
73567
17
26438
05631
.4
94369
27
34
11 28
48 32
67959
13
32041
73597
17
26403
05638
10. 05645
4
4
94362
26
;i5
8 11 20
3 48 40
9. 67982
14
10. 32018
9. 73627
18
10. 26873
9. 94355
25
86
11 12
48 48
68006
14
31994
73657
18
26343
05651
4
94349
24
87
11 4
48 56
68029
14
31971
78687
19
26318
05658
4
94342
23
88
10 56
49 4
68052
15
31948
73717
19
26283
05665
4
94335
22
39
10 48
49 12
68075
15
81925
73747
20
26253
05672
4
94828
21
20
40
8 10 40
3 49 20
9. 68098
16
10. 31902
9. 73777
20
10. 26223
10. 05679
5
9. 94321
41
10 32
49 28
68121
16
31879
73807
21
26193
05686
5
94314
19
42
10 24
49 36
68144
16
31856
73837
21
26163
05693
0
94307
18
48
10 16
49 44
68167
17
31833
78867
22
26133
05700
5
94300
17
44
10 8
49 52
68190
17
31810
73897
9. 73927
22
23
26103
10. 26073
05707
5
94293
9. 94286
16
15
45
8 10 0
3 50 0
9. 68213
17
10. 31787
10. 05714
5
46
9 52
50 8
68237
18
31763
78957
23
26043
05721
5
94279
14
47
9 44
50 16
68260
18
31740
78987
24
26013
05727
5
94278
13
48
9 36
50 24
68283
19
31717
74017
24
25983
05734
5
94266
12
49
50
9 28
50 32
68305
19
31695
74047
25
25953
05741
6
94259
11
8 9 20
3 50 40
9. 68328
19
10.31672
9. 74077
25
10. 25923
10. 05748
6
9. 94252
10
51
9 12
50 48
68351
20
31649
74107
26
25893
05755
6
94245
9
52
9 4
50 56
68374
20
31626
74137
26
25863
05762
6
94238
8
58
8 56
51 4
68397
21
31603
74166
27
25834
05769
6
94231
7
54
8 48
51 12
68420
21
31580
74196
27
25804
05776
6
94224
6
5
55
8 8 40
3 51 20
9. 68443
21
10. 31557
9. 74226
28
10. 25774
10. 05783
6 9.94217
56
8 32
51 28
68466
22
31534
74256
28
25744
05790
6
94210
4
57
8 24
51 36
68489
22
31511
74286
29
25714
05797
7
94203
8
58
8 16
51 44
68512
22
31488
74316
29
25684
05804
/
94196
2
59
8 8
51 52
68534
23
31466
74345
30
25655
05811
/
94189
1
60
8 0
52 0
68557
23
31443
74375
30
25625
05818
7
94182
0
M
M.
Hour p. M.
Hour A. M.
Cosine.
DIfl.
Secant.
Cotangent, j Diff.
Tangent.
Cosecant.
Diff.
Sine.
118°
A
A
B B
c
C 61° 1
Seconds of time
1"
2«
8- 1 4»
5'
6»
7-
fA
Prop, parts of cols, i B
Ic
8
4
1
6
8
2
9 12
11 15
3 3
15
19
4
17
23
5
20
26
6
TABLE 44.
[Page 637
Log. Sines, Tangents, and Secants.
29°
A
A
B B
C
C 160°
M.
0
Hour A. M.
Hour p. M.
Sine.
DifF. Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
8 8 0
3 52 0
9. 68557
0
10. 31443
9. 74375
0
10. 25625
10. 05818
0
9. 94182
60
1
7 52
52 8
68580
0
31420
74405
0
25595
05825
0
94175
59
?.
7 44
52 16
68603
1
31397
74435
1
25565
05832
0
94168
58
8
7 36
52 24
68625
1
31375
74465
1
25535
05839
0
94161
57
4
7 28
52 32
68648
1
31352
74494
9. 74524
2
2
25506
05846
0
94154
56
55
5
8 7 20
3 52 40
9. 68671
2
10. 31329
10. 25476
10. 05853
9. 94147
fi
7 12
52 48
68694
2
31306
74554
3
25446
05860
94140
54
7 4
52 56
68716
3
31284
74583
3
25417
05867
94133
53
8
6 56
53 4
68739
3
31261
74613
4
25387
05874
94126
52
9
6 48
53 12
68762
3
31238
74643
4
25357
05881
94119
51
10
8 6 40
3 53 20
9. 68784
4
10. 31216
9. 74673
5
10. 25327
10. 05888
9.94112
50
n
6 32
53 28
68807
4
31193
74702
5
25298
05895
94105
49
ii>
6 24
53 36
68829
4
31171
74732
6
25268
05902
94098
48
18
6 16
53 44
68852
5
31148
74762
6
252.38
05910
2
94090
47
14
15
6 8
53 52
68875
5
31125
74791
9. 74821
7
25209
0.5917
10. 0.5924
2
2
94083
46
45
8 6 0
3 54 0
9. 68897
6
10. 31103
7
10. 25179
9. 94076
16
5 52
54 8
68920
6
31080
74851
8
25149
05931
2
94069
44
17
5 44
54 16
68942
6
31058
74880
8
25120
05938
2
94062
43
1«
5 36
54 24
68965
7
31035
74910
9
25090
05945
2
94055
42
19
5 28
54 32
68987
7
31013
74939
9
25061
05952
2
94048
41
90
8 5 20
3 54 40
9. 69010
7
10. 80990
9. 74969
10
10. 25031
10. 05959
2
9. 94041
40
9^
5 12
54 48
69032
8
30968
74998
10
25002
05966
3
94034
39
99
5 4
54 56
69055
8
30945
75028
11
24972
05973
3
94027
38
9'^
4 56
55 4
69077
9
30923
75058
11
24942
05980
3
94020
37
24
4 48
55 12
69100
9
9
30900
75087
12
24913
0.5988
3
94012
36
9h
8 4 40
3 55 20
9. 69122
10. 30878
9. 75117
12
10. 24883
10. 05995
3
9. 94005
3b
9f\
4 32
55 28
69144
10
. 30856
75146
13
24854
06002
3
93998
34
91
4 24
55 36
69167
10
30833
75176
13
24824
06009
3
93991
33
?8
4 16
55 44
69189
10
30811
75205
14
24795
06016
3
93984
32
29
4 8
55' 52
69212
11
30788
75235
14
24765
06023
3
93977
31
80
8 4 0
3 56 0
9. 69234
11
10. 30766
9. 75264
15
10. 24736
10. 06030
4
9. 93970
30
81
3 52
56 8
69256
12
30744
75294
15
24706
06037
4
93963
29
82
3 44
56 16
69279
12
30721
75323
16
24677
06045
4
93955
28
88
3 36
56 24
69301
12
30699
75353
16
24647
06052
4
93948
27
34
3 28
56 32
69323
13
30677
75382
17
24618
06059
10. 06066
4
4
9.3941
26
85
8 3 20
3 56 40
9. 69345
13
10. 30655
9.75411
17
10. 24-589
9. 93934
25
86
3 12
56 48
69368
13
30632
75441
18
24559
06073
4
93927
24
87
3 4
56 56
69390
14
30610
75470
18
24530
06080
4
93920
23
88
2 56
57 4
69412
14
30588
75500
19
24500
06088
5
93912
22
39
40
2 48
57 12
69434
15
30566
75529
19
24471
06095
5
93905
21
20
8 2 40
3 57 20
9. 69456
15
10. 30544
9. 75558
20
10. 24442
10. 06102
6
9. 93898
41
2 32
57 28
69479
15
30521
75588
20
24412
06109
5
93891
19
42
2 24
57 36
69501
16
30499
75617
21
24383
06116
5
93884
18
48
2 16
57 44
69523
16
30477
75647
21
24353
06124
5
93876
17
44
45
2 8
57 52
69.545
16
17
30455
75676
22
24324
06131
5
93869
.16
15
8 2 0
3 58 0
9. 69567
10. 30433
9. 75705
22
10. 24295
10. 06138
5
9. 93862
46
1 52
58 8
69589
17
30411
75735
23
24265
06145
5
93855
14
47
1 44
58 16
69611
17
30889
75764
23
24236
06153
6
93847
13
48
1 36
58 24
69633
18
30867
75793
24
24207
06160
6
93840
12
49
1 28
58 32
69655
18
19
30845
75822
24
24178
06167
6
938.33
11
10
50
8 1 20
3 58 40
9. 69677
10. 30323
9. 75852
25
10. 24148
10. 06174
6
9. 93826
51
.1 12
58 48
69699
19
30801
75881
25
24119
06181
6
93819
9
52
1 4
58 56
69721
19
30279
75910
26
24090
06189
6
9.3811
8
53
0 56
59 4
69743
20
30257
75939
26
24061
06196
6
93804
7
54
55
0 48
59 12
69765
20
30235
75969
27
24031
06203
6
93797
6
8 0 40
3 59 20
9. 69787
20
10. 30213
9. 75998
27
10. 24002
10. 06211
7
9. 93789
5
56
0 32
59 28
69809
21
30191
76027
28
23973
06218
7
93782
4
57
0 24
59 36
69831
21
30169
76056
28
28944
06225
7
98775
3
58
0 16
59 44
69853
22
30147
76086
29
23914
06232
7
93768
2
59
0 8
59 52
69875
22
30125
76115
29
23885
06240
7
93760
1
60
M.
0 0
4 0 0
69897
22
30103
76144
29
23856
06247
7
93753
0
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
119°
A
A
B B
C
C 60° 1
Seconds of time
Prop, parts of cols.-jB
C
Page 638j
TABLE 44.
Log.
Sines, Tangents, and Secants.
80°
A
A
B
B
C
C 1490
M.
Hour A.M.
Hour p. M.
Sine.
Diflf.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
8 0 0
4 0 0
9. 69897
0
10. 30103
9. 76144
0
10. 23856
10. 06247
0
9. 93753
60
1
7 59 52
0 8
69919
0
30081
76173
0
23827
06254
^i
93746
59
2
59 44
0 16
69941
1
30059
76202
1
23798
06262
0 '
93738
58
3
59 36
0 24
69963
1
30037
76231
1
23769
06269
0
93731
57
4
5
59 28
7 59 20
0 m
4 0 40
69984
9. 70006
1
2
30016
10. 29994
76261
2
23739
06276
10. 06283
0 '
93724
9. 93717
56
55
9. 76290
2
10. 23710
6
59 12
0 48
70028
2
29972
76319
3
23681
06291
93709
54
7
59 4
0 56
70050
3
29950
76348
3
23652
06298
1
93702
53
8
58 56
1 4
70072
3
29928
76377
4
23623
06305
93695
52
9
58 48
1 12
70093
3
29907
76406
4
23594
06313
93087
51
10
7 58 40
4 1 20
9. 70115'
4
10. 29885
9. 76435
5
10. 23565
10. 06320
9. 93680
50
11
58 32
1 28
70137
4
29863
76464
5
23536
06327
93673
49
12
58 24
1 36
70159
4
29841
76493
6
23507
06335
936()5
48
18
58 16
1 44
70180
5
29820
76522
6
23478
06342
2
93658
47
14
58 8
1 52
70202
5
5
29798
10. 29776
76551
7
23449
10. 23420
06350
2
93650
9. 93643
46
45
15
7 58 0
4 2 0
9. 70224
9. 76580
7
10. 06357
2
16
57 52
2 8
70245
6
29755
76609
8
23391
063(>4
2
93636
44
17
57 44
2 16
70267
6
29733
76639
8
23361
06372
2
93628
43
18
57 36
2 24
70288
6
29712
76668
9
23332
06379
2
93621
42
19
57 28
2 32
4 2 40
70310
7
29690
76697
9
23303
06386
2
93614
9. 93606
41
40
20
7 57 20
9. 70332
7
10. 29668
9. 76725
10
10. 23275
10. 06394
2
21
57 12
2 48
70353
8
29647
76754
10
23246
06401
3
93599
39
22
57 4
2 56
70375
8
29625
76783
11
23217
06409
3
93591
38
23
56 56
3 4
70396
8
29604
76812
11
23188
06416,
3
93584
37
24
56 48
3 12
70418
9
29582
76841
12
23159
10. 23130
06423
3
93577
36
25
7 56 40
4 3 20
9. 70439
9
10. 29561
9. 76870
12
10. 06431
3
9. 93569
35
26'
56 32
3 28
70461
9
29539
76899
13
23101
06438
3
93562
34
27
56 24
3 36
70482
10
29518
76928
13
23072
06446
3
93554
33
28
56 16
3 44
70504
10
29496
76957
13
23043
06453
3
93547
32
29
56 8
3 52
70525
10
29475
76986
14
23014
06461
4
93539
9. 93532
31
30
30
7 56 0
4 4 0
9. 70547
11
10. 29453
9. 77015
14
10. 22985
10. 06468
4
31
55 52
4 8
70568
11
29432
77044
15
22956
06475
4
93525
29
32
55 44
4 16
70590
11
29410
77073
15
22927
06483
4
93517
28
33
55 36
4 24
70611
12
29389
77101
16
22899
06490
4
93510
27
34
55 28
4 32
70633
9.70654
12
29367
77130
16
22870
06498
4
93502
26
35
7 55 20
4 4 40
13
10. 29346
9. 77159
17
10. 22841
10. 06505
4
9. 93495
25
36
55 12
4 48
70675
13
29325
77188
17
22812
06513
4
93487
24
37
55 4
4 56
70697
13
29303
77217
18
22783
06520
5
93480
23
38
54 56
5 4
70718
14
29282
77246
18
22754
06528
5
93472
22
39
54 48
5 12
70739
14
29261
77274
19
22726
06535
5
93465
21
20
40
7 54 40
4 5 20
9. 70761
14
10. 29239
9. 77303
19
10. 22697
10. 0a543
5
9. 93457
41
54 32
5 28
70782
15
29218
77332
20
22668
06550
5
93450
19
42
54 24
5 36
70803
15
29197
77361
20
22639
06558
5
93442
18
43
54 16
5 44
70824
15
29176
77390
21
22610
06565
5
93435
17
44
54 8
5 52
70846
16
16
29154
10.29133
77418
21
22582
10. 22553
06573
5
93427
9. 93420
16
15
45
7 54 0
4 6 0
9. 70867
9. 77447
22
10. 06580
6
46
53 52
6 8
70888
16
29112
77476
22
22524
06588
6
93412
14
47
53 44
6 16
70909
17
29091
77505
23
22495
06595
6
93405
13
48
53 36
6 24
70931
17
29069
77533
23
22467
06603
6
93397
12
49
50
53 28
7 53 20
6 32
70952
9.70973
18
18
29048
10. 29027
77562
9. 77591
24
22438
06610
6
" 6
93390
9. 93382
11
10
4 6 40
24
10. 22409
10.06618
51
53 12
6 48
70994
18
29006
77619
25
22.381
06625
6
93375
9
52
53 4
6 56
71015
19
28985
77648
25
22352
06633
6
93367
8
53
52 56
7 4
71036
19
28964
77677
26
22323
06640
7
93360
7
54
55
52 48
7 12
71058
19
28942
77706
26
26
22294
10. 22266
06648
7
93352
6
5
7 52 40
4 7 20
9. 71079
20
10. 28921
9. 77734
10. 06656
7
9. 93344
56
52 32
7 28
71100
20
28900
77763
27
22237
06663
7
93337
4
57
52 24
7 36
71121
20
28879
77791
27
22209
06671
7
93329
3
58
52 16
7 44
71142
21
28858
77820
28
22180
06678
7
93322
2
59
52 8
7 52
71163
21
'28837
77849
28
22151
06686
7
93314
1
60
52 0
8 0
71184
21
28816
77877
29
22123
06693
7
93307
0
M.
Hour p. M
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
jDiff.
Sine.
M.
120^
A
A
B
B
C
C 69° 1
Seconds of time
1«
2-
8*
4«
&•
6«
J'
A
Prop, parts of cols.^B
Ic
3
4
1
5
7
2
8
11
3
11
14
4
13
18
5
16
22
6
19
25
7
TABLE 44.
[Page 639
Log. Sines, Tangents, and Secants.
31°
A A
B
B
C
C 148°
M.,
Hour A. M.
Hour P.M.
Sine.
Diflf.
Cosecant.
Tangent. Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
7 52 0
4 8 0
9.71184
0
10. 28816
9. 77877
0
10. 22123
10. 06693
0
9. 93307
60
1
51 52
8 8
71205
0
28795
77906
0
22094
06701
0
98299
59
9,
51 44
8 16
71226
1
28774
77935
1
22065
06709
0
93291
58
8
51 36
8 24
71247
1
28753
77963
1
22087
06716
0
93284
57
4
51 28
8 32
71268
1
28732
77992
2
22008
06724
93276
56
55
5
7 51 20
4 8 40
9. 71289
2 jlO. 28711
9. 78020
2
10. 21980
10. 06731
1 i 9. 93269 1
fi
51 12
8 48
71310
2 1 28690
78049
3
21951
06739
93261
54
7
51 4
8 56
71331
2 ! 28669
78077
3
21923
06747
93253
58
S
50 56
9 4
71352
3 28648
78106
4
21894
06754
93246
52
9
10
50 48
9 12
4 9 20
71378
3 28627
•3 110.28607
78135 1 4
21865
06762
93238
51
50
7 50 40
9. 71393
9. 78168
5
10. 21887
10. 06770
1 9.93280
11
50 32
9 28
71414
4 ' 28586
78192
5
21808
06777
1 ; 93223
49
12
50 24
9 36
71435
4 28565
78220
6
21780
06785
2 93215
48
IS
50 16
9 44
71456 i 4 ! 28544
78249
6
21751
06793
2 93207
47
14
50 8
9 52
71477
5
5
28523
78277
9. 78306
7
21723
06800
10. 06808
2 93200
2 9.93192"
46
45
15
7 50 0
4 10 0
9. 71498
10. 28502
t
10. 21694
16
49 52
10 8
71519 5 28481
78334
8
21666
06816
2 93184
44
17
49 44
10 16
71539
6 ; 28461
78863
8
21637
06823
2 , 93177
43
18
49 36
10 24
71560
6 1 28440
78391
9
21609
06831
2 93169
42
19
20
49 28
10 32
71581
9. 71602
7
7
28419
78419
9
9
21581
06839
2 93161
41
40
7 49 20
4 10 40
10. 28398
9. 78448
10. 21552
10. 06846
3 9.93154
?.\
49 12
10 48
71622
7
28378
78476
10
21524
06854
3 93146
39
22
49 4
10 56
71643 8
28357
78505
10
21495
06862
3 93138
38
28
48 56
11 4
71664 ! 8
28336
78533
11
21467
06869
3 93131
37
24
48 48
11 12
71685
8
28315
78562 11
21438
06877
3 93123
36
35
25
7 48 40
4 11 20
9. 71705
9
10. 28295
9. 78590 12
10. 21410
10. 06885
3 9.93115
26
48 32
11 28
71726
9 [ 28274
78618 12
21382
06892
3 93108
34
27
48 24
11 36
71747
9 28253
78647 13
21358
06900
3 93100
33
28
48 16
11 44
71767
10 28233
78675 ! 13
21325
06908
4 93092
32
29
48 8
11 52.
71788
10
28212
10. 28191
78704
14
14
21296
06916
4
4
93084
31
30
80
7 48 0
4 12 0
9. 71809
10
9. 78732
10. 21268
10. 06923
9. 93077
81
47 52
12 8
71829
11 1 28171
78760 15
21240
06931
4 93069
29
82
47 44
12 16
71850
11 1 28150
78789 ; 15
21211
06939
4 93061
28
88
47 36
12 24
71870
11 1 28130
78817 16
21188
06947
4 98053
27
34
47 28
12 32
71891
12 I 28109
78845 i 16
21155
06954
4
5
93046
26
25
85
7 47 20
4 12 40
9. 71911
12 110.28089
9.78874 ! 17
10. 21126
10. 06962
9. 98038
86
47 12
12 48
71932
12 1 28068
78902 17
21098
06970
5 93030
24
87
47 4
12 56
71952
13 28048
78930 17
21070
06978
5 93022
23
88
46 56
13 4
71973
13 28027
78959 18
21041
06986
5 93014
22
39
46 48
13 12
71994
13 1 28006
78987 t 18
21013
10. 20985
06993
10. 07001
5
5
93007
21
40
7 46 40
4 13 20
9.72014 1 14 10.27986
9.79015 19
9. 92999
20
41
46 32
13 28
72034 ! 14 27966
79043 19
20957
07009
5 92991
19
42
46 24
13 36
72055
14 27945
79072 20
20928
07017
5 92983
18
48
46 16
13 44
72075
15 27925
79100 20
20900
07024
6 ; 92976
17
44
46 8
13 52
72096
15 i 27904
79128 21
9. 79156 21
20872
07032
6 ! 92968
16
15
45
7 46 0
4 14 0
9. 72116
15
10. 27884
10. 20844
10. 07040
6 9. 92960
46
45 52
14 8
72137
16
27863
79185 22
20815
07048
6 1 92952
14
47
45 44
14 16
72157
16
27848
79213 22
20787
07056
6 1 92944
13
48
45 36
14 24
72177
16
27823
79241 23
20759
07064
6 1 92936
12
49
50
45 28
7 45 20
14 82
4 14 40
72198
17 27802
79269 1 23
20731
07071
6 92929
11
10
9.72218 i 17 10.27782
9.79297 1 24
10. 20703
10. 07079
6 9.92921
51
45 12
14 48
72238 1 18 1 27762
79326 1 24
20674
07087
7 1 92913
9
52
45 4
14 56
72259 18 27741
79354 25
20646
07095
7 ! 92905
8
58
44 56
15 4
72279 1 18 27721
79382 25
20618
07103
7 92897
1
54
55
44 48
15 12
4 15 20
72299
19 27701
19 10.27680
79410 26
20590
10. 20562
07111
10.07119
7 I 92889
7 19.92881
6
5
7 44 40
9. 72320
9. 79438
26
56
44 32
15 28
72340 i 19
27660
79466
26
205;w
07126
7 92874
4
57
44 24
15 36
72360 ; 20
27640
79495
27
20505
07134
7 92866
3
58
44 16
15 44
72381 20
27619
79523
27
20477
07142
7 92858
2
59
44 8
15 52
72401 1 20
27599
79551
28
20449
07150
8
92850
1
60
44 0
16 0
72421
21
27579
79579
28
20421
07158
8
92842
0
M.
Hour p. M.
Hour A.M.
Cosine.
DiflF.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
121°
A A
B
B
C
C 58° 1
Seconds of time
1» 2"
3«
4»
5«
6' 7"
Prop, parts of cols. B
1 c
3 5 8
4 i 7 11
1 2 3
10 13
14 18
4 h
15 j 18
21 1 25
6 ' 7
Page 640]
TABLE 44.
Log. Sines, Tangents, and Secants.
82°
A
A
B
B
C
C
147°
M.
Hour A. M.
Hour p. M.
Sine. 1 Diff.
Cosecant.
Tangent. Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
60
0
7 44 0
4 16 0
9. 72421
0
10. 27579
9.79579 0
10. 20421
10. 07158
0
9. 92842
1
48 52
16 8
72441
0
27559
79607 0
20398
07166
0
92834
59
9
48 44
16 16
72461
1
27539
79635 1
20365
07174
0
92826
58
8
43 86
16 24
72482
1
27518
79663 1
20337
07182
0 92818
57
4
5
43 28
16 3»
72502
1
27498
79691
2
20309
07190
1
92810
56
55
7 43 20
4 16 40
9. 72522 2
10. 27478
9. 79719
2
10. 20281
10. 07197
1
9. 92803
H
43 12
16 48
72542 2
27458
79747
8
20258
07205
1
92795
54
7
48 4
16 56
72562 2
27438
79776
3
20224
07213
1
92787
53
8
42 56
17 4
72582 3
27418
79804 4
20196
07221
1
92779
52
9
10
42 48
17 12
72602 3
27398
79832 i 4
20168
07229
1
92771
9. 92768
51
50
7 42 40
4 17 20
9. 72622 3
10. 27878
9. 79860 5
10. 20140
10. 07237
1
11
42 32
17 28
72643 4
27857
79888 5
20112
07245
1
92755
49
12
42 24
17 36
72668 ; 4
27887
79916 6
20084
07258
2
92747
48
18
42 16
17 44
72688 4
27317
79944 ; 6
20056
07261
2
92739
47
14
15
42 8
17 52
72708
5
5
27297
79972
'9. 80000
7
7
20028
07269
10. 07277
2
2
92731
9. 92728
46
45
7 42 0
4 18 0
9. 72723
10. 27277
10.20000
U)
41 52
18 8
72743 5
27257
80028
7
19972
07285
2
92715
44
17
41 44
18 16
72768 6
27237
80056
8
19944
07293
2
92707
48
18
41 36
18 24
72788 6
27217
80084
8
19916
07301
2
92699
42
19
20
41 28
7 41 20
18 32
72808 6
27197
80112
9
19888
07309
3
92691
41
40
4 18 40
9.72828 7
10. 27177
9.80140 1 9
10. 19860
10. 07817
3 i 9. 92683
21
41 12
18 48
72848 7
27157
80168 1 10
19832
07325
3 ! 92675
39
22
41 4
18 56
72863 7
27137
80195 10
19805
07338
3 ' 92667
38
28
40 56
19 4
72883 , 8
27117
80223 11
19777
07:341
8 ; 92659
87
24
40 48
19 12
72902 8
27098
80251 11
19749
07349
8 i 92651
36
25
7 40 40
4 19 20
9.72922 8
10. 27078
9.80279 12
10. 19721
10. 07857
8 i 9. 92648
35
26
40 82
19 28
72942 9
27058
80307 12
19693
07365
8 ! 926:35
34
27
40 24
19 36
72962 9
27038
80335 13
19665
07873
4
92627
33
28
40 16
19 44
72982 i 9
27018
80868 13
19687
07381
4
92619
32
29
80
40 8
19 52
78002
10
10
26998
10. 26978
80391 18
9.80419 14
19609
07389
4
92611
9. 92603
31
80
7 40 0
4 20 0
9. 73022
10. 19581
10. 07397
4
81
39 52
20 8
73041 : 10
26959
80447 14
19553
07405
4
92595
29
82
39 44
20 16
78061 ; 11
26989
80474 15
19526
07413
4
92587
28
88
89 36
20 24
78081 11
26919
80502 , 15
19498
07421
4
92579
27
34
39 28
20 82
78101 11
26899
80580 : 16
19470
07429
5 ! 92571
26
85
7 39 20
4 20 40
9.78121 12
10. 26879
9.80558 1 16
10. 19442
10. 07487
5 (9.92568
25
86
39 12
20 48
78140 12
26860
80586 17
19414
07445
5 ! 92555
24
87
89 4
20 56
73160 12
26840
80614 17
19886
07454
5 1 92546
23
88
38 56
21 4
73180 1 13
26820
80642 1 18
19358
07462
5 ! 92538
22
89
40
38 48
21 12
73200 i 13
26800
80669 18
9.80697 j 19
19831
07470
5
5~
92580
21
7 38 40
4 21 20
9. 78219 13
10. 26781
10. 19808
10. 07478
9. 92522
20
41
88 82
21 28
73239 14
26761
80725 1 19
19275
07486
6 1 92514
19
42
88 24
21 86
73259 ! 14
26741
80753 1 20
19247
07494
6 92506
18
48
88 16
21 44
78278 : 14
26722
80781 : 20
19219
07502
6 92498
17
44
45
38 8
"7'38 0
21 52
4 22 0
73298 15
26702
80808 20
19192
07510
6 92490
16
9.73818 15
10. 26682
9.80886 1 21
10. 19164
10. 07518
6
9. 92482
15
46
37 52
22 8
78387 15
26663
80864 i 21
19136
07527
6
92478
14
47
37 44
22 16
78857 1 16
26643
80892 i 22
19108
07535
6
92465
13
48
87 36
22 24
78377 ' 16
26628
80919 ! 22
19081
07543
6
92457
12
49
37 28
22 32
73396 16
26604
80947 j 28
19058
07551
7
"^7"
92449
11
10
50
7 37 20
4 22 40
9.73416 17
10. 26584
9.80975 1 28
10. 19025
10. 07559
9. 92441
51
87 12
22 48
73435 1 17
26565
81003
24
18997
07567
/
92483
9
52
37 4
22 56
7:3455 i 17
26545
81030
24
18970
07575
7
92425
8
58
36 56
23 4
73474 18
26526
81058
25
18942
07584
7
92416
7
54
36 48
23 12
73494 i 18
26506
81086
25
18914
07592
7
92408
6
5
55
7 36 40
4 28 20
9.73518 ; 18
10. 26487
9.81113
26
10. 18887
10. 07600
7
9. 92400
56
36 32
28 28
78533 19
26467
81141
26
18859
07608
8
92392
4
57
86 24
23 36
78552 i 19
26448
81169
26
18831
07616
8
92884
8
58
36 16
23 44
78572 19
26428
81196
27
18804
07624
8 1 92376
2
59
36 8
23 52
73591 20
26409
81224 27
18776
07638
8 92367
1
60
M.
36 0
24 0
73611 20
26389
81252 ! 28
18748
07641
8
92359
0
Hour p. M.
Hour A. M.
Cosine. Dili.
Secant.
Cotangent. Diff.
Tangent.
Ccsecant.
Diff.
Sine.
M.
1-220
A
A
B
B
C
C
57°
Seconds of time
1»
2»
8>
4»
6<
6>
7'
fA
Prop, parts of cols. iB
Ic
2
3
1
6
7
2
7
10
3
10
14
4
12
17
5
15
21
6
17
24
7
TABLE U.
[Page 641
Log. Sines, Tangents, and Secants.
83°
A
A
B
B
C
C 146°
M.
0
Hour A. M.
Hour P. M.
Sine.
Diff.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Difl.
Cosine.
M.
7 36 0
4 24 0
9. 73611
0
10. 26389
9. 81252
0
10. 18748
10. 07641
0
9. 92359
60
1
35 52
24 8
73630
0
26370
81279
0
18721
07649
0
92351
59
'?
35 44
24 16
73650
1
26350
81307
1
18693
07657
0
92343
58
8
35 36
24 24
73669
1
26331
81335
1
18665
07665
0
92335
57
4
35 28
24 32
73689
1
26311
81362
2
18638
07674
1
92326
56
5
7 35 20
4 24 40
9. 73708
2
10. 26292
9. 81390
2
10. 18610
10. 07682
1
9. 92318
55
6
35 12
24 48
73727
2
26273
81418
3
18582
07690
1
92310
54
7
35 4
24 56
73747
2
26253
81445
3
18555
07698
1
92302
53
8
34 56
25 4
73766
3
26234
81473
4
18527
07707
1
92293
52
9
10
34 48
25 12
73785
3
26215
81500
4
18500
07715
1
92285
51
50
7 34 40
4 25 20
9. 73805
3
10. 26195
9. 81528
5
10. 18472
10. 07723
1
9. 92277
n
34 32
25 28
73824
3
26176
81556
5
18444
07731
2
92269
49
12
34 24
25 36
73843
4
26157
81583
5
18417
07740
2 92260
48
18
34 16
25 44
73863
4
26137
81611
6
18389
07748
2
92252
47
14
15
34 8
25 52
73882
4
26118
81638
6
18362
07756
2
92244
46
7 34 0
4 26 0
9. 73901
5
10. 26099
9. 81666
7
10. 18334
10. 07765
2
9. 92235
45
Ifi
33 52
26 8
73921
• 5
26079
81693
7
18307
07773
2
92227
44
17
33 44
26 16
73940
5
26060
81721
8
18279
07781
2
92219
43
18
33 36
26 24
73959
6
26041
81748 8
18252
07789
3
92211
42
19
20
33 28
26 32
73978
6
26022
81776
9
18224
07798
3
92202
41
7 33 20
4 26 40
9.73997
6
10. 26003
9. 81803
9
10. 18197
10. 07806
3
9. 92194
40
21
33 12
26 48
74017
7
25983
81831
10
18169
07814
3
92186
39
22
33 4
26 56
74036
7
25964
81858
10
18142
07823
3
92177
38
28
32 56
27 4
74055
7
25945
81886
11
18114
07831
3
92169
37
24
32 48
27 12
74074
8
25926
81913
11
18087
07339
3
92161
36
25
7 32 40
4 27 20
9.74093
8
10. 25907
9. 81941
11
10. 18059
10. 07848
3
9. 92152
35
26
32 32
27 28
74113
8
25887
81968
12
18032
07856
4
92144
34
27
32 24
27 36
74132
9
25868
81996
12
18004
07864
4
92186
33
28
32 16
27 44
74151
9
25849
82023
13
17977
07873
4
92127
32
29
32 8
27 52
74170
9
25830
82051
13
17949
07881
4
92119
31
80
7 32 0
4 28 0
9. 74189
10
10. 25811
9. 82078
14
10. 17922
10. 07889
4
9.92111
30
81
31 52
28 8
74208
10
25792
82106
14
17894
07898
4
92102
29
82
31 44
28 16
74227
10
25773
82133
15
17867
07906
4
92094
28
88
31 36
28 24
74246
10
25754
82161
15
17839
07914
5
92086
27
34
31 28
28 32
74265
11
25735
82188
16
17812
07923
5
92077
26
85
7 31 20
4 28 40
9. 74284
11 10.25716
9. 82215
16
10. 17785
10. 07931
5
9. 92069
25
8H
31 12
28 48
74303
11 25697
82243
16
17757
07940
5
92060
24
87
31 4
28 56
74322
12 25678
82270
17
17730
07948
5
92052
23
88
30 56
29 4
74341
12 25659
82298
17
17702
07956
5
92044
22
39
30 48
29 12
74360
12 25640
82325
18
17675
07965
6
92035
9. 92027
21
20
40
7 30 40
4 29 20
9. 74379
13
10. 25621
9. 82352
18
10. 17648
10. 07973
6
41
30 32
29 28
74398
13
25602
82380
19
17620
07982
6
92018
19
42
30 24
29 36
74417
13
25583
82407
19
17593
07990
6
92010
18
48
30 16
29 44
74436
14
25564
82435
20
17565
07998
6
92002
17
44
45
30 8
29 52
74455
14
25545
82462 I 20
17538
10. 17511
08007
6
91993
16
7 30 0
4 30 0
9. 74474
14
10. 25526
9. 82489
21
10. 08015
6
9. 91985
15
46
29 52
30 8
74493
15
25507
82517
21
17483
08024
6
91976
14
47
29 44
30 16
74512
15
25488
82544
22
17456
08032
/
91968
13
48
29 36
30 24
74531
15
25469
82571
22
17429
08041
7
91959
12
49
29 28
30 32
74549
16
25451
82599
22
17401
08049
/
91951
11
50
7 29 20
4 30 40
9. 74568
16
10. 25432
9. 82626
23
10. 17374
10. 08058
7
9. 91942
10
51
29 12
30 48
74587
16
25413
82653
23
17347
08066
/
91934
9
52
29 4
30 56
74606
17
25394
82681
24
17319
08075
7
91925
8
53
28 56
31 4
74625
17
25375
82708
24
17292
08083
/
91917
/
54
55
28 48
31 12
74644
17
25356
82735
25
17265
08092
8
91908
9. 91900
6
0
7 28 40
4 31 20
9. 74662
17
10. 25338
9. 82762
25
10. 17238
10. 08100
8
56
28 32
31 28
74681
18
25319
82790
26
17210
08109
8
91891
4
57
28 24
31 36
74700
18
25300
82817
26
17183
08117
8
91888
3
58
28 16
31 44
74719
18
25281
82844
27
17156
08126
8
91874
' 2
59
28 8
31 52
74737
19
25263
82871 i 27
17129
08134
8
91866
1
60
28 0
32 0
74756
19
25244
82899 27
17101
08143
8
91857
0
M.
Hour P. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent. Difl.
Tangent.
Cosecant.
Difl.
Sine. M. 1
123=
A
A
B
B
c
C 66° 1
Seconds of time
1'
2»
3»
4"
5»
6«
7«
fA
Prop, parts of cols. <B
[c
2
3
1
6
7
2
7
10
3
10
14
4
12
17
5
14
21
6
17
24
7
22489—03-
-41
Page 642]
TABLE 44.
Log. Sines, Tangents, and Secants.
84°
A
A
B
B
C
C
145°
M.
Hour A.M.
Hour p. M.
Sine.
Difl.
Cosecant
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
0
7 28 0
4 32 0
9. 74756
0
10. 25244
9. 82899
0
10. 17101
10. 08143
0
9. 91857
60
1
27 52
32 8
74775
0
25225
82926
0
17074
08151
0
91849
59
2
27 44
32 16
74794
1
25206
82953
1
17047
08160
0
91840
58
3
27 36
32 24
74812
1
25188
82980
1
17020
08168
0
91832
57
4
5
27 28
32 'S»
74831
1
25169
83008
2
16992
08177
91823
56
55
7 27 20
4 32 40
9. 74850
2
10. 25150
9. 83035
2
10. 16965
10. 08185
9. 91815
6
27 12
32 48
74868
2
25132
83062
3
16938
08194
91806
54
7
27 4
32 56
74887
2
25113
83089
3
16911
08202
91798
53
8
26 56
33 4
74906
2
25094
83117
4
16883
08211
91789
52
9
26 48
33 12
74924
3
25076
83144
4
16856
08219
91781
51
50
10
7 26 40
4 33 20
9. 74943
3
10. 25057
9. 83171
5
10. 16829
10. 08228
9.91772
11
26 32
33 28
74961
3
25039
83198
5
16802
08237
2 91763
49
12
26 24
33 36
74980
4
25020
83225
5
16775
08245
2 91755
48
13
26 16
33 44
74999
4
25001
83252
6
16748
08254
2 91746
47
14
15
26 8
33 52
4 34 0
75017
4
24983
83280
6
7
16720
10. 16693
08262
10. 08271
2 91738
2 9.91729
46
45
7 26 0
9. 75036
5
10. 24964
9. 83307
16
25 52
34 8
75054
5
24946
83334
7
16666
08280
2 91720
44
17
25 44
34 16
75073
5
24927
83361
8
16639
08288
2 91712
43
18
25 36
34 24
75091
6
24909
83388
8
16612
08297
3 1 91703
42
19
25 28
34 32
75110
6
24890
83415
9
16585
10. 16558
08305
3
3
91695
41
40
20
7 25 20
4 34 40
9. 75128
6
10. 24872
9.83442
9
10. 08314
9. 91686
21
25 12
34 48
75147
6
24853
83470
9
16530
08323
3 91677
.39
22
25 4
34 56
75165
7
24835
83497
10
16503
08331
3 91669
38
23
24 56
35 4
75184
7
24816
83524
10
16476
08340
3 ' 91660
37
24
24 48
35 12
75202
7
24798
83551
11
16449
08349
3
91651
9. 91643
36
35
25
7 24 40
4 35 20
9. 75221
8
10. 24779
9. 83578
11
10. 16422
10.08357
4
26
24 32
35 28
752.39
8
24761
83605
12
16395
08366
4 91634
.34
27
24 24
35 36
75258
8
24742
83632
12
16368
08375
4 j 91625
33
28
24 16
35 44
75276
9
24724
83659
13
16341
08383
4 1 91617
32
29
30
24 8
35 52
75294
9
24706
83686
13
14
16314
08392
4 ! 91608
31
30
7 24 0
4 36 0
9. 75313
9 10.24687
9. 83713
10. 16287
10. 08401
4 9.91599
31
32
23 52
36 8
75331
9
24669
83740
14
16260
08409
4
91591
29
23 44
36 16
75350
10
24650
83768
14
16232
08418
5
91582
28
33
23 36
36 24
75368
10
24632
83/795
15
16205
08427
5
91573
27
34
23 28
36 32
75386
10
24614
83822
15
16178
08435
5
91565
26
25
35
7 23 20
4 36 40
9. 75405
11
10. 24595
9. 83849
16
10. 16151
10. 08444
5
9. 91556
36
23 12
36 48
75423
11
24577
83876
16
16124
08453
5
91547
24
37
23 4
36 56
75441
11
24559
83903
17
16097
08462
5
91538
23
38
22 56
37 4
75459
12 1 24541
83930
17
16070
08470
5
91530
22
39
40
22 48
7 22 40
37 12
4 37 20
75478
12
24522
10. 24504
83957
18
16043
08479
6
91521
21
20
9. 75496
12
9. 83984
18
10. 16016
10. 08488
6
9.91512
41
22 32
37 28
75514
13 i 24486
84011
18
15989
08496
6
91504
19
42
22 24
37 36
75533
13 24467
84038
19
15962
08505
6
91495
18
43
22 16
37 44
75551
13 24449
84065
19
15935
08514
6
91486
17
44
45
22 8
7 22 0
37 52
4 38 0
75569
9. 75587
13
14
24431
84092
20
15908
08523
6 : 91477
16
10.24413
9.84119
20
10. 15881
10. 08531
7 9.91469
15
46
21 52
38 8
75605
14 24395
84146
21
15854
08540
7 91460
14
47
21 44
38 16
75624
14 2.^76
15 24358
84173
21
15827
0a549
7 91451
13
48
21 36
38 24
75642
84200
22
15800
08558
7 ; 91442
12
49
21 28
38 32
75660
15
15
24340
84227
22
15773
08567
7
91433
9. 91425
11
10
50
7 21 20
4 38 40
9. 75678
10. 24322
9. 84254
23
10. 15746
10. 08575
7
51
21 12
38 48
75696
16 24304
84280
23
15720
08584
7 \ 91416
9
52
21 4
38 56
75714
16 24286
84307
23
15693
08593
8 91407
8
53
20 56
39 4
75733
16 24267
84334
24
15666
08602
8 91398
7
54
20 48
39 12
75751
17 24249
17 10.24231
84361
24
25
15639
10715612
08611
8
91389
9. 91381
6
5
55
7 20 40
4 39 20
9. 75769
9. 84388
10. 08619
8
56
20 32
39 28
75787
17 i 24213
84415
25
15585
08628
8 91.372
4
57
20 24
39 36
75805
17
24195
84442
26
15558
08637
8 91363
3
58
20 16
39 44
75823
18
24177
84469
26
15531
08646
8 i 91354
2
59
20 8
39 52
75841
18
24159
84496
27
15504
08655
9
91.345
1
60
M.
20 0
40 0
75859
18
24141
84523
27
15477
08664
9
91336
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Diff.
Sine.
124=
A
A
B
B
C
C
56
Seconds of time
1' »
g. 4.
S-
e*
7«
(A
Prop, parts of cols. <B
Ic
2 5
3 7
1 2
7 9
10 14
3 , 4
11
17
6
14
20
7
16
24
8
TABLE 4A.
[Page 643
]
Log.
Sines, Tangents, and Secante.
86°
A
A
B
B
C
C 144°
M.
0
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff. Cotangent.
Secant.
Diff. Cosine.
M.
7 20 0
4 40 0
9. 75859
0
10. 24141
9. 84523
0 10. 15477
10. 08664
0 9.91886
60
1
19 52
40 8
75877
0
24128
84550
0 15450
08672
0
91328
59
^
19 44
40 16
75895
1
24105
84576
1 1 15424
08681
0
91319
58
8
19 36
40 24
75913
1
24087
84608
1
15397
08690
0
91810
57
4
5
19 28
40 32
75981
9. 75949
1
24069
84630
2
2
15870
10. 15348
08699
10. 08708
91801
56
55
7 19 20
4 40 40
1
10. 24051
9. 84657
9. 91292
6
19 12
40 48
75967
2
24088
84684
8
15316
08717
91288
54
7
19 4
40 56
75985
2
24015
84711
8
15289
08726
91274
53
8
18 56
41 4
76008
2
28997
84788
4
15262
08784
91266
52
9
18 48
41 12
76021
3
28979
84764
4
15236
08743
91257
51
50
10
7 18 40
4 41 20
9. 76089
3
10. 28961
9. 84791
4
10. 15209
10. 08752
2
9. 91248
n
18 32
41 28
76057
3
28943
84818
5
15182
08761
2
91239
49
12
18 24
41 86
76075
4
28925
84845
5
15155
08770
2
91280
48
18
18 16
41 44
76093
4
28907
84872
6
15128
08779
2
91221
47
14
18 8
41 52
76111
4
28889
84899
6
15101
08788
2
2
91212
46
45
15
7 18 0
4 42 0
9. 76129
4
10. 28871
9. 84925
7
10. 15075
10. 08797
9. 91203
16
17 52
42 8
76146
5
23854
84952
7
15048
08806
2
91194
44
17
17 44
42 16
76164
5
28886
84979
8
15021
08815
3
91185
48
18
17 36
42 24
76182
5
28818
85006
8
14994
08824
3
91176
42
19
20
17 28
42 32
76200
9. 76218
6
6
23800
10. 28782
85033
9. 85059
8
9
14967
10. 14941
08838
10. 08842
3
3
91167
9.91L58
41
40
7 17 20
4 42 40
21
17 12
42 48
76236
6
28764
85086
9
14914
08851
3
91149
89
22
17 4
42 56
76253
6
23747
85113
10
14887
08859
8
91141
88
28
16 56
48 4
76271
7
23729
85140
10
14860
08868
3
91182
37
24
25
16 48
7 16 40
48 12
76289
7
23711
85166
11
14884
08877
4
91128
36
4 48 20
9. 76307
7
10. 28698
9. 85193
11
10. 14807
10. 08886
4
9.91114
85
26
16 82
48 28
76324
8
28676
85220
12
14780
08895
4
91105
34
27
16 24
43 86
76342
8
28658
85247
12
14753
08904
4
91096
33
28
16 16
48 44
76360
8
2.3640
85273
12
14727
08918
4
91087
32
29
80
16 8
48 52
76378
9
23622
85300
9. 85327
13
13
14700
08922
10. 08981
4
5
91078
31
30
7 16 0
4 44 0
9. 76895
9
10. 28605
10. 14678
9. 91069
31
15 52
44 8
76418
9
28587
85354
14
14646
08940
5
91060
29
82
15 44
44 16
76431
9
28569
85380
14
14620
08949
5
91051
28
88
15 86
44 24
76448
10
23552
85407
15
14593
08958
5
91042
27
84
85
15 28
7 15 20
44 32
76466
9. 76484
10
10
2:3534
85434
15
16
14566
08967
5
91033
-26
4 44 40
10. 23516
9.85460
10. 14540
10. 08977
5
9. 91023
25
86
15 12
44 48
76501
11
23499
85487
16
14513
08986
5
91014
24
37
15 4
44 56
76519
11
2;W81
85514
16
14486
08995
6
91005
28
38
14 56
45 4
76587
11
2;W68
85540
17
14460
09004
6
90996
22
89
40
14 48
.7" 14 40"
45 12
76554
12
12
28446
85567
9.85594
17
18
14438
09018
6
90987
21
20
4 45 20
9. 76572
10. 28428
10. 14406
10. 09022
6
9. 90978
41
14 32
45 28
76590
12
28410
85620
18
14880
09031
6
90969
19
42
14 24
45 86
76607
12
28893
85647
19
14853
09040
6
90960
18
43
14 16
45 44
76625
18
23375
85674
19
14826
09049
6
90951
17
44
45
14 8
7 14 0
45 52
4 46 0
76642
9. 76660
13
13
28858
10.28840
85700
9. 85727
20
20"
14800
10. 14273
09058
7
90942
16
15
10. 09067
7
9. 90938
46
13 52
46 8
76677
14
28328
85754
20
14246
09076
7
90924
14
47
13 44
46 16
76695
14
28305
85780
21
14220
09085
7
90915
13
48
13 36
46 24
76712
14
23288
85807
21
14193
09094
7
90906
12
49
13 28
46 32
76730
14
15
23270
10.28253
85884
9:85860
22
22
14166
10. 14140
09104
10. 09113
7
8
90896
11
10
50
7 13 20
4 46 40
1 9. 76747
9. 90887
51
13 12
46 48
76765
15
23285
85887
28
14113
09122
8
90878
9
52
13 4
46 56
76782
15
2.3218
85918
23
14087
09181
8 : 90869
8
53
12 56
47 4
76800
16
23200
85940
24
14060
09140
8 90860
7
54
55
12 48
7 12 40
47 12
4 47 20
76817
16
16
23188
10.23165
85967
9.85998
24
14088
09149
10.09158
8
8
90851
6
1 9. 76835
24 10.14007
9. 90842
5
56
12 32
47 28
1 76852
17
23148
86020
25 13980
09168
8
90882
4
57
12 24
47 36
76870
17
23180
86046
25 13954
09177
9
90828
3
58
12 16
47 44
76887
17
23113
86078
26 13927
09186
9
90814
2
59
12 8
47 52
76904
17
28096
86100
26 13900
09195
9
90805
1
60
12 0
48 0
76922
18
23078
86126
27 18874
09204
9
90796
0
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff. Tangent.
Cosecant.
Diff.
Sine.
126°
A
A
B
B
C
' "M
Seconds of time 1'
L'» 3' 4'
o»
6^
7'
Prop, parts of cols.'jB
[0
2
3
1
4
7
2
7
10
3
9
13
5
11
17
6
13
20
7
16
23
8
Page 644]
TABLE U.
Log. Sines, Tangents, and Secants.
86°
A
A
B
B
C
C 148° 1
M.
0
Hour A. M. Hour p. m.
Sine.
Diff.
Closecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
7 12 0 4 48 0
9. 76922
0
10. 23078
9. 86126
0
10. 13874
10. 09204
0
9. 90796
60
1
11 52 48 8
76939
0
23061
86153
0
13847
09213
0 ' 90787
59
2
11 44 48 16
76957
1
23043
86179
1
13821
09223
0 1 90777
58
3
11 36 1 48 24
76974
1
23026
86206
1
13794
09232
0
90768
57
4
5
11 28
7 11 20
48 3^
76991
1
23009
86232
2
13768
09241
1
90759
56
55
4 48 40
9.77009
1
10. 22991
9. 86259
2
10. 13741
10. 09250
1
9. 90750
6
11 12 48 48
77026
2
22974
86285
3
13715
09259
1
90741
54
1
11 4 1 48 56
77043
2
22957
86312
3
13688
09269
1
90731
53
8
10 56 1 49 4
77061
2
22939
86338
4
13662
09278
1
90722
52
9
10
10 48
49 12
77078
9. 77095
3
3
22922
10. 22905
86365
4
13635
09287
1
90713
51
50
7 10 40
4 49 20
9. 86392
4
10. 13608
10. 09296
2
9.90704
11
10 32
49 28
77112
3
22888
86418
5
13582
09306
2
90694
49
12
10 24
49 36
77130
3
22870
86445
5
13555
09315
2
90685
49
13
10 16
49 44
77147
4
22853
86471
6
13529
09324
2
90676
47
14
10 8
49 52
77164
4
22836
86498
6
7
13502
10. 13476
09333
2
2
90667
9. 90657
46
45
15
7 10 0
4 50 0
9. 77181
4
10. 22819
9. 86524
10. 09343
16
9 52
50 8
77199
5
22801
86551
/
13449
09352
2
90648
44
17
9 44
50 16
77216
5
22784
86577
7
13423
09361
3
90639
43
18
9 36
50 24
77233
5
22767
86603
8
13397
09370
3
90630
42
19
20
9 28
50 32
4 50 40
77250
5
22750
86630
9. 86656
8
13370
09380
3
90620
41
7 9 20
9. 77268
6
10. 22732
9
10. 13344
10. 09389
3
9. 90611
40
21
9 12
50 48
77285
6
22715
86683
9
13317
09398
3
90602
39
22
9 4
50 56
77302
6
22698
86709
10
13291
09408
3
90592
38
23
8 56
51 4
77319
7
22681
86736
10
13264
09417
4
90583
37
24
25
8 48
51 12
4 51 20
77336
7
22664
86762
11
13238
09426
4
90574
36
35
7 8 40
9. 77353
/
10. 22647
9. 86789
11
10.13211
10. 09435
4
9.90565
26
8 32
51 28
77370
7
22630
86815
11
13185
09445
4
90555
34
27
8 24
51 36
77387
8
22613
86842
12
13158
09454
4
90546
33
28
8 16
51 44
77405
8
22595
86868
12
13132
09463
4
90537
32
29
3b
8 8
51 52
77422
8
22578
86894
13
13
13106
09473
5
90527
4. 90518
31
30
7 8 0
4 52 0
9. 77439
9
10. 22561
9. 86921
10. 13079
10. 09482
5
31
7 52
52 8
77456
9
22544
86947
14
13053
09491
5
90509
29
32
7 44
52 16
77473
9
22527
86974
14
13026
09501
5
90499
28
33
7 36
52 24
77490
9
22510
87000
15
13000
09510
5
90490
27
34
35^
7 28 1 52 32
77507
10
22493
87027
15
12973
09520
5
90480
26
7 7 20
4 52 40
9. 77524
10
10. 22476
9. 87053
15
10. 12947
10. 09529
5
9. 90471
25
36
7 12
52 48
77541
10
22459
87079
16
12921
09538
6
90462
24
37
7 4
52 56
77558
11
22442
87106
16
12894
09548
6
90452
23
38
6 56
53 4
77575
11
22425
87132
17
12868
09557
6
90443
22
39
40
6 48
53 12
77592
11
22408
87158
17
12842
09566
6
90434
21
20
7 6 40
4 53 20
9. 77609
11
10. 22391
9. 87185
18
10. 12815
10. 09576
6
9. 90424
41
6 32
53 28
77626
12
22374
87211
18
12789
09585
6
90415
19
42
6 24
53 36
77643
12
22357
87238
18
12762
09595
7
90405
18
43
6 16
53 44
77660
12
22340
87264
19
12736
09604
7
90396
17
44
45
6 8
53 52
77677
13 i 22323
87290
19
20
12710
10. 12683
09614
7
90386
16
15
7 6 0
4 54 0
9. 77694
13 10.22306
9. 87317
10. 09623
9. 90377
46
5 52
,54 8
77711
13 22289
87^3
20
12657
09632
7
90368
14
47
5 44
54 16
77728
13 22272
87369
21
12631
09642
7
90358
13
48
5 36
54 24
77744
14 22256
87396
21
12604
09651
7
90349
12
49
50
5 28
54 32
77761
14
14
22239
87422
22
22
12578
10. 12552
09661
8
8
90339
11
10^
7 5 20
4 54 40
9. 77778
10. 22222
9. 87448
10. 09670
9. 90330
51
5 12
54 48
77795
15
22205
87475
22
12525
09680
8
90320
9
52
5 4
54 56
77812
15
22188
87501
23
12499
09689
8
90311
8
53
4 56
55 4
77829
15
22171
87527
23
12473
09699
8
90301
7
54
4 48
55 12
4 55 20
77846
15
16
22154
87554
24
24
12446
10. 12420
09708
8
9
90292
9. 90282
6
5
55
7 4 40
9. 77862
10. 22138
9. 87580
10.09718
56
4 32
55 28
' 77879
16
22121
87606
25
12394
09727
9
90273
4
57
4 24
55 36
77896
16
22104
87633
25
12367
09737
9
90263
3
58
4 16
55 44
77913
16
22087
87659
26
12341
09746
9
90254
2
59
4 8
55 52
77930
17
22070
87685
26
12315
09756
9
90244
1
60
4 0
56 0
77946
17
22054
87711
26
12289
09765
9
90235
0
M. Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
126°
A
A
B
B
C
C
58°
Seconds of time 1"
2«
8'
4"
o"
6*
'1
fA 2
Prop, parts of cols. -{B 3
Ic 1
4
7
2
6
10
4
9
13
5
11 13 15
17 20 '■ 23
6 7 8
TABLE U.
iPage 645
Log.
Sines, Tangents, and Secants.
87°
A
A B
B
C
C 142°
M.
Hour A.M.
Hour p. M.
Sine.
Difl.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Difl.
Cosine.
M.
0
7 4 0
4 56 0
9. 77946
0
10. 22054
9. 87711
0
10. 12289
10. 09765
0
9. 90235
60
1
3 52
56 8
77963
0
22037
87738
0
12262
09775
0
90225
59
2
3 44
56 16
77980
1
22020
87764
1
12286
09784
0
90216
58
8
8 36
56 24
77997
1
22003
87790
1
12210
09794
0
90206
57
4
3 28
56 82
78013
1
21987
87817
2
12188
09803
2^
90197
56
5
7 3 20
4 56 40
9. 78030
1
10. 21970
9. 87843
2
10. 12157
10.09813
9. 90187
oo
6
3 12
56 48
78047
2
21953
87869
3
12131
09822
90178
54
7
3 4
56 56
78063
2
21937
87895
3
12105
09832
90168
53
8
2 56
57 4
78080
2
21920
87922
3
12078
09841
90159
52
9
2 48
57 12
78097
2
21903
87948
4
12052
10. 12026
09851
90149
9. 90139
51
50
10
7 2 40
4 57 20
9. 78113
3
10. 21887
9. 87974
4
iO. 09861
2
n
2 32
57 28
78130
3
21870
88000
o
12000
09870
2
90130
49
12
2 24
57 36
78147
3
218.58
88027
5
11978
09880
2
90120
48
18
2 16
57 44
78163
4
21837
88053
6
11947
09889
2
90111
47
14
2 8
57 52
78180
4
21820
88079
6
11921
09899
2
90101
46
15
7 2 0
4 58 0
9. 78197
4
10. 21803
9. 88105
7
10. 11895
10. 09909
2
9. 90091
45
16
1 52
58 8
78213
4
21787
88131
7
11869
09918
3
90082
44
17
1 44
58 16
78230
5
21770
88158
1
11842
09928
3
90072
43
18
1 36
58 24
78246
5
21754
88184
8
11816
09937
3
90063
42
19
1 28
58 32
78263
5
21737
88210
8
11790
09947
3
90053
41
40
20
7 1 20
4 58 40
9. 78280
5
10.21720
9. 88236
9
10. 11764
10. 09957
3
9. 90043
21
1 12
58 48
78296
6
21704
88262
9
11738
09966
3
90084
39
22
1 4
58 56
78313
6
21687
88289
10
11711
09976
4
90024
38
23
0 56
59 4
78329
6
21671
88315
10
11685
09986
4
90014
37
24
0 48
59 12
78346
t
21654
88341
10
11659
09995
10. 10005
4
4
90005
36
35
25
7 0 40
4 59 20
9. 78362
7
10. 21638
9. 88367
11
10. 11638
9. 89995
26
0 32
59 28
78379
7
21621
88393
11
11607
10015
4
89985
34
27
0 24
59 36
78395
7
21605
88420
12
11580
10024
4
89976
33
28
0 16
59 44
78412
8
21588
88446
12
11554
10034
5
89966
32
29
0 8
59 52
78428
8
21572
88472
13
11528
10044
5
89956
31
30
80
7 0 0
5 0 0
9.78445
8
10. 21555
9. 88498
13
10. 11502
10. 10053
5
9. 89947
81
6 59 52
0 8
78461
9
21539
88524
14
11476
10063
5
89937
29
82
59 44
0 16
78478
9
21522
88550
14
11450
10073
5
89927
28
88
59 86
0 24
78494
9
21506
88577
14
11428
10082
5
89918
27
34
59 28
0 32
78510
9
10
21490
88603
15
15
11397
iO. 11371
10092
10. 10102
5
6
89908
9. 89898
26
25
85
6 59 20
5 0 40
9. 78527
10. 21473
9. 88629
36
59 12
0 48
78543
10
21457
88655
16
11845
10112
6
89888
24
87
59 4
0 56
78560
10
21440
88681
16
11819
10121
6
89879
23
88
58 56
1 4
78576
10
21424
88707
17
11293
10131
6
89869
22
39
58 48
1 12
78592
11
21408
88733
17
11267
10141
6
89859
21
20
40
6 58 40
5 1 20
9. 78609
11
10. 21391
9. 88759
17
10. 11241
10. 10151
6
9. 89849
41
58 32
1 28
78625
11
21375
88786
18
11214
10160
7
89840
19
42
58 24
1 36
78642
12
21358
88812
18
11188
10170
7
89880
18
48
58 16
1 44
78658
12
21342
88838
19
11162
10180
7
89820
17
44
45
58 8
6 58 0
1 52
78674
9. 78691
12
21326
88864
9. 88890
19
20
11136
10. 11110'
10190
10. 10199
~7~
89810
16
15
5 2 0
12
10. 21809
9. 89801
46
57 52
2 8
78707
13
21293
88916
20
11084
10209
7
89791
14
47
57 44
2 16
78723
13
21277
88942
20
11058
10219
8
89781
13
48
57 36
2 24
78739
13
21261
88968
21
11032
10229
8
89771
12
49
50
57 28
6 57 20
2 32
5 2 40
78756
9. 78772
13
14
21244
88994
9. 89020
21
22
11006
10. 10980
10239
10. 10248
8
8
89761
11
10
10. 21228
9. 89752
51
57 12
2 48
78788
14
21212
89046
22
10954
10258
8
89742
9
52
57 4
2 56
78805
14
21195
89073
23
10927
10268
8
89732
8
53
56 56
8 4
78821
15
21179
89099
23
10901
10278
9
89722
7
54
55
56 48
3 12
5 3 20
78837
15
21163
10. 21147
89125
24
24
10875
10. 10849"
10288
10.10298
9
9
89712
9. 89702
6
5
6 56 40
9. 78853
15
9. 89151
56
56 32
3 28
78869
15
21181
89177
24
10823
10307
9
89693
4
57
56 24
8 86
78886
16
21114
89203
25
10797
10317
9
89683
8
58
56 16
3 44
78902
16
21098
89229
25
10771
10327
9
89678
2
59
56 8
3 52
78918
16
21082
89255
26
10745
10337
10
89668
1
60
56 0
4 0
78934
16
21066
89281
26
10719
10347
10
89658
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
127°
A
A B
B
C
C 52° 1
Seconds of time
1»
23
33 48
5'
«'
7'
Prop, parts of col8.<B
•>
3
1
•1
7
6 8
10 13
4 5
10
16
6
12
20
7
14
23
8
Page 646]
TABLE 44.
Log. Sines, Tangents, and Secants.
88°
A
A
B
B C
C 141°
M.
Hour A. M.
Hour p. M.
Sine.
Difl.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Difl.
Cosine.
M.
0
6 56 0
5 4 0
9. 78934
0
10. 21066
9. 89281
0
10. 10719
10. 10347
0
9. 89653
60
1
55 52
4 8
78950
0
21050
89307
0
10693
10357
0
89643
59
o
55 44 4 16 1
78967
1
21033
89333
1
10667
10367
0
89633
58
3
55 36
4 24
78983
1
21017
89359
1
10641
10376
1
89624
57
4
55 28
4 32 1
78999
1
1
21001
10. 20985
89385
2
10615
10. 10589
10386
10. 10396
1
1
89614
9.89604
56
55'
5
6 55 20
5 4 40
9. 79015
9. 89411
2
6
55 12
4 48
79031
2
20969
89437
3
10563
10406
1
89594
54
7
55 4
4 56
79047
2
20953
89463
3
10537
10416
1
89584
53
8
54 56
5 4
79063
2
20937
89489
3
10511
10426
1
89574
52
9
54 48
5 12
79079
2
20921
89515
■ 4
10485
10436
2
89564
51
50
10
6 54 40
5 5 20
9.79095
3
10. 20905
9. 89541
4
10. 10459
10. 10446
2
9. 89554
11
54 32
5 28
79111
3 ! 20889
89567
5
10433
10456
2
89544
49
12
54 24
5 36
79128
3 20872
89593
5
10407
10466
2
89534
48
13
54 16
5 44
79144
3 , 20856
89619
6
10381
10476
2
89524
47
14
15
54 8
5 52
79160
4
4"
20840
89645
6
6
10355
10486
10. 10496
2
3
89514
46
>45
6 54 0
5 6 0
9. 79176
10. 20824
9. 89671
10. 10329
9. 89504
16
53 52
6 8
79192
4
20808
89697
7
10303
10505
3
89495
44
17
53 44
6 16
79208
0
20792
89723
/
10277
10515
3
89485
43
18
53 36
6 24
79224
0
20776
89749
8
10251
10525
3
89475
42
19
53 28
6 32
79240
5
20760
89775
8
10225
10535
3
3
89465
41
20
6 53 20
5 6 40
9. 79256
5
10. 20744
9. 89801
9
10. 10199
10. 10545
9. 89455
40
21
53 12
6 48
79272
6
20728
89827
9
10173
10555
4
89445
39
22
53 4
6 56
79288
6
20712
89853
10
10147
10565
4
89435
38
23
52 56
7 4
79304
6 ' 20696 1
89879
10
10121
10575
4
89425
37
24
52 48
7 12
79319
6
20681
89905
10
10095
10585
4
89415
36
35
25
6 52 40
5 7 20
9. 79335
7
10. 20665
9. 89931
11
10. 10069
10. 10595
4
9. 89405
26
52 32
7 28
79351
7
20649
89957
11
10043
10605
4
89395
34
27
52 24
7 36
79367
7 20633
89983
12
10017
10615
5
89385
33
28
52 16
7 44
79383
/
20617
90009
12
09991
10625
5
89375
32
29
30
52 8
7 52
79399
8
20601
10. 20585
90035
13
09965
10636
5
89364
31
30
6 52 0
5 8 0
9. 79415
8
9. 90061
13
10. 09939
10. 10646
5
9. 89354
31
51 52
8 8
79431
8
20569
90086
13
09914
10656
5
89344
29
32
51 44
8 16
79447
8
20553
90112
14
09888
10666
5
89334
28
33
51 36
8 24
79463
9
20537
90138
14
09862
10676
6
89324
27
34
51 28
8 32
79478
9 ; 20522
90164
15
09836
10686
6
89314
26
35
6 51 20
5 8 40
9. 79494
9 10.20506
9. 90190
15
10. 09810
10. 10696
6
9. 89304
25
36
61 12
8 48
79510
10 20490
90216
16
09784
10706
6
89294
24
37
51 4
8 56
79526
10 20474
90242
16
09758
10716
6
89284
23
38
50 56
• 9 4
79542
10 ' 20458
90268
16
09732
10726
6
89274
22
39
40
50 48
6 50 40
9 12
5 9 20
79558
10
20442
90294
17
09706
10736
7
89264
9. 89254
21
20
9. 79573
11
10. 20427
9. 90320
17
10. 09680
10. 10746
7
41
50 32
9 28
79589
11
20411
90346
18
09654
10756
7
89244
19
42
50 24
9 36
79605
11 20395
90371
18
09629
10767
7
89233
18
43
50 16
9 44
79621
11 ! 20379
90397
19
09603
10777
7
89223
17
44
50 8
9 52
79636
12 \ 20364
90423
19
09577
10787
7
89213
16
15
45
6 50 0
5 10 0
9. 79652
12 10.20348
9. 90449
19
10. 09551
10. 10797
8
9. 89203
46
49 52
10 8
79668
12
20332
90475
20
09525
10807
8
89193
14
47
49 44
10 16
79684
12
20316
90501
20
09499
10817
8
89183
13
48
49 36
10 24
79699
13
20301
90527
21
09473
10827
8
89173
12
49
49 28
10 32
79715
.13
20285
90553
21
09447
10838
8
89162
11
10
50
6 49 20
5 10 40
9. 79731
13
10. 20269
9. 90578
22
10. 09422
10. 10848
8
9. 89152
51
49 12
10 48
79746
14
20254
90604
22
09396
10858
9
89142
9
52
49 4
10 56
79762
14
20238
90630
22
09370
10868
9
89132
8
53
48 56
11 4
79778
14
20222
90656
23
09344
10878
9
89122
7
54
48 48
11 12
79793
14
20207
90682
23
09318
10888
9
89112
6
5
55
6 48 40
5 11 20
9. 79809
15
10. 20191
9. 90708
24
10. 09292
10. 10899
9
9. 89101
56
48 32
11 28
79825
15
20175
90734
24
09266
10909
9
89091
4
57
48 24
11 36
79840
15
20160
90759
25
09241
10919
10
89081
3
58
48 16
11 44
79856
15
20144
90785
25
09215
10929
10
89071
2
59
48 8
11 52
79872
16
20128
90811
26
09189
10940
10
89060
1
60
48 0
12 0
79887
16
20113
90837
26
09163
10950
10
89050
0
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Difl.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant,
Difl.
Sine.
128'
A
A
B
B C
C
51°
Seconds of time
1«
2'
8<
4»
&>
6»
7'
Prop, parts of cols.-jB
Ic
2
3
1
4
6
3
6
10
4
8
13
5
10
16
6
12
19
8
14
23
9
TABLE 44.
[Page 647
Log.
Sines, Tangents, and Secants.
89°
M.
A
A
B B
C
C 140°
Hour A. M.
Hour P. M.
Sine.
Difl.
Cosecant.
Tangent. , Difl. , Cotangent.
Secant.
Diff.
Cosine.
M.
0
6 48 0
5 12 0
9. 79887
0
10. 20113
9. 90837
0 10.09163
10. 10950
0
9. 89050
60
1
47 o2
12 8
79903
0
20097
90863
0 09137
10960
0
89040
59
2
47 44
12 16
79918
1
20082
90889
1 09111
10970
0
89030
58
3
47 36
12 24
79934
1
20066
90914
1 09086
10980
1
89020
57
4
5
47 28
6 47 20
12 32
5 12 40
79950
9.799(55
1
1
20050
10.20035"
90940 2 09060
9.90966 2 10.09034
10991
10. 11001
1
89009
56
55
1
9. 88999
6
47 12
12 48
79981
2
20019
90992 3 ' 09008
11011
1
88989
54
7
47 4
12 56
79996
2
20004
91018 3 1 08982
11022
1
88978
53
8
46 56"
13 4
80012
2
19988
91043 3 08957
11032
1
88968
52
9
46 48
13 12
80027
2
19973
91069
4 08931
11042
2
88958
51
50
10
6 46 40-
5 13 20
9. 80043
3
10. 19957
9. 91095
4 10.08905
10. 11052
2
9. 88948
11
46 32
13 28
80058
3
19942
91121
5 08879
11063
2
88937
49
12
46 24
13 36
80074
3
19926
91147
5 08853
11073
2
88927
48
13
46 16.
13 44
80089
3
19911
91172
6 08828
11083
2
88917
47
14
15
46 8
13 52
80105
9. 80120
4
4
19895
10. 19880
91198 1 6
08802
11094
2
3
88906
9. 88896
46
45
6 46 0
5 14 0
9.91224 1 6
10. 08776
10. 11104
16
45 52
14 8
80136
4
19864
91250 ; 7
08750
11114
3
88886
44
17
45 44
14 16
80151
4
19849
91276 1 7
08724
11125
, 3
88875
43
18
45 36
14 24
80166
5
19834
91301 1 8
08699
11135
3
88865
42
19
20
45 28
6 45 20
14 32
5 14 40
80182
9.80197
5
5
19818
10. 19803
91327 i 8
9.91353 i 9
• 08673
11145
3
3
88855
9. 88844
41
40
10. 08647
10.11156
21
45 12
14 48
80213
5
19787
91379 ; 9 08621
11166
4
88834
39.
22
45 4
14 56
80228
6
19772
91404
9 08596
11176
4
88824
38
23
44 56
15 4
80244
6
19756
91430
10 1 08570
11187
4
88813
37
24
25
44 48
6 44 40
15 12
5 15 20
80259
6
6
19741
91456
9. 91482
10 08544
11197
10. 11207
4
4
88803
9788793
36
35
9. 80274
10. 19726
11
10. 08518
26
44 32
15 28
80290
7
19710
91507
11
08493
11218
5
88782
34
27
44 24
15 36
80305
7
19695
91533 12
08467
11228
5
88772
33
28
44 16
15 44
80320
7
19680
91559 12
08441
11239
5
88761
32
29
44 8
15 52
80336
7
19664
91585 12
08415
11249
5
88751
31
30
6 44 0
5 16 0
9. 80351
8
10. 19649
9. 91610 13
10. 08390
10. 11259
5
9. 88741
30
31
43 52
16 8
80366
8
19634
91636 13
08364
11270
5
88730
29
32
43 44
16 16
80382
8
19618
91662 14
08338
11280
6
88720
28
33
43 36
16 24
80397
8
19603
91688 14
08312
11291
6
88709
27
34
35
43 28
6 43 20
16 32
5 16 40
80412
9. 80428
9
9
19588
10. 19572
91713 15
08287
11301
6
6
88699
9. 88688
26
25"
9.91739 15
10. 08261
10. 11312
36
43 12
16 48
80443
9
19557
91765 15 : 08235
11322
6
88678
24
37
43 4
16 56
80458
9
19542
91791 16 1 08209
11332
6
88668
23
38
42 56
17 4
80473
10
19527
91816
16 i 08184
11343
7
88657
22
39
40
42 48
17 12
80489
9. 80504
10
10
19511
10. 19496
91842
9. 91868
17 ! 08158
17 10.08132
11353
/
88647
21
20
6 42 40
5 17 20
10. 11364
7
9. 88636
41
42 32
17 28
80519
10
19481
91893
18 ! 08107
11374
/
88626
19
42
42 24
17 36
80534
11
19466
91919
18
08081
11385
7
88615
18
43
42 16
. 17 44
80550
11
19450
91945
18
08055
11395
7
88605
17
44
45
42 8
6 42 0
17 52
5 18 0
80565
9. 80580
11
19435
91971
19
08029
11406
8
88594
16
12
10. 19420
9. 91996
19 10.08004
10. 11416
8
9. 88584
15
46
41 52
18 8
80595
12
19405
92022
20
07978
11427
8
88573
14
47
41 44
18 16
80610
12
19390
92018
20
07952
11437
8
88563
13
48
41 36
18 24
80625
12
19375
92073
21
07927
11448
8
88552
12
49
50
41 28
6 41 20
18 32
5 18 40
80641
9. 80656
13
13
19359
10. 19344
92099
21
07901
11458
10.11469
9
9
88542
11
10
9. 92125 21
10. 07875
9. 88531
51
41 12
18 48
80671
13
19329
92150 22 i 07850
11479
9
88521
9
52
41 4
18 56
80686
13
19314
92176 22
07824
11490
9
88510
8
53
40 56
19 4
80701
14
19299
92202
23
07798
11501
9
88499
7
54
55
40 48
6 40 40
19 12
5 19 20
80716
14
14
19284
92227
23
07773
11511
9
88489
6
5
9. 80731
10. 19269
9. 92253
24 :10. 07747
10. 11522
10
9. 88478
56
40 32
19 28
89746
14
19254
92279
24
07721
11532
10
88468
4
57
40 24
19 36
80762
15
19238
92304
24
07696
11543
10
88457
3
58
40 16
19 44
80777
15
19223
92330
25
07670
11553
10
88447
2
59
40 8
19 52
80792
15
19208
92356
25
07644
11564
10
88436
1
60
40 0
20 0
80807
15
19193
92381
26
07619
11575
10
88425
0
M.
Hour p. M.
Hour A. M.
Cosine.
Difl.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
129°
A
A
B B
C
C 50° j
Seconds of time
1»
2»
3'
4»
5»
6»
7«
Prop, parts of cols.^B
2
3
1
4
6
3
6
10
4
8
13
6
10
16
7
12
19
8
13
23
9
Page 648J
TABLE 44.
Log.
Sines, Tangents, and Secants.
40°
A
A
B B
C
C
189°
M.
Hour A.M.
Hour p. M.
Sine. DIff.
j Cosecant.
Tangent.
Diff. 1 Cotangent.
decant.
Diff.
Cosine.
M.
0
6 40 0,
6 20 0
9. 80807 1 0
10. 19193
9. 92381
0 10.07619
10. 11575
0
9. 88425
60
1
39 52
20 8
S0822 0
19178
92407
0 07593
11585
0
88415
59
2
39 44
20 16
80837 0
19163
92433
1 07567
11596
0
88404
58
3
39 36
20 24
S0852 1
19148
92458
1 07542
11606
1
88394
57
4
39 28
20 32^
80867 1 1
i 19133
92484
2
07516
10.07490
11617
10.11628
1
1
88383
9. 88372
56
55
5
6 39 20
5 20 40
9.80882 i 1
10. 19118
9. 92510
2
6
39 12
20 48
80897
1
1 19103
92535
3
07465
11638
1
88362
54
7
39 4
20 56
80912
2
I 19088
92561
3
07439
11649
1
88351
53
8
38 56
21 4
80927
2
1 19073
92587
3
07413
11660
1
88340
52
9
38 48
21 12
80942 ; 2
19058
92612
4
07388
11670
2
88330
51
10
6 38 40
5 21 20
9. 80957
2
10. 19043
9. 92638
4 ilO. 07362
10. 11681
2
9. 88319
50
11
38 32
21 28
80972
3
' 19028
92663
o
07337
11692
2
88308
49
12
38 24
21 36
80987 ''. 3
19013
92689
5
07311
11702
2
88298
48
13
38 16
21 44
81002 ' 3
18998
92715
6
07285
11713
2
88287
47
14
38 8
21 52
81017 i 3
18983
92740
6
07260
11724
10. li7:S4
3
3
88276
9. 88266
46
45
15
6 38 0
5 22 0
9.81032 i 4
10. 18968
9. 92766
6 10.07234
16
37 52
22 8
81047 ' 4
18953
92792
7
07208
11745
3
88255
44
17
37 44
'22 16
81061 4
18939
92817
t
07183
11756
3
88244
43
18
37 36
22 24
81076
4
18924
92843
8
07157
11766
3
88234
42
19
37 28
22 32
81091
5
18909
92868
8
07132
11777
3
88223
41
20
6 37 20
5 22 40
9. 81106
0
10. 18894
9. 92894
9 10.07106
10. 11788
4
9. 88212
40
21
37 12
22 48
81121
5
18879
92920
9
07080
11799
4
88201
39
22
37 4
22 56
81136
5
18864
92945
9
07055
11809
4
88191
38
23
36 56
23 4
81151
6
18849
92971
10
07029
11820
4
88180
37
24
36 48
23 12
81166
6
18834
92996
10
07004
11831
4
88169
36
35
25
6 36 40
5 23 20
9.81180
6
10. 18820
9. 93022
11
10. 06978
10. 11842
4
9. 88158
26
36 32
23 28
81195
6
18805
93048
11 06952
11852
5
88148
34
27
36 24
23 36
81210
i
18790
93073
12
06927
11863
5
88137
33
28
36 16
23 44
81225
i
18775
93099
12
06901
11874
5
88126
32
29
"30
36 8
23 52
81240
7
18760
10. 18746
93124
12
13
06876
11885
10.11895
5
5
88115
31
30
6 36 0
5 24 0
9. 81254
7
9. 93150
10. 06850
9. 88105
31
35 52
24 8
81269
8
18731
93175
13
06825
11906
6
88094
29
32
35 44
24 16
81284
8
18716
93201
14
06799
11917
6
88083
28
33
35 36
24 24
81299
8
18701
93227
14
06773
11928
6
88072
27
34
35 28
24 32
81314
8
18686
93252
14
15
06748
11939
6
88061
26
25
35
6 35 20
5 24 40
9. 81328
9
10. 18672
9. 93278
10. 06722
10. 11949
6
9,88051
36
35 12
24 48
81343
9
18657
93303
15
06697
11960
6
88040
24
37
35 4
24 56
81358
9
18642
93329
16
06671
11971
7
88029
23
38
34 56
25 4
81372
9
18628
93354
16
06646
11982
7
88018
22
39
34 48
25 12
81387
10
18613
93380
17
06620
10. 06594
11993
7
88007
21
20
40
6 34 40
5 25 20
9. 81402
10
10. 18598
9. 93406
17
10. 12004
7
9. 87996
41
34 32
25 28
81417
10
18583
93431
17
06569
12015
7
87985
19
42
34 24
25 36
81431
10
18569
93457
18
06543
12025
8
87975
18
43
34 16
25 44
81446
11
18554
93482
18
06518
12036
.8
87964
17
44
45
34 8
25 52
81461
9. 81475
11
11
18539
10.18525
93508 1 19
06492
12047
8
87953
9. 87942
16
15"
6 34 0
5 26 0
9. 93533 19 10. 06467 |
10. 12058
8
46
33 52
26 8
81490
11
18510
93559 ■ 20
06441
12069
8
87931
14
47
33 44
26 16
81505
12
18495
93584 20
06416
12080
8
87920
13
48
33 36
26 24
81519
12
18481
93610 20
06390
12091
9
87909
12
49
33 28
26 32
5 26 40
81534
9. 81549
12
18466
93636 21
06364
12102
10.12113
9
9
87898
11
10
50
6 33 20
12
10. 18451
9. 93661 21 10. 06339 |
9. 87887
51
33 12
26 48
81563
13
18437
93687 22
06313
12123
9
87877
9
52
33 4
26 56
81578
13
18422
93712
22
06288
12134
9
87866
8
53
32 56
27 4
81592
13
18408
93738
23
0<J262
12145
10
87855
7
54
32 48
27 12
5 27 20
81607
9.81622
13
14
18393
10. 18378
93763
9.93789
23
06237
12156
10. 12167
10
10
87844
9. 87833
6
5
55
6 32 40
23 10.06211 1
56
32 32
27 28
81636
14
18364
93814
24
06186
12178
10
87822
4
57
32 24
27 36
81651
14
18349
93840
24
06160
12189
10
87811
3
58
32 16
27 44
81665
14
18335
93865
25
06135
12200
10
87800
2
59
32 8
27 52
81680
15
18320
93891
25
06109
12211
11
87789
1
60
32 0
28 0
81694
15
18306
93916
26
06084
12222
11
87778
0
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Difl.
Secant.
Cotangent. Diff.
Tangent.
Cosecant.
Diff.
Sine.
180'
)
A
A
B B
C
C
49°
Seconds of time 1 ■
Prop, parts of cols.-jB
C
TABLE 44.
[Page 649
Log.
Sines, Tangents, and Secants.
41°
A
A
B B
C
C 138°
M.
Hour A. M.
; Hour p. m.
Sine.
Diff.
Cosecant.
Tangent.
Diff. Cotangent.
Secant.
Diff.
Cosine.
M.
0
6 32 0
5 28 0
9. 81694
0
10. 18306
9. 93916
0
10. 06084
10. 12222
0
9. 87778
60
1
31 52
28 8
81709
0
18291
93942
0
06058
12233
0
87767
59
9
31 44
28 16
81723
: 0
18277
93967
1
06033
12244
0
87756
58
8
31 36
: 28 24
81738
1
18262
93993
1
06007
12255
87745
57
4
31 28
I 28 32
81752
1
18248
94018
2
05982
12266
87734
56
5
6 31 20
5 28 40
9. 81767
! 1
10. 18233
9. 94044
2
10. 05956
10. 12277
9. 87723
55
6
31 12
28 48
81781
1
18219
94069
3
05931
12288
87712
54
/
31 4
28 56
81796
2
18204
94095
3
05905
12299
87701
53
8
30 56
29 4
81810
2
18190
94120
3
05880
12310
87690
52
9
To
30 48
29 12
81825
2
18175
10. 18161
94146
4
05854
12321
2
87679
9. 87668
51
50
6 30 40
5 29 20
9. 81839
2
9. 94171
4
10. 05829
10. 12332
2
11
30 32
29 28
81854
3
18146
94197
5
05803
12343
2
87657
49
12
30 24
29 36
81868
3
18132
94222
5
05778
12354
2
87646
48
13
^30 16
29 44
81882
3
18118
94248
6
05752
12365
2
87635
47
14
15
30 8
29 52
81897
3
18103
94273
6
6
05727
10. 05701
12376
10. 12387
3
3
87624
9.87613
46
45
6 30 0
5 30 0
9. 81911
4
10. 18089
9. 94299
16
29 52
30 8
81926
4
18074
94324
7
05676
12399
3
87601
44
17
29 44
30 16
81940
4
18060
94350
7
05650
12410
3
87590
43
18
29 36
30 24
81955
4
18045
94375
8
05625
12421
3
87579
42
19
20
29 28
30 32
81969
5
18031
94401 { 8
05599
12432
4
87568
41
6 29 20
5 30 40
9. 81983
5
10. 18017
9. 94426
8
10. 05574
10. 12443
4
9. 87557
40
21
29 12
30 48
81998
5
18002
94452
9
05548
12454
4
87546
39
22
29 4
30 56
82012
5
17988
94477
9
05523
12465
4
87535
38
23
28 56
31 4
82026
5
17974
94503
10
05497
12476
4
87524
37
24
28 48'
31 12
82041
6
17959
94528
9. 94554
10
05472
12487
4
87513
36
35
25
6 28 40
5 31 20
9. 82055
6
10. 17945
11 ilO. 05446
10. 12499
5
9. 87501
26
28 32
31 28
82069
6
17931
94579
11
05421
12510
5
87490
34
27
28 24
31 36
82084
6
17916
94604
11
05396
12521
5
87479
33
28
28 16
31 44
82098
7
17902
94630
12
05370
12532
5
87468
32
29
30
28 8
6 28 0
31 52
5 32 0
82112
7
7
17888
10. 17874
94655
9.94681
12
05345
12543
5
87457
31
30
9. 82126
13
10. 05319
10. 12554
6
9. 87446
31
27 52
32 8
82141
t
17859
94706
13
05294
12566
6
87434
29
32
27 44
32 16
82155
8
17845
94732
14
05268
12577
6
87423
28
33
27 36
32 24
82169
8
17831
94757
14
05243
12588
6
87412
27
34
35
27 28
32 32
82184
8
17816
94783
14
05217
12599
6
87401
26
25
6 27 20
5 32 40
9. 82198
8
10. 17802
9. 94808
15 110.05192
10. 12610
7
9. 87390
36
27 12
32 48
82212
9
17788
94834
15
05166
12622
7
87378
24
37
27 4
32 56
82226
9
17774
94859
16
05141
12633
7
87367
23
38
26 56
33 4
82240
9
17760
94884
16
05116
12644
7
87356
22
39
40
26 48
33 12
82255
9
17745
94910
17
05090
12655
10. 12666
7
87345
21
20
6 26 40
5 33 20
9. 82269
10
10. 17731
9. 94935
17
10. 05065
7
9. 87334
41
26 32
33 28
82283
10
17717
94961
17
05039
12678
8
87322
19
42
26 24
33 36
82297
10
17703
94986
18
05014
12689
8
87311
18
43
26 16
33 44
82311
10
17689
95012
18
04988
12700
8
87300
17
44
45"
26 8
33 52
82326
10
17674
95037
19
04963
12712
8
87288
16
15
6 26 0
5 34 0
9. 82340
11
10. 17660
9. 95062
19
10. 04938
10. 12723
8
9.87277
46
25 52
34 8
82354
11
17646
95088
20 04912
12734
9
87266
14
47
25 44
34 16
82368
11
17632
95113
20 04887
12745
9
87255
13
48
25 36
34 24
82382
11
17618
95139 20 1 04861
12757
9
87243
12
49
50
25 28
34 32
82396
9. 82410
12
12
17604
10. 17590
95164
21
21
04836
12768
10. 12779
9
87232
11
10
6 25 20
5 34 40
9. 95190
10. 04810
9
9. 87221
51
25 12
34 48
82424
12
17576
95215
22
04785
12791
10
87209
9
52
25 4
34 56
82439
12
17561
95240
22
04760
12802
10
87198
8
53
24 56
35 4
82453
13
17547
95266
22
04734
12813
10
87187
7
54
24 48
35 12
82467
13
13
17533
95291
23
04709
10. 04683
12825
10. 12836
10
10
87175
6
5
55
6 24 40
5 35 20
9. 82481
10. 17519
9.95317
23
9. 87164
56
24 32
35 28
82495
13
17505
95342
24
04658
12847
10
87153
4
57
24 24
35 36
82509
14
17491
95368
24
04632
12859
11
87141
3
58
24 16
35 44
82523
14
17477
95393
25
04607
12870
11
87130
2
59
24 8
35 52
82537
14
17463
95418
25
04582
12881
11
87119
1
60
M.
131-
24 0
36 0
82551
14
17449
95444
25
04556
12893
11
87107
0
Hour p. M.
Hour A.M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
A
A
B B
C
C 48° 1
Seconds of time
U
2'
3>
4» 1 5" 6»
7»
Prop, parts of cols. ■{ B
2
3
1
4
6
3
6
10
4
7
13
6
9
16
11
19
8
12
22
10
Page 650]
TABLE 44.
Log.
Sines, Tangents, and Secants.
42°
A
A
B
B
C
C
187°
M.
Hour A. H.
Hour p. M.
Sine.
Difif.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Diff. 1 Cosine.
M.
0
6 24 0
5 36 0
9. 82551
0
10. 17449
9. 95444
0
10. 04556
10. 12893
0
9. 87107
60
1
23 52
36 8
82565
0
17435
95469
0
04531
12904
0
87096
59
2
23 44
36 16
82579
0
17421
95495
1
04505
12915
0
87085
58
3
23 36
36 24
82593
17407
95520
1
04480
12927
87073
57
4
5'
23 28
36 ^
82607
17393
95545
2
2
04455
12938
10.12950
"r
87062.
56
55
6 23 20
5 36 40
9. 82621
10. 17379
9. 95571
10. 04429
9. 87050
6
23 12
36 48
82635
17365
95596
3
04404
12961
1 \ 87039
54
7
23 4
36 56
82649
2
17351
95622
3
04378
12972
1 ; 87028
53
8
22 56
37 4
82(563
2
17337
95647
3 i 04353
12984
2 87016
52
9
10
22 48
37 12
82677
2
17323
95672
4 i 04328
12995
2 87005
51
6 22 40
5 37 20
9. 82691
2
10. 17309
9. 95698
4
10. 04302
10. 13007
2
9. 86993
50
11
22 32
37 28
82705
3
17295
95723
5
04277
13018
2
86982
49
12
22 24
37 36
82719
3
17281
95748
5
04252
13030
2
86970
48
13
22 16
37 44
82733
3
17267
95774
5
04226
1.3041
3
86959
47
14
15
22 8
37 52
5 38 0
82747
3
17253
95799
9. 95825
6
04201
13053
3
3"
86947
46
45
6 22 0
9. 82761
3
10. 17239
6
10.04175
10.13064
9. 86936
16
21 52
38 8
82775
4
17225
95850
7 i 04150
13076
3
86924
44
17
21 44
38 16
82788
4
17212
95875
7 04125
13087
3
86913
43
18
21 36
38 24
82802
4
17198
95901
8 1 04099
13098
3
86902
42
19
20
21 28
6 21 20
38 32
82816
4
17184
95926
8 j 04074
13110
4
86890
41
40
5 38 40
9. 82830
5
10. 17170
9. 95952
8 10.04048
10. 13121
4
9. 86879
21
21 12
38 48
82844
5
17156
95977
9 1 04023
13133
4
86867
39
22
21 4
38 56
82858
5
17142
96002
9
03998
13145
4
86855
38
23
20 56
39 4
82872
5
17128
96028
10
03972
13156
4
86844
37
24
20 48
39 12
82885
6
17115
96053
10
11
03947
10. 03922
13168
5-
5
86832
9. 86821
36
35
25
6 20 40
5 39 20
9. 82899
6
10. 17101
9. 96078
10.13179
26
20 32
39 28
82913
6
17087
96104
11
03896
13191
5
86809
34
27
20 24
39 36
82927
6
17073
96129
11
03871
13202
5
86798
33
28
20 16
39 '44
82941
6
17059
96155
12
03845
13214
5
86786
32
29
30
20 8
39 52
82955
7
17045
96180
12
03820
13225
6
86775
31
30^
6 20 0
5 40 0
9. 82968
7
10. 17032
9. 96205
13
10. 03795
10. 13237
6 ! 9. 86763
31
19 52
40 8
82982
t
17018
96231
13
03769
13248
6
86752
29
32
19 44
40 16
82996
7
17004
96256
14
03744
1.3260
6
86740
28
33
19 36
40 24
83010
8
16990
96281
14
03719
13272
6
86728
27
34
35
19 28
40 32
5 40 40
83023
8
8
16977
96307
14
03693
13283
7
86717
26
6 19 20
9. 83037
10. 16963
9. 96332
15 110.03668
10. 13295
7
9. 86705
25
36
19 12
40 48
83051
8
16949
96357
15
03643
13306
1
86694
24
37
19 4
40 56
83065
8
16935
96383
16
03617
13318
1
86682
23
38
18 56
41 4
83078
9
16922
96408
16
03592
13330
7
86670
22
39
40
18 48
6 18 40
41 12
83092
9
16908
96433
16
03567
13341
10. 13353
8
8
86659
21
20
5 41 20
9. 83106
9
10. 16894
9. 96459
17
10. 03541
9. 86647
41
18 32
41 28
83120
9
16880
96484
17
03516
13365
8
86635
19
42
18 24
41 36
83133
10
16867
96510
18
03490
13376
8
86624
18
43
18 16
41 44
83147
10
16853
965.35
18
03465
1,3388
8
86612
17
44
45
18 8
6 18 0^
41 52
83161
9. 83174
10
10
16839
96560
19
03440
13400
10.13411
8
9
86600
9. 86589
16
15
5 42 0
10. 16826
9. 96586
19 10.03414
46
17 52
42 8
83188
11
16812
96611
19 I 03389
13423
9
86577
14
47
17 44
42 16
83202
11
16798
96636
20
03364
13435
9
86565
13
48
17 36
42 24
83215
11
16785
96662
20
03338
1.3446
9
86554
12
49
17 28
42 32
83229
11
11
16771
96687
21
21
03313
10. 03288
1.3458
10. 13470
9
To
86542
11
10
50
6 17 20
5 42 40
9. 83242
10. 16758
9. 96712
9. 86530
51
17 12
42 48
83256
12
16744
96738
22
03262
13482
10
86518
9
52
17 4
42 56
83270
12
16730
96763
22
03237
13493
10
86507
8
53
16 56
43 4
83283
12
16717
96788
22
03212
13505
10 ! 86495
7
54
55
16 48
6 16 40
43 12
83297
12
13
16703
10. 16690
96814
23
03186
13517
10
fl
86483
6
5 43 20
9. 8.3310
9. 96839
23
10. 03161
10. 1.3528
9. 86472
5
56
16 32
43 28
83324
13
16676
96864
24
03136
13540
11 1 86460
4
57
16 24
43 36
83338
13
16662
96890
24
03110
13552
11 86448
3
58
16 16
43 44
83351
13
16649
96915
25
03085
13564
11
86436
9
59
16 8
43 52
83365
14
16635
96940
25
03060
13575
11
86425
1
60
M.
16 0
44 0
83378
14
16622
96966
25
03034
13587
12
86413
0
M.
Hour P.M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Diff.
Sine.
182
0
A
A
B
B
C
C
47°
Seconds of time
1>
2>
3«
4'
5' 6'
7'
Prop, parts of cols. < B
Ic
2
3
1
3
6
3
6
10
4
7
13
6
9
16
10
19
9
12
•22
10
TABLE U.
[Page 651
Log.
Sines, Tangents, and Secants.
43°
A
A
B
B
C
C 136°
M.
0
Hour A. M.
Hour P.M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
60
6 16 0
5 44 0
9. 88378
0
10. 16622
9. 96966
0
10. 03034
10. 13587
0
9. 86413
1
15 52
44 8
88392
0
16608
96991
0
08009
13599
0
86401
59
2
15 44
44 16
88405
0
16595
97016
1
02984
13611
0
86889
58
8
15 36
44 24
88419
1
16581
97042
1
02958
13623
86877
57
4
15 28
44 82
88432
1
16568
97067
2
02933
13634
86366
9. 86354
56
55
5
6 15 20
5 44 40
9. 88446
1
10. 16554
9. 97092
2
10. 02908
10. 13646
6
15 12
44 48
88459
1
16541
97118
3
02882
13658
86342
54
7
15 4
44 56
88473
2
16527
97143
3
02857
13670
86330
58
H
14 56
45 4
83486
2
16514
97168
3
02832
13682
2
86818
52
9
14 48
45 12
83500
2
16500
97193
4
4
02807
18694
2
86806
51
50
10
6 14 40
5 45 20
9. 83513
2
10. 16487
9. 97219
10. 02781
10. 13705
2
9. 86295
11
14 32
45 28
83527
2
16478
97244
5
02756
13717
2
86288
49
12
14 24
45 86
83540
8
16460
97269
5
02731
18729
2
86271
48
18
14 16
45 44
83554
3
16446
97295
5
02705
18741
3
86259
47
14
15
14 8
45 52
88567
9. 83581
3
3
16488
97320
6
02680
10. 02655
18753
10.13765
3
86247
46
45
6 14 0
5 46 0
10. 16419
9. 97345
6
3
9. 86235
16
13 52
46 8
83594
4
16406
97871
7
02629
13777
3
86223
44
17
13 44
46 16
83608
4
16892
97896
7-
02604
13789
3
86211
48
18
13 36
46 24
83621
4
16379
97421
8
02579
13800
4
86200
42
19
20
13 28
6 18 20
46 82
83634
4
16366
10.16352
97447
"9. 97472
8
02553
13812
4
86188
41
40
5 46 40
9. 83648
4
8
10. 02528
10. 13824
4
9. 86176
21
18 12
46 48
88661
5
16839
97497
9
02503
13836
4
86164
39
22
13 4
46 56
83674
5
16326
97528
9
02477
13848
4
86152
38
23
12 56
47 4
83688
5
16312
97548
10
02452
13860
5
86140
37
24
12 48
47 12
83701
5
16299
97573
9. 97598
10
02427
13872
10. 13884
5
86128
36
25
6 12 40
5 47 20
9. 88715
6
10. 16285
11
10. 02402
5
9.86116
35
26
12 32
47 28
83728
6
16272
97624
11
02376
13896
5
86104
84
27
12 24
47 36
88741
6
16259
97649
11
02351
13908
5
86092
88
28
12 16
47 44
88755
6
16245
97674
12
02326
13920
6
86080
82
29
12 8
47 52
83768
6
7
16282
97700
12
02300
13982
6
86068
9. 86056
31
80
80
6 12 0
5 48 0
9. 83781
10. 16219
9. 97725
13
10. 02275
10. 18944
6
81
11 52
48 8
83795
7
16205
97750
18
02250
13956
6
86044
29
82
11 44
48 16
83808
7
16192
97776
13
02224
13968
6
86082
28
33
11 36
48 24
83821
/
16179
97801
14
02199
18980
7
86020
27
34
85
11 28
6 11 20
48 32
83834
8
8
16166
97826
14
02174
10. 02149
18992
7
86008
9. 85996
26
25
5 48 40
9. 83848
10. 16152
9. 97851
15
10. 14004
7
m
11 12
48 48
83861
8
16139
97877
15
02123
14016
7
85984
24
37
11 4
48 56
83874
8
16126
97902
16
02098
14028
7
85972
23
38
10 56
49 . 4
88887
8
16118
97927
16
02073
14040
8
85960
22
39
40
10 48
6 10 40
49 12
83901
9
9
16099
10. 16086
97953
9.97978
16
17
02047
14052
10. 14064
8
85948
21
5 49 20
9. 83914
10. 02022
8
9. 85986
20
41
10 32
49 28
83927
9
16073
98003
17
01997
14076
8
85924
19
42
10 24
49 86
83940
9
16060
98029
18
01971
14088
8
85912
18
48
10 16
49 44
83954
10
16046
98054
18
01946
14100
9
85900
17
44
45
10 8
49 52
88967
10
10
16088
98079
19
01921
10. 01896
14112
9
85888
9. 85876
16
15
6 10 0
5 50 0
9. 88980
10. 16020
9. 98104
19
10. 14124
9
46
9 52
50 8
88993
10
16007
98180
19
01870
14136
9
85864
14
47
9 44
50 16
84006
10
15994
98155
20
01845
14149
9
85851
18
48
9 36
50 24
84020
11
15980
98180
20
01820
14161
10
85839
12
49
50
9 28
50 32
84033
11
15967
98206
21
21
01794
14173
10
85827
9. 85815
11
10
6 9 20
5 50 40
9. 84046
11
10. 15954
9. 98281
10. 01769
10. 14185
10
51
9 12
50 48
84059
11
15941
98256
22
01744
14197
10
85803
9
52
9 4
50 56
84072
12
15928
98281
22
01719
14209
10
85791
8
58
8 56
51 4
84085
12
15915
98307
22
01693
14221
11
85779
7
54
8 48
51 12
84098
12
15902
98382
23
01668
14234
11
85766
6
55
6 8 40
5 51 20
9. 84112
12
10. 15888
9. 98357
23
10. 01648
10. 14246
11
9. 85754
5
56
8 32
51 28
84125
12
15875
98383
24
01617
14258
11
85742
4
57
8 24
51 36
84188
18
15862
98408
24
01592
14270
11
85780
8
58
8 16
51 44
84151
13
15849
98438
24
01567
14282
12
85718
2
59
8 8
51 52
84164
13
15886
98458
25
01542
14294
12
85706
1
60
8 0
52 0
84177
IS
15823
98484
25
01516
14307
12
85693
0
M.
Hour p. M.
Hour A. M.
Cosine.
Diflf.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
133°
A
A
B
B
C
C 46°n
Seconds of time
1»
2s
3»
4»
6» 6'
T
Prop, parts of cols.<B
2
3
2
3
6
3
5
9
5
7
13
6
8 10
16 19
8 9
12
22
11
Page 652]
TABLE 44.
Log.
Sines, Tangents, and Secants.
44°
A
A
B
B
C
C
185°
M.
Hour A. M.
Hour p. M.
Sine.
Difl.
Cosecant.
Tangent. Diff.
Cotangent.
Secant.
iDiff.
Cosine.
M.
60
0
6 8 0
5 52 0
9. 84177
0
10. 15823
9. 98484 0
10. 01516
10. 14807
1 0
9. 85693
1
7 52
52 8
84190
0
15810
98509 0
01491
14319
0
85681
59
2
7 44
52 16
84203
0
15797
98534
1
01466
14331
0
85669
58
3
7 36
52 24
84216
1
15784
98560
1
01440
14343
i 85657
57
4
5
7 28
6 7 20
52 34
84229
9.84242
1
15771
98585
2
01415
14355
1 85645
56
5 52 40
1
10. 15758
9. 98610
2
10. 01390
10. 14368
9. 85682
55
(3
7 12
52 48
84255
1
15745
98635
8
01865
14380
85620
54
t
7 4
52 56
84269
2
15731
98661 3
01839
14892
85608
53
8
6 56
53 4
84282
2
15718
98686 3
01314
14404
2
85596
52
9
6 48
53 12
84295
2
15705
98711 4
01289
14417
2
85583
9. 85571
51
50
6 6 40
5 53 20
9. 84308
2
10. 15692
9. 98787 4
10. 01263
10. 14429
2
11
6 32
53 28
84321
2
15679
98762 5
01238
14441
2
85559
49
12
6 24
53 36
84334
3
15666
98787
5
01213
14458
2
85547
48
18
6 16
53 44
84347
3
15653
98812
5
01188
14466
3
85534
47
14
6 8
53 52
84360
3
15640
98888
6
01162
14478
3
85522
46
15
6 6 0
5 54 0
9. 84373
3
10. 15627
9. 98868
6
10. 01137
10. 14490
3
9. 85510
45
16
5 52
54 8
84385
3
15615
98888
7
01112
14503
3
85497
44
17
5 44
54 16
84398
4
15602
98913
7
01087
14515
4
85485
43
18
5 36
54 24
84411
4
15589
98989
8
01061
14527
4
85478
42
19
20"
5 28
54 32
84424
4
15576
98964
8
01086
14540
4
85460
41
40
6 5 20
5 54 40
9. 84437
4
10. 15563
9. 98989
8
10. 01011
10. 14552
4
9. 85448
21
5 12
54 48
84450
5
15550
99015 i 9
00985
14564
4
85436
89
22
5 4
54 56
84463
5
15537
99040 1 9
00960
14577
5
85423
38
23
4 56
55 4
84476
o
15524
99065 10
00985
14589
5
85411
37
24
4 48
55 12
84489
5
15511
99090 10
00910
14601
5
85399
36
25
6 4 40
5 55 20
9. 84502
5
10. 15498
9.99116 11
10. 00884
10. 14614
5
9. 85386
35
26
4 32
55 28
84515
6
15485
99141 11
00859
14626
5
85874
34
27
4 24
55 36
84528
6
15472
99166 11
00834
14689
6
85361
33
28
4 16
55 44
84540
6
15460
99191 12
00809
14651
6
85349
32
29
30
4 8
55 52
84553
6
15447
99217 12
00783
14663
6
85887
81
30
6 4 0
5 56 0
9. 84566
6
10. 15434
9. 99242
13
10. 00758
10. 14676
6
9. 85824
31
3 52
56 8
84579
7
15421
99267
13
00733
14688
6
85312
29
32
3 44
56 16
84592
7
15408
99298
13
00707
14701
7
85299
28
33
3 36
56 24
84605
7
15395
99318
14
00682
14713
7
85287
27
34
35
3 28
56 32
84618
7
15382
99348
14
00657
14726
7
85274
26
25
6 3 20
5 56 40
9. 84630
8
10. 15370
9. 99368
15
10. 00632
10. 14738
7
9. 85262
36
3 12
56 48
84643
8
15857
99394
15
00606
14750
7
85250
24
37
3 4
56 56
84656
8
15844
99419
16
00581
14763
8
85237
23
38
2 56
57 4
84669
8
15331
99444
16
00556
14775
8
85225
22
39
40
2 48
57 12
84682
8
15318
99469
16
00531
14788
8
85212
21
20
6 2 40
5 57 20
9. 84694
9
10. 15306
9.99495 1 17
10. 00505
10. 14800
8
9. 85200
41
2 32
57 28
84707
9
15293
99520 17
00480
14813
8
85187
19
42
2 24
57 36
84720
9
15280
99545 18
00455
14825
9
85175
18
43
2 16
57 44
84733
9
15267
99570
18
00430
14838
9
85162
17
44
2 8
57 52
84745
9
15255
99596
19
19
00404
14850
9
85150
16
15
45
6 2 0
5 58 0
9. 84758
10
10. 15242
9. 99621
10. 00379
10. 14868
9
9. 85137
46
1 52
58 8
84771
10
15229
99646
19
00354
14875
10
85125
14
47
1 44
58 16
84784
10
15216
99672
20
00828
14888
10
85112
18
48
1 36
58 24
84796
10
15204
99697
20
00803
14900
10
85100
12
49
1 28
58 32
84809
11
15191
99722
21
00278
10. 00253
14918
10
85087
11
Id
50
6 1 20
5 58 40
9. 84822
11
10. 15178
9. 99747 21
10. 14926
10
9. 85074
51
1 12
58 48
84835
11
15165
99773
21
00227
14938
11
85062
9
52
1 4
58 56
84847
11
15153
99798
22
00202
14951
11
85049
8
53
0 56
59 4
84860
11
15140
99823
22
00177
14963
11
85087
7
54
55
0 48
59 12
84873
12
12
15127
99848
9. 99874 ^
28
00152
14976
11
11
85024
9. 85012"
6
5
6 0 40
5 59 20
9. 84885
10.15115
28
10. 00126
10. 14988
56
0 32
59 28
84898
12
15102
99899
24
00101
15001
12
84999
4
57
0 24
59 36
84911
12
15089
99924
24
00076
15014
12
84986
3
58
0 16
59 44
84923
12
15077
99949
24
00051
15026
12
84974
9
59
0 8
59 52
84936
13
15064
99975
25
00025
15039
12
84961
1
60
0 0
6 0 0
84949
13
15051
10.00000
25
' 00000
15051
12
84949
0
M.
M.
Hour p. M.
Hour A.M.
Cosine.
Difl.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
134°
A
A
B
B
C
C
45°
Seconds of time !• 2"
8»
4*
5-
«•
7"
11
22
11
fA 2 3
Prop, parts of cols.^B i 3 6
|C 2 1 3
5
9
5
6
13
6
8
16
8
10
19
9
OfVTHE
UNIVFRRITV
HOME USE
CIRCULATION DEPARTMENT
MAIN LIBRARY
This book is due on the last date stamped below,
l-month loans may be renewed by calling 642-3405.
6-month loans may be recharged by bringing books
to Circulation Desk.
Renewals and recharges may be made 4 days prior
to due date.
ALL BOOKS ARE SUBJECT TO RECALL 7 DAYS
AFTER DATE CHECKED OUT.
im^
44SIS.
gBMiBi iwa?"'^
LD21 — A-40jn-12,'74
(S2700L)
General Library
University of California
Berkeley
I:
I
YD 15^70
//
/
/
k
r.
Live Music
Archive
Librivox
Free Audio
Metropolitan Museum
Cleveland
Museum of Art
Internet
Arcade
Console Living Room
Open Library
American
Libraries
TV News
Understanding
9/11